High-brilliance high-polarization γ rays based on Compton scattering are of great significance in broad areas, such as nuclear physics, high-energy physics, astrophysics, etc. However, the transfer mechanism of spin angular momentum in the transition from linear through weakly into strongly nonlinear processes is still unclear, which severely limits the simultaneous control of brilliance and polarization of high-energy γ rays. In this work, we clarify the transfer mechanism in the transition regions and put forward a clear way to efficiently manipulate the polarization of emitted photons. We find that to simultaneously generate high-energy, high-brilliance, and high-polarization γ rays, it is better to increase the laser intensity for the initially spin-polarized electron beam. However, for the case of employing the initially spin-nonpolarized electron beam, in addition to increasing laser intensity, it is also necessary to increase the energy of the electron beam. Because the γ photon polarization emitted through the single-photon absorption channel is mainly attributed to the spin transfer of laser photons, while in multi-photon absorption channels, the electron spin plays a major role. Moreover, we confirm that the signature of γ-ray polarization can be applied to observing the nonlinear effects (multi-photon absorption) of Compton scattering with moderate-intensity laser facilities.

Polarized γ rays are powerful probes for basic research and applications.1–5 For instances, polarized photons below 1 MeV enable the crystallographic probing and the biomedical imaging with femtosecond time resolution.4 In the energy range of several MeV to tens of MeV, polarized photo-induced nuclear reactions are highly effective in studying nuclear physics, transmutation, and astrophysics.6–9 Furthermore, polarized γ rays can be readily deployed for testing the interaction between two real photons leading to the linear Breit–Wheeler (BW) electron–positron pair production10–13 and photon–photon elastic scattering.14,15 For energy scales ranging from hundreds of MeV to GeV, polarized γ rays are significant for probing vacuum birefringence.16–19 

Traditionally, polarized γ-ray sources are mainly obtained via synchrotron radiation,4,20 bremsstrahlung,21,22 and linear Compton scattering (LCS).23–26 For synchrotron radiation facilities, higher-energy electrons are required due to insertion devices such as undulators or wigglers with a wavelength λ of a few centimeters. This requirement arises because the energy of γ rays, denoted as εγ, is proportional to ε e 2 λ,27,28 where ε e is the electron energy. Compared with bremsstrahlung, LCS is characterized by good directionality, collimation, and high polarization.29 However, the low scattering probability sets a practical limit for the maximum flux no larger than 1010 photons/s.8 

Recently, a rapidly advanced high-power laser technique30–33 promoted the research of high-energy and high-brilliance polarized γ rays,34–36 where the interaction mechanism transitions from the linear to the nonlinear regime.37–40 At an intermediate laser intensity, polarized γ rays can be generated by spin-nonpolarized (SNP) electron beams via weakly nonlinear CS (NLCS).41–44 Furthermore, the stronger laser field scattered with initially spin-polarized (SP) electron beams enables the generation of more brilliant high-polarization γ rays in strong NLCS.45 Importantly, in the near future, experiments, such as LUXE at DESY46 and E320 at FACET-II,47 will be performed using the conventionally accelerated ε e  10 GeV electron beam in collision with dozens up to hundreds of TW (corresponding to the laser invariant intensity a 0 10) laser pulses to probe the transition from a linear to a strongly nonlinear QED regime. Moreover, all-optical PW up to 10 PW laser facilities have also been commissioned or will soon be online.48,49 However, there is no charted transfer mechanism of spin angular momentum (SAM) in the transition from linear through weakly into strongly nonlinear CS. Therefore, the simultaneous control of brilliance and polarization of high-energy γ rays is still a great challenge.

In this paper, the manipulation of γ-ray polarization in CS employing the S(N)P ultrarelativistic electron beam is investigated. We analyze the transfer mechanism of SAM in the transition regions from linear through weakly nonlinear to strongly nonlinear Compton scattering. We find that the polarization is predominantly contributed by the electron (laser photon) spin via the multi-photon (single-photon) absorption channel (see Figs. 1 and 2). And, SNP electrons in a high-intensity laser pulse can also generate high-brilliance high-polarization γ photons (see Fig. 3). The transfer mechanism of SAM is also valid in the generation of vortex γ photons due to the same radiation dynamics as the plane wave γ photons.50 Moreover, the polarization of γ photons radiated by the electrons with different initial spin states proceeds in different ways in LCS and strong NLCS, respectively, which can give a clear signature of the nonlinear effects in CS with moderate-intensity laser facilities (see Fig. 5).

FIG. 1.

(a) Distribution of the total differential radiation rate log 10 d 2 W rad d t d δ in CP laser vs the laser invariant intensity a0 and energy ratio parameter δ, where ω L = 1.55 eV and ε e = 10 GeV. The four lines indicate the first four cutoffs δ n = 1 , 2 , 3 , 4, respectively. (b) Average number of absorbed laser photons log 10 n ¯ vs a0 and δ. The black-solid lines indicate the contour lines of n ¯  10, 100, and 1000, respectively. Ratios of (c) C 1 C 0 and (d) | C 2 | | C 2 | + C 3 ( C 3 > 0) vs a0 and δ, respectively. The black-dotted line in (d) indicates the spin contribution of the laser is equal to that of an electron to the γ photon, i.e., | C 2 | | C 2 | + C 3 = 0.5.

FIG. 1.

(a) Distribution of the total differential radiation rate log 10 d 2 W rad d t d δ in CP laser vs the laser invariant intensity a0 and energy ratio parameter δ, where ω L = 1.55 eV and ε e = 10 GeV. The four lines indicate the first four cutoffs δ n = 1 , 2 , 3 , 4, respectively. (b) Average number of absorbed laser photons log 10 n ¯ vs a0 and δ. The black-solid lines indicate the contour lines of n ¯  10, 100, and 1000, respectively. Ratios of (c) C 1 C 0 and (d) | C 2 | | C 2 | + C 3 ( C 3 > 0) vs a0 and δ, respectively. The black-dotted line in (d) indicates the spin contribution of the laser is equal to that of an electron to the γ photon, i.e., | C 2 | | C 2 | + C 3 = 0.5.

Close modal
FIG. 2.

Average helicity h ¯ γ of the emitted photons vs a0 and δ for two different examples of (a) the laser helicity hL = 1 and initial electron helicity h e = 1, and (b) hL = 1 and he = 0, respectively. The laser and electron-beam parameters are the same as those in Fig. 1.

FIG. 2.

Average helicity h ¯ γ of the emitted photons vs a0 and δ for two different examples of (a) the laser helicity hL = 1 and initial electron helicity h e = 1, and (b) hL = 1 and he = 0, respectively. The laser and electron-beam parameters are the same as those in Fig. 1.

Close modal
FIG. 3.

(a)–(c) Generation of γ photons in the realistic laser pulse with peak intensity a 0 , peak = 1 vs the coordinate time t (T0) and γ photon energy ε γ with distributions of (a) and (b) the yields log 10 d N γ dtd ε γ and average helicity h ¯ γ for he = 0, and (c) h ¯ γ for h e = 1, respectively, where T0 is the laser period. The magenta solid line in (a) indicates the average intensity a ¯ 0 sensed by the spatially distributed electron beam vs t (T0). (d)–(f) The physical representations and other laser and electron-beam parameters are the same as those in (a)–(c) respectively, except a 0 , peak = 10. Comparisons of (g) energy spectra d N γ/d ε γ with relative deviation Δ γ and (h) h ¯ γ between the cases of a 0 , peak = 1 and a 0 , peak = 10 vs ε γ, respectively, where Δ γ = ( N h e = 1 N h e = 0 ) / N h e = 0 and N = d N γ / d ε γ. Other laser and electron-beam parameters are given in the text.

FIG. 3.

(a)–(c) Generation of γ photons in the realistic laser pulse with peak intensity a 0 , peak = 1 vs the coordinate time t (T0) and γ photon energy ε γ with distributions of (a) and (b) the yields log 10 d N γ dtd ε γ and average helicity h ¯ γ for he = 0, and (c) h ¯ γ for h e = 1, respectively, where T0 is the laser period. The magenta solid line in (a) indicates the average intensity a ¯ 0 sensed by the spatially distributed electron beam vs t (T0). (d)–(f) The physical representations and other laser and electron-beam parameters are the same as those in (a)–(c) respectively, except a 0 , peak = 10. Comparisons of (g) energy spectra d N γ/d ε γ with relative deviation Δ γ and (h) h ¯ γ between the cases of a 0 , peak = 1 and a 0 , peak = 10 vs ε γ, respectively, where Δ γ = ( N h e = 1 N h e = 0 ) / N h e = 0 and N = d N γ / d ε γ. Other laser and electron-beam parameters are given in the text.

Close modal

The paper is organized as follows. Section II gives a brief description of the radiation probability of a photon as well as the polarization in CS. Section III presents the theoretical analysis of the manipulation of γ-ray polarization. This is followed by the numerical analysis of the polarized γ-ray manipulation considering the radiation reaction during the propagation of the electrons through the laser field. The diagnosis of nonlinear effects in CS is also discussed. Section IV summarizes our results.

In this work, we consider the collision system of an ultrarelativistic electron beam colliding head-on with an intense laser field, of which the intensity is depicted by an invariant parameter a 0 = | e | E rms / ( m e ω L ),51,52 with the charge e and rest mass me of the electron, E rms = E 2 1 / 2, E, and ωL are the root-mean-squared (rms) electric field, electric field, and frequency of the laser field, respectively. In CS, the invariant parameter characterizing the quantum effects is χ e | e | ( F μ ν p e ν ) 2 / m e 3 2 ω L a 0 ε e / m e 2,51,52 with the field tensor F μ ν and four-vector momentum p e = ( ε e , p e ) of the electron. Relativistic units with c = = 1 are used throughout.

