## Towards a versatile active wavelength converter for all-optical networks based on quasi-phase matched intra-cavity difference-frequency generation |

Optics Express, Vol. 21, Issue 23, pp. 27933-27945 (2013)

http://dx.doi.org/10.1364/OE.21.027933

Acrobat PDF (3248 KB)

### Abstract

The availability of reconfigurable all-optical wavelength converters for an efficient and flexible use of optical resources in WDM (wavelength division multiplexing) networks is still lacking at present. We propose and report preliminary results on a versatile active technique for multiple and tunable wavelength conversions in the 1500-1700 nm spectral region. The technique is based on combining broadband quasi-phase matched intra-cavity parametric single-pass difference-frequency generation close to degeneracy in a diode-pumped tunable laser. A periodically poled stoichiometric lithium tantalate crystal is used as the nonlinear medium, with a parametric pump wave generated in a continuous-wave self-injection locked Cr^{3+}:LiCAF tunable laser operating at around 800 nm.

© 2013 Optical Society of America

## 1. Introduction

1. S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. **14**(6), 955–966 (1996). [CrossRef]

5. X. Qin and Y. Yang, “Multicast connection capacity of WDM switching networks with limited wavelength conversion,” IEEE/ACM Trans. Netw. **12**(3), 526–538 (2004). [CrossRef]

1. S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. **14**(6), 955–966 (1996). [CrossRef]

_{2}mixes with a local oscillator at a frequency ω

_{1}and generates converted (output) waves at ω

_{3}= ω

_{1}± ω

_{2.}The filter then selects either ω

_{1}+ ω

_{2}(sum-frequency generation, SFG) or ω

_{1}− ω

_{2}(DFG).

_{1}and ω

_{2}(pump and signal respectively) interact in a nonlinear medium and give raise to a third wave (idler) at the difference-frequency ω

_{3}= ω

_{1}− ω

_{2}. The pump, signal, and idler waves, play the role of the local oscillator and of the input and output waves respectively. It is well known from nonlinear optics theory that if the pump wave intensity remains continuous during a second-order the conversion process (or at every time), then the output channel preserves the intensity modulation of the input channel with fidelity (undistorted), provided that the pump wave remains essentially undepleted during the DFG nonlinear interaction process. In the undepleted case, DFG conversion efficiency remains independent of the input signal intensity as it will be shown in (1) [6].

7. M. H. Chou, J. Hauden, M. A. Arbore, and M. M. Fejer, “1.5-microm-band wavelength conversion based on difference-frequency generation in LiNbO_{3} waveguides with integrated coupling structures,” Opt. Lett. **23**(13), 1004–1006 (1998). [CrossRef] [PubMed]

_{low}/P

_{high}between the powers associated to the “on” and “off” levels [8]. The amplitude distortion can affect even more seriously in possible multilevel advanced digital modulation formats under present study [9

9. S. Walklin and J. Conradi, “Multilevel Signaling for Increasing the Reach of 10 Gb/s Lightwave Systems,” J. Lightwave Technol. **17**(11), 2235–2248 (1999). [CrossRef]

10. R. Muñoz, R. Martínez, and R. Casellas, “Challenges for GMPLS lightpath provisioning in transparent optical networks: Wavelength constraints in routing and signaling,” IEEE Commun. Mag. **47**(8), 26–34 (2009). [CrossRef]

^{3+}-doped colquiriite family (Cr

^{3+}:LiSAF, Cr

^{3+}:LiCAF and Cr

^{3+}:LisGAF) [11

11. S. A. Payne, L. L. Chase, H. W. Newkirk, L. K. Smith, and W. F. Krupke, “LiCaA1F_{6}:Cr^{3+}: A Promising New Solid-state Laser Material,” IEEE J. Quantum Electron. **24**(11), 2243–2252 (1988). [CrossRef]

11. S. A. Payne, L. L. Chase, H. W. Newkirk, L. K. Smith, and W. F. Krupke, “LiCaA1F_{6}:Cr^{3+}: A Promising New Solid-state Laser Material,” IEEE J. Quantum Electron. **24**(11), 2243–2252 (1988). [CrossRef]

13. M. Tsunekane, M. Ihara, N. Taguchi, and H. Inaba, “Analysis and design of widely tunable diode-pumped Cr:LiSAF lasers with external grating feedback,” IEEE J. Quantum Electron. **34**(7), 1288–1296 (1998). [CrossRef]

14. H. Maestre, A. J. Torregrosa, and J. Capmany, “Intracavity Cr^{3+}:LiCAF + PPSLT optical parametric oscillator with self-injection-locked pump wave,” Laser Phys. Lett. **10**(3), 035806 (2013). [CrossRef]

_{adj}in Fig. 1(b).

