Amplitude and phase measurements of optical signals using a coherent technique.

Nigel G. Walker, J.E. Carroll

‘Six-port’ techniques developed at microwave frequencies have been used to measure the relative phase and amplitude of optical signals with approximately 130 photons energy at 633 nm. Applications include phase measurements in coherent optical communication systems.

B. V. K. Vijaya Kumar

Yoshihiro Ogawa

We study the bound and antibound states of two excitons in a GaAs single quantum well by two-dimensional coherent spectroscopy. We also propose a method to directly observe the amplitude and phase (real and imaginary parts) of optical fields by using a heterodyne interference technique and through synchronized detection of the interference signals. In this scheme, the mechanical fluctuation of an unstabilized interferometer does not affect the measurement. In addition, the amplitude and phase of the optical fields, resulting from the coherent interactions between light and matter, are directly obtained by comparing a reference heterodyne beating signal by using a two-phase lock-in amplifier. By using this method, the bound and antibound states of two excitons are observed. It is expected that the excitons are localized to the quantum islands and the lateral confinement induces the large repulsive energy between the two excitons.

A. A. Vishenskii, I. A. Deriugin, Vitaliy N. Kurashov

M. T. DiMario, Elohim Becerra

Samuel H. Knarr, Daniel J. Lum, James Schneeloch +1 more

Optical phase spaces represent fields of any spatial coherence and are typically measured through phase-retrieval methods involving a computational inversion, optical interference, or a resolution-limiting lenslet array. Recently, a weak-values technique demonstrated that a beam's Dirac phase space is proportional to the measurable complex weak value, regardless of coherence. These direct measurements require raster scanning through all position-polarization couplings, limiting their dimensionality to less than 100 000 [C. Bamber and J. S. Lundeen, Phys. Rev. Lett. 112, 070405 (2014)]. We circumvent these limitations using compressive sensing, a numerical protocol that allows us to undersample, yet efficiently measure, high-dimensional phase spaces. We also propose an improved technique that allows us to directly measure phase spaces with high spatial resolution with scalable frequency resolution. With this method, we are able to easily and rapidly measure a 1.07-billion-dimensional phase space. The distributions are numerically propagated to an object in the beam path, with excellent agreement for coherent and partially coherent sources. This protocol has broad implications in quantum research, signal processing, and imaging, including the recovery of Fourier amplitudes in any dimension with linear algorithmic solutions and ultra-high-dimensional phase-space imaging.