Interplay of diffraction and nonlinear effects in the propagation of ultrashort pulses

Abstract

We investigate the interplay of diffraction and nonlinear effects during the propagation of very short light pulses. Adapting the factorization approach to the problem at hand by keeping the transverse-derivative terms apart from the residual nonlinear contributions we derive an unidirectional propagation equation which is valid for weak dispersion and reduces to the slowly-evolving-wave-approximation in the case of paraxial rays. A comparison of the numerical simulation results for the two equations shows pronounced differences when self-focusing plays an important role. We devote special attention to modelling the propagation of ultrashort terahertz pulses taking into account diffraction as well as Kerr-type and second-order nonlinearities. Comparing the measured and simulated wave forms we deduce the value of the nonlinear refractive index of lithium niobate in the terahertz region to be three orders of magnitude larger than in the visible part of the spectrum.

Estimations of Low-Inertia Cubic Nonlinearity Featured by Electro-Optical Crystals in the THz Range

“…However, THz pulses feature the duration of 1-2 ps and the thermal nonlinearity contribution is small as it has high-inertia nature. It has been shown both analytically [7,8] and experimentally [9] that regarding THz frequency range, the nonlinearity of the vibrational nature contributes to the overall cubic (third-order) nonlinearity the most, which occurs owing to its low inertia (of the order of or less than 1 ps).…”

The nonlinearity of the refractive index of optical media in the terahertz spectral range

“…It has been predicted theoretically [2] that the THz nonlinear response of crystals is extremely large as a consequence of a strong vibrational contribution. An indirect assessment of n 2 for lithium niobate at THz frequencies was reported in [3], leading to a value of approximately 10 -11 cm 2 /W. We find that n 2 = 4.0 × 10 -11 сm 2 /W, which is approximately 3 orders of magnitude larger that the value 2.4×10 -14 cm 2 /W in the NIR spectral range [4].…”

Mapping the lattice-vibration potential using terahertz pulses

“…In Fig. 3 we show the result (solid line) together with the result of using the cycle averaged expression (13) with β = 0 and also the curve obtained by neglecting the reflection in substrate. We observe considerable difference of the last curve compared to the other two which is a consequence of rather large substrate refraction index.…”

“…Development and application of sources of short, intense radiation in the terahertz region [1,2,3,4,5] makes possible observation of vibrational and electronic excitations in various materials [6,7,8,9,10,11] and quantification of nonlinear effects in pulse propagation [12,13,14]. This offers the possibility of studying material properties responsible for nonlinear effects in the frequency region previously not accessible and potentially even manipulating these properties by induced phase transition.…”