Intensity dependent prism coupling of slab waveguides

3.4 Intensity dependent prism coupling of slab waveguides

The principle of prism coupling is sketched in Fig. 2. Nonlinear prism coupling occurs when the incident intensity I is so large that the refractive index of the film n f becomes intensity dependent. Similarly, the absorption coefficient of the film α f can also change because of increased two-photon absorption, for example. The quantitative evaluation of the nonlinear refractive index n 2 and nonlinear absorption coefficient α 2 is described in detail elsewhere. 20,21 A crucial step in the evaluation of n 2 and α 2 is the determination of the thickness of the air-gap between the prism base and the film surface which is accomplished by simulation of the angular dependence of the reflected intensity I R . Fig. 6 shows an example of intensity dependent prism coupling. The minimum of the resonance coupling angle θ shifts with increasing energy of the incident laser pulses. This is directly related to a change of n f . The resonance curve also becomes deeper due to an increase of α f . The intensity-dependent shifts of the coupling curves were fully reversible at the input laser pulse energy below a certain limiting value which was approximately 3 µJ for 1064 nm λ 1600 nm and 1 µJ for λ 1064 nm. The knowledge of the air-gap thickness enables the evaluation of the average intensity I gw in the waveguide. 20,21 Fig. 7 shows examples of the changes in refractive index ∆n f and absorption coefficient ∆ α f at wavelengths 830 nm and 1064 nm as a function of I gw . The data of ∆n f and ∆ α f increase linearly with I gw which is typical for a cubic nonlinear optical process and allow the evaluation of n 2 and α 2 of the waveguide. A remarkably large ∆n f up to 10 -3 with complete reversibility of the coupling curves was observed at 1064 nm. We like to point out that the optically induced changes of n and α observed here have a pure electronic origin, i.e. they are not thermally induced because of the short pulse duration 20 ps and low repetition rate 10 Hz of our laser system. Furthermore, thermal “nonlinearities” would normally show ∆n 0 only. The intensity dependent prism coupling experiments were performed in the range 680 nm λ 1600 nm. The spectral dependences of the nonlinear absorption coefficient α 2 and nonlinear refractive index n 2 are shown in Fig. 8. Very large values of α 2 were observed at wavelengths around 800 - 850 nm that are caused by two-photon absorption. At λ 1000 nm, α 2 decreases strongly and does not show any other significant resonance. At λ 1000 nm the value of α 2 is smaller than 10 -8 cmW. Negative n 2 values were observed at λ 980 nm. Around 980 nm, n 2 is zero and becomes positive at longer wavelengths. The maximum of n 2 = 2.2 ± 0.4 x 10 -13 cm 2 W was observed at λ = 1080 nm. At λ 1100 nm, the n 2 values decrease monotonically. -10,2 -10,0 -9,8 -9,6 -9,4 -9,2 0,6 0,7 0,8 0,9 1,0 λ = 1064 nm 0.1 µ J 1.0 µ J 2.0 µ J I R [ a .u .] θ [deg.] Fig. 6. Prism coupling curves of a waveguide of MEH-PPV-4 on a fused silica substrate M w = 40,300 gmol, film thickness 590 nm, laser wavelength λ = 1064 nm. The TE mode was excited at different pulse energies given in the inset. Symbols represent the experimental data and lines are the numerical fits. The air-gap thickness d a = 340 nm was evaluated from the curve at 0.1 µJ and held constant afterwards. Only n f and α f of the film were varied to fit the measurements at different energies 0.1 µJ: n f =1.65925, α f = 0.2 cm -1 ; 1.0 µJ: n f =1.65960, α f = 14 cm -1 ; 2.0 µJ: n f =1.6603, α f = 17.4 cm -1 . 1 2 3 4 5 6 7 -0,3 0,0 0,3 0,6 0,9 1,2 a λ = 830 nm λ = 1064 nm λ = 1064 nm ∆ α ∆ α ∆ α ∆ α f [ c m -1 ] I gw [GWcm 2 ] ∆∆∆∆ n f [ 1 -3 ] 1 2 3 4 5 6 7 4 8 12 16 20 b λ = 830 nm Fig. 7. Optically induced and fully reversible changes in a refractive index ∆n f and of b absorption coefficient ∆ α f at laser wavelengths 830 nm open circles and 1064 nm full squares as a function of the average intensity I gw in the waveguide of MEH-PPV-4 TE mode. We interpret the main spectral features of the dispersions of α 2 and n 2 as being due to two processes: 21 First, the broad maximum of α 2 at approximately 830 nm is caused by two-photon absorption, which is in good agreement with the peak observed in the two-photon excitation spectra of the fluorescence, see Section 3.5. Second, the negative n 2 data from 680 to 950 nm are assigned to saturable absorption, which is the dominant nonlinear optical process that occurs for intense laser pulses at the long-wavelength tail of the main absorption band displayed in Figs. 3b and 4, respectively. 3.5 Two-photon excited fluorescence spectroscopy of MEH-PPV solutions To verify the α 2 data, we performed two-photon excited fluorescence experiments with a solution of MEH-PPV-4 in toluene concentration: 3 by weight. At laser wavelengths between 700 nm and 1000 nm, the fluorescence intensity recorded at 600 nm scales with the square of the intensity of the laser pulses which allows the calculation of the imaginary part of the cubic nonlinearity Im[ χ 3 ] in arbitrary units. The two-photon fluorescence excitation spectrum is shown in Fig. 8 for comparison with the α 2 data. The agreement of both spectra is excellent. This means that the chromophores of MEH-PPV behave very similar in the solid state film as compared to the solution state which indicates that aggregation of chromophores does not have significant influence on the nonlinear optical spectra of MEH-PPV. Furthermore, the relative experimental error of Im[ χ 3 ] is much smaller than that of α 2 . Therefore, the more accurate values can be used to evaluate the figures of merit with reduced experimental error as shown in Section 3.7. 0,0 0,5 1,0 1,5 2,0 -6 -4 -2 2 600 700 800 900 1000 1100 1200 -8 -6 -4 -2 2 4 b n 2 [ 1 -4 c m 2 G W ] λ λ λ λ [nm] 600 700 800 900 1000 1100 1200 0,0 0,1 0,2 0,3 αααα 2 [ 1 3 c m G W ] a αααα 2222 [ c m G W ] n 2 [ 1 -5 c m 2 G W ] Fig. 8. Nonlinear optical spectra of MEH-PPV measured at the laser wavelength λ. a Comparison of data of α 2 from nonlinear prism coupling films of 4, full large dots, left scale, from two-photon excitation spectra of fluorescence solutions of 4, open circles, arbitrary units scaled to the peak of film data, error bars are smaller than symbol size, and from z-scan solution of 6, small dots, right scale. b Dispersion of n 2 from nonlinear prism coupling films of 4, full large dots, left scale, and z-scan solution of 6, small dots, right scale.

3.6 Z-scan experiments of MEH-PPV solutions