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Optics Letters

Balancing interferometers with slow-light elements

Alireza Marandi, Brian T. Lantz, Robert L. Byer

Published Mar 9, 2011• 4 citations
Publisher

Abstract

In this Letter we show that interferometers with unbalanced arm lengths can be balanced using optical elements with appropriate group delays. For matched group delays of the arms, the balanced interferometer becomes insensitive to the frequency noise of the source. For experimental illustration, a ring resonator is employed as a slow-light element to compensate the arm-length mismatch of a Mach-Zehnder interferometer. An arm-length mismatch of 9.4 m is compensated by a ring resonator with a finesse of 70 and a perimeter of 42 cm.

DOI
10.1364/ol.36.000933

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In this Letter we show that interferometers with unbalanced arm lengths can be balanced using optical elements with appropriate group delays. For matched group delays of the arms, the balanced interferometer becomes insensitive to the frequency noise of the source. For experimental illustration, a ring resonator is employed as a slow-light element to compensate the arm-length mismatch of a Mach-Zehnder interferometer. An arm-length mismatch of 9.4 m is compensated by a ring resonator with a finesse of 70 and a perimeter of 42 cm.
We demonstrate a slow-light augmented unbalanced Mach-Zehnder interferometer (MZI) which can be used to enhance very significantly the sensitivity of measuring the frequency shift in a laser. The factor of enhancement depends on the group index of the slow-light medium, the degree of imbalance between the physical lengths of the two arms of the MZI, and the spectral width of the laser. For a laser with a quantum noise limited spectral width, the group index has to be larger than the finesse of the laser cavity in order to achieve enhancement in measurement sensitivity. For the reported results, slow-light effect is produced by employing electro-magnetically induced transparency via coherent population trapping in a paraffin coated vapor cell of Rb atoms, with a maximum group index of ~2170. The maximum enhancement factor realized is ~70. This differs from the theoretically expected value of ~183 by a factor of ~2.6. This discrepancy can be attributed to effects of unidentified excess noise, and the fact that the test laser spectral width may not the quantum noise limited. Much larger values can potentially be obtained by modifying the apparatus, and using cold atoms for producing the slow-light effect. The sensitivity of any sensor that relies on measuring the frequency shift of a laser can be enhanced substantially using this technique. These include, but are not limited to, gyroscopes and accelerometers based on a conventional ring laser or a superluminal ring laser, and detectors for virialized ultra-light field dark matter.
An analytical approach is reported that describes previously observed fast-light regimes in linear and passive Mach-Zehnder interferometers (MZI) where the optical path difference is due to a different length of the branches. Approximate expressions are developed for the transmission coefficient and group delay spectral functions valid for frequencies close to the transmission minima ${\ensuremath{\omega}}_{\mathrm{min}}$, where these regimes occur. It is found that the group delay at ${\ensuremath{\omega}}_{\mathrm{min}}$ verifies a simple scaling law. We demonstrate that slow light cannot arise in this system, and that tunneling and superluminal regimes appear only for low-loss devices, where the attenuation drives the change in the propagation regimes. The propagation of a sinusoidally modulated pulse train through the MZI is described, and relevant figures of merit, which are intrinsic to the system and universal for any operative spectral range, are determined. The theoretical approach is illustrated by simulations of a silicon-based interferometer designed for advancing pulses at 1.55 \ensuremath{\mu}m. Also, previously reported experimental results in the radiofrequency range are interpreted in the framework of the model.
We report the experimental observation of dispersion transition from abnormal dispersion (fast light) to normal dispersion (slow light) in a side-coupled ring resonator. We reveal that the transition from fast light to slow light can occur, when the tuned loss of the resonator results in the experience from the undercoupled regime to the overcoupled regime. Also, we experimentally fabricate the fiber side-coupled ring resonator, and measure the group delay of the resonator by coupling the resonator to a fiber Mach-Zehnder interferometer (MZI). The measured experimental results demonstrate the dispersion transition, and are in good agreement with the corresponding theoretical results. The sidecoupled resonator with the tunable dispersion (group delay) can exploited for optical storage devices, slow light Fourier transform (FT) interferometric spectrometers, white light cavities (WLCs), optical switches, optical routers, and optical sensors.
We report the group velocity control of light in optical fiber by gain-imbedded unbalanced fiber Mach–Zehnder interferometer. Slow and fast light effects were observed at the frequencies near the minimum of the transmission spectrum. Controllable group velocity between 0.719 c to 0.620 c ( c is the light speed in a vacuum) was obtained via the cross-intensity modulation effect, by changing the gain index in the long arm. With the power compensation provided by the introduced Erbium doped fiber, this proposal offers a simple and operable solution to realize lossless slow and fast light propagation in optical fiber.
We propose and demonstrate a method for manipulation of group velocity from slow-to-fast light (SFL) in a two-beam Mach–Zehnder interferometer in radio frequency (RF) regime. The subluminal, superluminal, and tunneling propagation regimes occur in a narrow frequency band around the resonance frequency of the interferometer where destructive interference occurs. Importantly, the group velocity at the resonance frequency can be controlled by simply adjusting the transmission magnitude of the signals from the two beams, without changing the length of the interferometer. Models that fully describe the SFL effects in the microwave interferometer system are developed and closed-form expressions for the prediction of group delays at the resonance frequency are obtained. The simple and effective method is verified through numerical calculations and experimental measurements. We also demonstrate that the proposed method applies to a microwave cavity interferometer. A proof-of-concept experiment is performed using a custom open-ended coaxial cable resonator (OE-CCR). Positive and negative group delays are experimentally measured when the resonator is set at different coupling states.