We investigate the photothermoelastic response of ZnTe and GaP crystals irradiated by THz-frequency radiation from a quantum cascade laser. We present a full theoretical description of this interaction that agrees well with the measured response

Alhathlool, R

Awang, AH

Davies, AG

Dean, P

Khanna, SP

Kundu, I

Li, LH

Linfield, EH

P. Dean

A. H. Awang

I. Kundu

R. Alhathlool

S. P. Khanna

L. H. Li

E. H. Linfield

A. G. Davies

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Photothermoelastic response of zincblende crystals to radiation from a THz-frequency quantum cascade laser

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This is a repository copy of Photothermoelastic response of zincblende crystals to radiation from a THz-frequency quantum cascade laser.White Rose Research Online URL for this paper:http://eprints.whiterose.ac.uk/80897/Version: Accepted VersionProceedings Paper:Dean, P, Awang, AH, Kundu, I et al. (5 more authors) (2013) Photothermoelastic response of zincblende crystals to radiation from a THz-frequency quantum cascade laser. In: International Conference on Infrared, Millimeter, and Terahertz Waves, IRMMW-THz. 38th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz), 1-6 September 2013, Mainz, Germany. IEEE . ISBN 9781467347174 https://doi.org/10.1109/IRMMW-THz.2013.6665428eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version - refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher’s website. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. Abstract—We investigate the photothermoelastic response of ZnTe and GaP crystals irradiated by THz-frequency radiation from a quantum cascade laser.  We present a full theoretical description of this interaction that agrees well with the measured response. I. INTRODUCTION AND BACKGROUND he use of optically-sampled crystals for the detection of terahertz (THz) frequency radiation has become widespread within applications such as THz time-domain spectroscopy.  The most commonly adopted detection scheme exploits the linear electro-ptic (EO) (or „Pockels‟) effect in noncentrosymmetric crystals whereby the THz field induces a birefringence in the crystal (typically ZnTe) that can be probed optically.  Electro-optic crystals have also been applied to incoherent and coherent sampling of THz fields generated using a quantum cascade laser (QCL) source.  Interestingly, an incoherent interaction mechanism of thermal origin has recently been identified using a standard EO sampling arrangement with a ZnTe crystal and a THz QCL source [1]. In this paper we further investigate this interaction in ZnTe and GaP crystals illuminated by a QCL source emitting at 2.2 THz.  Our results indicate a photothermoelastic origin of the interaction, whereby the stress distribution established through localised heating of the crystal induces a change in optical birefringence via the photoelastic response of the crystal.  We have developed a comprehensive model of this previously unexplored mechanism, which shows good agreement with experimental data. II.  EXPERIMENT AND RESULTS The photothermoelastic response of (110)-orientated ZnTe and GaP crystals with thicknesses L=1.9 mm and 1 mm, respectively, were investigated experimentally using a QCL source emitting at 2.2 THz.  Radiation from the QCL was focused onto each crystal, and a 778 nm probe beam was employed to sample the induced birefringence optically using a balanced sampling arrangement [2].  Both the THz beam and the probe beam were linearly polarized parallel to the [-1,1,0] direction of the crystal, which in turn was oriented parallel to the polarisation axis of the Wollaston prism.  The QCL device was operated in pulsed mode, emitting an average power ~845 たW.  The pulse trains were electrically modulated in the frequency range 10 Hz–3 kHz, with lock-in detection of the photodiode response being employed.   Fig. 1. (a) Contour plot showing the spatial variation of the photodiode signal  measured across the y−z plane (the (110) plane) of the ZnTe crystal.  The origin (0,0) corresponds to the centre of the THz beam.  (b) Spatial variation of the (normalized) photodiode signal calculated using the photothermoelastic model for the same experimental conditis. By translating the focusing lens in our apparatus, the probe beam could be scanned across the crystal surface in two dimensions.  Using this approach the spatial variation of the measured response, relative to the position of the focussed THz beam, was investigated.  Figure 1(a) shows a contour plot of the photodiode signal measured across an area of 1.4 mm  P. Dean,1,* A. H. Awang,2 I. Kundu,1 R. Alhathlool,1 S. P. Khanna,1 L. H. Li,1 E. H. Linfield,1 and A. G. Davies1 1School of Electronic and Electrical Engineering, University of Leeds, Leeds LS2 9JT, UK 2Universiti Teknologi MARA (UiTM), 40450 Shah Alam, Selangor Darul Ehsan, Malaysia Email: *p.dean@leeds.ac.uk Photothermoelastic response of zincblende crystals to radiation from a THz-frequency quantum cascade laser T 1.4 mm on the surface of the ZnTe crystal (defined as the y−z plane), for a laser modulation frequency of 40 Hz.  