We demonstrate the generation of single-cycle longitudinally polarized terahertz pulses with field amplitudes in excess of 11 kV/cm using the interferometric recombination of two linearly polarized terahertz beams. High field strength transversely polarized pulses were generated by optical rectification in a matched pair of magnesium-oxide doped stoichiometric lithium niobate (MgO:SLN) crystals with a reversal in the χ333(2) orientation. The discontinuity in χ333(2) produces a polarity flip in the transverse field; the longitudinal field produced as a consequence of the transverse field discontinuity was measured in the far-field. Both the spatial and temporal profiles of the measured longitudinally polarized terahertz radiation were consistent with the propagation of the transverse discontinuity.

There is a great deal of interest in utilizing the longitudinal electric field component of radially polarized sources for particle acceleration.1–3 Recent demonstrations of acceleration with terahertz radiation within waveguides, with 7 keV acceleration in 3 mm,4 have increased the interest in high electric field strength terahertz sources. In recent years, magnesium-oxide doped stoichiometric lithium niobate (MgO:SLN) has become a popular non-linear material for use in the generation of linearly polarized terahertz radiation with a high peak electric field strength.5–9 Electric field amplitudes in excess of 1 MV/cm have been demonstrated by employing a pulse-front tilt pumping scheme to enable the coherent transverse addition of the Cherenkov terahertz emission.10,11 Whilst other non-linear crystal sources have been shown to produce terahertz radiation with similar electric field amplitudes,12 the wide availability of 800 nm Ti:Sapphire lasers makes MgO:SLN more attractive as a terahertz source. Such sources are however transverse linearly polarized. In order to apply these sources to accelerator applications conversion to a mode with a longitudinally polarized component, such as a radially polarized mode, is required.

Radially polarized terahertz beams have been produced using radially biased photo-conductive antennas13–17 and an air-plasma generation technique,18 with Cliffe et al.17 reporting the largest longitudinal electric field amplitude of 2.22 kV/cm. Such beams have also been produced at optical wavelengths by the interferometric recombination of multiple linearly polarized beams.19 Tidwell et al.19 split a single linearly polarized 10 μm laser beam into multiple beams and rotated the polarization of the individual beams before recombining them to form a radially polarized mode. The use of such radially polarized laser pulses for free space accelerator applications has been proposed.3,20,21 Limitations imposed by the short temporal cycle durations of optical radiation however significantly reduces the interaction length. The technique of combining radiation with different linear polarization states has also been applied to radiation within the terahertz regime. Imai et al.22 used a segmented gallium phosphide (GaP) electro-optic generation crystal to generate a radially polarized terahertz beam with a longitudinal electric field amplitude of 30 V/cm. Nanni et al.4 have also recently reported using a segmented waveplate to convert a linearly polarized terahertz pulse into a radially polarized few-cycle pulse. The use of such time-shifting segmented waveplates is however not applicable to the generation of radially polarized single-cycle pulses. Pálfalvi et al.23 proposed a method of terahertz radiation acceleration that involved an evanescent wave traveling on the boundary between a vacuum and dielectric material. Whilst this method is able to maintain phase matching between the terahertz radiation and particle bunch, the presence of the dielectric material, in this case MgO:SLN, causes a lowering of the terahertz electric field through strong terahertz absorption.5 Generating a large longitudinal electric field component whilst still maintaining the single-cycle nature of the pulsed terahertz radiation would present a distinct advantage for particle acceleration as it would enable a higher accelerating peak electric field and a higher acceleration efficiency for short (sub-ps) electron bunches.

In this letter, we demonstrate the generation of single-cycle longitudinally polarized terahertz pulses with electric field amplitudes of 11.7 kV/cm. As a radially segmented MgO:SLN generation scheme was impractical with a single pump beam, we employed the interferometric recombination of two polarity inverted terahertz pulses effectively forming a Hermite-Gaussian 01 (HG01) spatial mode. This was generated using a single near-infrared laser beam with a pulse energy of 0.8 mJ. As this method does not require the use of terahertz waveplates, it enabled the full bandwidth of the terahertz pulse to be utilized to generate a single-cycle temporal profile. The spatial, temporal, and polarization properties of the generated radiation are compared with those obtained from terahertz beam propagation simulations.

From the free space constraint, E=0, the longitudinal electric field component of a source is given by

Ez(x,y,zobs,t)=zobsE(x,y,z,t)dz,
(1)

where zobs is the observation plane, Ez(x,y,zobs,t) is the longitudinally polarized electric field component, is the transverse spatial gradient, and E(x,y,z,t) is the transversely polarized electric field component. This polarization component can be maximized by increasing the transverse electric field gradient. We achieved such a transverse gradient by the interferometric recombination of two polarity flipped linearly polarized terahertz pulses. This polarity flip was achieved by using two 5 mm × 5 mm × 9.81 mm MgO:SLN crystals with opposite [001] axis polarities, as commonly found within periodically polled MgO:SLN.24 

