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Optics Letters

Linearized quantum-fluctuation theory of spectrally filtered optical solitons

Antonio Mecozzi, Prem Kumar

Published Aug 15, 1997• 47 citations
Publisher

Abstract

We study the quantum fluctuations of an optical nonlinear Schrödinger soliton after spectral filtering. The photon-number-bandwidth correlation of the emerging soliton produces squeezing in the photon number of the filtered soliton. Bandwidth oscillations caused by the interference of the soliton with the quantum-noise continuum, however, give oscillations of the photon-number squeezing and, in addition, prevent achievement of arbitrarily high values of squeezing through spectral filtering.

DOI
10.1364/ol.22.001232

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Summary form only given.Spectral filtering of optical solitons has been demonstrated to squeeze their photon-number uncertainty up to a measured value of 3.8 dB. The squeezing has been explained in terms of an uneven spectral distribution of photon-number noise caused by the Kerr nonlinearity of the fiber. Some indication for correlations among different frequency components has been found in a numerical analysis. We present the first experimental evidence for such spectral correlations. The experimental setup is shown. Pulses of 130 fs centered at 1.5 /spl mu/m are launched into a 2.9-m polarization-presenting single-mode optical fiber with energies close to the fundamental soliton energy.
We report the photon-number squeezing of optical solitons. 2.7 ps pulses were launched as solitons down a 1.5 km optical fiber. For energies slightly above that of fundamental solitons, they broadened spectrally due to self-phase modulation caused by ${\ensuremath{\chi}}^{(3)}$ nonlinearities. Filtering away outlying components of the broadened spectra squeezed the soliton's photon-number fluctuations to 2.3 dB (41%) below the shot-noise limit. Accounting for losses, this corresponds to 3.7 dB (57%) photon-number squeezing. A quantum field-theoretic model shows that the outlying spectral components have large energy fluctuations, so that their removal causes squeezing.
The quantum dynamics of coherent optical pulses are studied using a nondiagonal coherent-state generalized PPP representation including photon-phonon interactions. Photon-number squeezing of coherent quantum solitons using spectral filtering is theoretically predicted. It is shown that Raman noise does not significantly reduce photon-number squeezing produced by spectral filtering of 1-ps fundamental coherent quantum solitons in optical fibers. Coherent NsechNsechNsech pulses with N>1N>1N>1 can show a larger reduction in photon-number fluctuations even at room temperature. The reduction in quantum noise for N>1N>1N>1 is not restricted to photon number and an improvement of more than 3 dB is also found for the quadrature-phase squeezed soliton experiments using a fiber Sagnac interferometer at 77 K.
We study the quantum-noise properties of spectrally filtered solitons in optical fibers. Perturbation theory, including a quantum description of the continuum, is used to derive a complete analytical expression for the second-order correlator of the amplitude quadrature. This correlator is subsequently used to optimize the frequency response of the filter numerically in order to achieve the minimum photon-number noise. For propagation distances up to three soliton periods, the length at which the best noise reduction occurs, a square filter is found to be approximately optimum. For longer distances, more-complicated filter shapes are predicted for the best noise reduction.
The nonlinear optical Kerr effect, acting on optical pulses in fibres, creates spectral sidebands and noise correlations between these sidebands. The reduction of photon-number fluctuations of these pulses below the shot-noise limit by spectral filtering is well established in the anomalous dispersion regime which allows for soliton formation. Here it is demonstrated that a significant quantum-noise reduction with spectral filtering can also be reached for pulses in the normal dispersion regime. The filter function was optimized and the power dependence of the noise reduction was investigated. The best squeezing result is (1.2 ± 0.2) dB (corresponding to (2.6 ± 0.7) dB inferred for 100% detection efficiency).
Photon number squeezing of spectrally filtered optical solitons has been observed in the sub-picosecond regime, where the Raman effect changes the internal quantum structure of each pulse. 160 fs pulses were propagated down a 10 m optical fibre of anomalous group velocity dispersion. At energies below the soliton energy subsequent spectral filtering with an optical band-pass squeezed the directly detected photocurrent fluctuations to 3.2 ± 0.1 dB (52%) below the shot-noise limit. This implies 4.5 dB (65%) of soliton photon number squeezing, if detection losses are taken into account. Using a spectral edge filter the spectral components of the pulses are shown to contribute asymmetrically to the squeezing due to stimulated Raman scattering.