15. D. S. Hum and M. M. Fejer, “Quasi-phasematching,” C. R. Phys. **8**(2), 180–198 (2007). [CrossRef]

15. D. S. Hum and M. M. Fejer, “Quasi-phasematching,” C. R. Phys. **8**(2), 180–198 (2007). [CrossRef]

16. C. R. Fernández-Pousa and J. Capmany, “Dammann grating design of domain-engineered lithium niobate for Equalized wavelength conversion grids,” IEEE Photon. Technol. Lett. **17**(5), 1037–1039 (2005). [CrossRef]

17. N. O’Brien, M. Missey, P. Powers, V. Dominic, and K. L. Schepler, “Electro-optic spectral tuning in a continuous-wave, asymmetric-duty-cycle, periodically poled LiNbO3 optical parametric oscillator,” Opt. Lett. **24**(23), 1750–1752 (1999). [CrossRef] [PubMed]

18. A. J. Torregrosa, H. Maestre, C. R. Fernández-Pousa, and J. Capmany, “Electro-Optic Reconfiguration of Quasi-Phase Matching in a Dammann Domain Grating for WDM Applications”, Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 1–9, 1790–1791 (2008). [CrossRef]

_{QPM}in Fig. 1(b). Waveguide QPM devices have been also reported which would help in miniaturization [7

7. M. H. Chou, J. Hauden, M. A. Arbore, and M. M. Fejer, “1.5-microm-band wavelength conversion based on difference-frequency generation in LiNbO_{3} waveguides with integrated coupling structures,” Opt. Lett. **23**(13), 1004–1006 (1998). [CrossRef] [PubMed]

19. M. H. Chou, K. R. Parameswaran, M. M. Fejer, and I. Brener, “Multiple-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO_{3} waveguides,” Opt. Lett. **24**(16), 1157–1159 (1999). [CrossRef] [PubMed]

20. R. G. Smith, “Theory of intracavity optical second-harmonic generation,” IEEE J. Quantum Electron. **6**(4), 215–223 (1970). [CrossRef]

21. J. Capmany, J. A. Pereda, V. Bermúdez, D. Callejo, and E. Diéguez, “Laser frequency converter for continuous-wave tunable Ti:sapphire lasers,” Appl. Phys. Lett. **79**(12), 1751–1753 (2001). [CrossRef]

## 2. Experimental set-up

22. U. Demirbas, D. Li, J. R. Birge, A. Sennaroglu, G. S. Petrich, L. A. Kolodziejski, F. X. Kaertner, and J. G. Fujimoto, “Low-cost, single-mode diode-pumped Cr:colquiriite lasers,” Opt. Express **17**(16), 14374–14388 (2009). [CrossRef] [PubMed]

23. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J. Appl. Phys. **39**(8), 3597–3641 (1968). [CrossRef]

^{2}~67. This made it difficult to achieve a good beam overlap between the pump and laser beams reducing the overall laser efficiency of the laser [24

24. W. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B **5**(7), 1412–1423 (1988). [CrossRef]

22. U. Demirbas, D. Li, J. R. Birge, A. Sennaroglu, G. S. Petrich, L. A. Kolodziejski, F. X. Kaertner, and J. G. Fujimoto, “Low-cost, single-mode diode-pumped Cr:colquiriite lasers,” Opt. Express **17**(16), 14374–14388 (2009). [CrossRef] [PubMed]

*P*≅ 10 mW/0.0025 = 4W. With a better mode overlap between the 665 nm red pump diode and the Cr:LiCAF fundamental mode values around

_{p}*P*~30 W have been already reported [22

_{p}22. U. Demirbas, D. Li, J. R. Birge, A. Sennaroglu, G. S. Petrich, L. A. Kolodziejski, F. X. Kaertner, and J. G. Fujimoto, “Low-cost, single-mode diode-pumped Cr:colquiriite lasers,” Opt. Express **17**(16), 14374–14388 (2009). [CrossRef] [PubMed]

13. M. Tsunekane, M. Ihara, N. Taguchi, and H. Inaba, “Analysis and design of widely tunable diode-pumped Cr:LiSAF lasers with external grating feedback,” IEEE J. Quantum Electron. **34**(7), 1288–1296 (1998). [CrossRef]