The experimental setup employed a 1 kHz regenerative amplifier system which produced 1.8 mJ of 800 nm radiation with a pulse duration of 50 fs for generation and detection of terahertz radiation. The laser beam was split into a pump and probe beam with the pump beam providing 90% of the laser radiation to generate the terahertz radiation. A pulse-front tilt pumping scheme was employed, whereby the pump beam was incident upon a 1800 lines per mm holographic grating. The angle of incidence was set to 29° which caused the m = −1 diffraction order to be reflected at an angle of 70°. A pulse-front tilt of 77° was present within this diffraction order upon the grating surface which was one-to-one imaged into the two MgO:SLN generation crystals by a 2-in. diameter 100 mm focal length lens. Due to the refractive index of MgO:SLN, this produced a pulse-front tilt of 63° within the crystals. Figure 1 shows a schematic diagram of the terahertz generation scheme. As can be seen, two MgO:SLN crystals were vertically stacked with their [001] axes aligned pointing in opposite vertical directions. The crystals were both pumped by the same vertically polarized laser pulse centered at the intersection of the crystals surfaces. The terahertz radiation beam generated within the crystals was collected by a 2-in. diameter gold coated parabolic mirror with an effective focal length of 75 mm. The radiation was then focused by a second 2-in. diameter gold coated parabolic mirror with an effective focal length of 100 mm. The probe beam passed through a temporal delay stage before it was recombined with the terahertz radiation using a 2-in. diameter 60:40 (reflective:transmissive) pellicle beamsplitter and used to detect the generated terahertz pulse with a standard electro-optic detection technique. For the electro-optic detection, a zinc telluride (ZnTe) crystal cut with either a (110) or (100) orientation was employed, with a 0.5 mm thick (110)-cut crystal being used to detect transversely polarized terahertz radiation and a 2 mm thick (100)-cut crystal being used for longitudinally polarized detection. A 1-in. diameter plano-convex lens was placed behind an iris which was situated on a vertical translation stage within the probe beam path 1 m before the electro-optic detection setup. This enabled the vertical translation of the probe beam over the ZnTe crystal surface, thus allowing a spatial map of the terahertz radiation to be formed.

FIG. 1.

Schematic diagram of the experimental setup showing the generation and detection of the terahertz radiation. Inset (a) shows a conceptual diagram of the longitudinally polarized terahertz generation scheme. Two MgO-doped stoichiometric lithium niobate crystals (labelled crystal 1 and 2) were placed on top of each other with their [001] axes pointing in opposite vertical directions. Inset (b) shows a conceptual diagram of the terahertz radiation detection scheme with a vertical probe beam offset.

FIG. 1.

Schematic diagram of the experimental setup showing the generation and detection of the terahertz radiation. Inset (a) shows a conceptual diagram of the longitudinally polarized terahertz generation scheme. Two MgO-doped stoichiometric lithium niobate crystals (labelled crystal 1 and 2) were placed on top of each other with their [001] axes pointing in opposite vertical directions. Inset (b) shows a conceptual diagram of the terahertz radiation detection scheme with a vertical probe beam offset.

Close modal

Figure 2(a) shows the transversely polarized terahertz electric fields measured with the (110)-cut ZnTe crystal at a range of vertical sampling positions of the probe beam. As can be seen, the polarity of the temporal profile flips as the probe beam was scanned through the center of the detection crystal. On the mirror symmetry axis, the transverse fields will cancel; off-axis however the cancellation is not complete due to the different phase shifts coming from each source crystal and a transverse field pattern similar to a HG01 mode is observed. The terahertz transverse peak electric field amplitude was determined to be 48.4 kV/cm using an absolute field strength calibration.25 The spatial and temporal profiles of the measured transversely polarized terahertz radiation agreed with the simulated data (shown in Fig. 2(b)). A wavefront curvature can be seen in both the simulated and measured data which are attributed to the measurement being taken before the terahertz focal plane. Figure 2(c) shows the corresponding power spectra. Both spectra have a peak at approximately 0.4 THz and display a large bandwidth typically attributed to single-cycle pulses. The detected longitudinal electric field component is shown in Fig. 3, where the red circles indicate the measured data whilst the black line shows the calculated waveform. The measured longitudinal temporal electric field exhibits a phase shift with respect to the transverse field, as explained by Winnerl et al.14 The longitudinal electric field was found to have a peak amplitude of 11.7 kV/cm, thus giving a longitudinal to transverse electric field amplitude ratio of 0.24. This is lower than the value of 0.89 measured by Cliffe et al.17 and is attributed to the different terahertz transport and focusing optics used along with the transverse mode not being fully radially polarized. The electric field amplitude value was calibrated as described by Cliffe et al.17 using

ETHz=ΔII0λ2πn3r41L1t,
(2)

where ETHz is the terahertz electric field amplitude, ΔI is the difference in the photodiode signals in the presence of the terahertz radiation, I0 is the total signal on the photodiodes in the absence of terahertz radiation, r41 is the electrooptic co-efficient of ZnTe, n = 2.85 and is the refractive index of ZnTe at λ = 800 nm, and t is the transmission coefficient for longitudinally polarized electric fields given by t = 2/[nTHz(1+nTHz)].

