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Optics Letters

Polarization-based balanced heterodyne detection method in a Sagnac interferometer for precision phase measurement

Ke-Xun Sun, Eric K. Gustafson, M. M. Fejer, Robert L. Byer

Published Sep 1, 1997• 31 citations
Publisher

Abstract

We describe a balanced heterodyne detection method for a Sagnac interferometer that uses a polarization-dependent beam splitter. The signal and the local oscillator are orthogonally polarized components of a single laser beam, permitting the detection of the signal by subtraction of two photocurrents produced in appropriate polarization projections. Using this scheme, we experimentally demonstrate a phase measurement with a sensitivity of 9x10(-10) rad/ radicalHz. The measurement is robust in the presence of laser frequency noise, as a result of preserving the common-path nature of the Sagnac interferometer, and of laser-amplitude noise, as a result of balanced detection.

DOI
10.1364/ol.22.001359

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Journal of the Optical Society of America•Sep 1, 1982•41 citations
We describe a balanced heterodyne detection method for a Sagnac interferometer that uses a polarization-dependent beam splitter. The signal and the local oscillator are orthogonally polarized components of a single laser beam, permitting the detection of the signal by subtraction of two photocurrents produced in appropriate polarization projections. Using this scheme, we experimentally demonstrate a phase measurement with a sensitivity of 9x10(-10) rad/ radicalHz. The measurement is robust in the presence of laser frequency noise, as a result of preserving the common-path nature of the Sagnac interferometer, and of laser-amplitude noise, as a result of balanced detection.
A differential-phase decoder (DPD) together with a polarization common-path optical heterodyne interferometer is set up. Based on this interferometric configuration and a novel balanced-detector scheme, the performance of the quantum-noise-limited differential-phase decoder is demonstrated and analyzed. The minimum-detectable differential phase is on the order of 10(-7) rad/sqrt Hz when a 2.5 mW He-Ne laser is used. Verified experimentally, the DPD is immune to the common-phase noise induced by an electro-optic phase modulator or by thermal disturbance within the interferometer. This signifies that the minimum-detectable differential phase can become 10(-8) rad/sqrt Hz if a 300 mW continuous wave laser is employed instead.
We experimentally study optical homodyne and heterodyne detections with the same setup, which is flexible to manipulate the signal sideband modulation. When the modulation only generates a single signal sideband, the light field measurement by mixing the single sideband at ω0 ±? with a strong local oscillator at the carrier frequency ω0on a beam splitter becomes balanced heterodyne detection. When two signal sidebands at ω0 ±? are generated and the relative phase of the two sidebands is locked, this measurement corresponds to optical balanced homodyne detection. With this setup, we may confirm directly that the signal-to-noise ratio with heterodyne detection is two-fold worse than that with homodyne detection. This work will have important applications in quantum state measurement and quantum information.
A novel frequency stabilization method for external cavity diode lasers by using an all-pass polarization-split Sagnac loop is proposed. This scheme uses a quarter waveplate to convert the incident beam to a circularly polarized beam, and a polarization beam splitter for the input and output of the Sagnac loop. The two beams with perpendicular polarizations counter-propagate in the loop and experience different absorption of the Rb cell; therefore, the Sagnac loop output beam is converted into elliptical polarization. The dispersion phase shift induced by Rb saturation absorption can be obtained by balanced polarization-divided detection of the Sagnac loop output beam. The experimental results showed the feasibility and merits of the new method. This scheme is simple, robust, low-cost, and has potential applications in atomic physics experiments.
Summary form only given. We present a novel multi-port balanced homodyne interferometer scheme, that can simultaneously determine the quadrature phases of the signal beam. This interferometer consists of two identical balanced homodyne interferometers, in which the local oscillators of the corresponding interferometers, have /spl pi//2 phase difference with respect to each other. In this scheme, two identical interferometers for quadrature measurements are constructed by the use of the corresponding polarization components of the signal and local oscillator beams, i.e., principal polarizations of the signal and local oscillator beams are used as independent interferometers. A /spl pi//4 phase shift between the reflected and transmitted polarization components at a polarizing beamsplitter, which was observed in our experiment, was used to provide two local oscillators with /spl pi//2 phase difference. Output interference signals from the corresponding. balanced interferometers, I and Q, respectively, can be written as, I=/spl eta/|E/sub LO/|E/sub s/| cos(/spl Delta//spl phi/),Q=/spl eta/|E/sub LO/|E/sub s/|sin(/spl Delta//spl phi/), where /spl eta/ is the quantum efficiency of photodiode, |E/sub s/| and |E/sub LO/| are the amplitude of signal and local oscillator beam, respectively, and /spl Delta//spl phi/ is the phase difference between signal and local oscillator.
The phase noise affecting the beat photocurrent produced by coherent detection of a single-frequency laser field with a time-delayed and frequency-shifted image of itself in a heterodyne two-wave interferometric system using a single-mode optical fiber is investigated as a function of source spectrum and phase-decorrelation time under the assumptions of quantum laser phase noise and high-local-oscillation level. The influence on the photocurrent spectrum of partial correlation between detected fields is pointed out. These calculations are an extension of a previously reported high-resolution spectroscopic method and account for the phase-noise limitation in unbalanced heterodyne fiber sensors and heterodyne-transmission receivers with an optical reference wave generated from the received signal. An experimental study is reported consisting of a Mach–Zender-type interferometer employing a single-frequency amplitude-stabilized laser, an acousto-optical single-side-band modulator for frequency shifting one of the arms, and several lengths of single-mode optical fiber to decorrelate the detected fields partially. Results are found to be in good agreement with theory.