When electrons scatter with a laser field, they may absorb single or multiple low-energy laser photons and then emit a high-energy γ photon via CS. The rate for an electron emitting a single photon in a monochromatic field is given as38,
d W d t = W 0 n = 1 0 δ n d δ 0 2 π d φ F 0 n + j = 1 3 ( F j n ξ j + G j n ζ j ) + i , j = 1 3 H i j n ζ i ξ j ,
(1)
where W0 =  α m e 2 a 0 2 / ( 16 ε eff ) , ε eff = ε e + a 0 2 ω L / Λ is the effective energy of the initial electron in the laser field, δ = ( k L · k γ ) / ( k L · p e ) ε γ / ε e is the energy ratio parameter, Λ = 2 ( k L · p e ) / m e 2 is an invariant variable, φ is the azimuthal scattering angle, α is the fine structure constant, kL and k γ are the four-momenta of the laser photon and emitted photon, and n is the number of absorbed laser photons (nth harmonics), respectively. According to the energy-momentum conservation q e + n k L = q e + k γ, the cutoff energy fraction (nth Compton edge) is derived as δ n = 2 n ( k L · p e ) m e 2 ( 1 + a 0 2 ) + 2 n ( k L · p e ) when the emitted photon is along the propagation direction of the initial electron.38,53 Here, q e = p e + a 0 2 m e 2 2 ( k L · p e ) k L and q e = p e + a 0 2 m e 2 2 ( k L · p e ) k L are the four-quasimomenta of the initial and final electrons, and p e = ( ε e , p e ) is the four-momenta of the final electron. The sums in Eq. (1) running from 1 to 3 are over the terms related to the polarization properties of final particles, which can be specified by three real numbers ( ξ j for the emitted photon and ζ j for the final electron, with j = 1, 2, and 3). Here, ξ j and ζ j are defined with respect to the unit-basis vectors ( e ̂ 1 , e ̂ 2 , e ̂ 3) and ( g ̂ 1 , g ̂ 2 , g ̂ 3) for the final photon and electron, respectively. For the emitted photon, e ̂ 3 is along the emitted photon momentum n ̂ = k γ | k γ | with the emitted photon momentum k γ , e ̂ 1 = E ̂ n ̂ ( n ̂ E ̂ ) and e ̂ 2 = e ̂ 3 × e ̂ 1 with the unit vector E ̂ = E | E | along the electric field E. For the final electron, in the collision system, g ̂ j (j = 1, 2, 3) are g ̂ 1 = p e × p e | p e × p e | , g ̂ 3 = p e | p e |, and g ̂ 2 = g ̂ 3 × g ̂ 1, respectively. The terms of F k n , H k n, and G k n ( k = 0 , 1 , 2 , 3) for cases of the circularly polarized (CP) laser and the linearly polarized (LP) laser are detailed in Ref. 38. For the limit of a 0 2 0, the radiation rate coincides with the result known for the LCS case.38,54,55
For the polarization of the final photon, it is necessary to distinguish the polarization ξ j f of the final photon, resulting from the scattering process itself, from the detected polarization ξ j , which enters the effective cross section and essentially represents the properties of the detector.38,56 According to the usual rules,56 after summing over the polarization states of the final electron, one can obtain the Stokes parameters of the final photon as follows:
ξ j f = F j F 0 , F 0 = n F 0 n , F j = n F j n ; j = 1 , 2 , 3.
(2)
These Stokes parameters ξ j f are also defined with the unit-basis vectors ( e ̂ 1 , e ̂ 2 , e ̂ 3).
After averaging over the azimuthal angle ( φ) and summing over the final particles' polarizations ( ζ j and ξ j ), the total radiation rate is obtained as follows:
d W rad d t = 4 W 0 n = 1 0 δ n d δ F 0 n .
(3)
The average polarization states of the emitted photon equal to
ξ ¯ 1 f = n F 1 n n F 0 n , ξ ¯ 2 f = n F 2 n n F 0 n , ξ ¯ 3 f = n F 3 n n F 0 n ,
(4)
where F k n (k = 0, 1, 2, and 3) are the average values of F k n over φ.
To clarify the transfer mechanism of SAM in the transition regions from linear through weakly nonlinear into strongly nonlinear CS, which has not been investigated well in previous works, we analyze the spin contributions of the laser and electron to the γ photon helicity by merging and reorganizing formulas F k n (k = 0, 1, 2, and 3) in Ref. 38. For the case of the CP laser, i.e., ξ 1 i = ξ 3 i = 0 and ξ 2 i = h L = ± 1 , F 1 n = F 3 n = 0, therefore, the emitted photons have no degree of linear polarization. Also, F 0 n = C 0 n + h L h e C 1 n and F 2 n = h L C 2 n + h e C 3 n. Here, ξ j i (j = 1, 2, and 3) are polarization states of the laser photon and are defined with unit-basis vectors ( e ̂ 1 , L , e ̂ 2 , L , e ̂ 3 , L), where, e ̂ 3 , L is along the direction of laser propagation, e ̂ 1 , L is perpendicular to e ̂ 3 , L, and e ̂ 2 , L = e ̂ 3 , L × e ̂ 1 , L. Here, hL is the laser photon helicity, h e = 2 ζ p e | p e | is the helicity of the electron with initial spin ζ, and C k n (k = 0, 1, 2, and 3) are given as57,
C 0 n = 4 a 0 2 J n 2 + ( 2 + v 2 1 + v ) ( J n 1 2 + J n + 1 2 2 J n 2 ) ,
(5)
C 1 n = ( 1 2 v v n ) v ( 2 + v ) 1 + v ( J n 1 2 J n + 1 2 ) ,
(6)
C 2 n = ( 1 2 v v n ) ( 2 + v 2 1 + v ) ( J n 1 2 J n + 1 2 ) ,
(7)
C 3 n = 4 v 1 + v 1 a 0 2 J n 2 + v ( 2 + v ) 1 + v ( J n 1 2 + J n + 1 2 2 J n 2 ) ,
(8)
here, J n s are Bessel functions with the argument zn defined as
z n = 2 n a 0 1 + a 0 2 v v n ( 1 v v n ) ,
(9)
where v = δ / ( 1 δ ) and the maximum value of v for a given n is v n = n Λ / ( 1 + a 0 2 ). Therefore, the average helicity of the emitted γ photon is determined by38,57
h ¯ γ = ξ ¯ 2 f = h L C 2 + h e C 3 C 0 + h L h e C 1 ,
(10)
where C k = n = 1 C k n ( k = 0 , 1 , 2 , 3).

Let us illustrate the transfer mechanism of SAM in CS from linear to strongly nonlinear processes by employing the CP laser (see Fig. 1). For a 0 O ( 0.1 ), there is a distinct edge at the end of the first harmonic followed by smaller probabilities of higher harmonics [see Figs. 1(a) and 1(b)]. For instance, for a 0 = 0.1 , d 2 W rad d t d δ 10 5.31 at δ 0.192 is two orders of magnitude smaller than d 2 W rad d t d δ 10 3.01 at δ = δ 1 0.190, and for larger δ, d 2 W rad d t d δ is smaller, where Wrad is the radiation probability after summing over the polarization states of the final particles and averaging over the initial electron spin with d 2 W rad d t d δ = 4 W 0 C 0, and δ1 is the first Compton edge of the emitted photon. Therefore, for a 0 O ( 0.1 ), the electron absorbs almost only one laser photon and radiates a γ photon with δ δ 1, i.e., the scattering process is LCS. For a 0 O ( 1 ), the process of absorbing dozens of laser photons appears with d 2 W rad d t d δ 10 2.99 and the average number of absorbed laser photons is n ¯ = n n · C 0 n n C 0 n 10 (corresponding to δ 0.4), termed as weak NLCS. As a0 increases to O(10), due to W rad a 0 2, the electron will have a greater probability of absorbing thousands of laser photons to emit a higher energy γ photon with d 2 W rad d t d δ 10 1.22 and n ¯ 1000 (corresponding to δ 0.55), described as strong NLCS. Therefore, electrons will radiate more brilliant γ rays in a higher intensity laser field. Note that the electron quivers in the transverse direction under the high-intensity laser field with a 0 1. Therefore, the electron obtains an effective mass m e * = m e 1 + a 0 2 while propagating in the laser field.53 Hence, the nth Compton edge δn can also be expressed as δ n = 2 n ( k L · p e ) m e * 2 + 2 n ( k L · p e ) and their gaps of harmonic cutoffs are obtained as Δ δ n = δ n δ n 1 1 / m e * 2. Then, as the laser intensity a0 increases, the electron effective mass m e * increases, and the edge locations δn of the emission spectrum and their gaps Δ δ n are both decreasing. As a result, in a higher intensity laser field, the energy cutoffs of the emitted photon shift toward the lower energy region for absorbing a certain number of laser photons, and the harmonic structures become more closely spaced. Therefore, the distinct harmonic structures become smoother due to the increased effective mass of the electron in stronger NLCS. Note that the trends of harmonic cutoffs as well as the laser intensity are crucial for manipulating high-quality polarized γ photons and testing the nonlinear effects in strong NLCS (see Figs. 2 and 5, which will be discussed later). In addition, the impact of electron spin on the radiation rate weakens as the laser intensity increases. For instances, for a 0 = 0.1, the radiation probability of the longitudinally spin-polarized (LSP) electrons (satisfying h L h e = 1) at the first edge can be increased by Δ W i = ( W i LSP W i SNP ) / W i SNP = C 1 C 0 20 %, yet, for a 0 = 10 , Δ W i 0 [see Fig. 1(c)], where W i LSP ( W i SNP) is the radiation probability of LSP (SNP) electrons with d 2 W i LSP d t d δ = 4 W 0 ( C 0 + h L h e C 1 ).

The electron spin plays an increasingly significant role in the transfer of SAM with stronger nonlinear effects. The entanglement term C 1 C 0 of the laser helicity and electron spin in the γ-photon helicity Eq. (10) mainly operates at the end of the first few harmonics and decreases as a0 increases. While C 1 C 0 can reach to −0.68 at δ = 0.7 for a 0 = 0.1, it is irrelevant due to the relatively low radiation probability with d 2 W rad d t d δ 10 25 [see Figs. 1(a) and 1(c)]. Therefore, the helicity of emitted γ photon is mainly related to the independent laser helicity term C2 and the electron spin term C3. For emitted photons with δ δ 1 at any a0, the laser helicity contribution | C 2 | | C 2 | + C 3 1 and correspondingly the electron spin contribution C 3 | C 2 | + C 3 = 1 | C 2 | | C 2 | + C 3 0, i.e., regardless of whether the scattering process is linear or not, the average helicity of γ photons via the single-photon absorption channel is almost completely determined by the laser [see Fig. 1(d)]. When electrons simultaneously absorb dozens of laser photons, higher energy γ photons are emitted, where the contribution of laser helicity gradually decreases and the electron spin comes into play, i.e., the SAM transfer enters a competitive stage of the laser and electron for controlling the γ-photon polarization [see the black-dotted line in Fig. 1(d), which almost corresponds to n ¯ 10 in Fig. 1(b)]. As the number of absorbed laser photons continues to increase, the electron spin plays a dominant role in the SAM transfer, for instance, as n ¯ increases up to 1000, | C 2 | | C 2 | + C 3 0.05 and C 3 | C 2 | + C 3 0.95 at δ = 0.55 for a 0 = 10.

The transfer mechanism of SAM indicates a way to manipulate the polarization of γ rays. For LSP ( h e = 1) electrons scattered with the CP (hL = 1) laser, in LCS ( a 0 0.1), the emitted photons are almost completely radiated via the single-photon absorption channel and helicities are mainly contributed by the laser [see Fig. 2(a)]. In the low-energy parts of the first harmonic, γ photons are radiated in the forward scattering with average helicity h ¯ γ h L = 1, while near the edge h ¯ γ h L = 1 via the backward scattering. This behavior, obtained as the limit of a small number of absorbed photons during an NLCS event, also exists in the LCS.58 As a0 increases, the interaction process transitions into the NLCS regime, due to δ 1 1 / a 0 2, the energy regions of h ¯ γ 1 of radiated photons via the single-photon absorption channel tend toward lower energy areas with smaller δ. For a certain a 0 1, γ photons with high energy ( δ δ 100) obtain increasingly high h ¯ γ transferred by the electron spin. For the case of he = 1, the helicity behavior is similar to that of h e = 1 but slightly different especially at the end of the first few harmonics with a 0 1 due to the entanglement term of the laser helicity and electron spin [see Fig. 6(a) in  Appendix A]. If electrons are SNP (he = 0), h ¯ γ of γ photons is only provided by the laser helicity. Therefore, h ¯ γ of high-energy γ photons via multi-photon absorption channels ( n ¯ 10) gradually decreases as a0 increases, for instance, at δ = 0.3 , h ¯ γ 0.40 and −0.03 for a 0 = 1 and 10, respectively [see Fig. 2(b)]. Note that in the NLCS, the polarization of emitted photons in the linear region ( δ δ 1) is averaged over all possible multi-photon absorption channels (see Fig. 7 in  Appendix B). For instance, h ¯ γ shifts up to −0.76 from −1 near the first harmonic edge ( δ δ 1) for a 0 = 1, while, h ¯ γ 0.53 for a 0 = 10 [see Figs. 7(d) and 7(f) in  Appendix B].

The above-mentioned analytical discussions are based on the single-photon emission of electrons with ε e = 10 GeV. However, the transfer mechanism also holds true for other electron energies. The slight difference lies in the positions of harmonic edges and the average number of absorbed laser photons (see Fig. 8 in  Appendix C). Moreover, for LP γ photons generated in the LP laser, the competition between the laser and electron for controlling the γ photon polarization also exists (see Fig. 10 in  Appendix E).

