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Optics Express

Measurement of the spectrally-resolved absolute phase difference between orthogonal optical modes using a nonlinear beat signal

A. Gosteva, M. Haiml, Ursula Keller

Published Oct 31, 2005• 2 citations
Publisher

Abstract

On the basis of white-light interferometry with spectrally integrated detection and Fourier transform (FT) analysis, we demonstrate a novel technique for measuring the spectrally-resolved absolute phase difference between orthogonal optical modes with milliradian precision. The phase difference is evaluated from a nonlinear beat signal, occurring in the phase spectrum when independent interferograms, formed by individual modes, are recorded simultaneously. Although scanning white-light FT interferometry is a linear technique in general, the nonlinear beat signal is due to spectral amplitude variations in each mode. These proof-of-principle absolute phase difference measurements were carried out with polarization and spatial fiber modes.

DOI
10.1364/opex.13.008913

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On the basis of white-light interferometry with spectrally integrated detection and Fourier transform (FT) analysis, we demonstrate a novel technique for measuring the spectrally-resolved absolute phase difference between orthogonal optical modes with milliradian precision. The phase difference is evaluated from a nonlinear beat signal, occurring in the phase spectrum when independent interferograms, formed by individual modes, are recorded simultaneously. Although scanning white-light FT interferometry is a linear technique in general, the nonlinear beat signal is due to spectral amplitude variations in each mode. These proof-of-principle absolute phase difference measurements were carried out with polarization and spatial fiber modes.
The unambiguous determination of optical refractive indices of metamaterials is a challenging task for device applications and the study of new optical phenomena. We demonstrate here simple broadband phase measurements of metamaterials using spectrally and spatially resolved interferometry. We study the phase response of a π-shaped metamaterial known to be an analog to electromagnetically induced transparency. The measured broadband interferograms give the phase delay or advance produced by the metamaterial in a single measurement. The presented technique offers an effective way of characterizing optical metamaterials including nonlinear and gain-metamaterial systems.
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Interferometry has long been used to measure the phase of light signals. Combined with a heterodyne detection scheme, it allows to simultaneously and unambiguously record amplitude and phase variations. In this work, we exploit these well-known techniques to evaluate the nonlinear phase induced by the optical Kerr effect during the propagation of a laser pulse in a nonlinear medium. We show that the nonlinear index can easily be retrieved when the accumulated phase remains small, but counter-intuitive results can be observed at higher powers.
The power spectrum of an optical field can be acquired without a spectrally resolving detector by means of Fourier-transform spectrometry, based on measuring the temporal autocorrelation of the optical field. Analogously, we here perform temporal envelope measurements of ultrashort optical pulses without time resolved detection. We introduce the technique of Fourier transform chronometry, where the temporal envelope is acquired by measuring the frequency autocorrelation of the optical field in a linear interferometer. We apply our technique, which is the time-frequency conjugate measurement to Fourier-transform spectrometry, to experimentally measure the pulse envelope of classical and single-photon light pulses.
Abstract A phase-sensitive detection scheme for optical fields is described, which allows for the simultaneous measurement of orthogonal field quadratures. The recent achievement of -radian cross-phase shifts between a single photon and a second light field has opened the door to quantum computing protocols which utilize photonic quantum bits. Optical phase measurements play an integral role in these schemes. The detection scheme presented here was designed to measure such transient phase shifts of a laser field as it interacts with another light field through a cloud of laser-cooled Rb atoms. In place of conventional spatial interferometry, which is very sensitive to mechanical instabilities, the scheme utilizes beat-note interferometry to improve on the robustness of the measurement. Beat-note interferometry serves to map a signal from a THz-frequency carrier onto a radio-frequency carrier. A variant of 8-port optical homodyne detection, the scheme then uses IQ demodulation, a well-established technique in communications engineering, to extract amplitude information for both the in-phase (I) and quadrature-phase (Q) components of the radio-frequency signal. This IQ data can then be used to extract any amplitude variation and/or phase shifts of the original THz-frequency optical field. The technique is illustrated here by simultaneously measuring the absorption and dispersion experienced by an optical beam as it passes through a cloud of laser-cooled atoms, which have been prepared in a state of electromagnetically-induced transparency. A thorough characterization of the measurement is presented, which identifies the dominant noise sources and illustrates the utility of IQ demodulation in eliminating noise. This scheme has been used to measure rad phase shifts on nanosecond time scales.