18. A. J. Torregrosa, H. Maestre, C. R. Fernández-Pousa, and J. Capmany, “Electro-Optic Reconfiguration of Quasi-Phase Matching in a Dammann Domain Grating for WDM Applications”, Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 1–9, 1790–1791 (2008). [CrossRef]

^{2}of transverse cross-section was used and placed in the middle of the second arm. The poling period is 22.1 μm with a duty cycle of 0.5 for up and down domains, and had its facets antireflection coated in a small band around ~800 nm and for 1500-1700 nm. The nonlinear crystal was mounted in an oven to be held at a controlled temperature in order to reach the phase matching condition and to reduce possible photorefractive effects. The pump wave generated (790-800 nm) is polarized along the z-axis direction to participate in a QPM-type 0 process (mixing of waves all with extraordinary polarization) with an external signal wave presenting the same polarization, and then taking advantage of the SLT highest nonlinear tensor coefficient

*d*

_{33}= 12.9 pm/V (similar to the case of co-doping with MgO [25

25. I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, “Linear and nonlinear optical properties of MgO:LiTaO_{3},” Appl. Phys. B **96**(2-3), 423–432 (2009). [CrossRef]

## 3. QPM bandwidth and efficiency

23. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J. Appl. Phys. **39**(8), 3597–3641 (1968). [CrossRef]

*P*,

_{i}*P*and

_{s}*P*are the idler, signal and pump powers respectively,

_{p}*d*is an effective nonlinear coefficient of the material which can be made to account also for the wave vector mismatch Δ

_{eff}*k*=

*k*− (

_{p}*k*+

_{i}*k*) in the interaction,

_{s}*L*the length of the nonlinear crystal,

*n*and

_{p}*n*the refractive indices of the nonlinear material for the pump and signal wavelengths respectively,

_{s}*λ*and

_{s}*λ*the signal and idler vacuum wavelengths respectively, and

_{i}*ε*

_{0}and

*c*the dielectric constant and speed of light in vacuum respectively. The last term

*h*(

*ξ*) is a focusing factor (known as Boyd-Kleinmann focusing factor) that lies between 0.8 and 1 for 1 ≤

*ξ*≤ 7, where

*ξ*=

*L*/

*b*with

*L*being the crystal length and

*b*the confocal parameter (twice the Rayleigh range) [23

23. G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J. Appl. Phys. **39**(8), 3597–3641 (1968). [CrossRef]

*d*be a function of the wave-vector mismatch Δ

_{eff}*k*and of the material nonlinear coefficient:Here

*d**(

*z*) is the spatial distribution of the effective nonlinear coefficient along the propagation coordinate

*z*once accounted for the polarization of the waves, a fact that is taken into account by using in

*d** the usual sub-index notation

*d*proposed by Kleinmann for the components of the nonlinear tensor [27]. In (2) we assume a collinear interaction and thus have removed the vector notation. Because

_{ij}*d** = 0 outside the nonlinear crystal, the integration limits in (2) may be expanded to ± ∞ and (2) gives then (1/

*L*) times the Fourier Transform of the spatial distribution of the nonlinear coefficient in the crystal i.e.,

*L*

^{2}) times the power spectrum of

*d**(

*z*), and is limited by the nonlinear crystal length

*L*through Parseval’s theorem [16

16. C. R. Fernández-Pousa and J. Capmany, “Dammann grating design of domain-engineered lithium niobate for Equalized wavelength conversion grids,” IEEE Photon. Technol. Lett. **17**(5), 1037–1039 (2005). [CrossRef]

29. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. **28**(11), 2631–2654 (1992). [CrossRef]

*d**(

*z*) remains constant along the interaction path and gives the usual efficiency expression

*k*= 0, with a PM bandwidth in the Δ

*k*reciprocal space set by the sinc

^{2}function. In general, we will refer to the

*d**(

*z*) =

*d*

_{33}(

*z*) for all interacting waves polarized parallel to the ferroelectric c-axis and propagating perpendicular to it (Type 0 QPM), and changes sign between ± |

*d*

_{33}| (the highest valued diagonal component of the nonlinear tensor) at every domain reversal i.e., at every place in the crystal where the spontaneous polarization changes its “up” or “down” orientation parallel or antiparallel to the ferroelectric + c-axis. In general,