To summarize, if electrons are SP, one can increase the laser intensity to generate high-energy, high-brilliance, and high-polarization γ rays. However, for SNP electrons, due to the energy regions δ δ 1 ε e for a certain a0, apart from the high-intensity laser, higher energy electrons are also required to produce the similar high-quality γ rays, where the polarization is mainly contributed by the laser via the single-photon absorption channel. Importantly, when the scattering process satisfies the rotational symmetry around the collision axis, e.g., in the case of CP laser, the angular momentum conservation holds and one could expect the generation of vortex γ photons with intrinsic orbital angular momentum (OAM) via multi-photon absorption channels. In the monochromatic CP laser, γ photons corresponding to the nth harmonic carry OAM l γ = n h L + h e h e h γ with the final electron helicity h e . Since the radiation dynamics of the vortex γ photons are the same as those of the plane wave γ photons,50 the transfer mechanism of SAM discussed above is still valid. However, the electrons are required to possess coherence in the transverse plane with axial symmetry in order to attain vortex γ photons. In theory, such a transverse coherence for the final electron can be achieved using the generalized measurement. In this scenario, the momentum azimuthal angle of the final electron is not measured, such that the final γ photon assumes a vortex state carrying OAM.59,60

The SAM transfer mechanisms of LCS and weak NLCS presented above are consistent with the existing experimental data. However, the SAM transfer mechanism of strong NLCS will be verified as the fast-paced development of high-intensity laser facilities. For LCS, polarized γ photons have been generated with low-intensity laser devices,61 such as BNL-ATF,23 SPring-8,24 NewSUBARU,25 UVSOR-III,26 etc. In these LCS experiments mentioned above, the polarization degree of the emitted photons near the peak of the spectra exceeds 99%. The experimental results coincide with the SAM transfer mechanism in LCS, indicating that the polarization of the emitted photons is mainly transferred by the laser spin. Near the edge of the first harmonic with δ δ 1, the average polarization states of γ photons are | ξ ¯ 2 f | = ξ 2 i = 100 % and ξ ¯ 1 f = ξ ¯ 3 f = 0 for the CP laser, and ξ ¯ 1 f ξ ¯ 2 f = 0 and ξ ¯ 3 f ξ 3 i = 100 % for the LP laser [see Figs. 2(b) and 7(b) in  Appendix B and Fig. 10(b) in  Appendix E]. For weak NLCS, the CP- or LP-emitted photons have been obtained experimentally in an all-optical moderate-intensity laser setup ( a 0 0.86 1) by tuning the polarization state of the driving laser,62 where the average linear polarization degree of the emitted photons is 75 (±3)% within 18.2 mrad. The experimental results are consistent with the SAM transfer mechanism in weak NLCS, wherein the polarization of emitted photons is still mainly transferred by the laser spin, albeit with a slightly decreased contribution [see Figs. 2(b) and 7(d) in  Appendix B]. For strong NLCS, the transfer mechanism of the γ-photon polarization from the electron spin has not been confirmed. Subsequently, the verification plan is proposed based on current and upcoming high-intensity ( a 0 10) laser setups, utilizing either conventional accelerator setups, such as LUXE at DESY46 and E320 at FACET-II,47 or all-optical configurations in the colliding-beams geometry, such as ELI-NP,63 SILEX-II,64 Apollon,65 SULF,66 etc. We allow the high-intensity laser to collide head-on with the LSP and SNP electron beams, using each setup, respectively, and then measure the polarization degree of the high-energy γ photons. If the polarization degree of high-energy γ photons emitted by the LSP electrons increases with energy (from the middle to the rear segments of the spectra), while in the case of the SNP electrons, the high-energy γ photons are nearly nonpolarized [see Figs. 2 and 3(h)], then the transfer mechanism of SAM in strong NLCS will be verified. The high-energy LSP electrons can be generated in a controllable laser wakefield acceleration scheme,67–73 in which a pre-polarized gas target can be prepared experimentally via ultraviolet photodissociation of a hydrogen-halogen molecule.74–77 

The generation of CP γ rays via different CS mechanisms in a realistic laser pulse is detailed in Fig. 3. In the region of a 0 10, we employ the method of locally monochromatic approximation (LMA) to simulate the scattering process57 [For the strong NLCS ( a 0 1), the computational cost of evaluating very high-order harmonics restricts the implementation of the LMA and the locally constant field approximation (LCFA) method is appropriate].49,51,52,78 The LMA method, which has been benchmarked against exact calculations in pulses and has been extended to include chirped pulses under a “slowly varying chirp” approximation,79,80 treats the fast dynamics related to the carrier frequency of the plane wave exactly, but uses a local expansion to describe the slow dynamics associated with the pulse envelope.81 The focused Gaussian left-hand CP laser pulse (hL = 1) propagating along the – z direction is employed with peak intensity a 0 , peak = 1, wavelength λ 0 = 0.8 μm, pulse duration τ = 10 T 0 (full width at half maximum) with the period T0, and beam waist (the radius at which the intensity falls to 1/e2 of its central value) w 0 = 5 μm. The normalized amplitude is79,
a 0 , gauss ( X ) = a 0 , peak f ( t + z ) 1 + ( z z R ) 2 exp [ r 2 w 0 2 ( 1 + ( z z R ) 2 ) ] ,
(11)
where z R = π w 0 2 / λ 0 is the Rayleigh length, and X = ( t , r , z ) with r = ( x , y ) is the four-dimensional coordinate. The pulse envelope is f ( t + z ) = exp [ ( t t shift + z 2 σ τ ) 2 ], where σ τ = τ / 2 ln 2 and the constant tshift is the pulse shift in the coordinates to make sure that the electrons are initially outside of the laser pulse, and we neglect the wavefront curvature and Gouy phase. On the longitudinal propagation axis, let X = ( 0 , r , 0 ) be the origin of the laser, i.e., the initial time and position, thus, one gets z t shift / 2 and f ( t + z )  1 at t = t shift / 2. The head-on collision (along + z direction) cylindrical electron beam is uniformly distributed between z = l e and z = 0 μm in the longitudinal direction with the beam length l e = 3 μm, initial kinetic energy ε ¯ e = 10 GeV, energy spread Δ ε e / ε ¯ e = 12 %, and electron number N e = 5 × 10 6. The distribution in the transverse direction has a Gaussian profile with the radius r e = 2 μm. The collision polar angle with respect to the laser propagation direction is θ e = 180 ° with angular divergence Δ θ e = 0.2 mrad. Such electron bunches can be obtained via laser wakefield acceleration.82–85 To ensure that the electron beam is initially outside of the laser pulse, we have t shift / 2 = 4 σ τ = 4 τ / 2 ln 2 34 T 0.

In the laser pulse, the intensity sensed by electrons changes in real time and is strongest at t 35 T 0, which is larger than t shift / 2 34 T 0 due to the electron beam with a certain length, and copious γ rays are radiated at t 35 T 0 [see Fig. 3(a)]. According to Eq. (11), the normalized amplitude a 0 , gauss of the focused Gaussian laser not only depends on the time t but also on the space positions ( r , z) in longitudinal and transverse directions. Therefore, we calculate the average intensity a ¯ 0 sensed by the spatially distributed electron beam in real time. For SNP electrons, the helicities of γ photons come from the laser. In the front of the laser pulse with t 23 T 0 and the average intensity a ¯ 0 0.1, electrons only radiate a small amount of high polarized γ photons due to the low-radiation probability of the LCS regime [see Figs. 3(a) and 3(b)]. The polarization directions of γ photons with ε γ 1 GeV ( δ 0.1) and ε γ < 1 GeV ( δ < 0.1) are opposite [see Figs. 2(b) and 3(b)]. For 23 T 0 t 35 T 0 , a ¯ 0 gradually increases to 1 and since δ 1 1 / a 0 2 the energy regions of h ¯ γ h L = 1 decrease from ε γ 2 GeV to 1 GeV. There are high-energy γ photons radiated by electrons absorbing dozens of laser photons and h ¯ γ of GeV γ photons decreases from 1 to 0.43 due to the decline of the transfer efficiency of the driving laser. As t continues to increase, a ¯ 0 begins to decrease and the trends of radiated spectra and helicities of γ photons are basically symmetrical with those of t 35 T 0. Therefore, the final h ¯ γ of γ photons is the average result of the laser pulse effect, and the first few harmonics are smoothed out and the h ¯ γ of γ photons with ε γ 2 GeV is about −0.53 which is higher than h ¯ γ 0.43 of the plane wave with a 0 = 1 [see Fig. 2(b) and the green-solid line in Fig. 3(h)]. For LSP electrons,67–73 the helicities of γ photons contributed by the CP laser are almost identical to the case of SNP electrons for all energy regions radiated at both ends of the laser pulse with t 23 T 0 and t 49 T 0 and ε γ 1 GeV radiated at the middle of the laser pulse with 23 T 0 t 49 T 0. However, at the middle of the laser pulse, the γ photons with ε γ 1 GeV receive helicities from the scattering electrons and h ¯ γ linearly falls (rises) as ε γ increases for h e = 1 (he = 1) [see Fig. 3(c), the blue-dash-dotted line in Fig. 3(h), and Figs. 6(b) and 6(c) in  Appendix A]. In addition, the relative deviation of energy spectra Δ γ can reach 30% (−30%) for h e = 1 (he = 1) [see the red dash-dotted line in Fig. 3(g)].

Usually, one can increase the laser intensity to obtain high-brilliance γ rays. For instance, the γ-photon yields in CS with a 0 , peak = 10 are two to three orders of magnitude higher than that of the a 0 , peak = 1 case [see Figs. 3(d) and 3(g)]. The yield and helicity distributions are not completely symmetric due to the radiation reaction. Importantly, SNP electrons can also generate high-brilliance high-polarization γ rays with the energy scale of keV to MeV [see Fig. 3(e) and the black-solid line in Fig. 3(h)]. Similar to the a 0 , peak = 1 case, one gets | h ¯ γ | h L = 1 for γ photons via linear and weakly nonlinear CS at the front and rear of the laser pulse. During 23 T 0 t 49 T 0, the scattering sequentially undergoes weakly nonlinear, strongly nonlinear, and again weakly nonlinear processes. At about 35T0, due to δ 1 1 / a 0 2, the energy regions of h ¯ γ h L = 1 drop below 100 keV, which is much smaller than that in the plane wave case ( ε γ = δ ε e  10 MeV) in Fig. 2, due to radiation reaction. Meanwhile, electrons experience the strongest field and have larger probabilities of absorbing thousands of laser photons to radiate higher energy γ photons [see Fig. 3(g)]. For ε γ 1 GeV, h ¯ γ decreases from −0.28 at t 23 T 0 to −0.05 at t 35 T 0 since the transfer efficiency of laser helicity decreases as a0 increases. The corresponding brilliances B (average helicities h ¯ γ) are 1.49 × 10 20 (0.98), 1.14 × 10 21 (0.59), and 5.23 × 10 21 (0.16) photons/(s · mm2 · mrad2 · 0.1% bandwidth) for ε γ = 100 keV, 1, and 10 MeV, respectively. Such polarized beams can be readily deployed to the near-future photon–photon colliders, e.g., the Beijing electron–positron collider (BEPC) in IHEP,86 for studying linear Breit–Wheeler pair production13 and elastic photon–photon scattering.15 Note that the difference in the average helicity of the emitted photons in the linear region ( ε γ ε ¯ e δ 1) between LCS, weak NLCS, and strong NLCS can be attributed to the combined effects of multi-photon absorption channels and radiation reaction. The effects of multi-photon absorption channels lead to the average helicity of emitted photons in the linear region shifting upward compared to that of the LCS (see Fig. 7 in  Appendix B). The helicity of emitted photons is averaged over those photons radiated by the electrons with a wide energy spread caused by the radiation reaction (see Fig. 9 in  Appendix D). For LSP electrons, the γ photons spectra are almost identical to the case of he = 0 with Δ γ 5 % at ε γ = 9 GeV [see the red-solid line in Fig. 3(g)]. However, electrons transfer SAM to high-energy γ photons with ε γ 1 GeV via strong NLCS and h ¯ γ is linearly falling (rising) as ε γ in the case of h e = 1 (he = 1) and reaches 1 (1) at ε γ = 9 GeV [see Fig. 3(f), the red-dash-dotted line in Fig. 3(h), and Figs. 6(d) and 6(e) in  Appendix A]. Note that with a 0 , peak = 10, the LCFA method commonly used to simulate strong NLCS performs poorly not only in radiation spectra but also in γ-photon polarization (see Fig. 11 in  Appendix F).

The generation of the second-generation γ photons radiated by positron–electron pairs, which are produced by the first-generation γ photons during the propagation in laser pulse via nonlinear BW (NLBW), is shown in Fig. 4. The decay probability of γ photons into positron–electron pairs in a laser field is characterized by an invariant parameter χ γ | e | ( F μ ν k γ ν ) 2 / m e 3 2 a 0 ε γ ω L / m e 2 with the four-vector momentum k γ = ( ε γ , k γ ) of the γ photon. For a 0 10 and ε γ 10 GeV, χ γ 1.18, therefore, only a very small fraction of the first-generation γ photons generated by high-energy electrons via NLCS decay into positron–electron pairs.51 For instance, the ratio of the number of positrons to one of the first-generation γ photons is N p / N γ 1 st 3.3 × 10 4, where Np and N γ 1 st are the total numbers of the positrons via NLBW and the first-generation γ photons via NLCS, respectively [spectra of the positrons d N p / d ε p and the first-generation γ photons d N γ 1 st / d ε γ are shown in Figs. 4(a) and 4(b), respectively]. As a result, the proportion P = d N γ 2 nd / d ε γ d N γ 1 st / d ε γ + d N γ 2 nd / d ε γ 0.03 of the second-generation γ photons radiated by positron–electron pairs is very small, where d N γ 2 nd / d ε γ is the number of the second-generation γ photons [see Figs. 4(b) and 4(c)]. Therefore, the final yields and polarization of γ photons are almost the same as those of the first-generation γ photons.

