This work presents a theoretical analysis of the generation of twisted terahertz (THz) radiation using laser-bunched relativistic electron beams in a magnetic wiggler. By employing a laser-bunched relativistic electron beam, which introduces a transverse modulation to the electron beam density, and a magnetic wiggler, which induces a transverse deflection to the electron trajectories, the generation of twisted THz radiation is achieved. The interaction between the modulated electron beam and the magnetic field leads to the emission of THz photons with a twisted phase structure. The findings of this study provide valuable insights into the generation and manipulation of twisted THz radiation contributing to the advancement of THz technology and its diverse applications.

## I. INTRODUCTION

THz radiation has garnered a great deal of attention recently due to its potential applications in spectroscopy, imaging, and communications, among other fields. Its frequency range extends from infrared to microwaves.^{1–3} The ability to manipulate the properties of THz radiation opens up new avenues for technological advancement. One such route is the generation of twisted THz radiation also known as vortex beams, which has an orbital angular momentum (OAM) that is precisely specified. The field of orbital angular momentum (OAM) has gained significant attention since 1992, when Allen *et al.*^{4} demonstrated that Laguerre–Gaussian (LG) beams have an orbital angular momentum of $l\u210f$ per photon, where $l$ is the topological charge of the OAM mode. The characteristics of such laser beams are an annular spatial profile with a central dark spot and a wavefront that spirals in a corkscrew-like manner along the beam's propagation direction.^{5,6} Twisted THz radiation has enormous potential for applications that rely on the special features of OAM-carrying beams.^{7–9} For example, in communication systems, utilizing the OAM of THz radiation can dramatically boost data capacity and improve security measures.^{10,11} Furthermore, the ability to adjust the OAM of THz radiation can provide increased structural and chemical research capabilities in spectroscopy and imaging.^{12,13} Recently, many different strategies have been presented to generate twisted THz waves.^{14–16} Sobhani *et al.* studied the cross-focusing of two twisted coaxial laser beams to create a resonant vortex THz beam. Vortex THz radiation can be produced more effectively by adjusting the laser and plasma parameters. It is also shown that as the beating frequency approaches the plasma frequency, the THz radiation amplitude increases.^{17} Laser-plasma vortex interactions provide a new path toward THz vortex beams, where emission qualities are tuned and angular momentum transfer is guided by the helical density.^{18,19} Shobani *et al.* further investigated the generation of twisted THz radiation by two nonlinear currents that are triggered by a static electric field. By structuring the radiation into a Laguerre–Gaussian envelope, one can create new potential for THz applications by modifying the plasma density.^{20}

On the other hand, it has also been shown that Bunched beams present a compelling solution to the growing need for compact and controllable THz sources.^{21–23} Kumar *et al.* provided a formalism for the controllable generation of coherent THz radiation through the use of a magnetic wiggler and a relativistic electron beam regulated by two laser beams. At around $\u22481.9$ THz, they were able to attain a maximum value of conversion efficiency of the order $\u223c 10 \u2212 7.$^{24} Hasanbeigi studied the production of coherent THz radiation from the interaction of a helical wiggler pumped with a bunched relativistic electron beam. They found that the injected beam's radius, axial velocity, and ion-channel density all increased with the highest THz power.^{25} Li *et al.* reported the simulation of a single-pass free electron laser (FEL) powered by a THz-pulse-train photoinjector, which produces a strong narrow-band THz source with a wide tuning range of frequency of radiation. According to simulation results, this FEL can provide power outputs in the few tens of megawatts and pulse energy in the several tens of micro-joules at frequencies between 0.5 and 5 THz.^{26} Zhen *et al.* suggested a technique for producing strong subpicosecond density bunching in high-intensity relativistic electron beams that is based on slice energy spread modulation. The adjustable beam's radiation can cover the frequency range of 1–10 THz with high power, as demonstrated by both theory and simulations.^{27}

In this research paper, we explore the generation of twisted THz radiation using a laser-bunched relativistic electron beam in a magnetic wiggler. Incorporating a magnetic wiggler further enhances the efficiency and control over the generation process enabling the precise manipulation of the radiation's OAM. Two laser pulses interact with a modulator within the electron beam path. These pulses transfer energy to the electrons through the modulator, modulating their energy levels. This energy modulation results in a corresponding modulation of their velocities, with higher energies translating to faster speeds. As a consequence, electrons with similar velocities tend to cluster together, forming bunches with higher densities compared to surrounding regions. This prebunched electron beam then enters a magnetic wiggler. The wiggler's alternating magnetic field exerts a transverse force on the electrons, causing them to oscillate perpendicular to their direction of travel. This oscillatory motion generates electromagnetic radiation in the THz range.

Section II establishes expressions for velocity modulation and density modulation of an electron beam under the influence of twisted laser beams. Section III delves into the derivation of an expression for the nonlinear current generated within this modulated beam. Section IV outlines the calculation of radiated power resulting from this interaction. Finally, Secs. V and VI, respectively, present the key results and draw conclusions from the analysis.

