Short pulses properties and chirp
This window helps translating between spectral and temporal width of short fourier-limited laser pulses.
In addition it calculates the amount of chirp such a pulse accumulates in a certain amount of glass. For Gaussian pulses it also estimates the resulting pulse broadening.
In addition it calculates the amount of chirp such a pulse accumulates in a certain amount of glass. For Gaussian pulses it also estimates the resulting pulse broadening.
In the first section calculations concerning the transform-limited pulse are performed.
The pulse shape can be chosen to be either of gaussian or sech^2 (hyperbolic secant squared) type. These pulses have different time bandwidth products and different relations between pulse duration and second order autocorrelation width.
Pulse durations can be translated into spectral widths, autocorrelation width into pulse durations, spectral widths into autocorrelation widths ...etc.
The following relations apply :
The pulse shape can be chosen to be either of gaussian or sech^2 (hyperbolic secant squared) type. These pulses have different time bandwidth products and different relations between pulse duration and second order autocorrelation width.
Pulse durations can be translated into spectral widths, autocorrelation width into pulse durations, spectral widths into autocorrelation widths ...etc.
The following relations apply :
- time_bandwidth = FWHM_pulseduration * FWHM_frequency
- FWHM_wavelength = wavelength^2*FWHM_frequency/c
- FWHM_autocorrelation = ACfactor*FWHM_pulseduration
In the second section glass properties for the above selected center wavelength are calculated. The index of refraction is calculated from a Sellmeier formula and for the different dispersion parameters the Sellmeier formula is numerically differentiated.
The following formulas are used:
The following formulas are used:
- optical_path = thickness*index
- GV = c/n/(1+wavelength/index*(d_index/d_wavelength))
- GD = thickness/GV
- GVD = wavelength^3/2/Pi/c^2*(d^2_index/d_wavelength^2)
- GDD = thickness*GVD
In the third section the pulse duration of the chirped pulse is calculated from the GDD. This calculation neglects contributions from higher order dispersion.
For Gaussian pulses the following formulas are used:
For Gaussian pulses the following formulas are used:
- FWHM_chirped_pulse = FWHM_pulseduration*sqrt(1+(thickness*GVD)
- ^2/FWHM_pulseduration^4*16*(ln(2))^2)
- chirped_time_bandwidth = FWHM_chirped_pulse * FWHM_frequency FWHM_chirped_autocorrelation = ACfactor*FWHM_chirped_pulse
The broadening calculations for sech^2 pulses are retieved from the Gaussian ones. However, they are only empirical modifications and not directly derived from a Taylor expansion.