FIG. 4.

(a) Energy spectra d N p / d ε p of positrons generated by the first-generation γ photons via NLBW. (b) Energy spectra d N γ / d ε γ of γ photons. Black and green solid lines indicate the spectra of the first-generation ( d N γ 1 st / d ε γ) and second-generation ( d N γ 2 nd / d ε γ) γ photons, respectively. (c) Proportion of the second-generation γ photons P = d N γ 2 nd / d ε γ d N γ 1 st / d ε γ + d N γ 2 nd / d ε γ.

FIG. 4.

(a) Energy spectra d N p / d ε p of positrons generated by the first-generation γ photons via NLBW. (b) Energy spectra d N γ / d ε γ of γ photons. Black and green solid lines indicate the spectra of the first-generation ( d N γ 1 st / d ε γ) and second-generation ( d N γ 2 nd / d ε γ) γ photons, respectively. (c) Proportion of the second-generation γ photons P = d N γ 2 nd / d ε γ d N γ 1 st / d ε γ + d N γ 2 nd / d ε γ.

Close modal

In addition, the vacuum birefringence (VB) effect on the polarization of γ photons can also be neglected. For CP γ photons radiated in CP laser pulse, the unit-basis vector ( e ̂ 1 , e ̂ 2 , e ̂ 3) rotates due to the rotation of the polarization direction of the CP laser field, and then the VB effect cancels out. For LP γ photons, since the polarization of the emitted photons is mainly along the polarization direction of the LP laser field, ξ 1 f 0 is very small. The VB effect is related to ξ 1 f and ξ 2 f but not to ξ 3 f.17 Therefore, the VB effect is not included in the calculation code.

As mentioned above, the nonlinear effects increase with the laser intensity. In experiments to test the nonlinear effects of CS, the main methods involve measuring the energy spectra of scattered electrons or emitted photons. However, visible harmonic structures of the final particles cannot be detected in strong NLCS as seen in experiments conducted for weak NLCS at SLAC.37 The reason is that the gaps of harmonic cutoffs decrease as a0 increases and the harmonic structures become smoother in stronger NLCS. In addition, the method of measuring γ-photon energy spectra requires the use of the highest possible laser intensity to generate high-energy γ photons exceeding the energy cutoffs evaluated by the LCS.34,36 Therefore, detecting the nonlinear effects of CS in the experiment remains a crucial issue. The relevant theoretical studies predict different behaviors of the nonlinear effects in CS compared with the linear case,87,88 also primarily focusing on the energy spectra of emitted photons. However, the polarization of the emitted photons introduces another dimension to the investigation of nonlinear effects in CS.

An alternative method is proposed for testing the nonlinear effects in CS by detecting the polarization degree of γ photons (see Fig. 5). The polarization behavior of γ photons is studied in such a setup, where a moderate-intensity laser pulse collides head-on with an electron beam, considering the energy and angular spreads and the radiation reaction effect. In LCS, the first cutoff is δ LCS = Λ / ( 1 + Λ ) 4 ε e ε L / ( m e 2 + 4 ε e ε L ) and higher harmonics (n > 1) disappear. Therefore, there is a distinct edge at ε γ , edge = δ LCS ε e = 1.9 GeV, which is smaller than 2.5 GeV of the numerical result due to the initial electron energy spread [see the red-solid line in Fig. 5(c)]. In addition, the helicities of the emitted photons are almost completely derived from the laser, and due to the opposite scattering direction, h ¯ γ at both ends of the spectra are anti-parallel. Because of the radiation reaction, ε γ , edge and the turning points from h ¯ γ 1 to −1 decrease as t increases [see Figs. 5(a) and 5(b)]. As a result, for 10 MeV ε γ 1 GeV, h ¯ γ is averaged to a smaller polarization degree [see the green-solid line in Fig. 5(d)]. Therefore, the strongly nonlinear effects not only broaden the spectra but also change the helicity distribution of radiated γ photons compared with the LCS process [see Figs. 5(c) and 5(d)]. Importantly, the polarization of γ photons exhibits notably distinct behaviors even in the overlapped energy regions predicted by the LCS and strong NLCS, respectively. Therefore, the method of detecting the polarization degree of γ photons reduces the need for higher energy γ photons beyond the LCS cutoff. As a result, the polarization degree of γ photons can serve as a diagnostic tool to test the nonlinear effects in CS with the use of currently available laser facilities. Moreover, if electrons are LSP, the nonlinear signals will be more sensitive. For instance, the electron spin hardly affects the γ-photon helicity in the LCS process, while, in strong NLCS, LSP electrons will absorb abundant laser photons and transfer SAM to high-energy γ photons [see Fig. 5(d)].

FIG. 5.

Distributions of γ photons predicted by LCS for SNP electrons (he = 0) with (a) the yields log 10 d N γ dtd ε γ and (b) average helicity h ¯ γ, respectively. (c) and (d) Comparisons of energy spectra d N γ/d ε γ and h ¯ γ predicted by LCS and NLCS, respectively. The laser and electron-beam parameters are the same as those in Figs. 3(d)–3(f).

FIG. 5.

Distributions of γ photons predicted by LCS for SNP electrons (he = 0) with (a) the yields log 10 d N γ dtd ε γ and (b) average helicity h ¯ γ, respectively. (c) and (d) Comparisons of energy spectra d N γ/d ε γ and h ¯ γ predicted by LCS and NLCS, respectively. The laser and electron-beam parameters are the same as those in Figs. 3(d)–3(f).

Close modal

Therefore, the transfer mechanism of SAM can offer an alternative approach for testing the nonlinear effects in CS using presently accessible laser facilities. For instance, the collision of SNP high-energy electrons with a moderate-intensity CP laser pulse ( a 0 10) will enable the experimental study of nonlinear effects in CS by detecting the average circular polarization degree ξ ¯ 2 f of γ photons. If ξ ¯ 2 f transitions gradually from 100% to −100% as the energy of the emitted photons increases, the scattering processes of electrons will exhibit LCS. Conversely, if ξ ¯ 2 f decreases from 100% to approximately 0, the nonlinear effects in CS will be tested [see Fig. 5(d)].

In conclusion, we have investigated the transfer mechanism of SAM in CS from linear through weakly into strongly nonlinear regimes. We have found that the SAM transfer is related to the number of absorbed laser photons. The polarization of emitted photons via the single-photon absorption channel is mainly contributed by the driving laser, and the contribution gradually decreases as the number of scattered laser photons increases, meanwhile, the electron spin plays an increasingly important role in the SAM transfer. The transfer mechanism gives us a clear direction for simultaneously manipulating the brilliance and polarization of high-energy γ rays, which can be applied to the study of nuclear physics, high-energy physics, astrophysics, etc. Moreover, we have shown that detecting the SAM of particles can help us observe the nonlinear effects of strong-field QED processes with currently feasible laser facilities.

The work was supported by the National Natural Science Foundation of China (Grants Nos. U2267204 and U2241281), and the Foundation of Science and Technology on Plasma Physics Laboratory (Grant No. JCKYS2021212008), and the Shaanxi Fundamental Science Research Project for Mathematics and Physics (Grant No. 22JSY014).

The authors have no conflicts to disclose.

Yu Wang: Conceptualization (equal); Data curation (equal); Investigation (equal); Writing – original draft (equal). Mamutjan Ababekri: Conceptualization (equal); Formal analysis (equal); Writing – review & editing (equal). Feng Wan: Conceptualization (equal); Formal analysis (equal); Writing – review & editing (equal). Jia-Xing Wen: Formal analysis (equal); Writing – review & editing (equal). Wen-Qing Wei: Formal analysis (equal); Writing – review & editing (equal). Zhong-Peng Li: Formal analysis (equal); Writing – review & editing (equal). Hai-Tao Kang: Formal analysis (equal); Writing – review & editing (equal). Bo Zhang: Conceptualization (equal); Funding acquisition (equal); Writing – review & editing (equal). Yong-Tao Zhao: Formal analysis (equal); Writing – review & editing (equal). Wei-Min Zhou: Conceptualization (equal); Funding acquisition (equal); Writing – review & editing (equal). Jian-Xing Li: Conceptualization (equal); Funding acquisition (equal); Investigation (equal); Project administration (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Impact of electron spin (he = 1) on h ¯ γ of γ photons in the transition regime is shown in Fig. 6. When the LSP electron beam scatters with the CP (hL = 1) laser field, h ¯ γ of emitted γ photons via the single-photon absorption channel is almost unaffected by the electron spin, i.e., h ¯ γ h L = 1 in the low-energy parts of the first harmonic and h ¯ γ h L = 1 near the end. As the number of absorbed photons increases, the electron spin begins to participate in the competition with the laser. As the average number of the absorbed laser photons increases up to n ¯ 100, the electron spin mostly contributes to the high-energy γ photon and h ¯ γ is anti-parallel to the case of h e = 1 [see Figs. 2 and 6(a)]. In the realistic laser pulse, for both a 0 , peak = 1 and a 0 , peak = 10 , h ¯ γ of γ photons rises as ε γ increases in the medium- to high-energy regions. h ¯ γ with ε γ 1 GeV for a 0 , peak = 1 is the same as the case of he = 0, while due to δ 1 1 / a 0 2, for a 0 , peak = 10, in the range of ε γ 0.36 GeV, h ¯ γ is the same as in the case of he = 0 [see Figs. 3 and 6(b)–6(e)].

FIG. 6.

(a) Average helicity of γ photons h ¯ γ in the monochromatic plane wave vs a0 and δ, with hL = 1 and he = 1. The other laser and electron-beam parameters are the same as those in Fig. 1. (b) and (c) h ¯ γ of γ photons emitted by the LSP (he = 1) electron beam in the realistic laser pulse with a 0 , peak = 1. (b) h ¯ γ vs the coordinate time t (T0) and the energy ε γ of γ photons, and (c) comparisons of h ¯ γ vs ε γ for differently initial electron helicities he = 0, he = 1, and h e = 1, respectively. The other laser and electron-beam parameters are the same as those in Fig. 3. (d) and (e) The physical representations and other laser and electron-beam parameters are the same as those in (b) and (c) except a 0 , peak = 10.

FIG. 6.

(a) Average helicity of γ photons h ¯ γ in the monochromatic plane wave vs a0 and δ, with hL = 1 and he = 1. The other laser and electron-beam parameters are the same as those in Fig. 1. (b) and (c) h ¯ γ of γ photons emitted by the LSP (he = 1) electron beam in the realistic laser pulse with a 0 , peak = 1. (b) h ¯ γ vs the coordinate time t (T0) and the energy ε γ of γ photons, and (c) comparisons of h ¯ γ vs ε γ for differently initial electron helicities he = 0, he = 1, and h e = 1, respectively. The other laser and electron-beam parameters are the same as those in Fig. 3. (d) and (e) The physical representations and other laser and electron-beam parameters are the same as those in (b) and (c) except a 0 , peak = 10.

Close modal

In the NLCS, the polarization of the emitted photons in the linear region is averaged over all possible multi-photon absorption channels. The polarization of γ photons radiated by the single-photon absorption channel in NLCS is almost identical to that of the artificially squeezed LCS, which can be considered as the limit of NLCS as a 0 2 0 and n = 1.38 As the first harmonic edge of NLCS δ 1 1 / a 0 2, δ1 decreases as a0 increases. For instance, δ1 decreases from 0.191 for a 0 = 0.1 to 2.30 × 10 3 for a 0 = 10. Therefore, artificially squeezing the LCS helicity by a factor of S = δ LCS / δ 1 along δ yields a result that is nearly identical to that of the single-photon absorption channel in the NLCS [see the black-dash-dotted and green-dotted lines in Figs. 7(b), 7(d), and 7(f)]. The squeezing factors S are about 1.0, 1.80, and 81.96 for a 0 = 0.1, 1, and 10, respectively. Note that the polarization of γ photons radiated by the single-photon absorption channel is mainly determined by the laser spin. Due to the multi-photon absorption effect in the NLCS, in the following paragraphs, we analyze the photon polarization with respect to the laser intensity regime.

