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IEEE Journal of Quantum Electronics

Gain characteristics of coherent optical amplifiers using a Mach-Zehnder interferometer with Kerr media

Wataru Imajuku, Atsushi Takada

Published Jan 1, 1999• 16 citations
Publisher

Abstract

This paper investigates the gain characteristics of coherent optical amplifiers that amplify only one of two quadrature phase components in an input signal light according to the phase of pump light. It is constructed around a Mach-Zehnder interferometer with Kerr media. To heuristically obtain the design parameters of the coherent optical amplifier, small-signal analysis is adapted to the Mach-Zehnder interferometer with Kerr media. The theoretical results are then compared to experimental results and shown to agree well, which confirms the validity of this design approach. By utilizing low-loss and high-nonlinearity silica fiber as the Kerr medium and optimizing its length, a coherent optical amplifier is constructed that yields high-gain (up to 26 dB) operation.

DOI
10.1109/3.798089

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This paper investigates the gain characteristics of coherent optical amplifiers that amplify only one of two quadrature phase components in an input signal light according to the phase of pump light. It is constructed around a Mach-Zehnder interferometer with Kerr media. To heuristically obtain the design parameters of the coherent optical amplifier, small-signal analysis is adapted to the Mach-Zehnder interferometer with Kerr media. The theoretical results are then compared to experimental results and shown to agree well, which confirms the validity of this design approach. By utilizing low-loss and high-nonlinearity silica fiber as the Kerr medium and optimizing its length, a coherent optical amplifier is constructed that yields high-gain (up to 26 dB) operation.
The noise figure (NF) of a phase-sensitive parametric amplifier using a nonlinear Mach-Zehnder interferometer (NMZI) with Kerr media is analyzed for amplitude-modulation signals. In the analysis, the distributed loss of the Kerr media and the excess noise of the pump light are taken into account. As for the distributed loss of the Kerr media, the quantum Langevin equation for the NMZI is derived and solved. The results elucidate a simple degradation factor in the NF representation of the amplifier. This factor implies that the NF can be less than the standard quantum limit (SQL) of 3 dB, even if the total loss of the Kerr media exceeds 3 dB. As for the excess noise of the pump light, the semi-classical small signal analysis is utilized. The results clearly indicate that the signal-to-noise ratio of the pump light must be four times higher than that of the input signal in order to realize a low-noise optical amplifier under the SQL of 3 dB.
We present an extension of Glauber's theory of the Mach-Zehnder interferometer with optical amplifiers placed in each of its internal paths. Conditions are derived for the achievement of maximum fringe visibility with amplifiers of general linear characteristics. The effects of the phase-conjugated and the phase-preserved components of the amplified light are elucidated for the contrasting cases of coherent and number-state inputs. Particular attention is paid to the minimization of amplifier noise in the limit of high gain.
Quantum mechanical arguments show that any optical amplifier must add noise to the amplified beam of light.For the case of a high gain amplifier with a coherent (Poissonian) input, the signal-to-noise ratio of the amplified beam must be at least two times smaller than that of the incident beam.We review the theoretical basis of this prediction.We also describe the results of our experimental investigations of the noise properties of optical amplifiers that utilize the nonlinear optical response of strongly driven atomic transitions.
The characteristics of the quantum optical complementarity principle and the coherence of the photons generated in a Mach-Zehnder interferometer with two degenerate optical parametric amplifiers are analysed. The photon statistics and the phase fluctuation of the combined states are analysed in a homodyning Mach-Zehnder interferometer with two degenerate optical parametric amplifiers. By analysing the photon statistics, the mean-square phase fluctuation and the fringe visibility, the complementarity is considered as a function of the gain and input phase, when the amplified input is a coherent state containing one photon, on average. It is also considered when the input is a number state with one photon.
Optical amplification in optical fibers by means of degenerate four-wave mixing (DFWM) is studied by classical equations. A balanced interferometer is used to mix and separate the signal and the pump. Exact solutions are obtained even with pump depletion. If the cross-phase modulation is small, the signal power gain varies as the square of the pump self-phase shift. This gain can be sizable for moderate fiber lengths and laser powers, before the onset of stimulated Raman scattering. We have experimentally verified these calculations with a Sagnac interferometer, comprising a 300 m long polarization-preserving fiber, emitting pulses with 100-200 W peak power and 100-200 nsec duration. We have measured a signal power gain of 22 (13.3 dB); this value correlated well with a pump self-phase shift of 3π/2 measured in a separate two-wavelength experiment. This system can be used for squeezing fluctuations of the signal quadrature which is not amplified. We have performed a classical derivation of squeezing, based upon a geometrical study of the transformation of the signal phasor. The results are in agreement with those of more elaborate quantum-mechanical derivations.
This work discusses the single-intensity and difference-intensity detection schemes for lossy Mach–Zehnder Interferometer (MZI) and gives the corresponding optimal conditions to achieve the best phase measurements. The interferometer is fed by a coherent state in one port and a vacuum state in the other. When the core parameters (reflectivities, phase difference) are optimal, the phase sensitivity of these two detection schemes can reach a generalized precision bound: the standard interferometric limit (SIL). In the experiment, we design an MZI with adjustable beam splitters to verify the phase sensitivity optimization compared to the conventional MZI with 50:50 beam splitters. The sensitivity improvements at loss rates from 0.4 to 0.998 are demonstrated based on difference-intensity detection, matching the theoretical results well. With a loss up to 0.998 in one arm, we achieve a sensitivity improvement of 2.5 dB by adjusting reflectivity, which equates to a 5.5 dB sensitivity improvement in single-intensity detection. Such optimal phase measurement methods provide practical solutions for the correct use of resources in lossy interferometers.