We consider the non-linear generation of THz with tilted pulse-fronts in three dimensions and show that, contrary to the widely held expectations, coherent phase matching can be obtained for pulse-front tilt angles other the Cherenkov angle

Jamison, S. P.

Snedden, E. W.

Walsh, D. A.

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Abstract—We consider the non-linear generation of THz with tilted pulse-fronts in three dimensions and show that, contrary to the widely held expectations, coherent phase matching can be obtained for pulse-front tilt angles other the Cherenkov angle. I. INTRODUCTION    ffecient generation of high-field strength THz pulses are of interest for non-linear THz spectroscopy, and for application to THz driven particle acceleration. For many of the widely used non-linear materials with large non-linear coefficients phase-matching conditions preclude co-linear phase matching. For transversely narrow optical pump beams materials such as LiNbO3 give rise to THz emission in a Cherenkov cone around the drive laser. For transversely extended beams tilted pulse fronts are required to maintain efficient generation, and also have the desirable result of producing a planar front THz emission. The generation of THz with tilted pulse fronts has been widely studied and exploited for over a decade [1-6]. It is generally accepted that to obtain the efficiency gains the pulse front tilt must match the Cherenkov angle of the material.  Recently, Walsh et al demonstrated a ‘travelling source’ THz generation concept for particle acceleration [7]. The generation scheme explicitly utilized a pulse-front tilt with tilt angle exceeding the Cherenkov angle, raising questions on the nature of the phase-matching efficiency. Here we show analytically, and also numerically through finite-difference time-domain modeling examples, that pulse-front tilt generation can meet the phase-matching condition whenever the tilt-angle exceeds the Cherenkov angle. II. RESULTS   Previous derivations of Cherenkov angle pulse-front tilt phase-matching have generally started from a two dimensional construction, requiring that the phase-fronts of the generated THz coherently reinforce in the 2-dimensional plane[1]. Similarly, published numerical modeling of the generation process has tended to assume a two-dimensional symmetry [2,3]. However for a 1-dimesional ‘pencil-beam’ excitation a 3 dimensional Cherenkov cone of emission is produced. By an explicitly three-dimensional construction of the Huygens-like emission throughout a finite, 3-dimensional volume it is possible to show analytically that constructive interference (i.e. phase-matching) can be obtained whenever the pulse-front tilt exceeds the Cherenkov angle. In Fig 1 we show results from a three dimensional FDTD modeling with pulse-front tilt equal to, and exceeding, the cherenkov angle. A planar wave THz emission is obtained in both cases, and with equal efficiency and field strength. REFERENCES   [1] Hebling, J., Almasi, G., Kozma, I.Z. Velocity matching by pulse front tilting for large area THz-pulse generation. Opt. Express. 10, 1161-1166 (2002) [2] M.I. Baakunov, S.B. Bodrov, A.V. Maslov, M. Hangyo.Theory of terahertz generation in a slab of electro-optic material using an ultrashort laser pulse focused to a line. Phys Rev B 76, 085346 (2007) [3] M.I. Bakunov, M.V. Tsarev, E.V. Mashkovich. Terahertz difference-frequency generation by tilted amplitude front excitation. Optics Express 20 28573 (2012) [4] Fulop, J. A., Palfalvi, L., Hoffmann, M. C. & Hebling, J. Towards generation of mJ-level ultrashort THz pulses by optical rectification. \Opt. Express 19, 15090-15097 (2011). [5] Hebling, J. Yeh, K-L, Hoffmann, M.C., Bartal, B., Nelson, K.A. Generation of high-power terahertz pulses by tilted pulse front excitation and their application possibilities. J. Opt. Soc. Am B, 25, 6 (2008) [6] Hirori, H., Doi, A., Blanchard, F. & Tanaka, K. Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3. Appl. Phys. Lett. 98, 091106 (2011). [7]. D.A. Walsh, D.S. Lake, E.W. Snedden, M.J. Cliffe, D.M. Graham and S.P. Jamison, “Demonstration of sub-luminal propagation of single-cycle terahertz pulses for particle acceleration,” Nature Communications, vol. 8, pp. 421, 2017.  Steven P. Jamison1, David A. Walsh2, Edward W. Snedden2 1Department of Physics, Lancaster University, Lancaster LA1 4YW, United Kingdom 2Accelerator Science and Technology Centre, Science and Technology Facilities Council, Daresbury Laboratory, Warrington, WA4 4AD, UK Tilted Pulse-Front Phase-matching in Three Dimensions: Overcoming The Cherenkov Angle Restrictions E Fig. 1. THz generation of a planar front with differing pulse front tilt angle. Optical pulse propagation direction is in the z-direction. (a) with pulse-front tilt matching the Cherenkov angle of the material, with tilt in the z-x plane. (b) with a pulse front tilt exceeding the Cherenkov angle. The pulse-front tilt has projection components in both the zx- and zy-planes. The angle projected into the zx-plane is at the Cherenkov angle.    

Tilted Pulse-Front Phase-matching in Three Dimensions:Overcoming The Cherenkov Angle Restrictions

https://eprints.lancs.ac.uk/id/eprint/131089/1/IRMMW_THz2018_abstract_Jamison.pdf

Tilted Pulse-Front Phase-matching in Three Dimensions:Overcoming The Cherenkov Angle Restrictions

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