Abstract: An electronic circuit includes signal processing electronics. The electronic circuit receives an electrical signal generated by a photodetector based on a light beam from a location on a material including a signal of interest and one or more modulation frequencies. The electronic circuit discriminates a portion of the electrical signal proportional to a characteristic of the signal of interest from other components of the electrical signal using a low pass filter with a transfer function including a notch at a notch frequency corresponding to one of the modulation frequencies. The electronic circuit determines a value for the characteristic of the signal of interest from the discriminated portion of the electrical signal. The signal processing electronics further outputs the value of the characteristic of the signal of interest.

Abstract: A method determines the number of layers in a sample material. The method includes measuring, as a function of two or more wavelengths, a four-wave mixing (FWM) spectrum of the sample material. The method further includes using the FWM spectrum to determine a thickness of the sample material, wherein the thickness is a number of layers in the sample material.

Abstract: An electronic circuit includes signal processing electronics. The electronic circuit receives an electrical signal generated by a photodetector based on a light beam from a location on a material including a signal of interest and one or more modulation frequencies. The electronic circuit discriminates a portion of the electrical signal proportional to a characteristic of the signal of interest from other components of the electrical signal using a low pass filter with a transfer function including a notch at a notch frequency corresponding to one of the modulation frequencies. The electronic circuit determines a value for the characteristic of the signal of interest from the discriminated portion of the electrical signal. The signal processing electronics further outputs the value of the characteristic of the signal of interest.

Abstract: A method is presented for determining path length fluctuations in an interferometer using a reference laser with an arbitrary frequency with respect to the measured light. The method includes: injecting reference light along signal paths of the interferometer; measuring interference between the reference light at an output of the interferometer; determining an optical phase difference between the reference light in the two signal paths of the interferometer by measuring intensity modulation of the interference between the reference light and subtracting an intended frequency modulation from the measured intensity modulation; accumulating an unwrapped phase difference between the reference light in the two signal paths of the interferometer, where the unwrapped phase difference is defined in relation to a reference; and determining path length fluctuation of light in the interferometer using the unwrapped phase difference.

Abstract: A method is presented for determining path length fluctuations in an interferometer using a reference laser with an arbitrary frequency with respect to the measured light. The method includes: injecting reference light along signal paths of the interferometer; measuring interference between the reference light at an output of the interferometer; determining an optical phase difference between the reference light in the two signal paths of the interferometer by measuring intensity modulation of the interference between the reference light and subtracting an intended frequency modulation from the measured intensity modulation; accumulating an unwrapped phase difference between the reference light in the two signal paths of the interferometer, where the unwrapped phase difference is defined in relation to a reference; and determining path length fluctuation of light in the interferometer using the unwrapped phase difference.

Abstract: A method is presented for determining an offset frequency of a frequency comb. The method includes: generating a beam of light with a waveform that repeats regularly in the time domain and exhibits a frequency comb in the frequency domain; directing the beam of light towards a point of incidence on a material; and detecting oscillation of a photocurrent in the material that is caused by the beam of light. Of note, the beam of light has an optical bandwidth that includes light propagating at a first frequency and at a second frequency, where the first frequency is less than the second frequency and the ratio of the second frequency to the first frequency is n:m, where n=m+i, m is an integer greater than one, and n and i are positive integers. Additionally, the material has a band gap and the band gap is not more than n times the first frequency.

Abstract: A method is presented for determining an offset frequency of a frequency comb. The method includes: generating a beam of light with a waveform that repeats regularly in the time domain and exhibits a frequency comb in the frequency domain; directing the beam of light towards a point of incidence on a material; and detecting oscillation of a photocurrent in the material that is caused by the beam of light. Of note, the beam of light has an optical bandwidth that includes light propagating at a first frequency and at a second frequency, where the first frequency is less than the second frequency and the ratio of the second frequency to the first frequency is n:m, where n=m+i, m is an integer greater than one, and n and i are positive integers. Additionally, the material has a band gap and the band gap is not more than n times the first frequency.

Abstract: Dual laser frequency combs can rapidly measure high resolution linear absorption spectra. However, one-dimensional linear techniques cannot distinguish the sources of resonances in a mixture of different analytes, nor separate inhomogeneous and homogeneous broadening. These limitations are overcome by acquiring high resolution multi-dimensional non-linear coherent spectra with frequency combs.

Abstract: Dual laser frequency combs can rapidly measure high resolution linear absorption spectra. However, one-dimensional linear techniques cannot distinguish the sources of resonances in a mixture of different analytes, nor separate inhomogeneous and homogeneous broadening. These limitations are overcome by acquiring high resolution multi-dimensional non-linear coherent spectra with frequency combs.

Abstract: Disclosed is a system and method for stabilizing the carrier-envelope phase of the pulses emitted by a femtosecond mode-locked laser by using the powerful tools of frequency-domain laser stabilization. Control of the pulse-to-pulse carrier-envelope phases was confirmed using temporal cross correlation. This phase stabilization locks the absolute frequencies emitted by the laser, which is used to perform absolute optical frequency measurements that were directly referenced to a stable microwave clock.

Abstract: Disclosed is a system and method for stabilizing the carrier-envelope phase of the pulses emitted by a femtosecond mode-locked laser by using the powerful tools of frequency-domain laser stabilization. Control of the pulse-to-pulse carrier-envelope phases was confirmed using temporal cross correlation. This phase stabilization locks the absolute frequencies emitted by the laser, which is used to perform absolute optical frequency measurements that were directly referenced to a stable microwave clock.