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Physical Review A

Reply to “Comment on ‘Thermal phase noise in Fabry-Pérot resonators and fiber Bragg gratings’ ”

George Skolianos, Michel J. F. Digonnet

Published Jul 17, 2015• 0 citations

Abstract

The previous Comment clarifies a few key points that were unclear in an earlier paper by its authors, in particular their definitions of phase and of phase noise. We now agree that this earlier paper was modeling the resonance-frequency fluctuations of a Fabry-Perot resonator, whereas our article [Phys. Rev. A 89, 033818 (2014)] was modeling the noise in the phase of the resonator's output field. In light of the Comment, the two pictures are indeed consistent. The resonance-frequency fluctuations are independent of group index, whereas the phase noise in the output field is proportional to group index. This important dependence was pointed out in our paper [Phys. Rev. A 89, 033818 (2014)]. From a more physical standpoint, we argue that phase noise can be described without resorting to the concept of signal-to-noise ratio and that, although the phase noise is of course in part a property of the fiber itself, its group-index dependence is introduced solely by the resonator.

DOI: 10.1103/physreva.92.017802

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The previous Comment clarifies a few key points that were unclear in an earlier paper by its authors, in particular their definitions of phase and of phase noise. We now agree that this earlier paper was modeling the resonance-frequency fluctuations of a Fabry-Perot resonator, whereas our article [Phys. Rev. A 89, 033818 (2014)] was modeling the noise in the phase of the resonator's output field. In light of the Comment, the two pictures are indeed consistent. The resonance-frequency fluctuations are independent of group index, whereas the phase noise in the output field is proportional to group index. This important dependence was pointed out in our paper [Phys. Rev. A 89, 033818 (2014)]. From a more physical standpoint, we argue that phase noise can be described without resorting to the concept of signal-to-noise ratio and that, although the phase noise is of course in part a property of the fiber itself, its group-index dependence is introduced solely by the resonator.

We report a rigorous derivation of the power spectral density (PSD) spectrum of the phase noise in the transmitted and reflected signals of a Fabry-P\'erot (FP) interferometer. In transmission off and on resonance, the PSD at low frequencies is found to be simply equal to the PSD of the single-pass phase noise (the phase noise acquired by a signal that has traveled once through the FP interferometer) times

{({n}_{g}/n)}^{2}

, where

{n}_{g}

is the group index and

n

the phase index of the light inside the FP interferometer. Equivalently, the phase noise (in radians) is equal to the single-pass phase-noise times

{n}_{g}/n

. This result states that the phase noise is proportional to the number of passes light makes through the FP interferometer, as expected physically. This simple expression provides a quick means of calculating the phase noise in a linear Fabry-P\'erot interferometer of any length in the range of frequencies of interest to the most applications. At high frequencies, we show that the PSD spectrum can also be expressed in a simple closed-form expression on resonance, but that off resonance it must be calculated numerically. Numerical simulations show that the PSD oscillates between 3 dB below the low-frequency PSD and 3 dB below the single-pass PSD. Equivalent expressions are derived for the phase noise in the signal reflected by a Fabry-P\'erot interferometer, which is found to have the same magnitude at low frequencies, but to be typically significantly lower at high frequencies.

The spectra, coherence properties, and intensity fluctuations of waves generated by reflections of a noisy probe field from a phase-conjugate Fabry-Perot resonator are discussed. The emphasis of the analysis is on the spectral response of the resonator. The results obtained are in fill agreement with those derived using specific noise models in the time domain. Advantages of the frequency-domain analyses include full tractability of general probe-wave noise models and fast convergence of numerical computations. The reflected-wave coherence properties reveal an interesting periodic structure due to multiple intracavity reflections. The intensity fluctuation levels, which depend on the statistical models, are calculated explicitly for pure Markovian phase noise and Gaussian amplitude noise of the probe. Combinations of these two, yielding simple laser models, and other extensions of noise effects in phase-conjugate resonators are briefly discussed.>

We discuss and clarify the concept of dephasing in the many-Hilbert-space approach to the quantum measurement problem. We argue that the phase randomization provoked by a detecting macroscopic device is responsible for the loss of quantum coherence, and that the ``collapse of the wave function'' is to be regarded as a statistical process for the accumulated distribution over many events. In stressing the fundamental differences between our approach and the Copenhagen interpretation, we counter the objections put forward by Johnston [preceding Comment, Phys. Rev. A 48, 2497 (1993)], whose standpoint is essentially similar to the Copenhagen one.

This paper presents properties of all-optical bistable fibre switch using two fibre Bragg gratings and rare earth elements doped optical fiber. It is not possible to obtain bistable properties at low switching power level in case of a single fibre grating. In this article the method of optical switching that uses all-optical switch has been proposed. It has been achieved by varying the refractive index of nonlinear optical material as a result of light signal amplitude changes. Presented optical bistable device can be used both in contemporary optically switched networks as well as in optoelectronic sensors, owing to their high achievable resolution.