As can be seen, the sign of the signal alternates in adjacent quadrants of the crystal surface and reaches a maximum magnitude at a critical radius along the ±45º diagonals.  The intensity is also seen to vanish towards zero at the centre of the THz beam. The absolute value of the phase delay between orthogonal components of the probe beam can be obtained from the photodiode response.  Fig. 2 shows the optical phase delays measured as a function of laser modulation frequency, at the positions of maximum response (see Fig. 1), for the ZnTe and GaP crystals.  As can be seen, the measured response decreases with modulation frequency の and tends towards an inverse relationship at higher frequencies.  A similar behavior has been observed previously [1] using a 3.2 THz QCL, and is symptomatic of a thermal response.  Fig. 2. Optical phase delay measured as a function of pulse modulation frequency for ZnTe and GaP crystals using a 2.2 THz QCL. III.  THEORETICAL MODEL AND DISCUSSION We have developed a theoretical description of the measured response based on a photoelastic modulation of the optical birefringence arising from the stress distribution that is thermally-induced in the crystal upon localised THz irradiation.  Our model predicts a modulation of the birefringence given by the relationship     232 3442 sin 22 2B Bnn BB        , (1) in which n is the refractive index and g is the angle between the [-1,1,0] direction of the crystal (the y−axis) and the major axis of the index ellipsoid induced through the photothermoelastic mechanism.  The tensor components of the perturbation to the optical indicatrix, expressed in single-suffix (matrix) notation, are given by  i ij jk kB p s   , (2) where pij are the components of the forth order photoelastic tensor and sjk are the components of the fourth order elastic compliance tensor.  The components of the second rank stress tensor jk are obtained by modeling the crystal as an isotropic thin disk subject to a radial temperature distribution determined by the Gaussian profile of the THz beam [3]. As such, 〉n, 〉Bi and jk vary in three dimensions by virtue of attenuation of the THz power as the beam propagates through the crystal, as well as through the spatial distribution of the stress field in the y−z plane (the (110) plane of the crystal). Figure 1(b) shows the spatial variation of the photodiode signal predicted using our model for the ZnTe crystal.  The prediction is seen to agree well with the experimentally-determined spatial variation shown in Fig. 1(a).  It should be noted that such a spatial variation is dependent upon the establishment of a radially-varying stress field in the (110) plane of the anisotropic crystal, and would not arise through a simple temperature-dependence of the refractive indices. The measured response depends not only on the photoelastic properties of the crystal but also on the magnitude of the temperature modulation induced by the incident THz radiation.  Our model also allows us to define a figure-of-merit for the response, at the position corresponding to the maximum signal, that depends on crystal properties including the elastic constant s44, the photoelastic constant p44, the volumetric heat capacity とC, the thermal expansion coefficient gth, the THz absorption coefficient g and Young‟s modulus Y :   3 44 44 1 LthYn p s eFOMC  (3) For ZnTe and GaP we obtain values for the FOM of 6.9  10 12 J-1m3 and 3.0  10-12 J-1m3 at 2.2 THz, respectively (see Fig. 1).  By comparison, the measured phase delays for these crystals are h=6.7  10-7 and 3.0  10-7 at  = 1 kHz, in good agreement with the ratio of figures of merit. IV.  CONCLUSION We have investigated the photothermoelastic response of ZnTe and GaP crystals to QCL radiation at a frequency 2.2 THz, and developed a theoretical description of this mechanism that models the experimental data well. ACKNOWLEDGMENTS We are grateful for support from EPSRC (UK), the Royal Society, the Wolfson Foundation, and the European Research Council grant „NOTES‟. REFERENCES [1] A. van Kolck, M. Amanti, M. Fischer, M. Beck, J. Faist, and J. Lloyd-Hughes, “Thermo-optic detection of terahertz radiation from a qu ntum cascade laser,” Appl. Phys. Lett., vol. 97, 251103, Dec. 2010. [2] Q. Wu and X. C. Zhang, “Ultrafast electro-optic field sensors,” Appl. Phys. Lett., vol. 68, pp. 1604−1606, March 1996. [3] B. A. Boley and J. H. Weiner, Theory of thermal stresses, New York: John Wiley & Sons, 1960. 

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Photothermoelastic response of zincblende crystals to radiation from a THz-frequency quantum cascade laser

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