Description:

This is the first book to provide 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.

Contents

   

      Acknowledgments

1  Introduction   

2  Properties of single-mode optical fibers    

2.1  Mode profile                                    

2.2  Loss                                                

2.3  Propagation constant and dispersion   

2.4  Longitudinal fluctuations of the zero-dispersion wavelength                                     

2.5  Temperature dependence of the zero-dispersion wavelength                                    

2.6  Fiber birefringence                            

2.7  Nonlinearities                                   

2.8  Types of fiber used for OPA work     

References                                                                                                           

3  Scalar OPA theory                     

3.1  Introduction                                      

3.2  Types of fiber OPA                           

3.3  Derivation of the OPA equations and γ 

3.4  Scaling laws

3.5  Solution of the two-pump OPA equations                                                               

3.6  Theory for one-pump OPA                 

3.7  Case of no dispersion with loss    

3.8  Solutions for degenerate OPAs     

3.9  Conclusion                                

References                                

4  Vector OPA theory                                

4.1  Introduction                                      

4.2  Isotropic fibers                                 

4.3  Fibers with constant birefringence       

4.4  Fibers with random birefringence        

4.5  Conclusion                                       

References                                 

5  The optical gain spectrum                 

5.1  Introduction                                

5.2  The effect of pump power on gain bandwidth                                                         

5.3  The effect of fiber dispersion on the gain spectru

5.4  OPAs with similar gain spectra     

5.5  Equivalent gain spectra for OPAs using pumps with different SOPs                          

5.6  Saturated gain spectra                        

5.7  Fibers with longitudinal dispersion variations                                                           

5.8  Fibers with constant linear birefringence                                                                

5.9  Few-mode fibers                               

References                                         

                                                                                                                                     

6  The nonlinear Schrödinger equation

6.1  Introduction                                

6.2  Derivation of the NLSE for an isotropic fiber                                                          

6.3  Derivation of the NLSE for a birefringent fiber                                                      

6.4  Analytic solutions of the scalar NLSE  

6.5  Including the Raman gain in the NLSE 

6.6  Numerical solutions of the NLSE by the split-step Fourier method                           

6.7  Applications of the SSFM to fibers with longitudinal variations                                

6.8  Sources of SSFM software                

6.9  Conclusion                                       

References                                       

7  Pulsed-pump OPAs                             

7.1  Introduction                                      

7.2  The quasi-CW regime                        

7.3  The split-step Fourier method             

7.4  Important pulse shapes                      

7.5  Examples of pulsed-pump OPAs         

7.6  Conclusion                                       

References                                     

8  OPO theory                              

8.1  Introduction                        

8.2  Fiber OPO theory                

8.3  Conclusion                          

References                         

9   Quantum noise figure of fiber OPAs                                                                         

9.1  Introduction                        

9.2  Quantum-mechanical derivation of the OPA equations                                             

9.3  Noise figure of non-degenerate fiber OPAs

9.4  Wavelength exchange                                                                                                

9.5  Noise figure of degenerate fiber OPAs                                                                   

9.6  Effect of Raman gain on OPA noise figure                                                             

9.7  Conclusion                          

References                         

10 Pump requirements                          

10.1  Introduction                                    

10.2  Pump power requirements                

10.3  Polarization considerations                

10.4  Pump amplitude fluctuations (pump RIN)                                                             

10.5  Pump phase or frequency fluctuations                                                                  

10.6  Conclusion                                      

 References                                                                                                        

11 Performance results                         

11.1  Introduction                             

11.2  Pulsed devices                          

11.3  CW devices                              

References                               

12 Potential applications of fiber OPAs and OPOs                                                         

12.1  Introduction                             

12.2  OPAs in optical communication  

12.3  OPAs in high-power wavelength conversion

12.4  OPOs                                      

References                                     

13 Nonlinear crosstalk in fiber OPAs          

13.1  Introduction                             

13.2  Four-wave mixing                     

13.3  Cross-gain modulation               

13.4  Coherent crosstalk                    

13.5  Cross-phase modulation             

13.6  Conclusion                               

References                                     

14 Distributedparametric amplification 14.1Introduction

14.2DPA experiment in75 kmof DSF

14.3Possible extensions ofDPA14.4Conclusion

15 Prospects forfuture developments15.1Introduction15.2Fibers

15.3Pumps

15.4SBS suppression

15.5Integrated optics

15.6Pump resonators15.7Discrete or distributed parametric amplification?

15.8Conclusion

Appendices

A.1General theoremsfor solving typical OPA

A.2The WKBapproximation

A.3Jacobian ellipticfunction solutions

A.4Solution of fourcoupled equations for the six-wave model

A.5 Summary of usefulequations

Index