FIG. 7.

(a) Transition rates R of all possible channels n R n and the single-photon absorption channel R n = 1, respectively, and (b) average helicities h ¯ γ of all possible channels ∑n, the single-photon absorption channel and the LCS, respectively. (c)–(f) The physical representations and parameters are the same as those in (a) and (b) except a0. Other laser and electron-beam parameters are the same as those in Fig. 1.

FIG. 7.

(a) Transition rates R of all possible channels n R n and the single-photon absorption channel R n = 1, respectively, and (b) average helicities h ¯ γ of all possible channels ∑n, the single-photon absorption channel and the LCS, respectively. (c)–(f) The physical representations and parameters are the same as those in (a) and (b) except a0. Other laser and electron-beam parameters are the same as those in Fig. 1.

Close modal

For a 0 0.1, the transition rate R multi . ( δ ) n 2 R n ( δ ) of multi-photon absorption channels is about three orders of magnitude smaller than R n = 1 ( δ ) of the single-photon absorption channel [see Fig. 7(a)], which dominates the transition rate R ( δ ). Therefore, both the average helicity is almost identical to case of LCS [see Figs. 7(b)].

For a 0 1 , R multi . ( δ ) with δ δ 1 cannot be neglected [see Fig. 7(c)]. Therefore, the average helicity is significantly affected by the relative intensity of each channel and shifts upward (due to the contribution from multi-photon absorption channels) compared to the situation where LCS is artificially squeezed. For instance, the average helicity shifts up to h ¯ γ 0.76 from −1 at δ δ 1 [see Fig. 7(d)].

For a 0 10 , R multi . ( δ ) in the linear region ( δ δ 1) continues to increase [see Fig. 7(e)]. The deviation of h ¯ γ from the case of artificially squeezed LCS increases. For instance, h ¯ γ shifts up to −0.53 from −1 at δ δ 1, which is averaged over the multi-photon absorption channels [see Fig. 7(f)].

The above-mentioned analytical discussions are based on the single-photon emission of electrons with ε e = 10 GeV. However, the transfer mechanism also holds true for other electron energies (see Fig. 8). The slight difference is that the competed energy regions between laser and electron for controlling the γ-photon polarization are different. As δ 1 ε e for a certain a0, the energy of γ photon radiated by the electron with smaller ε e, of which the helicity is mostly determined by the laser, moves to the lower energy region. To obtain high-energy γ photons, the lower energy electrons need to absorb more laser photons. For instances, for a 0 = 10, electrons with ε e = 10 GeV radiate high-polarization γ rays with δ δ 1 2.35 × 10 3 via single-photon channel, while, for ε e = 1 GeV, δ δ 1 2.35 × 10 4. For high-energy γ photons, electrons with ε e = 10 GeV absorb laser photons with n ¯ 1000 to radiate γ photons with δ = 0.56, while, electrons with ε e = 1 GeV require n ¯ 10000 for the same δ.

FIG. 8.

(a) Distribution of the total differential radiation rate log 10 d 2 W rad d t d δ vs a0 and δ. The four lines indicate the first four cutoffs δ n = 1 , 2 , 3 , 4, respectively. (b) Average number of absorbed laser photons log 10 n ¯ vs a0 and δ. The black-solid lines indicate the contour lines of n ¯  10, 100, 1000, and 10 000, respectively. Ratios of (c) C 1 C 0 and (d) | C 2 | | C 2 | + C 3 ( C 3 > 0) vs a0 and δ, respectively. The black-dotted line indicates the spin contribution of the driving laser is equal to that of an electron to the γ photon, i.e., | C 2 | | C 2 | + C 3=0.5. (e) and (f) Average helicity of γ photons h ¯ γ in the monochromatic plane wave vs a0 and δ for two different examples of (e) hL = 1 and h e = 1, and (f) hL = 1 and he = 0, respectively. The electron initial energy ε e = 1 GeV, and other laser and electron-beam parameters are the same as those in Fig. 1.

FIG. 8.

(a) Distribution of the total differential radiation rate log 10 d 2 W rad d t d δ vs a0 and δ. The four lines indicate the first four cutoffs δ n = 1 , 2 , 3 , 4, respectively. (b) Average number of absorbed laser photons log 10 n ¯ vs a0 and δ. The black-solid lines indicate the contour lines of n ¯  10, 100, 1000, and 10 000, respectively. Ratios of (c) C 1 C 0 and (d) | C 2 | | C 2 | + C 3 ( C 3 > 0) vs a0 and δ, respectively. The black-dotted line indicates the spin contribution of the driving laser is equal to that of an electron to the γ photon, i.e., | C 2 | | C 2 | + C 3=0.5. (e) and (f) Average helicity of γ photons h ¯ γ in the monochromatic plane wave vs a0 and δ for two different examples of (e) hL = 1 and h e = 1, and (f) hL = 1 and he = 0, respectively. The electron initial energy ε e = 1 GeV, and other laser and electron-beam parameters are the same as those in Fig. 1.

Close modal

The presence of radiation reaction leads to differences in the average polarization of emitted photons within the linear region between strong NLCS ( a 0 , peak = 10) and weak NLCS ( a 0 , peak = 1).

For a 0 , peak = 1, the emitted photon number per electron is about 0.3 and the central energy of the radiating electrons is still around 10 GeV with the energy spread Δ ε e 2 GeV [see the red-dash-dotted line in Fig. 9(a)]. Therefore, the polarization of the emitted photons is averaged over those photons radiated by electrons with different energies. For instance, h ¯ γ shifts up to −0.51 at ε γ = ε ¯ e δ 1 1.06 GeV from h ¯ γ 0.76 of the case of ε e = 10 GeV, where ε ¯ e = 10 GeV is the central energy of the radiating electrons [see Fig. 9(b)].

FIG. 9.

(a) Comparisons of electron spectra dNe/d ε e vs the electron energy ε e for the initial electron beam before colliding with the laser pulse (the black solid line) and the radiating electrons in pulses with a 0 , peak = 1 (the red-dash-dotted line) and 10 (the green-dotted line), respectively. Comparisons of average helicity h ¯ γ vs ε γ for monoenergetic electrons with different energies and energy-spread electrons for (b) a 0 = 1 and (c) a 0 = 10, respectively. The energy spreads Δ ε e in (b) and (c) correspond to the red-dash-dotted and green-dotted lines in (a), respectively. h ¯ γ of emitted photons for monoenergetic electrons is the result in plane wave, while for the electron beam with energy spread, the result is in the laser pulse, and other laser and electron-beam parameters are the same as those in Fig. 3.

FIG. 9.

(a) Comparisons of electron spectra dNe/d ε e vs the electron energy ε e for the initial electron beam before colliding with the laser pulse (the black solid line) and the radiating electrons in pulses with a 0 , peak = 1 (the red-dash-dotted line) and 10 (the green-dotted line), respectively. Comparisons of average helicity h ¯ γ vs ε γ for monoenergetic electrons with different energies and energy-spread electrons for (b) a 0 = 1 and (c) a 0 = 10, respectively. The energy spreads Δ ε e in (b) and (c) correspond to the red-dash-dotted and green-dotted lines in (a), respectively. h ¯ γ of emitted photons for monoenergetic electrons is the result in plane wave, while for the electron beam with energy spread, the result is in the laser pulse, and other laser and electron-beam parameters are the same as those in Fig. 3.

Close modal

For a 0 , peak = 10, an electron emits approximately ten photons in the laser pulse. Consequently, multiple radiations lead to an expanded energy distribution of the radiating electrons, with an energy spread of Δ ε e 9.5 GeV [see the green-dotted line in Fig. 9(a)]. Meanwhile, as δ 1 ε e, the energies of the photons radiated by the single-photon absorption channel ( ε γ δ 1 ε e) decrease as ε e decreases. Therefore, h ¯ γ is averaged over those photons radiated by electrons with different energies and smoothly decreases from about 1 at ε γ 0.1 MeV to 0.08 at ε γ 22.7 MeV [see Fig. 9(c)].

For the LP laser (e.g., ξ 1 i = ξ 2 i = 0 and ξ 3 i = 1),38, F 1 n = 0 and
F 0 n = ( 1 1 δ + 1 δ ) f n s n 2 1 + a 0 2 g n ,
(E1)
F 2 n = δ ( 2 δ 1 δ f n s n 2 1 + a 0 2 g n ) ζ 3 ,
(E2)
F 3 n = 2 f n ( 2 + 2 c n s n 2 ) g n + ( 1 + c n ) 2 g n cos 2 φ ,
(E3)
and
f n = 0 2 π f n d φ 2 π , g n = 0 2 π g n d φ 2 π ,
(E4a)
s n = 2 r n ( 1 r n ) , c n = 1 2 r n , r n = δ ( 1 + a 0 2 ) ( 1 δ ) n Λ .
(E4b)
Here, = a 0 2 1 + a 0 2 and
f n = 4 [ A 1 ( n , a , b ) ] 2 4 A 0 ( n , a , b ) A 2 ( n , a , b ) ,
(E5a)
g n = 4 n 2 z n 2 [ A 0 ( n , a , b ) ] 2 ,
(E5b)
where the functions Ak were introduced in Ref. 89 as follows:
A k ( n , a , b ) = π π cos k ψ exp [ i ( n ψ a sin ψ + b sin 2 ψ ) ] d ψ 2 π .
(E6)
In the collision system one has a = z n 2 cos φ and b = δ 2 ( 1 δ ) Λ a 0 2. From Eq. (E2), we can see that in the LP laser the CP polarization of the emitted photon only is transferred by the LSP electrons.

For LP γ photons generated in the LP laser, the competition between the laser and electron for controlling the γ-photon polarization also exists (see Fig. 10). For instances, for SNP electrons in the LP laser field with a 0 O ( 0.1 ), the radiation probability of the first harmonic is three orders of magnitude greater than that of the second and is greater than that of other harmonics. As a result, the emitted photons are almost completely radiated via the single-photon absorption channel and obtain an almost entirely linear polarization at the end of the first harmonic with ξ ¯ 3 f 1 [see Figs. 10(a) and 10(b)]. As a0 increases to O(1), the absorption channels of dozens of laser photons occur and γ photons with higher energy are radiated, while ξ ¯ 3 f of γ photons at the first harmonic edge decreases to 0.88. Since the electron spin plays an increasingly significant role in multi-photon absorption channels, ξ ¯ 3 f decreases as δ δ 2 [see Figs. 10(c) and 10(d)]. In addition, for a 0 O ( 10 ), there are higher transition probabilities to radiate higher energy γ photons, and d 2 W rad d t d δ 7.6 at δ δ 1 = 0.0023 but with decreased ξ ¯ 3 f 0.64. Note that when the average number of absorbed laser photons n ¯ increases to 100, the LCFA method can perfectly predict the radiation probability and linear polarization of γ photons [see Figs. 10(g) and 10(h)]. Expectedly, ξ ¯ 3 f is falling to 0 as δ increases to 1 because of more polarization contribution from the electron [see Fig. 10(f)]. Therefore, to generate high-brilliance high-energy LP γ rays, we not only need to increase the laser intensity but also accelerate the electrons to high energies due to δ 1 ε e. Importantly, the spin effects of electrons on the liner polarization of radiated γ photons are balanced out in the LP laser pulse. However, if the γ photons can be separated, such as using an elliptically polarized laser pulse,45 the high polarization of γ photons at high-energy parts contributed by the transversely spin-polarized electrons via multi-photon absorption channels will be accessed.

FIG. 10.

Comparisons of transition probability R = d 2 W rad d t d δ and linear polarization ξ ¯ 3 f of γ photons in the LP laser via differently intense CS regimes vs δ, with (a) and (b) a 0 = 0.1, (c) and (d) a 0 = 1, and (e)–(h) a 0 = 10. The black and blue solid lines in (a)–(h) are analytical results in the monochromatic (MONO) plane wave38 and the red dash-dotted lines in (e)–(h) are predicted by the LCFA method.45 The other laser and electron-beam parameters are the same as those in Fig. 1.

