Goos–Hänchen shift of a mid-infrared femtosecond filament visualized by the laser coloration method

Abstract

We present the results of investigation of total internal reflection of a femtosecond light filament in a LiF crystal in the regime of anomalous group velocity dispersion. We measure the Goos–Hänchen shift of the filament in the vicinity of the critical angle for a single femtosecond pulse using the laser coloration method. The obtained experimental values are compared to several existing theoretical models.

Angular deviations: From a cubic equation to a universal closed formula to determine the peak position of reflected and (upper) transmitted beams

“…In this paper, by using the first order Taylor expansion of the Fresnel coefficients, we find an analytic expression for the intensity of the optical beam reflected by and (upper) transmitted through a dielectric prism, see Eq. ( 8) and (22). The closed expressions are then verified by numerical calculations for incidence near the Brewster angle showing an excellent agreement as can be seen in Figure 2.…”

“…This study also showed the lateral displacement dependence on the angular distribution shape of the incoming beam. The theoretical prediction were confirmed by the experiments described in [21,22].…”

“…Contrarily to what happens for the Brewster angles this zero in the denominator is not compensated by the zero in the Fresnel coefficient. This implies that, in the critical region, θ cri + δ / k w 0 , the first order expansion of the (upper) transmitted beam (22) and, consequently, the cubic equation obtained for the angular deviation (15), with β pol instead of α pol , is valid for δ ≥ 5. For these values of δ the main contribution to the (upper) transmitted beam comes from the real part of the Fresnel coefficient and, in this case, the first order expansion represents a good approximation for the beam.…”

“…The optical path of a Gaussian beam reflected by or transmitted trough a dielectric prism can easily be calculated by using the laws of geometric optics [1,2]. As the reflection and Snell laws surely represent a useful tool to describe the propagation of optical beams, they cannot be used to predict or explain phenomena like lateral displacements [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] and/or angular deviations [23][24][25][26][27][28][29][30][31][32][33][34].…”

“…In this case, it is common to use weak measurements to amplify the lateral displacements [17,21]. In the region of pure total reflection, the prediction of the Artmann formula were widely confirmed in the experiments [17,18,21,22]. Nevertheless, for incidence at critical angle, the Artmann lateral displacement tends to infinity and numerical calculations are needed to reproduce the experimental data.…”