Guohai Situ

Phase-space measurement and coherence synthesis of optical beams

Summary form only given. Phase-space optics allows simultaneous visualization of both space (x) and spatial frequency (k) information. This is in distinct contrast with normal measurements, such as normal images and Fourier transforms, which record intensities in x-space or k-space only. For coherent beams, which are fully described by a 2D complex function (e.g. amplitude and phase), a phase-space description is useful but redundant. For partially coherent beams, on the other hand, each position x in the beam can have its own local power spectrum, so that a 4D description is often necessary. This is particularly true for propagation, as the beam coherence determines the evolution of its intensity. While a variety of theories has been developed to describe phase-space properties [1], there has been very little progress on the experimental front. Pinhole (Hartmann) or lenslet (Shack-Hartmann) arrays are most commonly used, but the arrays force a trade-off between spatial and angular sampling, usually resulting in poor resolution [2] (and often reduced dynamic range [3]) in both domains. Here, we demonstrate an alternative method for obtaining 4D phase-space distributions quickly, without sacrificing resolution in either dimension [4].The experimental setup is shown in Fig. 1. For measurement, we record a spatial spectrogram (windowed Wigner distribution function) by using a Spatial Light Modulator (SLM) to scan an aperture across the transverse field of the beam. The method is simple, fast, and free of mechanical scanning errors and artifacts [5]. For coherence control, we use a second SLM as a dynamically changing local diffuser with spatially varying statistics, allowing design and creation of arbitrary phase-space distributions. An example is shown Fig. 2, in which each small region in {x} has a variable Gaussian distribution in {k}. Traditional measurements along the marginals of the 4D distribution, i.e. the intensity and power spectrum projections 1(x) = f f(x, k)dk and S(k) = f f(x, k)dx, miss the coherence properties within the volume of phase space. Measurement and control of such higher-dimensional beams will have applications in coherence holography, encoding, illumination, and display.

Observation of all-optical Berezinskii-Krosterlitz-Thouless crossover in a photonic lattice

We experimentally observe an all-optical Berezinskii-Kosterlitz-Thouless transition, in which vortices spontaneously appear due to nonlinear interactions. We show that the number of vortices and their correlations agree with predictions from mean-field theory.

Phase-space imaging of partially coherent beams in linear and nonlinear media

We demonstrate a phase-space imaging system that scans and Fourier transforms an aperture created by a spatial light modulator (SLM), and use it to investigate partially coherent beams as they propagate through linear and nonlinear media.

Fractional optics for image processing and measurement

Fractional optics involves the study of optical phenomena with fractional orders, for example, fractional Fourier transforms and fractional vortices. We review our work on the applications of fractional optics in image processing and measurement.

Phase-space Imaging of Partially Coherent beams with a Spatial Light Modulator

We develop an imaging system for measuring the local coherence length of partially coherent light beams. The 4D phase-space distributions are captured by scanning and Fourier-transforming an aperture created by a spatial light modulator(SLM).

Phase-space imaging of partially coherent beam propagation using a Spatial Light Modulator

We measure the phase-space of coherent and partially coherent light beams as they propagate. The 4D distributions are captured by scanning and Fourier-transforming an aperture created by a spatial light modulator(SLM).