Spectral interferometry
Spectral interferometry (SI) or frequency-domain interferometry is a linear technique used to measure optical pulses, with the condition that a reference pulse that was previously characterized is available.
This technique provides information about the intensity and phase of the pulses.
[1][2] A known (acting as the reference) and an unknown pulse arrive at a spectrometer, with a time delay
are the electric fields of the unknown and reference pulse respectively, the time delay can be expressed as a phase factor
The average spacing between fringes is inversely proportional to the time delay
[5] Compared to time-domain interferometry, SI presents some interesting advantages.
Firstly, by using a CCD detector or a simple camera, the whole interferogram can be recorded simultaneously.
Furthermore, the interferogram is not nullified by small fluctuations of the optical path, but reduction in the fringe contrast should be expected in cases of exposure time being bigger than the fluctuation time scale.
There have been efforts to measure pulse intensity and phase in both the time and the frequency domain by combining the autocorrelation and the spectrum.
This technique is called Temporal Information Via Intensity (TIVI)[7] and it involves an iterative algorithm to find an intensity consistent with the autocorrelation, followed by another iterative algorithm to find the temporal and spectral phases consistent with the intensity and spectrum, but the results are inconclusive.
It is frequently used for measuring the linear response of materials, such as the thickness and refractive index of normal dispersive materials,[8] the amplitude and phase of the electric field in semiconductor nanostructures[9] and the group delay on laser mirrors.
[4][14] This technique is not commonly used since it relies on a number of factors in order to obtain strong fringes during experimental processes.
Some of them include:[15] In cases of relatively long pulses, one can opt for Spectral Shearing Interferometry.
For this method, the reference pulse is obtained by sending its mirror image through a sinusoidal phase modulation.
Thus, the spectral derivative of the phase of the signal pulse which corresponds to the frequency-dependent group delay can be obtained.
For this method, the reference pulse should produce a mirror image of itself with a spectral shift, in order to provide the spectral intensity and phase of the probe pulse via a direct Fast Fourier Transform (FFT) filtering routine.
The self referencing is possible due to pulse shaping optimization and non-linear temporal filtering.
[19][20] It provides all the benefits associated with SI (high sensitivity, precision and resolution, dynamic and large temporal range) but, unlike the SPIDER technique, neither shear nor harmonic generation are necessary in order to be implemented.
For SRSI, the generation of a weak mirror image of the unknown pulse is required.
That image is perpendicularly polarized and delayed with respect to the input pulse.
Then, in order to filter the reference pulse in the time domain, the main portion of the pulse is used for cross-polarized wave generation (XPW) in a nonlinear crystal.
[21] The interference between the reference pulse and the mirror image is recorded and analyzed via Fourier transform spectral interferometry (FTSI).
[6] Known applications of the SRSI technique include the characterization of pulses below 15 fs.
[22] Frequency Resolved Optical Gating (FROG) is a technique that determines the intensity and phase of a pulse by measuring the spectrum of a particular temporal component of said pulse.
[23] This results in an intensity trace, related to the spectrogram of the pulse
FROG is commonly combined with Second Harmonic Generation (SHG) process (SHG-FROG).
[24] There is a variety of linear techniques that are based on the main principles of spectral interferometry.
