In which case thermal contributions to nonlinear refractive indices will be more. Z-scan performed with a 150 fs laser operating at 80 MHz or a nanosecond laser operating at 1 KHz.
lensing effect due to thermal energy basically depends on the pulse width as well as pulse repetition rate, energy with in the pulse and also on the material thermal properties material (thermal diffusion constant and thermo-optic coefficient and geometrical shape etc) and this effect is time dependent phenomenon. best way to get thermal energy from optical energy is by continuous illumination. even though large repetition rate is there for femto seocnd lase (80 MHz) as compare with nano second laser , the thermal energy will be more in nano second regime as compare with femto second due to long range continuous illumination.
here I have given some of the papers discussed about thermal lensing. they may helpful for understanding about thermo optical energy.
1. ‘‘Sensitive Measurement of Optical Nonlinearities Using a Single Beam’’;MANSOOR SHEIK-BAHAE, ALI A. SAID, TAI-HUE1 WEI, DAVID J. HAGAN AND E. w. VAN STRYLAND,IEEE JOURNAL OF QUANTUM ELECTRONICS. VOL. 26. NO. 4, APRIL 1990.
2. ‘‘Simultaneous determination of nonlinear optical and thermo-optic parameters of liquid samples’’,A. Santhi,Vinu V. Namboodiri,P. Radhakrishnan, and V. P. N. Nampoori, APPLIED PHYSICS LETTERS 89, 231113 (2006).
3. S. A. AKHMANOV, D. P. KRINDACH, A. V. NIGULIN, A. P. SUKHORUKOV,R. V. KHOKHLOV, ‘‘E-12-Thermal Self-Actions of Laser beams’’, IEEE JOCRNAL OF QUANTUM ELECTROSICS, OCTOBER 1968.
4. F. W. Dabby, T. K. Gustafson, J. R. Whinnery, Y. Kohanzadeh, and P. L. Kelley, ‘‘thermally self-induced phase modulation of laser beam’’, Applied Physics Letters 16, 362 (1970).
5. Dmitriy I. Kovsh, David J. Hagan and Eric W. Van Stryland, ‘‘Numerical modeling of thermal refraction in liquids in the transient regime’’, 12 April 1999 / Vol. 4, No. 8 / OPTICS EXPRESS 315.
6. Mauro Falconieri, ‘‘Thermo-optical effects in Z-scan measurements using high-repetition-rate lasers’’, J. Opt. A: Pure Appl. Opt.1 (1999) 662–667. Printed in the UK.
If memory serves me right, n2 depends on instantaneous power. Thermal lensing, however, depends on average power (since thermal process are relatively slow).
So to observe equivalent n2, both the 150 fs and the 1 ns pulses must have the same peak power. The latter is ~10^4 longer, so it carries 10^4 more energy per pulse.
The 1 kHz source has ~10^5 fewer pulses per second than the 80 MHz source. So the 1 ns source will have approximately ten times lower time-averaged power. By this back-of-the envelope estimate, the nanosecond source should have less thermal lensing.
But, my assumption is that thermalization is so slow, that hot spot relaxation takes several ms. If thermalization is faster than that, then the fs beam will have less thermal lensing.
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