Determination of nonlinear refractive indices by external self-focusing

Abstract

The nonlinear refractive index of benzene is determined by measuring the reduction of the beam divergence of picosecond ruby laser pulses when passing through a benzene sample. Time-integrated spatial beam profiles give an effective refractive index while time-resolved beam profiles measured with a streak camera allow the determination of the temporal evolution of the nonlinear refractive index. PACS:42.65, 42.65.J At high laser powers the refractive index of materials becomes intensity dependent. The spatial laser beam profile causes a spatial refractive index profile and leads to self-focusing [1][2][3][4][5][6]. The overall beam profile is responsible for whole-beam self-focusing while an intensity modulation of the spatial intensity distribution leads to a beam break-up (small-scale selffocusing) [5][6][7][8]. The combined effects of self-focusing and beam diffraction result in filament formation [1][2][3][4][5][9][10][11][12]. The self-focusing increases the pulse intensity enormously and enhances all nonlinear optical effects [13][14][15][16][17][18][19]. The abrupt rise of nonlinear optical effects is an indication of self-focusing and may be used to determine the self-focusing length. The determination of the nonlinear refractive index from the abrupt rise of nonlinear optical effects is complicated by the fact that either whole-scale self-focusing or small-scale selffocusing may act and the small-scale self-focusing parameters (ripple widths and modulation depths) are difficult to determine.The vagueness of whole-scale or small-scale selffocusing dynamics may be avoided by changing from internal self-focusing (focal point caused by nonlinear refractive index is inside sample) to external selffocusing (focal point is outside sample) [1 ]. In this case the nonlinear refractive index of the sample causes a reduction of the overall beam divergence and the effects of small ripples across the beam profile may be neglected.In our experiments we determine the reduction of beam divergence by comparing the beam diameters (FWHM) of two pulses at a certain distance behind the sample position, where one pulse passes through the sample and the other pulse is bypassed. Our timeresolved measurements of the beam diameters with a streak camera and a two dimensional readout system allow the study of the instantaneous and transient contributions to the nonlinear refractive index [12,18,20]. The effective time-averaged and the time-resolved nonlinear refractive index of benzene are measured with picosecond light pulses of a ruby laser. The reported time-averaged nonlinear refractive index coefficients n 2 of benzene vary by a factor of ten in the region between n 2 = 1.4x 10~2 1 m 2 V~2 and lxlO" 20 m 2 V-2

Electrodynamics, Topsy-Turvy Special Relativity, and Generalized Minkowski Constitutive Relations for Linear and Nonlinear Systems

“…For additional literature references and related work see [19][20][21][22][23][24][25][26][27][28]. A postulated model [29], applied to numerical simulation of rays in nonlinear media, was used in conjunction with experimental data [30] given in the literature, and close agreement of the experimental and simulation results was found. Our prototype linear model for constitutive relations is given by (23), or its spectral equivalent in one of the forms (24) or (27), whichever is more convenient at a given time, or the spatiotemporal convolution integral equivalent (28).…”

“…In this form it appears that the spectral event K interacts with other values K 1 .Whether one considers (30), involving differentiations in the spectral domain, or (33) with its K-domain non-local interactions, in any case these forms seem to have no bearing on physical models as we know them. It is noted that interactions in spectral space are possible in the case of nonlinear systems, discussed below, but not in the present case of linear systems.…”

Spectral modulation of stimulated Raman scattering signal: Beyond weak Raman pump limit

“…The constant factor in the expression for in Equation including N and vibrational transition polarizability was set to a value with which the numerically simulated SRL at the peak maximum (992 cm −1 ) best fits with the experimentally obtained SRL at several weak pump intensities <1 GW/cm 2 (see Figure S3). Numerical simulations were performed for two different cases with n 2 = 3.0 × 10 −21 m 2 /V 2 (benzene) and 10 times smaller n 2 = 3.0 × 10 −22 m 2 /V 2 to compare large and small XPM effects on the SRS spectrum. Here, the normal refractive index ( n 0 ) of liquid benzene is 1.482 at the wavelength of 930 nm .…”

Simulation of Hamiltonian light-beam propagation in nonlinear media

“…Practical schemes as described below force us to truncate Eq. (15) for the problem to be manageable. We will also consider only the fundamental harmonic, p ϭ Ϯ1.…”