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Physical Review A

Noise in refractive index enhancement

Deniz D. Yavuz, Nicholas Proite

Published Nov 7, 2008• 7 citations
Publisher

Abstract

By utilizing the interference between an absorptive resonance and an amplifying resonance, one can achieve an enhanced refractive index without an increase in absorption to the beam. We analyze noise added to the beam due to spontaneous emission while propagating through such an index enhanced medium. We find that, for a medium with a refractive index of $n$ and of length $L$, $\ensuremath{\approx}(n\ensuremath{-}1)(2\ensuremath{\pi}∕{\ensuremath{\lambda}}_{0})L$ noise photons are added to the beam.

DOI
10.1103/physreva.78.053811

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By utilizing the interference between an absorptive resonance and an amplifying resonance, one can achieve an enhanced refractive index without an increase in absorption to the beam. We analyze noise added to the beam due to spontaneous emission while propagating through such an index enhanced medium. We find that, for a medium with a refractive index of nnn and of length LLL, \ensuremath≈(n\ensuremath−1)(2\ensuremathπ∕\ensuremathλ0)L\ensuremath{\approx}(n\ensuremath{-}1)(2\ensuremath{\pi}∕{\ensuremath{\lambda}}_{0})L\ensuremath≈(n\ensuremath−1)(2\ensuremathπ∕\ensuremathλ0​)L noise photons are added to the beam.
We report a proof-of-principle experiment where the refractive index of an atomic vapor is enhanced while maintaining vanishing absorption of the beam. The key idea is to drive alkali atoms in a vapor with appropriate control lasers and induce a gain resonance and an absorption resonance for a probe beam in a two-photon Raman configuration. The strength and the position of these two resonances can be manipulated by changing the parameters of the control lasers. By using the interference between these two resonances, we obtain an enhanced refractive index without an increase in the absorption.
Introduction Most of the lightwave transmission systems operating today benefit fully from extensive deployment of optical amplifiers (OA). These components perform the amplification of optical intensity directly in the optical domain, without resorting to any electrical-domain regeneration. Optical amplifiers increase the average number of output photons per unit time by several orders of magnitude compared with the incoming signal intensity. However, as with every amplifying process, optical amplification cannot be achieved without paying back for the unavoidable noise power added to the signal intensity. As we will see in detail in Chapter 6, the optical amplification process comes with optical noise generated by spontaneous emission inside the active medium. The intensity of the optical signal is represented by the flux of the signal photon population. Conversely, the photons generated by the spontaneous emission process inside the optical cavity represent the noise photon population. The fundamental phenomenon supporting optical amplification is stimulated emission. The basic property of stimulated emission, making the great difference from spontaneous emission and enabling optical amplification, is the coherent nature of the photon generation process. Accordingly, both signal and noise photons go through the same multiplication process by means of stimulated emission. Unless the optical cavity where the stimulated emission takes place (the active cavity) presents selective features for enhancing the signal photon population relative to the spontaneous one, there is no way to avoid noise photons going through stimulated emission, filling most of the cavity population. As a consequence, both photon populations increase, leading respectively to amplified signal intensity and to amplified spontaneous emission intensity. It should be apparent that every noise photon can create a new identical noise photon as a result of stimulated emission, effectively increasing the noise intensity in the active optical cavity. This is the well-known mechanism of amplified spontaneous emission (ASE) noise in optical amplification. Any improvement in the optical amplifier structure devoted to increasing stimulated over spontaneous emission will probably increase the optical signal-to-noise ratio (OSNR) at the cavity output. The spectrum of gain characteristic of the optical active medium is usually wide enough to support an efficient amplification of the broadband spontaneous emission spectrum, leading to the broadband ASE noise power spectral density.
A two-photon emission of a medium with periodically time-dependent refractive index is considered. The emission results from the zero-point fluctuations of the medium. Usually this emission is very weak. However, it can be strongly enhanced if the resonant condition ω0ω_0ω0​ = 2.94 c/l0c/l_0c/l0​ is fulfilled (here ω0ω_0ω0​ and $l_0 $ are the frequency and the amplitude of the oscillations of the optical length of the medium, respectively). Besides, a medium with resonant oscillations of the optical length performs the phase conjugated reflection with high efficiency. A similar resonant enhancement of the two-quantum emission of other bosons is also predicted.
We consider the two-photon emission by a dielectric where refractive index n oscillates in time. The oscillations of n cause analogous oscillations of the optical length. The velocity of the latter oscillations, in principle, may be arbitrarily large. If the maximal velocity of these oscillations V is much less than the light velocity c then the intensity of the emission will increase with V . However, if it strongly exceeds c then the opposite dependence takes place as the zero-point fluctuations cannot appreciably react on such a fast oscillations. Therefore, the crossover for the dependence of the emission on V exists at V r ∼ c and a resonant enhancement of it is observed at this value of V . Our calculation gives V r ≈ 3 c .