FIG. 10.

Comparisons of transition probability R = d 2 W rad d t d δ and linear polarization ξ ¯ 3 f of γ photons in the LP laser via differently intense CS regimes vs δ, with (a) and (b) a 0 = 0.1, (c) and (d) a 0 = 1, and (e)–(h) a 0 = 10. The black and blue solid lines in (a)–(h) are analytical results in the monochromatic (MONO) plane wave38 and the red dash-dotted lines in (e)–(h) are predicted by the LCFA method.45 The other laser and electron-beam parameters are the same as those in Fig. 1.

Close modal

Comparison of the γ photons, respectively, predicted by the methods of LMA57,79,81 and LCFA45 is shown in Fig. 11. LCFA requires a 0 1 and a 0 3 χ e,51,90–92 therefore, the radiation at the two tails of the laser pulse is overestimated and the spectra calculated by LCFA are broader than the case of LMA. Interestingly, even when the above conditions are fulfilled, the γ-photon spectra predicted by the methods of LMA and LCFA also have differences in the region of ε γ ( χ e / a 0 3 ) ε e,93–96 where χ e 1.18 for the head-on collision scenario. As a result, the yields of low-energy photons ε γ 11.87 MeV are also overestimated near the peak intensity of the laser pulse [see Figs. 3(d), 11(a), and 11(d)]. Importantly, in the LCFA method, the helicity contribution from the CP laser is not included, therefore, one gets h ¯ γ = 0 for spin-nonpolarized electrons (he = 0) [see Fig. 11(b) and the green-solid line in Fig. 11(e)]. As expected, high-energy γ photons with ε γ 1 GeV radiated in the middle of the laser pulse obtain polarization from the LSP electrons [see Fig. 11(c) and the red-dash-dotted line in Fig. 11(e)], and the deviation Δ h ¯ γ = h ¯ γ LCFA h ¯ γ LMA decreases from 0.08 at ε γ 1 GeV to 0 at about 9 GeV.

FIG. 11.

Generation of γ photons predicted by the LCFA method with a 0 , peak = 10 vs the coordinate time t ( T 0 ) and the energy ε γ of γ photons, with (a) and (b) the yields of γ photons log 10 d N γ dtd ε γ and average helicity h ¯ γ for he = 0, and (c) h ¯ γ for h e = 1, respectively. The magenta solid line in (a) indicates the average intensity a ¯ 0 sensed by the spatially distributed electron beam vs t (T0). (d) and (e) Comparisons for d N γ / d ε γ and h ¯ γ predicted by the methods of LMA and LCFA, respectively. The other laser and electron-beam parameters are the same as those in Fig. 3.

FIG. 11.

Generation of γ photons predicted by the LCFA method with a 0 , peak = 10 vs the coordinate time t ( T 0 ) and the energy ε γ of γ photons, with (a) and (b) the yields of γ photons log 10 d N γ dtd ε γ and average helicity h ¯ γ for he = 0, and (c) h ¯ γ for h e = 1, respectively. The magenta solid line in (a) indicates the average intensity a ¯ 0 sensed by the spatially distributed electron beam vs t (T0). (d) and (e) Comparisons for d N γ / d ε γ and h ¯ γ predicted by the methods of LMA and LCFA, respectively. The other laser and electron-beam parameters are the same as those in Fig. 3.

