An applications-oriented review of optical parametric amplifiers in fiber communications is presented. The emphasis is on parametric amplifiers in general and single pumped parametric amplifiers in particular. While a theoretical framework based on highly efficient four-photon mixing is provided, the focus is on the intriguing applications enabled by the parametric gain, such as all-optical signal sampling, time-demultiplexing, pulse generation, and wavelength conversion. As these amplifiers offer high gain and low noise at arbitrary wavelengths with proper fiber design and pump wavelength allocation, they are also candidate enablers to increase overall wavelength-division-multiplexing system capacities similar to the more well-known Raman amplifiers. Similarities and distinctions between Raman and parametric amplifiers are also addressed. Since the first fiber-based parametric amplifier experiments providing net continuous-wave gain in the for the optical fiber communication applications interesting 1.5-/spl mu/m region were only conducted about two years ago, there is reason to believe that substantial progress may be made in the future, perhaps involving "holey fibers" to further enhance the nonlinearity and thus the gain. This together with the emergence of practical and inexpensive high-power pump lasers may in many cases prove fiber-based parametric amplifiers to be a desired implementation in optical communication systems.

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Fiber-based optical parametric amplifiers and their applications

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

By suitably choosing the fiber properties, and by tuning the pump wavelength near the fiber zero-dispersion wavelength, one can in principle generate a wide variety of one-pump fiber optical parametric amplifier gain spectra These can range from a very wide single region to two symmetric narrow gain regions far away from the pump We have experimentally verified these predictions With a highly nonlinear fiber, we have inferred the existence of gain over a single 400-nm region and measured a maximum on-off gain of 65 dB With a common dispersion-shifted fiber, we have obtained tunable gain regions less than 1 nm wide, up to 200 nm from the pump; we have also shifted these by several nanometers by lowering the fiber temperature to 0/spl deg/C

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Wide-band tuning of the gain spectra of one-pump fiber optical parametric amplifiers

We experimentally demonstrate, for the first time to our knowledge, a phase-sensitive amplifier based on frequency nondegenerate parametric amplification in optical fiber, where the input signal-idler pair is prepared all-optically. Using two fiber-optic parametric amplifier sections separated by a fiber-based wavelength-dependent phase shifter, we observe and investigate phase-sensitive gain profile in the 1550 nm region both experimentally and theoretically. The realized scheme automatically generates gain-defining phase that is environmentally stable, making it advantageous for building phase-sensitive transmission links.

Gain characteristics of a frequency nondegenerate phase-sensitive fiber-optic parametric amplifier with phase self-stabilized input

Q penalties due to pump phase modulation and pump RIN in fiber optic parametric amplifiers with non-uniform dispersion

We present an experimental study on four-wave mixing (FWM) between two signals within a two-pump fiber-optical parametric amplifier (2P-FOPA). We demonstrate that the intensity of FWM spurious tones depend strongly on the signal power and length of the nonlinear medium and present two regimes as a function of the pumps' power. We also compare the amounts of FWM as a function of channel spacing in the 2P-FOPA with or without pumps and show that the presence of parametric gain enhances FWM over a broad spectral range.

Spurious four-wave mixing in two-pump fiber-optic parametric amplifiers

The mathematical inequality which in quantum mechanics gives rise to the uncertainty principle between two non commuting operators is used to develop a spatial step-size selection algorithm for the Split-Step Fourier Method (SSFM) for solving Generalized Non-Linear Schrodinger Equations (G-NLSEs). Numerical experiments are performed to analyze the efficiency of the method in modeling optical-fiber communications systems, showing its advantages relative to other algorithms.

F.A. Callegari

Papers

Q penalties due to pump phase modulation and pump RIN in fiber optic parametric amplifiers with non-uniform dispersion

Spurious four-wave mixing in two-pump fiber-optic parametric amplifiers

Uncertainty relation for the optimization of optical-fiber transmission systems simulations

Influence of zero dispersion wavelength variations on cross-talk in single-pumped fiber optic parametric amplifiers

Amplification of 12 × 10 Gb/s WDM signals with negligible FWM crosstalk in a double-pumped fiber optical parametric amplifier