Generation of longitudinally-polarized terahertz pulses with field amplitudes exceeding 2 kV / cm

exceeding 2 kV/cm M. J. Cliffe, 2, a) A. Rodak, 2 D. M. Graham, 2 and S. P. Jamison 3 School of Physics and Astronomy and the Photon Science Institute, The University of Manchester, Manchester M13 9PL, United Kingdom The Cockcroft Institute, Sci-Tech Daresbury, Keckwick Lane, Daresbury, Warrington WA4 4AD, United Kingdom Accelerator Science and Technology Centre, Science and Technology Facilities Council, Darebsury Laboratory, Keckwick Lane, Daresbury, Warrington WA4 4AD, United Kingdom

Longitudinally-polarized radiation is commonly used in many applications including electron acceleration 1 , laser machining 2 , optical tweezers 3 and microscopy 4 .The above applications exploit the enhancement of the longitudinally-polarized field component 5,6 by the tight focusing of a radiially-polarized beam.In recent years there has been a push to develop such sources in the terahertz spectral region and a number of laser-driven terahertz sources, with strong longitudinally-polarized field components, have been reported including: velocitymismatched optical rectification 7 , a segmented GaP crystal 8 , an air plasma filament 9 and photo-conductive antennas with radial electrode geometries, both single gap 10 and interdigitated InP 11 and GaAs 12,13 structures.To date all demonstrations of longitudinally-polarized terahertz generation have produced longitudinal-field amplitudes of < 30 V/cm, with the exception of Minami et al. 9 who reported a field amplitude of 1 kV/cm by tightly focusing the terahertz radiation generated from an air plasma filament induced by a 4.5 mJ femtosecond optical laser pulse.
In this letter we report the results of a detailed characterization of a radially-polarized terahertz radiation source generated from a large-area GaAs photo-conducting antenna.By focusing the terahertz radiation we were able to obtain a longitudinal, on axis, component with a peak amplitude of 2.22 kV/cm using an optical laser pulse energy of 0.5 mJ; the laser fluence was below the photoconductive antenna saturation threshold, and the peak terahertz field amplitude was monitored as a function of laser fluence to further confirm this.
The experimental setup is shown schematically in Fig. 1.The terahertz pulses were generated using a radially-biased large-area GaAs photoconductive antenna.The antenna consisted of a 76 mm diameter, 500 µm thick semi-insulating GaAs (SI-GaAs) wafer with a circular central electrode, radius r = 10 mm, and a concentric annular outer electrode, r = 36 mm.A high-voltage bias was applied to the antenna by a custom-built pulsed voltage supply that provided up to 100 kV in a 9 µs pulse at a repetition rate of 250 Hz.A tworesistor potential divider was wired in parallel to the antenna to enable the monitoring of the voltage pulse on an oscilloscope, this allowed for both calibration of the voltage applied to the antenna and temporal synchronization of the photo-exciting laser.The laser system employed in this work was a regenerative amplifier system which provided 100 fs pulses with a central wavelength of 800 nm and a repetition rate of 500 Hz.The laser pulse train was divided into a pump and probe beam with the pump beam providing pulse energies of 500 µJ to photo-excite the antenna.An average photo-excitation fluence of 6.1 µJ/cm 2 was obtained across the annular active surface area of the antenna by expanding the pump beam using a combination of a diverging and focusing lens.Placing the antenna in the focusing pump enabled the terahertz phase front to adopt the radial time delay of the optical excitation pulse, generating a focusing terahertz wave.The emitted terahertz radiation was then routed to a 90 o off-axis parabolic mirror with an effective focal length of 76.2 mm where it was further focused; providing an effective numerical aperture of 0.32.The terahertz radiation was detected using an electro-optic detection scheme which utilized a co-linear focused probe beam that was combined with the terahertz radiation via a pellicle beamsplitter.The probe beam was focused by a 1 m focal length lens and had a 1/e 2 diameter of 155 µm which was measured by a knife-edge scan at the detection crystal position.Temporal waveforms were recorded at multiple sampling positions along the terahertz focal plane by translating both the probe beam and the electro-optic detection optics using manually-driven translation stages.To detect the radial components of the terahertz field a 2 mm thick (110) ZnTe crystal was employed, while a 2 mm thick (100) ZnTe crystal was utilized to detect the longitudinal field components.In both cases the azimuthal rotation of the crystals were set to maximize the terahertz signal as described by Winnerl et al. 12 .The features seen in the waveforms of Fig. 2 at a time delay of approximately 14.3 ps are due to a reflection of the emitted terahertz radiation in the GaAs wafer.The flip in relative polarity is attributed to a phase change of π upon reflection at the larger refractive index of the photo-excited plasma layer. 15,16Following the approach of Planken et al. 17 , the terahertz field amplitude can be related to the probe intensity in orthogonal polarizations, where L = 2 mm is the detection crystal thickness, n = 2.85 is the refractive index of ZnTe at λ = 800 nm, r 41 = 4.0 pm/V is the electro-optic coefficient of ZnTe 18 and T is the Fresnel transmission coefficient.For low signal-to-noise ratio measurements we observed the terahertz induced intensity changes with a lock-in amplifier.The differential probe signal, ∆S 250 ∝ ∆I, was measured at 250 Hz, while the reference signal, S 500 ∝ I 0 , was measured at 500 Hz.A correction factor, C = 1.36, was determined to account for the different lock-in responses at 250 Hz and 500 Hz, where C is dependent on the photo-diode response time.