Close modal
1.
A.
Simon
, “
Theory of polarized particles and gamma rays in nuclear reactions
,”
Phys. Rev.
92
,
1050
(
1953
).
2.
L. W.
Fagg
and
S. S.
Hanna
, “
Polarization measurements on nuclear gamma rays
,”
Rev. Mod. Phys.
31
,
711
(
1959
).
3.
F.
Zernike
, “
How I discovered phase contrast
,”
Science
121
,
345
(
1955
).
4.
A.
Rousse
,
C.
Rischel
, and
J.-C.
Gauthier
, “
Femtosecond x-ray crystallography
,”
Rev. Mod. Phys.
73
,
17
(
2001
).
5.
A.
Dean
,
D.
Clark
,
J.
Stephen
,
V.
McBride
,
L.
Bassani
,
A.
Bazzano
,
A.
Bird
,
A.
Hill
,
S.
Shaw
, and
P.
Ubertini
, “
Polarized gamma-ray emission from the Crab
,”
Science
321
,
1183
(
2008
).
6.
H.
Schwoerer
,
J.
Magill
, and
B.
Beleites
,
Lasers and Nuclei: Applications of Ultrahigh Intensity Lasers in Nuclear Science
(
Springer Science & Business Media
,
2006
), Vol.
694
.
7.
H. R.
Weller
,
M. W.
Ahmed
,
H.
Gao
,
W.
Tornow
,
Y. K.
Wu
,
M.
Gai
, and
R.
Miskimen
, “
Research opportunities at the upgraded HIγS facility
,”
Prog. Part. Nucl. Phys.
62
,
257
(
2009
).
8.
D.
Budker
,
J. C.
Berengut
,
V. V.
Flambaum
,
M.
Gorchtein
,
J.
Jin
,
F.
Karbstein
,
M. W.
Krasny
,
Y. A.
Litvinov
,
A.
Pálffy
,
V.
Pascalutsa
et al, “
Expanding nuclear physics horizons with the Gamma Factory
,”
Ann. Phys.
534
,
2100284
(
2022
).
9.
A.
Zilges
,
D.
Balabanski
,
J.
Isaak
, and
N.
Pietralla
, “
Photonuclear reactions–From basic research to applications
,”
Prog. Part. Nucl. Phys.
122
,
103903
(
2022
).
10.
G.
Breit
and
J. A.
Wheeler
, “
Collision of two light quanta
,”
Phys. Rev.
46
,
1087
(
1934
).
11.
Q.
Zhao
,
L.
Tang
,
F.
Wan
,
B.-C.
Liu
,
R.-Y.
Liu
,
R.-Z.
Yang
,
J.-Q.
Yu
,
X.-G.
Ren
,
Z.-F.
Xu
,
Y.-T.
Zhao
,
Y.-S.
Huang
, and
J.-X.
Li
, “
Signatures of linear Breit-Wheeler pair production in polarized γ γ collisions
,”
Phys. Rev. D
105
,
L071902
(
2022
).
12.
Q.
Zhao
,
Y.-X.
Wu
,
M.
Ababekri
,
Z.-P.
Li
,
L.
Tang
, and
J.-X.
Li
, “
Angle-dependent pair production in the polarized two-photon Breit-Wheeler process
,”
Phys. Rev. D
107
,
096013
(
2023
).
13.
J. D.
Brandenburg
,
J.
Seger
,
Z.
Xu
, and
W.
Zha
, “
Report on progress in physics: Observation of the Breit-Wheeler process and vacuum birefringence in heavy-ion collisions
,”
Rep. Prog. Phys.
86
,
083901
(
2023
).
14.
O.
Halpern
, “
Scattering processes produced by electrons in negative energy states
,”
Phys. Rev.
44
,
855
(
1933
).
15.
D.
Micieli
,
I.
Drebot
,
A.
Bacci
,
E.
Milotti
,
V.
Petrillo
,
M. R.
Conti
,
A. R.
Rossi
,
E.
Tassi
, and
L.
Serafini
, “
Compton sources for the observation of elastic photon-photon scattering events
,”
Phys. Rev. Accel. Beams
19
,
093401
(
2016
).
16.
T. N.
Wistisen
and
U. I.
Uggerhøj
, “
Vacuum birefringence by Compton backscattering through a strong field
,”
Phys. Rev. D
88
,
053009
(
2013
).
17.
S.
Bragin
,
S.
Meuren
,
C. H.
Keitel
, and
A.
Di Piazza
, “
High-energy vacuum Birefringence and Dichroism in an ultrastrong laser field
,”
Phys. Rev. Lett.
119
,
250403
(
2017
).
18.
F.
Wan
,
T.
Sun
,
B.-F.
Shen
,
C.
Lv
,
Q.
Zhao
,
M.
Ababekri
,
Y.-T.
Zhao
,
K. Z.
Hatsagortsyan
,
C. H.
Keitel
, and
J.-X.
Li
, “
Enhanced signature of vacuum birefringence in a plasma wakefield
,” arXiv:2206.10792 (
2022
).
19.
B.
Jin
and
B.
Shen
, “
Enhancement of vacuum birefringence with pump laser of flying focus
,”
Phys. Rev. A
107
,
062213
(
2023
).
20.
D. H.
Bilderback
,
P.
Elleaume
, and
E.
Weckert
, “
Review of third and next generation synchrotron light sources
,”
J. Phys. B
38
,
S773
(
2005
).
21.
R.
Schwengner
,
R.
Beyer
,
F.
Dönau
,
E.
Grosse
,
A.
Hartmann
,
A.
Junghans
,
S.
Mallion
,
G.
Rusev
,
K.
Schilling
,
W.
Schulze
, and
A.
Wagner
, “
The photon-scattering facility at the superconducting electron accelerator ELBE
,”
Nucl. Instrum. Methods Phys. Res. Sect. A
555
,
211
(
2005
).
22.
K.
Sonnabend
,
D.
Savran
,
J.
Beller
,
M.
Büssing
,
A.
Constantinescu
,
M.
Elvers
,
J.
Endres
,
M.
Fritzsche
,
J.
Glorius
,
J.
Hasper
,
J.
Isaak
,
B.
Löher
,
S.
Müller
,
N.
Pietralla
,
C.
Romig
,
A.
Sauerwein
,
L.
Schnorrenberger
,
C.
Wälzlein
,
A.
Zilges
, and
M.
Zweidinger
, “
The Darmstadt high-intensity photon setup (DHIPS) at the S-DALINAC
,”
Nucl. Instrum. Phys. Res. Sect. A
640
,
6
12
(
2011
).
23.
S.
Kashiwagi
,
M.
Washio
,
T.
Kobuki
,
R.
Kuroda
,
I.
Ben-Zvi
,
I.
Pogorelsky
,
K.
Kusche
,
J.
Skaritka
,
V.
Yakimenko
,
X.
Wang
et al, “
Observation of high-intensity X-rays in inverse Compton scattering experiment
,”
Nucl. Instrum. Phys. Res. Sect. A
455
,
36
(
2000
).
24.
T.
Nakano
,
J.
Ahn
,
M.
Fujiwara
,
H.
Kohri
,
N.
Matsuoka
,
T.
Mibe
,
N.
Muramatsu
,
M.
Nomachi
,
H.
Shimizu
,
K.
Yonehara
et al, “
Multi-GeV laser-electron photon project at SPring-8
,”
Nucl. Phys. A
684
,
71
(
2001
).
25.
K.
Horikawa
,
S.
Miyamoto
,
S.
Amano
, and
T.
Mochizuki
, “
Measurements for the energy and flux of laser Compton scattering γ-ray photons generated in an electron storage ring: NewSUBARU
,”
Nucl. Instrum. Phys. Res. Sect. A
618
,
209
(
2010
).
26.
H.
Zen
,
Y.
Taira
,
T.
Konomi
,
T.
Hayakawa
,
T.
Shizuma
,
J.
Yamazaki
,
T.
Kii
,
H.
Toyokawa
,
M.
Katoh
, and
H.
Ohgaki
, “
Generation of high energy gamma-ray by laser Compton scattering of 1.94-μm fiber laser in UVSOR-III electron storage ring
,”
Energy Procedia
89
,
335
(
2016
).
27.
M.
Bech
,
O.
Bunk
,
C.
David
,
R.
Ruth
,
J.
Rifkin
,
R.
Loewen
,
R.
Feidenhans'l
, and
F.
Pfeiffer
, “
Hard X-ray phase-contrast imaging with the compact light source based on inverse Compton x-rays
,”
J. Synchrotron Radiat.
16
,
43
(
2009
).
28.
J.
Als-Nielsen
and
D.
McMorrow
,
Elements of Modern X-Ray Physics
(
John Wiley & Sons
,
2011
).
29.
F.
Albert
,
S. G.
Anderson
,
D. J.
Gibson
,
C. A.
Hagmann
,
M. S.
Johnson
,
M.
Messerly
,
V.
Semenov
,
M. Y.
Shverdin
,
B.
Rusnak
,
A. M.
Tremaine
,
F. V.
Hartemann
,
C. W.
Siders
,
D. P.
McNabb
, and
C. P. J.
Barty
, “
Characterization and applications of a tunable, laser-based, MeV-class Compton-scattering γ-ray source
,”
Phys. Rev. ST Accel. Beams
13
,
070704
(
2010
).
30.
S.
Gales
,
K. A.
Tanaka
,
D. L.
Balabanski
,
F.
Negoita
,
D.
Stutman
,
O.
Tesileanu
,
C. A.
Ur
,
D.
Ursescu
,
I.
Andrei
,
S.
Ataman
,
M. O.
Cernaianu
,
L.
D'Alessi
,
I.
Dancus
,
B.
Diaconescu
,
N.
Djourelov
,
D.
Filipescu
,
P.
Ghenuche
,
D. G.
Ghita
,
C.
Matei
,
K.
Seto
,
M.
Zeng
, and
N. V.
Zamfir
, “
The extreme light infrastructure–nuclear physics (ELI-NP) facility: New horizons in physics with 10 PW ultra-intense lasers and 20 MeV brilliant gamma beams
,”
Rep. Prog. Phys.
81
,
094301
(
2018
).
31.
C. N.
Danson
,
C.
Haefner
,
J.
Bromage
,
T.
Butcher
,
J.-C. F.
Chanteloup
,
E. A.
Chowdhury
,
A.
Galvanauskas
,
L. A.
Gizzi
,
J.
Hein
,
D. I.
Hillier
et al, “
Petawatt and Exawatt class lasers worldwide
,”
High Power Laser Sci.
7
,
e54
(
2019
).
32.
J. W.
Yoon
,
C.
Jeon
,
J.
Shin
,
S. K.
Lee
,
H. W.
Lee
,
I. W.
Choi
,
H. T.
Kim
,
J. H.
Sung
, and
C. H.
Nam
, “
Achieving the laser intensity of 5.5 × 10 22 W/cm2 with a wavefront-corrected multi-PW laser
,”
Opt. Express
27
,
20412
(
2019
).
33.
J. W.
Yoon
,
Y. G.
Kim
,
I. W.
Choi
,
J. H.
Sung
,
H. W.
Lee
,
S. K.
Lee
, and
C. H.
Nam
, “
Realization of laser intensity over 1023 W/cm2
,”
Optica
8
,
630
(
2021
).
34.
G.
Sarri
,
D. J.
Corvan
,
W.
Schumaker
,
J. M.
Cole
,
A. D.
Piazza
,
H.
Ahmed
,
C.
Harvey
,
C. H.
Keitel
,
K.
Krushelnick
,
S. P. D.
Mangles
,
Z.
Najmudin
,
D.
Symes
,
A. G. R.
Thomas
,
M.
Yeung
,
Z.
Zhao
, and
M.
Zepf
, “
Ultrahigh brilliance multi-MeV γ-ray beams from nonlinear relativistic Thomson scattering
,”
Phys. Rev. Lett.
113
,
224801
(
2014
).
35.
K.
Khrennikov
,
J.
Wenz
,
A.
Buck
,
J.
Xu
,
M.
Heigoldt
,
L.
Veisz
, and
S.
Karsch
, “
Tunable all-optical quasimonochromatic Thomson x-ray source in the nonlinear regime
,”
Phys. Rev. Lett.
114
,
195003
(
2015
).
36.
W.
Yan
,
C.
Fruhling
,
G.
Golovin
,
D.
Haden
,
J.
Luo
,
P.
Zhang
,
B.
Zhao
,
J.
Zhang
,
C.
Liu
,
M.
Chen
,
S.
Chen
,
S.
Banerjee
, and
D.
Umstadter
, “
High-order multiphoton Thomson scattering
,”
Nat. Photonics
11
,
514
(
2017
).
37.
C.
Bula
,
K. T.
McDonald
,
E. J.
Prebys
,
C.
Bamber
,
S.
Boege
,
T.
Kotseroglou
,
A. C.
Melissinos
,
D. D.
Meyerhofer
,
W.
Ragg
,
D. L.
Burke
,
R. C.
Field
,
G.
Horton-Smith
,
A. C.
Odian
,
J. E.
Spencer
,
D.
Walz
,
S. C.
Berridge
,
W. M.
Bugg
,
K.
Shmakov
, and
A. W.
Weidemann
, “
Observation of nonlinear effects in Compton scattering
,”
Phys. Rev. Lett.
76
,
3116
(
1996
).
38.
D. Y.
Ivanov
,
G.
Kotkin
, and
V.
Serbo
, “
Complete description of polarization effects in emission of a photon by an electron in the field of a strong laser wave
,”
Eur. Phys. J. C
36
,
127
(
2004
).
39.
Y. I.
Salamin
,
S.
Hu
,
K. Z.
Hatsagortsyan
, and
C. H.
Keitel
, “
Relativistic high-power laser–matter interactions
,”
Phys. Rep.
427
,
41
(
2006
).
40.
H.
Xiao
,
C.-W.
Zhang
,
H.-B.
Sang
, and
B. S.
Xie
, “
Nonlinear Thomson scattering in an arbitrary polarized laser field with a background magnetic field
,”
Phys. Plasmas
30
,
053104
(
2023
).
41.
T. N.
Wistisen
and
A.
Di Piazza
, “
Numerical approach to the semiclassical method of radiation emission for arbitrary electron spin and photon polarization
,”
Phys. Rev. D
100
,
116001
(
2019
).
42.
B.
King
and
S.
Tang
, “
Nonlinear Compton scattering of polarized photons in plane-wave backgrounds
,”
Phys. Rev. A
102
,
022809
(
2020
).
43.
S.
Tang
,
B.
King
, and
H.
Hu
, “
Highly polarised gamma photons from electron-laser collisions
,”
Phys. Lett. B
809
,
135701
(
2020
).
44.
Y.
Wang
,
M.
Ababekri
,
F.
Wan
,
Q.
Zhao
,
C.
Lv
,
X.-G.
Ren
,
Z.-F.
Xu
,
Y.-T.
Zhao
, and
J.-X.
Li
, “
Brilliant circularly polarized γ-ray sources via single-shot laser plasma interaction
,”
Opt. Lett.
47
,
3355
(
2022
).
45.
Y.-F.
Li
,
R.
Shaisultanov
,
Y.-Y.
Chen
,
F.
Wan
,
K. Z.
Hatsagortsyan
,
C. H.
Keitel
, and
J.-X.
Li
, “
Polarized ultrashort brilliant multi-GeV γ rays via single-shot laser-electron interaction
,”
Phys. Rev. Lett.
124
,
014801
(
2020
).
46.
H.
Abramowicz
,
U.
Acosta
,
M.
Altarelli
,
R.
Assmann
,
Z.
Bai
,
T.
Behnke
,
Y.
Benhammou
,
T.
Blackburn
,
S.
Boogert
,
O.
Borysov
et al, “
Conceptual design report for the LUXE experiment
,”
Eur. Phys. J. Spec. Top.
230
,
2445
(
2021
).
47.
F.
Salgado
,
N.
Cavanagh
,
M.
Tamburini
,
D.
Storey
,
R.
Beyer
,
P.
Bucksbaum
,
Z.
Chen
,
A.
Di Piazza
,
E.
Gerstmayr
,
E.
Isele
et al, “
Single particle detection system for strong-field QED experiments
,”
New J. Phys.
24
,
015002
(
2022
).
48.
A.
Gonoskov
,
T. G.
Blackburn
,
M.
Marklund
, and
S. S.
Bulanov
, “
Charged particle motion and radiation in strong electromagnetic fields
,”
Rev. Mod. Phys.
94
,
045001
(
2022
).
49.
A.
Fedotov
,
A.
Ilderton
,
F.
Karbstein
,
B.
King
,
D.
Seipt
,
H.
Taya
, and
G.
Torgrimsson
, “
Advances in QED with intense background fields
,”
Phys. Rep.
1010
,
1
138
(
2023
).
50.
M.
Ababekri
,