*d**(

*z*) may be a periodic or aperiodic spatial function along the propagation path in collinear interactions. In case of a periodically poled crystal with a spatial period Λ (length of an up and down domain pair), the equivalent tuning curve for

*m*-order QPM becomes (Δ

*k*) = (2

*d*

_{33}/

*m*π)

^{2}·sin

^{2}(

*mD*π)·sinc

^{2}[(1/2)·(Δ

*k*−2π/Λ)·

*L*], where the case

*m*= 1 is referred to as first-order QPM and

*D*is the domain pair duty cycle factor defined as

*D*=

*x*/Λ. Due to even symmetry in the problem,

*x*is the length of any of the up or down domains indistinctly [29

29. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. **28**(11), 2631–2654 (1992). [CrossRef]

*D*= 0.5. The QPM efficiency curve shape and bandwidth (QPM tuning curve) results then identical to the birefringent case, and set by the crystal length

*L*. It should be apparently clear that the QPM efficiency conditions may be changed (reconfigured) by temperature changes or electro-optic changes in Δ

*k*, through the corresponding changes in the refractive indices of the material for the interacting waves (

*k*= 2π

_{j}*n*/

_{j}*λ*). It should also be apparently clear that aperiodic distributions change the shape of the QPM tuning curve and exchange amplitude for bandwidth keeping its area constant due to Parseval’s theorem if the absolute value of

_{j}*d**(

*z*) remains constant along the interaction path. There are some demonstrations of techniques that trade-off QPM bandwidth at the expense of nonlinear effective coefficient by using aperiodically poling patterns such as chirping the domain reversal distribution and others [15

15. D. S. Hum and M. M. Fejer, “Quasi-phasematching,” C. R. Phys. **8**(2), 180–198 (2007). [CrossRef]

16. C. R. Fernández-Pousa and J. Capmany, “Dammann grating design of domain-engineered lithium niobate for Equalized wavelength conversion grids,” IEEE Photon. Technol. Lett. **17**(5), 1037–1039 (2005). [CrossRef]

*k*-space or in the corresponding wavelength values of the interacting waves.

29. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. **28**(11), 2631–2654 (1992). [CrossRef]

30. M. H. Chou, I. Brener, K. R. Parameswaran, and M. M. Fejer, “Stability and Bandwidth Enhancement of Difference Frequency Generation (DFG)-based wavelength conversion by pump detuning,” Elec. Lett. **35**(12), 978–980 (1999). [CrossRef]

28. A. Bruner, D. Eger, M. B. Oron, P. Blau, M. Katz, and S. Ruschin, “Temperature-dependent Sellmeier equation for the refractive index of stoichiometric lithium tantalate,” Opt. Lett. **28**(3), 194–196 (2003). [CrossRef] [PubMed]

## 4. Results and discussion

*λ*= 1584 nm) of the pump wave and serves as a reference to illustrate the process. An apparent conversion efficiency ~−13 dB follows from the figure. However, one must keep in mind that the real conversion efficiency that is defined as

_{p}*η*=

*P*/

_{out}*P*cannot be directly read form the spectra. Because the spectra correspond to the output spectra, the input signal has undergone parametric gain, and its level relative to the output must be corrected as it does not correspond to the input level to the system. Every converted photon created annihilates a pump photon and adds a new photon to the output spectrum of the input wave. Thus, the real level of the input signal must be computed by carefully substracting to the output spectra of the input signal an amount similar to the energy created in the converted output. We estimated it to be around 0.5 dB by numerical integration. Thus, the conversion efficiency is closer to −12.5 dB than to the apparent −13 dB. As it will be discussed later, this conversion efficiency is in reasonable agreement with the conversion efficiency expected by modelling (−9 dB) in our experimental conditions.

_{in}## 5. Conclusion

## Acknowledgment

## References and links

1. | S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol. |

2. | J. M. Yates and M. P. Rumsewicz, “Wavelength converters in dynamically reconfigurable WDM networks,” IEEE Commun. Surv. Tutor. |

3. | K. C. Lee and V. Li, “A wavelength-convertible optical network,” J. Lightwave Technol. |

4. | H. S. Hamza and J. S. Deogun, “WDM optical interconnects: A balanced design approach,” IEEE/ACM Trans. Netw. |

5. | X. Qin and Y. Yang, “Multicast connection capacity of WDM switching networks with limited wavelength conversion,” IEEE/ACM Trans. Netw. |