With this approach the lock-in signal was consistent with direct observation of the photodiode change, ∆V /V .A maximum differential terahertz signal, ∆I/I 0 , of 0.13 was obtained with an applied bias voltage of 40 kV.Using Eq. 1 and taking T = 2.08 we obtained a maximum field amplitude of 2.5 kV/cm at a bias voltage of 100 kV.
Careful inspection of the χ (2) tensor for both (110) and (100) cut crystals as well both polarization geometries confirms the validity of Eq. 1 for both transversely-and longitudinallypolarized radiation detection schemes.The usual Fresnel transmission coefficient however is not valid for longitudinally-polarized radiation as the component of the electric field perpendicular to the interface is not continuous.By using the boundary condition for the electric displacement vector, i.e. that the perpendicular component is continuous across the interface, we can obtain the following transmission coefficient for longitudinally-polarized radiation, The transmission co-efficient of Eq. 2 is also consistent with the spatial compression of a pulsed field in the longitudinal direction, due to the reduced pulse velocity, and the necessary maintenance of ∂ ∂z E z = −∇ ⊥ E ⊥ within the crystal.Figure 3 (a) shows the measured longitudinal field as a function of sampling position and time delay for an applied bias of 40 kV.It exhibits a bipolar temporal structure and a unipolar transverse profile.For an applied bias of 40 kV the maximum differential terahertz signal, ∆I/I 0 , measured was 0.0205.This differential signal increased to 0.036 by increasing the applied bias to 100 kV.A peak longitudinal field amplitude of 1.26 kV/cm was therefore determined from the data shown in Fig. 3 (a), which increased to 2.22 kV/cm at a 100 kV bias.As it is known that a slightly tilted electro-optic sampling crystal can lead to a transverse field component being detected as a longitudinal field component, 8 it is important to ensure that any tilt of the detection crystal was minimized.This was achieved by ensuring the back reflection of probe beam from the ZnTe detection crystal followed the same path as the incoming probe beam.To further verify that the correct polarization state is being detected the expected longitudinal field was calculated from the measured transverse field components.From ∇ • E = 0 it follows that, where E r (r, z) is the radial component of the field.In order to calculate an expected longitudinal field from the data shown in Fig. 2. We integrate over time, t, instead of z by making the assumption that E(r, z, t) ≈ E(r, z − ct).Spatial profiles of the terahertz beam were taken at various z positions by moving the detection crystal through the focus; very little change in the spatial profile was observed within our scan range confirming the validity of this assumption.Using Eq. 3 and the measured transverse field data shown in Fig. 2 (a), which was measured at a transverse slice through the origin, r = 0, we calculate the expected longitudinal field as a function of r and z which is shown in Fig. 3 (b).Numerical artifacts at r = 0 that are due to 1 r have been removed by the truncation of r around this region.There is good agreement of both the spatial and temporal properties between the measured and calculated datasets as can be seen.This shows that any contribution from the transverse field components in the longitudinal detection due to a tilted electro-optic crystal has been minimized.
In order to verify that the detection crystal was positioned at the focal point of the terahertz radiation beam we recorded the spatial profile of the longitudinal terahertz field while moving the (100) ZnTe detection crystal along the direction of beam propagation with a micrometer-driven stage.We observed an increase in the beam diameter and a decrease in the peak field amplitude on both sides of the nominal focal position, hence confirming the optimal positioning of our detection crystal and the measurement of the maximum longitudinal field amplitude.
An average photo-excitation fluence of 6.1 µJ/cm 2 was used in this work, which is far below the saturation fluence of 40 µJ/cm 2 as determined by You et al. 19 .The terahertz field amplitude continuously decreased as the excitation laser fluence was decreased hence confirming we were operating below saturation.It therefore follows that higher field amplitudes could be obtained with modest laser pulse energies increasing towards saturation levels.We estimate that for our experimental arrangement a 6 times increase in the longitudinallypolarized field amplitude could be obtained before reaching the saturation fluence; potentially increasing the longitudinally-polarized field amplitude to 13.3 kV/cm.
In summary we have shown that it is possible to generate large longitudinally-polarized terahertz field amplitudes, in excess of 2 kV/cm, from a large-area photo-conductive antenna.
Expressions commonly used for transversely-polarized field analysis have been modified and correctly applied to longitudinally-polarized radiation.Scaling the pump laser towards saturation, this method is estimated to be capable of 6 fold higher longitudinal fields, with the possibility of even higher still if larger diameter photo-conductive antennas are considered.

FIG. 1 .
FIG. 1. (Color) Schematic diagram of the experimental setup.Inset shows the concentric arrangement of the antenna electrodes.

Figure 2 FIG. 2 .
Figure 2 shows the transverse terahertz field as a function of sampling position and time delay.A polarity flip in the field is observed as the sampling position is scanned through the

FIG. 3 .
FIG. 3. (Color) (a) Longitudinal electric field component of the terahertz source measured at the focal point.(b) Calculated longitudinal electric field component, truncation of r occurs within the dotted lines.