FIG. 2.

Transversely polarized terahertz waveforms (a) measured and (b) simulated for a range of vertical offsets from the detection image center, small on-axis oscillations are present due to the spatial grid having an offset from zero. All waveforms have been vertically offset for clarity. (c) Power spectra of the measured and simulated data for a vertical offset of 1 mm.

FIG. 2.

Transversely polarized terahertz waveforms (a) measured and (b) simulated for a range of vertical offsets from the detection image center, small on-axis oscillations are present due to the spatial grid having an offset from zero. All waveforms have been vertically offset for clarity. (c) Power spectra of the measured and simulated data for a vertical offset of 1 mm.

Close modal
FIG. 3.

Longitudinally polarized terahertz waveform measured (red circles) using a 2 mm-thick (100)-cut ZnTe crystal and calculated (black line) at the center of the detection image. Simulated waveform is normalized to the peak of the measured waveform to aid comparison. Inset shows longitudinally polarized waveforms measured at vertical offset positions of 2, 0, and −2 mm. Inset waveforms are vertically offset for clarity.

FIG. 3.

Longitudinally polarized terahertz waveform measured (red circles) using a 2 mm-thick (100)-cut ZnTe crystal and calculated (black line) at the center of the detection image. Simulated waveform is normalized to the peak of the measured waveform to aid comparison. Inset shows longitudinally polarized waveforms measured at vertical offset positions of 2, 0, and −2 mm. Inset waveforms are vertically offset for clarity.

Close modal

To verify the concept and to confirm that the correct spatial and temporal electric field distributions could be created within the focal region an electric field propagation simulation based on the Frensnel-Kirchhoff diffraction integral26 was developed. This simulation generated a three-dimensional electric field distribution throughout the focal region from a given two-dimensional electric field distribution. The simulation used an electric field profile of the transversely polarized terahertz radiation on the output surface which was taken to be of the form

E(x,y,ω)=ω2eω22σ2ex2σxy2σy,
(3)

where σ=1.9 THz. The spectral dependence agreed well with the result of a split-step terahertz generation simulation we have carried out using the method described by Hattori et al.27 Rather than using the results from the split-step simulation directly, the analytical form was used to enable resolution downscaling in order to reduce the computational requirements of the Fresnel-Kirchhoff calculation. The spatial dependence of the terahertz radiation at the output surface of the generation crystal was derived from the spatial profile of the pump laser beam projected onto the output surface. This surface field was then propagated, with radially varying phase delays imposed to model focusing effects, to a sequence of output planes around the focal region. From the transversely propagated electric field, the longitudinal component was calculated, as described by Eq. (1). The simulated power spectrum is shown in Fig. 2(c). As can be seen, the power spectrum has good agreement in both shape and bandwidth to the measured power spectrum.

Longitudinally polarized single-cycle terahertz pulses with electric field amplitudes of 11.7 kV/cm were generated using the well-known MgO:SLN tilted pulse-front pumping scheme. As such it can be assumed that the same scaling of the terahertz electric field will be observed with increasing the excitation fluence and cooling the MgO:SLN crystal to 10 K.28 It has been shown that cooling the generation crystal to 10 K can result in a factor of 5.8 increase in the terahertz field strength. Fülöp et al.28 have also shown that the electric field strength of the terahertz radiation can be further increased by a factor of 8 by temporally tuning the pump laser beam from 50 fs to 500 fs. Our experiment used a pump laser fluence at the surface of the generation crystals of 3.9 mJ/cm2. Saturation within MgO:SLN occurs around 15 mJ/cm2, thus enabling a further scaling by 3.8. These factors combined enable the method presented here to potentially scale such that terahertz radiation with peak longitudinal electric fields on the order of 1 MV/cm could be generated and propagated with a single-cycle temporal profile. As well as the scaling factors listed above there is also the possibility of using a much larger lithium niobate crystal such as the one used by Wu et al.5 These field amplitudes can be further increased by tighter focusing, with peak field amplitudes scaling as E1f; however, the Rayleigh range also scales with the same relationship. For particle acceleration, this increased field does not therefore necessarily lead to increased acceleration.

In summary, by using a matched pair of polarity inverted MgO:SLN crystals as an optical rectification source, we have demonstrated the generation of strong on-axis longitudinally polarized single-cycle terahertz radiation, with electric field amplitudes in excess of 11 kV/cm. In contrast to segmented waveplate sources, the single-cycle terahertz temporal profile is maintained hence maximizing the attainable electric field strength. The ability, through commonly employed techniques, to scale this generation method such that longitudinally polarized terahertz electric fields with field amplitudes in excess of 1 MV/cm has also been discussed. Calculations have shown a good agreement of the spatial and temporal profiles.

This work was supported by the United Kingdom Science and Technology Facilities Council (Grant No. ST/G008248/1); the Engineering and Physical Sciences Research Council (Grant No. EP/J002518/1); and the Accelerator Science and Technology Center through Contract No. PR110140. The data associated with the paper are openly available from The University of Manchester eScholar Data Repository: http://dx.doi.org/10.15127/1.301040.

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