Observation of the Lowest Lying Electric-Dipole-Allowed Two-Photon Resonance in C₆₀

Abstract

We use time-resolved degenerate four-wavemixing (DFWM) with femtosecond pulses in the wavelength range 0.74−1.7 μm to measure both phase and amplitude of all nonvanishing elements of the electronic third-order nonlinear optical susceptibility tensor c ijkl (−ω,ω,ω,−ω) of a 10 μm amorphous C60 film on a CaF2 substrate. Linear absorption is found to be less than 1% in this range. We find a single resonance in DFWM, the amplitudes and phases of which are fit well by a Lorentzian model of a two-photon resonance to a level 2.7 ± 0.1 eV above the ground level, with width 0.25 eV. The peak two-photon absorption coefficient is 0.02 cm/MW, essentially the same peak value as for bulk gallium arsenide, one of the strongest and most widely studied of the two-photon absorbers. Our results show there is only one two-photon allowed transition below 3.4 eV (as well as below the first one-photon transition), an unambiguous signature which is expected from theory. Theory assigns the symmetry Hg to this lowest lying two-photon state. We see a clearly nonresonant long-wavelength limit for the third-order optical susceptibility tensor which is 250 ± 70 times the known long-wavelength limit for fused quartz (our nonlinear standard). This result is at least an order-of-magnitude larger than any of several theoretical predictions.

Femtosecond, Frequency-Agile, Phase-Sensitive-Detected, Multi-Wave-Mixing Nonlinear Optical Spectroscopy Applied to π-Electron Photonic Materials

“…The large frequency shift between the input and signal beams in THG ensures that the signal is independent of laser pulse width and excited-state absorption. Unfortunately, as has been noted by Strohkendl et al., THG suffers from the unpredictable overlap of predictable three photon resonances with two photon resonances. Denoting the optical band gap as E g , one finds that THG is able to detect two-photon absorption free of interference from one- and three-photon resonances only for excited-state energies up to 2 / 3 E g .…”

“…We have modeled the two-photon resonances with the Placzek model, which was developed for the analysis of Raman resonances . We demonstrated its applicability to two-photon resonances in the case of C 60 . It permits calculation of all tensor components c ijkl in contrast to our one-photon resonance model which is presently limited to c 1111 .…”

“…For DFWM to be useful for the characterization of instantaneous optical nonlinearity, four modifications of traditional DFWM are required: (1) utilization of femtosecond (100 fs or less) pulses to minimize excited-state absorption, (2) implementation of phase-sensitive-detection to separate two-photon absorption from nonlinear refractive index contributions (i.e., to separate imaginary and real components of the third-order nonlinear optical susceptibility), (3) measurement of the nonlinear optical spectra over a significant range of wavelengths to permit the line shape of excitations (e.g., two photon) to be determined and to permit deconvolution of various resonances through spectral simulation, and (4) improvement of laser pulse-to-pulse stability for the realization of good signal-to-noise. In previous publications, , we have discussed the implementation of these features and have demonstrated the existence of a two-photon absorption for C 60 centered at an excitation wavelength of 0.93 μm (2.7 eV above the ground state). This is the only two-photon state detected for C 60 in the spectral range 0.7 to 2.0 μm.…”

Optical susceptibilities of supported indium tin oxide thin films

“…Strokhendl et al have applied this method to study 10 m thick C 60 films on 1 mm thick CaF 2 substrates and 3.1 m thick C 70 films on 1.49 mm thick fused silica substrates. [25][26][27][28] They showed that for the 3.1-10 m thick films, F Ϸ 1, and F Ϸ 0 for the 1 -1.49 mm thick substrates. The substrate's contribution to the I 6 signal did not need to be considered because its phase-mismatched signal amplitude was ϳ1% of the film's phase-mismatched signal amplitude.…”

“…These contributions can be separated using a method based on the different phase-matching conditions of the thin film and thick substrate. [25][26][27][28] As shown in Fig. 1, the phasematched signal I 4 propagates in a direction that satisfies geometric ͑phase-matching͒ conditions defined as k 1 + k 2 = k 3 + k 4 , where k i are the wave vectors of the corresponding optical beams i ͑k 4 is a wave vector of an optical signal, and k 1 -k 3 are the wave vectors of laser beams͒.…”