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arXiv:1902.06566

Phase Synchronization of Stimulated Raman Process in Optical Fiber For Long Pulse Regime

Partha Mondal, Shailendra Kumar Varshney

Published Feb 18, 2019• 0 citations
arXivHTMLPDF

Abstract

We investigate the evolution of coherence property of noise-seeded Stokes wave in short (< 1 ps) and long pulse (> 1 ps) regimes. Nonlinear equations expressing the evolution of pump and Stokes wave are solved numerically for both the regions. The simulations include quantum noise by incorporating noise seed in the pump field where one photon per mode with random phase. The spectral phase fluctuations of the Stokes wave for both the regions, are characterized by performing multiple simulations and finally, the degrees of first-order mutual coherence are calculated as a function of wavelength for different conditions. Our statistical analysis proclaim that noise-seeded stimulated Raman process, which plays the role in degradation of coherence in short pulse region, exhibits strong phase synchronization in long pulse regime. The manifestation of phase synchronization occurs by the transition of the Stokes wave from incoherent to coherent spectra in long pulse regime.

DOI
10.48550/arxiv.1902.06566

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We investigate the evolution of coherence property of noise-seeded Stokes wave in short (< 1 ps) and long pulse (> 1 ps) regimes. Nonlinear equations expressing the evolution of pump and Stokes wave are solved numerically for both the regions. The simulations include quantum noise by incorporating noise seed in the pump field where one photon per mode with random phase. The spectral phase fluctuations of the Stokes wave for both the regions, are characterized by performing multiple simulations and finally, the degrees of first-order mutual coherence are calculated as a function of wavelength for different conditions. Our statistical analysis proclaim that noise-seeded stimulated Raman process, which plays the role in degradation of coherence in short pulse region, exhibits strong phase synchronization in long pulse regime. The manifestation of phase synchronization occurs by the transition of the Stokes wave from incoherent to coherent spectra in long pulse regime.
Manifestations of quantum fluctuations in stimulated Raman scattering ( SRS ) have been intensively studied lately1. Quantum noise present in spontaneous scattering stimulates fluctuations both in phase and in amplitude characteristics of output Stokes emission. At present statistical properties of amplitude fluctuations are studied in detail and it is shown that in linear transient regime of SRS without pump depletion statistical scatter of Stokes energy Es has negative exponential distribution2. In saturation regime of SRS the amplitude fluctuations are almost suppressed simultaneously with pump depletion. The phase fluctuations manifest both in linear and in nonlinear SRS and produce beam pointing fluctuations3, a change in Stokes emission spectra from pulse to pulse4 and cause soliton appearance in Rayleigh component of SRS5. Phase noise is observed in saturation regime due to relation between phases of Stokes and phonon waves which is preserved in processes of stationary and quasistationary SRS amplification. Spectrum phase fluctuations manifest as fine structure of SRS spectrum4, fluctuations of average Stokes frequency and Stokes linewidth fluctuations. The evolution of phase fluctuations in time is determined by the nature of spontaneous scattering and polarization of Raman media and is of great interest as one can follow its development from vacuum modes level to saturation regime. However up to now this problem has not been studied yet.
Recently Swanson et al.1 have shown that, even in the transient regime of a Raman generator, when the Stokes pulses are nominally transform-limited, the mean frequency of the pulses fluctuates from pulse to pulse. The coherent modes model2 provides a simple, intuitive and computationally efficient method for determining the statistics of the Stokes light from a Raman generator. We use this model to calculate the probability density of the mean frequency of the Stokes pulse energy spectrum and show that it gives reasonable agreement with Swanson et al.'s experimental results. The spectral fluctuations in the transient regime arise because the excitation of high-order temporally coherent modes produces a time-dependent phase structure in the Stokes pulse. The phase of the Stokes field is more sensitive to the excitation of these high-order modes than is its amplitude, so that the pulse energy spectrum exhibits measurable fluctuations in the transient regime, even though the pulse temporal shape does not.3
In the coherent anti-Stokes Raman scattering process, the spectrum of the generated optical phonon depends on the degree of temporal correlation between the pump laser field and the Stokes field. When the two fields are strongly correlated, such as when the Stokes field is generated with stimulated Raman scattering (SRS), the spectral shape of the optical phonon is found experimentally and theoretically to be the same as the gain-narrowed Raman line shape because the laser phase fluctuations cancel out totally, leaving only the collisional noise in the SRS process. When the two fields are uncorrelated, the shape of the optical-phonon spectrum is found to be the same as the Raman line shape without gain narrowing. When two fields are partially correlated, then the two spectral components appear together. We provide a method to measure the degree of correlation between two optical fields that have different central frequencies. The theory developed to interpret the experimental results is an extension of the quantum theory of SRS to include anti-Stokes scattering. We show that only in the high-gain limit can the quantum fluctuations be thought of as arising from a classical noise process.
The light initially prepared in a coherent state runs the stimulated and spontaneous Raman processes in a second-order nonlinear medium. Using analytical expressions of field operators for the light modes, we determine the quantum statistical properties of the modes in the stimulated and spontaneous Raman processes. By a choice of phase, we obtain a boson-pair property correlating the pump and vibration modes and such a property correlating the pump and anti-Stokes modes. The Stokes and vibration modes exhibit the boson-pair property for all initial phase differences between the pump mode and the other ones. In the spontaneous Raman process only the Stokes and vibration modes show such a property.
A quantum theory of stimulated Raman scattering is presented that takes into account three-dimensional propagation and collisional dephasing, allowing the study of the spatial and temporal coherence properties of the generated Stokes light. Maxwell-Bloch equations for the Stokes field operator and the collective atomic operators are solved analytically under low-signal-gain conditions, where the laser field and the atomic ground states remain undepleted. The intensity and the space-time autocorrelation function of the Stokes field are calculated. The Stokes field is expanded into a set of statistically independent ``coherence modes,'' which are determined explicitly for the case of a cylindrically shaped pumped volume. The Stokes pulse energy W is found to fluctuate from pulse to pulse. The probability distribution function for pulse energies P(W) is calculated for a range of Fresnel numbers of the excited volume and collisional dephasing rates. For small values of Fresnel number and dephasing rate, P(W) is a negative exponential distribution. For large values of either, P(W) narrows and approaches a Gaussian-shaped distribution. This occurs because many independent modes contribute to the Stokes emission, making it spatially and/or temporally incoherent.
Stimulated Raman scattering is a quantum macroscopic process starting from unstable state. Any fluctuations, initial or boundary, classical or quantum in nature, lead to the macroscopic output fluctuations of the Stokes amplitude. Manifestation of these fluctuations in the statistics of the Stokes pulse energy and its spectrum have been studied extensively for the linear stage of the SRS [1]. Another fluctuation phenomena arises in nonlinear stage of the SRS - the random spikes, usually called soliton-like, are observed in the depleted pump [2]. Here we shown that the reason for these soliton-like spikes is the conservation of the relative phase Δϕ=ϕL−ϕS+ϕQ of the laser, Stokes and the polarization wanes [3].