R.-T.
Guo
,
F.
Wan
,
B.
Qiao
,
Z.
Li
,
C.
Lv
,
B.
Zhang
,
W.
Zhou
,
Y.
Gu
, and
J.-X.
Li
, “
Vortex γ photon generation via spin-to-orbital angular momentum transfer in nonlinear Compton scattering
,”
Phys. Rev. D
109
,
016005
(
2024
).
51.
V.
Ritus
, “
Quantum effects of the interaction of elementary particles with an intense electromagnetic field
,”
J. Sov. Laser Res.
6
,
497
(
1985
).
52.
V. N.
Baier
and
V.
Katkov
,
Electromagnetic Processes at High Energies in Oriented Single Crystals
(World Scientific, Singapore, 1998).
53.
C.
Bamber
,
S. J.
Boege
,
T.
Koffas
,
T.
Kotseroglou
,
A. C.
Melissinos
,
D. D.
Meyerhofer
,
D. A.
Reis
,
W.
Ragg
,
C.
Bula
,
K. T.
McDonald
,
E. J.
Prebys
,
D. L.
Burke
,
R. C.
Field
,
G.
Horton-Smith
,
J. E.
Spencer
,
D.
Walz
,
S. C.
Berridge
,
W. M.
Bugg
,
K.
Shmakov
, and
A. W.
Weidemann
, “
Studies of nonlinear QED in collisions of 46.6 GeV electrons with intense laser pulses
,”
Phys. Rev. D
60
,
092004
(
1999
).
54.
I. F.
Ginzburg
,
G. L.
Kotkin
,
S. L.
Panfil
,
V. G.
Serbo
, and
V. I.
Telnov
, “
Colliding γe and γ γ beams based on single-pass e+ e accelerators II. Polarization effects, monochromatization improvement
,”
Nucl. Instrum. Methods Phys. Res.
219
,
5
24
(
1984
).
55.
T.
Heinzl
,
D.
Seipt
, and
B.
Kämpfer
, “
Beam-shape effects in nonlinear Compton and Thomson scattering
,”
Phys. Rev. A
81
,
022125
(
2010
).
56.
V.
Berestetskii
,
E.
Lifshitz
, and
L.
Pitaevskii
,
Quantum Electrodynamics
, 3rd ed. (Nauka, Moscow,
1989
).
57.
K.
Yokoya
,
CAIN 2.42 User Manual
(
2011
).
58.
D.
Babusci
,
G.
Giordano
, and
G.
Matone
, “
Photon polarization properties in laser backscattering
,”
Phys. Lett. B
355
,
1
8
(
1995
).
59.
D.
Karlovets
,
S.
Baturin
,
G.
Geloni
,
G.
Sizykh
, and
V.
Serbo
, “
Generation of vortex particles via generalized measurements
,”
Eur. Phys. J. C
82
,
1008
(
2022
).
60.
D.
Karlovets
,
S.
Baturin
,
G.
Geloni
,
G.
Sizykh
, and
V.
Serbo
, “
Shifting physics of vortex particles to higher energies via quantum entanglement
,”
Eur. Phys. J. C
83
,
372
(
2023
).
61.
C. R.
Howell
,
M. W.
Ahmed
,
A.
Afanasev
,
D.
Alesini
,
J.
Annand
,
A.
Aprahamian
,
D.
Balabanski
,
S.
Benson
,
A.
Bernstein
,
C.
Brune
et al, “
International workshop on next generation gamma-ray source
,”
J. Phys. G
49
,
010502
(
2022
).
62.
Y.
Ma
,
J.
Hua
,
D.
Liu
,
Y.
He
,
T.
Zhang
,
J.
Chen
,
F.
Yang
,
X.
Ning
,
H.
Zhang
,
Y.
Du
, and
W.
Lu
, “
Compact polarized x-ray source based on all-optical inverse compton scattering
,”
Phys. Rev. Appl.
19
,
014073
(
2023
).
63.
K.
Tanaka
,
K.
Spohr
,
D.
Balabanski
,
S.
Balascuta
,
L.
Capponi
,
M.
Cernaianu
,
M.
Cuciuc
,
A.
Cucoanes
,
I.
Dancus
,
A.
Dhal
et al, “
Current status and highlights of the ELI-NP research program
,”
Matter Radiat. Extremes
5
,
024402
(
2020
).
64.
W.
Hong
,
S.
He
,
J.
Teng
,
Z.
Deng
,
Z.
Zhang
,
F.
Lu
,
B.
Zhang
,
B.
Zhu
,
Z.
Dai
,
B.
Cui
et al, “
Commissioning experiment of the high-contrast SILEX-II multi-petawatt laser facility
,”
Matter Radiat. Extremes
6
,
064401
(
2021
).
65.
K.
Burdonov
,
A.
Fazzini
,
V.
Lelasseux
,
J.
Albrecht
,
P.
Antici
,
Y.
Ayoul
,
A.
Beluze
,
D.
Cavanna
,
T.
Ceccotti
,
M.
Chabanis
,
A.
Chaleil
,
S. N.
Chen
,
Z.
Chen
,
F.
Consoli
,
M.
Cuciuc
,
X.
Davoine
,
J. P.
Delaneau
,
E.
d'Humières
,
J.-L.
Dubois
,
C.
Evrard
,
E.
Filippov
,
A.
Freneaux
,
P.
Forestier-Colleoni
,
L.
Gremillet
,
V.
Horny
,
L.
Lancia
,
L.
Lecherbourg
,
N.
Lebas
,
A.
Leblanc
,
W.
Ma
,
L.
Martin
,
F.
Negoita
,
J.-L.
Paillard
,
D.
Papadopoulos
,
F.
Perez
,
S.
Pikuz
,
G.
Qi
,
F.
Quéré
,
L.
Ranc
,
P.-A.
Söderström
,
M.
Scisciò
,
S.
Sun
,
S.
Vallières
,
P.
Wang
,
W.
Yao
,
F.
Mathieu
,
P.
Audebert
, and
J.
Fuchs
, “
Characterization and performance of the Apollon short-focal-area facility following its commissioning at 1 PW level
,”
Matter Radiat. Extremes
6
,
064402
(
2021
).
66.
Z.
Gan
,
L.
Yu
,
C.
Wang
,
Y.
Liu
,
Y.
Xu
,
W.
Li
,
S.
Li
,
L.
Yu
,
X.
Wang
,
X.
Liu
et al,
Progress in Ultrafast Intense Laser Science XVI
, edited by
K. M.
Kaoru Yamanouchi
and
L.
Roso
(Springer, Cham, 2021), Vol.
141
.
67.
J.
Vieira
,
C.-K.
Huang
,
W. B.
Mori
, and
L. O.
Silva
, “
Polarized beam conditioning in plasma based acceleration
,”
Phys. Rev. ST Accel. Beams
14
,
071303
(
2011
).
68.
M.
Wen
,
M.
Tamburini
, and
C. H.
Keitel
, “
Polarized laser-WakeField-accelerated kiloampere electron beams
,”
Phys. Rev. Lett.
122
,
214801
(
2019
).
69.
Y.
Wu
,
L.
Ji
,
X.
Geng
,
Q.
Yu
,
N.
Wang
,
B.
Feng
,
Z.
Guo
,
W.
Wang
,
C.
Qin
,
X.
Yan
,
L.
Zhang
,
J.
Thomas
,
A.
Hützen
,
A.
Pukhov
,
M.
Büscher
,
B.
Shen
, and
R.
Li
, “
Polarized electron acceleration in beam-driven plasma wakefield based on density down-ramp injection
,”
Phys. Rev. E
100
,
043202
(
2019
).
70.
Y.
Wu
,
L.
Ji
,
X.
Geng
,
Q.
Yu
,
N.
Wang
,
B.
Feng
,
Z.
Guo
,
W.
Wang
,
C.
Qin
,
X.
Yan
,
L.
Zhang
,
J.
Thomas
,
A.
Hützen
,
M.
Büscher
,
T. P.
Rakitzis
,
A.
Pukhov
,
B.
Shen
, and
R.
Li
, “
Polarized electron-beam acceleration driven by vortex laser pulses
,”
New J. Phys.
21
,
073052
(
2019
).
71.
Z.
Nie
,
F.
Li
,
F.
Morales
,
S.
Patchkovskii
,
O.
Smirnova
,
W.
An
,
N.
Nambu
,
D.
Matteo
,
K. A.
Marsh
,
F.
Tsung
,
W. B.
Mori
, and
C.
Joshi
, “
In Situ generation of high-energy spin-polarized electrons in a beam-driven plasma wakefield accelerator
,”
Phys. Rev. Lett.
126
,
054801
(
2021
).
72.
H.
Fan
,
X.
Liu
,
X.
Li
,
J.
Qu
,
Q.
Yu
,
Q.
Kong
,
S.
Weng
,
M.
Chen
,
M.
Büscher
,
P.
Gibbon
et al, “
Control of electron beam polarization in the bubble regime of laser-wakefield acceleration
,”
New J. Phys.
24
,
083047
(
2022
).
73.
T.
Sun
,
Q.
Zhao
,
F.
Wan
,
Y. I.
Salamin
, and
J.-X.
Li
, “
Generation of ultrabrilliant polarized attosecond electron bunches via dual-wake injection
,”
Phys. Rev. Lett.
132
,
045001
(
2024
).
74.
T. P.
Rakitzis
,
P. C.
Samartzis
,
R. L.
Toomes
,
T. N.
Kitsopoulos
,
A.
Brown
,
G. G.
Balint-Kurti
,
O. S.
Vasyutinskii
, and
J. A.
Beswick
, “
Spin-polarized hydrogen atoms from molecular photodissociation
,”
Science
300
,
1936
(
2003
).
75.
D.
Sofikitis
,
L.
Rubio-Lago
,
L.
Bougas
,
A. J.
Alexander
, and
T. P.
Rakitzis
, “
Laser detection of spin-polarized hydrogen from HCl and HBr photodissociation: Comparison of H- and halogen-atom polarizations
,”
J. Chem. Phys.
129
,
144302
(
2008
).
76.
D.
Sofikitis
,
C. S.
Kannis
,
G. K.
Boulogiannis
, and
T. P.
Rakitzis
, “
Ultrahigh-density spin-polarized H and D observed via magnetization quantum beats
,”
Phys. Rev. Lett.
121
,
083001
(
2018
).
77.
A. K.
Spiliotis
,
M.
Xygkis
,
M. E.
Koutrakis
,
D.
Sofikitis
, and
T. P.
Rakitzis
, “
Depolarization of spin-polarized hydrogen via collisions with chlorine atoms at ultrahigh density
,”
Chem. Phys. Impact
2
,
100022
(
2021
).
78.
F.
Wan
,
C.
Lv
,
K.
Xue
,
Z.-K.
Dou
,
Q.
Zhao
,
M.
Ababekri
,
W.-Q.
Wei
,
Z.-P.
Li
,
Y.-T.
Zhao
, and
J.-X.
Li
, “
Simulations of spin/polarization-resolved laser–plasma interactions in the nonlinear QED regime
,”
Matter Radiat. Extremes
8
,
064002
(
2023
).
79.
T. G.
Blackburn
,
A. J.
Macleod
, and
B.
King
, “
From local to nonlocal: Higher fidelity simulations of photon emission in intense laser pulses
,”
New J. Phys.
23
,
085008
(
2021
).
80.
T. G.
Blackburn
,
B.
King
, and
S.
Tang
, “
Simulations of laser-driven strong-field QED with Ptarmigan: Resolving wavelength-scale interference and γ-ray polarization
,”
Phys. Plasmas
30
,
093903
(
2023
).
81.
T.
Heinzl
,
B.
King
, and
A. J.
MacLeod
, “
Locally monochromatic approximation to QED in intense laser fields
,”
Phys. Rev. A
102
,
063110
(
2020
).
82.
W. P.
Leemans
,
A. J.
Gonsalves
,
H.-S.
Mao
,
K.
Nakamura
,
C.
Benedetti
,
C. B.
Schroeder
,
C.
Tóth
,
J.
Daniels
,
D. E.
Mittelberger
,
S. S.
Bulanov
,
J.-L.
Vay
,
C. G. R.
Geddes
, and
E.
Esarey
, “
Multi-GeV electron beams from capillary-discharge-guided subpetawatt laser pulses in the self-trapping regime
,”
Phys. Rev. Lett.
113
,
245002
(
2014
).
83.
G.
Xia
,
Y.
Nie
,
O.
Mete
,
K.
Hanahoe
,
M.
Dover
,
M.
Wigram
,
J.
Wright
,
J.
Zhang
,
J.
Smith
,
T.
Pacey
,
Y.
Li
,
Y.
Wei
, and
C.
Welsch
, “
Plasma wakefield acceleration at CLARA facility in Daresbury Laboratory
,”
Nucl. Instrum. Methods in Phys. Res. Sect. A
829
,
43
(
2016
).
84.
A. J.
Gonsalves
,
K.
Nakamura
,
J.
Daniels
,
C.
Benedetti
,
C.
Pieronek
,
T. C. H.
de Raadt
,
S.
Steinke
,
J. H.
Bin
,
S. S.
Bulanov
,
J.
van Tilborg
,
C. G. R.
Geddes
,
C. B.
Schroeder
,
C.
Tóth
,
E.
Esarey
,
K.
Swanson
,
L.
Fan-Chiang
,
G.
Bagdasarov
,
N.
Bobrova
,
V.
Gasilov
,
G.
Korn
,
P.
Sasorov
, and
W. P.
Leemans
, “
Petawatt laser guiding and electron beam acceleration to 8 GeV in a laser-heated capillary discharge waveguide
,”
Phys. Rev. Lett.
122
,
084801
(
2019
).
85.
F.
Li
,
T. N.
Dalichaouch
,
J. R.
Pierce
,
X.
Xu
,
F. S.
Tsung
,
W.
Lu
,
C.
Joshi
, and
W. B.
Mori
, “
Ultrabright electron bunch injection in a plasma wakefield driven by a superluminal flying focus electron beam
,”
Phys. Rev. Lett.
128
,
174803
(
2022
).
86.
T.
Takahashi
,
G.
An
,
Y.
Chen
,
W.
Chou
,
Y.
Huang
,
W.
Liu
,
W.
Lu
,
J.
Lv
,
G.
Pei
,
S.
Pei
et al, “
Light-by-light scattering in a photon-photon collider
,”
Eur. Phys. J. C
78
,
893
(
2018
).
87.
C.
Harvey
,
T.
Heinzl
, and
A.
Ilderton
, “
Signatures of high-intensity Compton scattering
,”
Phys. Rev. A
79
,
063407
(
2009
).
88.
C.
Maroli
,
V.
Petrillo
,
P.
Tomassini
, and
L.
Serafini
, “
Nonlinear effects in Thomson backscattering
,”
Phys. Rev. ST Accel. Beams
16
,
030706
(
2013
).
89.
A. I.
Nikishov
and
V. I.
Ritus
, “
Nonlinear effects in Compton scattering and pair production due to absorption of several quanta
,”
Zh. Eksperim. Teor. Fiz.
47
, 1130 (
1964
).
90.
V.
Baier
,
V.
Katkov
, and
V.
Strakhovenko
, “
Quantum radiation theory in inhomogeneous external fields
,”
Nucl. Phys. B
328
,
387
(
1989
).
91.
C. N.
Harvey
,
A.
Ilderton
, and
B.
King
, “
Testing numerical implementations of strong-field electrodynamics
,”
Phys. Rev. A
91
,
013822
(
2015
).
92.
V.
Dinu
,
C.
Harvey
,
A.
Ilderton
,
M.
Marklund
, and
G.
Torgrimsson
, “
Quantum radiation reaction: From interference to incoherence
,”
Phys. Rev. Lett.
116
,
044801
(
2016
).
93.
A.
Di Piazza
,
M.
Tamburini
,
S.
Meuren
, and
C. H.
Keitel
, “
Implementing nonlinear Compton scattering beyond the local-constant-field approximation
,”
Phys. Rev. A
98
,
012134
(
2018
).
94.
A.
Di Piazza
,
M.
Tamburini
,
S.
Meuren
, and
C. H.
Keitel
, “
Improved local-constant-field approximation for strong-field QED codes
,”
Phys. Rev. A
99
,
022125
(
2019
).
95.
A.
Ilderton
,
B.
King
, and
D.
Seipt
, “
Extended locally constant field approximation for nonlinear Compton scattering
,”
Phys. Rev. A
99
,
042121
(
2019
).
96.
A.
Ilderton
,
B.
King
, and
A. J.
MacLeod
, “
Absorption cross section in an intense plane wave background
,”
Phys. Rev. D
100
,
076002
(
2019
).