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Physical Review A

Intrapulse quantum spectral correlation of femtosecond optical pulses in optical fiber

Heongkyu Ju

Published Mar 14, 2012• 0 citations
Publisher

Abstract

Intrapulse quantum spectral correlation of photon numbers of a femtosecond optical pulse, which propagates a 5-m-long optical fiber, is presented in a matrix format for quantum noise study by numerical calculation. The calculation includes the higher-order optical effects such as intrapulse-stimulated Raman scattering and self-steepening effects, as well as self-phase modulation and group velocity dispersion. The quantum correlations between spectral components (spectral resolution of 0.7 nm) which evolve with the pulse energy are provided in a matrix format at soliton orders including the low orders, $N=0.1$ to 1.0 (a 0.1 step), to give the detailed properties of spectral correlation evolutions in the matrix format. It is shown that the photon-number correlations between spectral components near the pulse spectrum center form strong correlations of a square shape in the matrix, at a soliton order $N$ ($\ensuremath{\le}$0.4), and then are redistributed into those between spectral components near the spectrum wings such that the cross-shaped correlation pattern in the matrix begin to be visible at $N=0.5$ before their further redistribution as $N\ensuremath{\rightarrow}1.0$. In addition, significant anticorrelations can be increasingly extended to be found between spectral components near the spectrum center as $N\ensuremath{\rightarrow}1.0$, leading to the expectation that the degree of photon-number squeezing by spectral filtering for subsolitons can be lower than that for solitons. Intrapulse-stimulated Raman scattering that starts to become visible at around $N=0.6$ produces an asymmetric correlation structure with respect to the spectrum center in the correlation matrices while the relevant pulse self-frequency shift becomes visible at $N\ensuremath{\ge}0.8$. The calculation presented indicates that the measurement of nonlinear effects which are not detectable distinctly at the classical level is possible at the quantum level.

DOI
10.1103/physreva.85.033810

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Intrapulse quantum spectral correlation of photon numbers of a femtosecond optical pulse, which propagates a 5-m-long optical fiber, is presented in a matrix format for quantum noise study by numerical calculation. The calculation includes the higher-order optical effects such as intrapulse-stimulated Raman scattering and self-steepening effects, as well as self-phase modulation and group velocity dispersion. The quantum correlations between spectral components (spectral resolution of 0.7 nm) which evolve with the pulse energy are provided in a matrix format at soliton orders including the low orders, N=0.1N=0.1N=0.1 to 1.0 (a 0.1 step), to give the detailed properties of spectral correlation evolutions in the matrix format. It is shown that the photon-number correlations between spectral components near the pulse spectrum center form strong correlations of a square shape in the matrix, at a soliton order NNN (\ensuremath≤\ensuremath{\le}\ensuremath≤0.4), and then are redistributed into those between spectral components near the spectrum wings such that the cross-shaped correlation pattern in the matrix begin to be visible at N=0.5N=0.5N=0.5 before their further redistribution as N\ensuremath→1.0N\ensuremath{\rightarrow}1.0N\ensuremath→1.0. In addition, significant anticorrelations can be increasingly extended to be found between spectral components near the spectrum center as N\ensuremath→1.0N\ensuremath{\rightarrow}1.0N\ensuremath→1.0, leading to the expectation that the degree of photon-number squeezing by spectral filtering for subsolitons can be lower than that for solitons. Intrapulse-stimulated Raman scattering that starts to become visible at around N=0.6N=0.6N=0.6 produces an asymmetric correlation structure with respect to the spectrum center in the correlation matrices while the relevant pulse self-frequency shift becomes visible at N\ensuremath≥0.8N\ensuremath{\ge}0.8N\ensuremath≥0.8. The calculation presented indicates that the measurement of nonlinear effects which are not detectable distinctly at the classical level is possible at the quantum level.
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.
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.
Summary form only given. Recent experiments have demonstrated more than 50% of photon number squeezing of optical pulses by spectral filtering method in nonlinear optical fibers. For such squeezing quantum correlations between the spectral components of the pulses play a crucial role. The intermode correlations in the squeezed pulses are mainly induced by the second-order dispersion and the third-order nonlinearity (the self-phase modulation (SPM) effect) of fibers. We numerically study the dependence of the initial pulse waveform on spectral filtering squeezing and the optimization of pulses to obtain the further squeezing. Calculations are performed by solving the quantum nonlinear Schrodinger equation (QNLSE) in the positive P representation.
Recent experimental results on edge-filtered (also referred to as low- and high-pass filters) subpicosecond optical solitons have raised a number of theoretical questions concerning the origin of the reduced photon- number fluctuations. One of the main experimental results was that for long fibers, on the order of 100 soliton periods, the measured photon-number squeezing increased with propagation distance in contrast with theoretical calculations for picosecond solitons at that time. Here I present theoretical results on photon statistics of edge-filtered subpicosecond optical solitons. The numerical simulations include coupling to phonons via a Raman interaction, in addition to the electronic Kerr nonlinearity, and are in good agreement with the experimental data over the range of propagation distances investigated so far. The theoretical results clearly show that the phenomena observed are not related to long fiber propagation but to the Raman self-frequency shift and should be more clearly observable using cooled fiber.
Experimental demonstration of more than 50% photon-number squeezing obtained using microstructure fibers (MFs) , of which zero-dispersion wavelength locates at 820 nm, in a spectral filtering scheme with 40-fs laser pulses at /spl lambda/ = 810 nm is reported. The highest photon-number squeezing of -4.6 dB is obtained when a soliton-like Stokes Raman pulse, which broke up from the main pulse, exhibiting a self-frequency shift toward the longer wavelength, is preserved by low-pass spectral filtering from the white-light spectrum generated from the 30-cm MF.
We discuss the characteristics of photon-number squeezing generated in a spectrally filtered Raman Stokes pulse obtained from a nonlinear fiber. The Raman Stokes pulse generated from a microstructure fiber with a femtosecond input laser pulse exhibits far higher photon-number squeezing. We studied the quantum correlation established among the frequency modes in the Raman Stokes pulse by using numerical calculations and experiments. To design an intra-Stokes pulse quantum correlation through the optical nonlinearities of a fiber to obtain higher photon-number squeezing, we shaped the input laser pulse by using a self-learning closed-loop control approach.