## II. MODEL EQUATIONS

## III. NONLINEAR CURRENT DENSITY

A prebunched electron beam is introduced into a magnetic wiggler, having magnetic field, $ B \u2192 w= B 0( x \u0302+i y \u0302) e i k w z$ as shown in Fig. 2.

## IV. THz EMISSION AS AN ANTENNA

## V. RESULT AND DISCUSSION

The governing equation of twisted THz radiation using laser-bunched relativistic electron beams in a magnetic wiggler is modeled analytically. For a given set of parameters, $d=400\u2009\mu m,\u2009L=1\u2009cm, v 0 b=0.90c,\u2009 \gamma 0=2.29,\u2009 L b=0.40\u2009cm,\u2009 L w=0.40\u2009cm,\u2009 \lambda w=1.8\u2009mm, e E 0 / m \omega 1 c= e E 0 / m \omega 2 c=0.05,\u2009 \lambda 1=1.06\u2009\mu m,\u2009 \lambda 2=1.06(1+ \lambda 1 / \lambda THz )\mu m,\u2009 r b=18\u2009\mu m,\u2009 r 0=2\u2009\mu m,\u2009 \omega p 0 / \omega 1 = 10 \u2212 4,$ and a range of topological charge number of both lasers equation (16) has been calculated to demonstrate the THz radiation in a helical wiggler magnetic field. Figure 3 illustrates the normalized THz power behavior as a function of normalized frequency $ \omega / \omega 1$ for $ l 1= l 2=1,\u2009l=0$. The power initially exhibits a positive correlation with frequency, reaching a maximum value ( $2\xd7 10 \u2212 3$) at frequency $\u223c1.9$ THz, but as frequency gets high, a limit sets in due to the Bessel function. As frequency increases beyond a certain point, the system becomes less efficient in converting power and the transmitted power starts to decline. By increasing the beam velocity from $0.90c$ to $0.95c$, the THz power output can be enhanced by a factor of 1.9 with the peak shifting toward a higher frequency $\u223c4.2$ THz. Figure 4 plots the relationship between THz radiation power and frequency $ \omega / \omega 1$ for $ l 1= l 2=2,\u2009l=0$. The frequency and power are both normalized, making the plot more general. As the vortex charge number increases (from $ l 1= l 2=1$ to $ l 1= l 2=2$), the plot reveals that the peak power of the THz radiation gets significantly stronger. Not only does the power increase, but it also shifts toward higher frequencies. This is because at higher OAM, the intensity of the LG beam can be concentrated in a smaller region within the material. This intense region can trigger nonlinear optical effects that further enhance the generation of THz radiation. Figures 5 and 6 show the variation of normalized THz power as a function of normalized frequency $ \omega / \omega 1$ for $l\u22600$. The curve in this instance is increasing exponentially because the term $\psi (r,\phi ,z)$ in Eq. (16) has a dominant exponential component for $l\u22600$. THz power drops as beam velocity rises. THz power decreases as the number of lasers with increasing topological charge increases. This is because the relative phase between the lasers has a significant impact on the production of THz radiation for $l\u22600$. As Figs. 7 and 8 make clear, the relative Gouy phase causes a decrease in the amplitude of the THz radiation emission. The Gouy phase is the extra phase shift that a concentrated laser beam's finite size causes in various regions of the beam. A distinctive phase curvature is produced throughout the beam profile as a result. Because the Gouy phase introduces undesired phase deviations throughout the beam profile, it might interfere with phase matching. Because of this mismatch, there is less overlap between effective interaction zones, which lowers conversion efficiency and produces fewer THz. In simple terms, matching the topological numbers of the lasers maximizes their interaction and eliminates a major source of inefficiency, which results in a large increase in the amplitude of the generated THz radiation.

## VI. CONCLUSION

The generation of twisted THz radiation using a laser-bunched relativistic electron beam in a magnetic wiggler is explored in this study. Two laser pulses and a modulator are in contact within the electron beam path. These pulses modify the energy levels of the electrons by imparting energy through the modulator. This energy modulation, which also influences their velocities, converts higher energies into quicker speeds. This leads to the formation of bunches with higher densities than the surrounding areas when electrons traveling at similar speeds gather together. After being prebunched, the electron beam travels via a magnetic wiggler. The electrons oscillate perpendicular to their initial path of travel due to the transverse force of the wiggler's alternating magnetic field. This repetitive motion generates electromagnetic radiation in the THz range. In a laser-bunched relativistic electron beam system, our study uncovers the essential parameters controlling the production of twisted THz radiation, including the vital function of vortex charge number and beam velocity. As a result of this study, twisted THz radiation creation will be better understood and may be used practically in a number of scientific and technological domains. This research lays the groundwork for future developments and breakthroughs in the field of twisted THz radiation, which has a wide range of possible uses in biological spectroscopy, security screening, and THz imaging.

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

### Author Contributions

**Himani Juneja:** Conceptualization (equal); Data curation (equal); Formal analysis (equal); Software (equal); Supervision (equal); Writing – original draft (equal). **Anuraj Panwar:** Supervision (equal). **Prashant Chauhan:** Supervision (equal).

## DATA AVAILABILITY

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

## REFERENCES

*Optical Angular Momentum*