Chronocyclic tomography for measuring the amplitude and phase structure of optical pulses

Abstract

We describe a new method-chronocyclic tomography-for determining the amplitude and phase structure of a short optical pulse. The technique is based on measurements of the energy spectrum of the pulse after it has passed through a time-frequency-domain imaging system. Tomographic inversion of these measured spectra yields the time-frequency Wigner distribution of the pulse, which uniquely determines the amplitude and phase structure.

Time-dependent spectrum of a single photon and its positive-operator-valued measure

“…Whereas measuring the frequency of light has been relatively straightforward since Newton's days, measuring the time of arrival (on, say, a picosecond timescale) tends to be much harder. One nice way to achieve a high-resolution time measurement is to measure the frequency after first sending the photon through a time-to-frequency converter [17][18][19][20][21][22]. Here one first lets the photon propagate through a dispersive element that multiplies the spectral amplitude of the photon with a phase factor exp(−iαω 2 /2), with α a constant, and subsequently one applies a time-dependent phase modulation that multiplies the temporal amplitude with a similar phase shift exp(−iβt 2 /2) in the time-domain.…”

Ultrashort Pulse Characterization

“…In contrast to spectrographic methods, tomography methods utilize a direct inversion algorithm. The most thorough method projects rotations up to 2π and then performs an inverse Radon transform on all projections, see Figure 3.17b [80]. Due to bandwidth constraints, this technique has only been demonstrated for picosecond pulses.…”

The criterion of pulse reconstruction quality based on Wigner representation

“…It has been introduced using the analogy of ultrashort light pulses and quantum particles moving in a combined position-momentum phase space [20,21]. The Wigner distribution was used in pulse-characterization methods [22,23] and recently, it has also been applied for the interpretation of coherent optical spectroscopy such as photon and Raman echoes [24][25][26]. An example of a Wigner trace of a pulse with the Gaussian spectrum and cubic spectral phase is shown in Fig.…”