Yi-Ci Li1*, Yu-Ting Kuo1, Po-Yuan Huang1, Sidney S. Yang2, Cheng-I Lee3, Tai-Huei Wei1
1Department of Physics, National Chung Cheng University, Min-Hsiung, Chia-Yi, Taiwan
2Department of Materials and Optoelectronic Science, National Sun Yat-Sen University, Kaohsiung, Taiwan
3Department of Life Science, National Chung Cheng University, Min-Hsiung, Chia-Yi, Taiwan
* presenting author:李乙氣,
Using the Z-scan technique with femtosecond (fs) laser pulses, thermal lensing effect has been observed in simple molecular liquids such as carbon disulfide (CS2), water (H2O) and methanol (CH3OH). In this report, we quantitatively explain the mechanisms of the thermal lensing effect of these samples. The Z-scan measurements were conducted using the continuously output 82 MHz transform-limited laser pulses with a central wavelength of λ0 = 820 nm and a pulse duration of τ = 18 fs, measured at half-width at e-1 maximum (HWe-1M). The open aperture Z-scan results show no noticeable variations at the vicinity of focal point. This is understandable because pure CS2 is both linearly and nonlinearly transparent to the femtosecond pulses. Both water and methanol are weakly absorptive around 820 nm wavelength but nonlinearly transparent to the femtosecond pulses. The closed aperture Z-scan results show a peak on the -z side and a valley on the +z side. This signifies a negative lensing effect.
By treating the light-mater interaction in frequency domain, we propose a model which assigns the heat generation mechanism to non-radiative relaxation of molecular librations and vibrations, excited linearly or nonlinearly. Those molecular motions, whose mode frequencies fall within the bandwidth (350 cm-1 measured at HWe-1M) of our 18 fs pulse, can be excited by stimulated Raman scattering (SRS). On the other hand, linear absorption (LA) can induce the “combination mode” of the molecular motions, whose mode frequencies are beyond pulse bandwidth, if the combination of these mode frequencies matches photon energy of the laser.
Our model establishes a link between fs pulse intensity, first and third order polarization of simple molecular liquids. Using the susceptibility formalism, we simulate the intensity change of each frequency carried within a laser pulse. After a pulse train traverses the sample, accumulation of pulse energy per unit area can be calculated by repeatedly integrating the pulse intensity over frequency and summing over repetition number. The relaxation of excited molecular motions creates a temperature gradient driven acoustic wave which renders the lens-like density distribution in liquids. Based on Huygens-Fresnel principle, the closed aperture Z-scan results conducted with average power ranging between 240 and 270 milliwatt (mW) are quantitatively explained. Our results show that SRS dominates over LA in CS2, LA dominates over SRS in both H2O and CH3OH.

Keywords: thermal lensing effect, Z-scan, femtosecond laser