This book, published in 2007, provides comprehensive coverage of the theory and practice of OPAs and related devices, including fiber optical parametric oscillators (OPOs). After introducing the field, the theory and techniques behind all types of fiber OPAs are covered starting from first principles - topics include the scalar and vector OPA theory; the nonlinear Schrodinger equation; OPO theory; and quantum noise figure of fiber OPAs. Challenges of making fiber OPAs practical for a number of applications are discussed, and a survey of the state-of-the-art in feasibility demonstrations and performance evaluations is provided. The capabilities and limitations of OPAs; the potential applications for OPAs and OPOs, and prospects for future developments in the field are discussed. Theoretical tools developed in this text can also be applied to other areas of nonlinear optics. This is a valuable resource for researchers, advanced practitioners, and graduate students in optoelectronics.

Fiber Optical Parametric Amplifiers, Oscillators and Related Devices: The nonlinear Schrödinger equation

1. Introduction 2. Properties of single-mode optical fibers 3. Scalar OPA theory 4. Vector OPA theory 5. The optical gain spectrum 6. The nonlinear Schrodinger equation (NLSE) 7. Pulsed-pump OPAs 8. OPO theory 9. Quantum noise figure of fiber OPAs 10. Pump requirements 11. Performance results 12. Potential applications of fiber OPAs and OPOs 13. Nonlinear crosstalk in fiber OPAs 14. Distributed parametric amplification 15. Prospects for future developments Appendices: A.1 General theorems for solving typical OPA equations A.2 The WKB approximation A.3 Jacobian elliptic function solutions A.4 Solution of four coupled equations for the six-wave model A.5 Summary of useful equations.

Fiber Optical Parametric Amplifiers, Oscillators and Related Devices

For the first time, four different noise sources, which are amplified quantum noise, Raman phonon seeded excess noise, pump transferred noise (PTN), and pump residual noise, are considered simultaneously to model the wavelength-dependent noise figure in a single-pumped fiber optical parametric amplifier. An asymmetric signal NF spectrum induced by both Raman phonon seeded excess noise and Raman gain modified PTN is measured in the electrical domain. Theoretical results agree very well with the experimental data. The idler NF spectrum is also analyzed and measured, which shows a more symmetric profile.

Full characterization of the signal and idler noise figure spectra in single-pumped fiber optical parametric amplifiers

Raman amplification has been commercially utilized in optical transmission systems for more than a decade. The drive toward higher spectral density has increased the interest in Raman to improve system performance. This tutorial reviews the benefits of Raman amplification, defines methods to analyze system performance, and describes the issues involved with system deployment and operation.

Raman Amplification: An Enabling Technology for Long-Haul Coherent Transmission Systems

\n This study has demonstrated the simulative and analytical methods of bidirectional EDFA amplifiers in optical communication links in the optimum case. The output power, max. Q factor and light signal/noise ratio variations are clarified with pump power variations at the bidirectional amplification EDFA amplifier for the previous/proposed models at optimum EDFA length of 8 m. As well as the output power and max. Q factor variations with EDFA amplifier length variations are demonstrated at the bidirectional amplification EDFA amplifier for the previous/proposed models at various pump power levels. The optimum operation efficiency case is observed at 8 m EDFA amplifier length and 120 mW pumping power.

Simulative and analytical methods of bidirectional EDFA amplifiers in optical communication links in the optimum case

Electrical measurements of the noise figure of a fiber-optical parametric amplifier are presented and compared with optical measurements. The transfer of pump noise by four-wave mixing was clearly demonstrated. A numerical model was developed to simulate the transfer of pump noise and validated by these measurements. Using this model, we determine, for practical systems, a minimum required pump optical signal-to-noise ratio of 65 dB.

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Impact of pump OSNR on noise figure for fiber-optical parametric amplifiers

Pump-to-signal relative-intensity-noise (RIN) transfer in a forward-pumped Raman amplifier using polarization-combined diodes is measured and analyzed. For the first time, by means of experiment and simulations, we call attention to the impact of the polarized nature of stimulated Raman scattering on RIN transfer. We show that measuring the RIN at the output of a depolarized Raman pump and inserting this figure in the commonly used RIN transfer equation is not sufficient for good signal RIN prediction. Although depolarizing the Raman pump enables polarization-independent signal gain, proper modeling of RIN transfer should include the polarization dependence of the Raman effect and the polarization mode dispersion of the fiber.

RIN transfer in copumped Raman amplifiers using polarization-combined diodes

We demonstrate a novel convenient nondestructive method based on optical parametric amplification that allows retrieval of the zero-dispersion wavelength map along a short optical fiber span with a high-spatial resolution. The improved resolution relies on the high sensitivity to the local longitudinal dispersion fluctuations of the parametric high-gain spectrum.

Zero-dispersion Wavelength Mapping in Short Single-Mode Optical Fibers Using Parametric Amplification

Pump-to-signal relative intensity noise (RIN) transfer in copumped Raman amplifiers is analyzed. By means of simulations and experiments, the authors call attention to the impact of the polarized nature of stimulated Raman scattering on RIN transfer. Although depolarizing the Raman pump enables polarization-independent signal gain, the authors demonstrate that proper modeling of RIN transfer requires including the polarization dependence of the Raman effect and the polarization mode dispersion of the fiber. A second key phenomenon is emphasized. Besides the RIN transfer induced by Raman gain, pump RIN is also transferred to the signal via nonlinear gain. This phenomenon can be addressed as pump-signal cross-phase modulation since it essentially generates phase noise on the signal. For the first time, in this paper, a model of pump-to-signal RIN transfer that includes polarization and nonlinear gain is presented. The authors reveal the key influence of these factors that had been uncared for so far. Their analysis is supported by experimental data. Signal noise characteristics (RIN spectrum and high-resolution optical power spectrum) measured at the output of a copumped Raman amplifier were presented. The Raman pump is a pair of semiconductor diodes in the first two experiments and then a Raman fiber laser. For these two kinds of depolarized or unpolarized Raman pumps that are commonly used in the field, the authors emphasize the necessity of considering polarization for the good assessment of RIN transfer

Influence of polarization on pump-signal RIN transfer and cross-phase modulation in copumped Raman amplifiers

https://hal.archives-ouvertes.fr/hal-00269147/document

A. Durecu-Legrand

Papers

Impact of pump OSNR on noise figure for fiber-optical parametric amplifiers

RIN transfer in copumped Raman amplifiers using polarization-combined diodes

Zero-dispersion Wavelength Mapping in Short Single-Mode Optical Fibers Using Parametric Amplification

Influence of polarization on pump-signal RIN transfer and cross-phase modulation in copumped Raman amplifiers

Simple methods for crosstalk reduction in fiber optical parametric amplifiers