I think 6fs will spread to be about 30 fs if pass through 1 mm and about 56 fs if pass through the 2 mm of Bk7.
For 18 fs , it will be 22 fs if pass through 1 mm and about 24 fs if pass through the 2 mm of Bk7.
For 30 fs , it will be 31 fs if pass through 1 mm and about 32fs if pass through the 2 mm of Bk7.
What is your opinion and if you have some related papers please?
Up to the quadratic order of dispersion, the effect of propagation through material on the temporal duration of an initially-transform-limited Gaussian laser pulse is given by:
Tout=Tin*\sqrt[1+(4*(\alpha^2)*(z^2)/((Tin)4)]
where Tin is the starting pulse duration (Tin=TFWHM/(2*Sqrt[ln(2)])), Tout is the final pulse duration, z is the propagation length, and \alpha is the quadratic dispersion term given by
\alpha = (n'(\omega)/c) + (\omega * n''(\omega)/(2c))
where n is the index of refraction as a function of \omega, \omega is the angular frequency (evaluated after differentiation at the pulse's central frequency), and c is the speed of light.
For BK7 glass, and assuming that your Gaussian pulse has a central wavelength of 800 nm (the answer would be slightly different otherwise):
- A 6 fs pulse will spread to 21.5 fs through 1 mm of BK7 and to 41.7 fs through 2 mm of BK7.
- An 18 fs pulse will spread to 19.3 fs through 1 mm of BK7 and to 22.7 fs through 2 mm of BK7.
- A 30 fs will spread to 30.3 fs through 1 mm of BK7 and to 31.1 fs through 2 mm of BK7.
Remember, again, that the 1/e pulse duration rather than full-width-half-maximum (FWHM) pulse duration is used in this calculation.
To answer the question of "What is the difference between temporal dispersion of 6fs,18 fs and 30fs Gaussian pulses in glass?", the difference is the bandwidth: because a 6 fs pulse has a much broader bandwidth, the opposite ends of its spectrum will experience significantly different indices of refraction. Therefore, shorter pulses see their pulse durations increase more than longer pulses going through equal amounts of material.
See the link for more information.
http://optics.byu.edu/BYUOpticsBook_2015.pdf#page=189
Up to the quadratic order of dispersion, the effect of propagation through material on the temporal duration of an initially-transform-limited Gaussian laser pulse is given by:
Tout=Tin*\sqrt[1+(4*(\alpha^2)*(z^2)/((Tin)4)]
where Tin is the starting pulse duration (Tin=TFWHM/(2*Sqrt[ln(2)])), Tout is the final pulse duration, z is the propagation length, and \alpha is the quadratic dispersion term given by
\alpha = (n'(\omega)/c) + (\omega * n''(\omega)/(2c))
where n is the index of refraction as a function of \omega, \omega is the angular frequency (evaluated after differentiation at the pulse's central frequency), and c is the speed of light.
For BK7 glass, and assuming that your Gaussian pulse has a central wavelength of 800 nm (the answer would be slightly different otherwise):
- A 6 fs pulse will spread to 21.5 fs through 1 mm of BK7 and to 41.7 fs through 2 mm of BK7.
- An 18 fs pulse will spread to 19.3 fs through 1 mm of BK7 and to 22.7 fs through 2 mm of BK7.
- A 30 fs will spread to 30.3 fs through 1 mm of BK7 and to 31.1 fs through 2 mm of BK7.
Remember, again, that the 1/e pulse duration rather than full-width-half-maximum (FWHM) pulse duration is used in this calculation.
To answer the question of "What is the difference between temporal dispersion of 6fs,18 fs and 30fs Gaussian pulses in glass?", the difference is the bandwidth: because a 6 fs pulse has a much broader bandwidth, the opposite ends of its spectrum will experience significantly different indices of refraction. Therefore, shorter pulses see their pulse durations increase more than longer pulses going through equal amounts of material.
See the link for more information.
http://optics.byu.edu/BYUOpticsBook_2015.pdf#page=189
Building on the previous answer, Newport also has a nice discussion of it - https://www.newport.com/The-Effect-of-Dispersion-on-Ultrashort-Pulses/602091/1033/content.aspx
There are also online calculators that can give you exact values (search scientific calculator, laser or , dispersion) for any length and most often used materials. They usually either have preloaded optical properties for materials, (BK7, quartz, etc..) or at least a fields where you can enter n, n', n''....
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