6. | J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. Lett. |

7. | M. H. Chou, J. Hauden, M. A. Arbore, and M. M. Fejer, “1.5-microm-band wavelength conversion based on difference-frequency generation in LiNbO |

8. | For general aspects of fiber optics communications see G. P. Agrawal, |

9. | S. Walklin and J. Conradi, “Multilevel Signaling for Increasing the Reach of 10 Gb/s Lightwave Systems,” J. Lightwave Technol. |

10. | R. Muñoz, R. Martínez, and R. Casellas, “Challenges for GMPLS lightpath provisioning in transparent optical networks: Wavelength constraints in routing and signaling,” IEEE Commun. Mag. |

11. | S. A. Payne, L. L. Chase, H. W. Newkirk, L. K. Smith, and W. F. Krupke, “LiCaA1F |

12. | A. E. Siegman, “Laser injection locking,” in |

13. | M. Tsunekane, M. Ihara, N. Taguchi, and H. Inaba, “Analysis and design of widely tunable diode-pumped Cr:LiSAF lasers with external grating feedback,” IEEE J. Quantum Electron. |

14. | H. Maestre, A. J. Torregrosa, and J. Capmany, “Intracavity Cr |

15. | D. S. Hum and M. M. Fejer, “Quasi-phasematching,” C. R. Phys. |

16. | C. R. Fernández-Pousa and J. Capmany, “Dammann grating design of domain-engineered lithium niobate for Equalized wavelength conversion grids,” IEEE Photon. Technol. Lett. |

17. | N. O’Brien, M. Missey, P. Powers, V. Dominic, and K. L. Schepler, “Electro-optic spectral tuning in a continuous-wave, asymmetric-duty-cycle, periodically poled LiNbO3 optical parametric oscillator,” Opt. Lett. |

18. | A. J. Torregrosa, H. Maestre, C. R. Fernández-Pousa, and J. Capmany, “Electro-Optic Reconfiguration of Quasi-Phase Matching in a Dammann Domain Grating for WDM Applications”, Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 1–9, 1790–1791 (2008). [CrossRef] |

19. | M. H. Chou, K. R. Parameswaran, M. M. Fejer, and I. Brener, “Multiple-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO |

20. | R. G. Smith, “Theory of intracavity optical second-harmonic generation,” IEEE J. Quantum Electron. |

21. | J. Capmany, J. A. Pereda, V. Bermúdez, D. Callejo, and E. Diéguez, “Laser frequency converter for continuous-wave tunable Ti:sapphire lasers,” Appl. Phys. Lett. |

22. | U. Demirbas, D. Li, J. R. Birge, A. Sennaroglu, G. S. Petrich, L. A. Kolodziejski, F. X. Kaertner, and J. G. Fujimoto, “Low-cost, single-mode diode-pumped Cr:colquiriite lasers,” Opt. Express |

23. | G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J. Appl. Phys. |

24. | W. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B |

25. | I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, “Linear and nonlinear optical properties of MgO:LiTaO |

26. | H. Maestre, A. J. Torregrosa, C. R. Fernández-Pousa, J. A. Pereda, and J. Capmany, “Widely tuneable dual-wavelength operation of a highly doped erbium fiber laser based on diffraction gratings,” IEEE J. Quantum Electron. |

27. | R. L. Sutherland, D. G. McLean, and S. Kirkpatrick, |

28. | A. Bruner, D. Eger, M. B. Oron, P. Blau, M. Katz, and S. Ruschin, “Temperature-dependent Sellmeier equation for the refractive index of stoichiometric lithium tantalate,” Opt. Lett. |

29. | M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron. |

30. | M. H. Chou, I. Brener, K. R. Parameswaran, and M. M. Fejer, “Stability and Bandwidth Enhancement of Difference Frequency Generation (DFG)-based wavelength conversion by pump detuning,” Elec. Lett. |

31. | Telecommunication Standardization Sector of International Telecommunication Union, Recommendation ITU-T G.694.1, “Spectral grids for WDM applications: DWDM frequency grid” (2002). |

32. | SNLO nonlinear optics code available from A. V. Smith, Sandia National Laboratories, Albuquerque, NM 87185–1423. |

**OCIS Codes**

(160.2260) Materials : Ferroelectrics

(190.0190) Nonlinear optics : Nonlinear optics

(190.4223) Nonlinear optics : Nonlinear wave mixing

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: June 12, 2013

Revised Manuscript: October 13, 2013

Manuscript Accepted: October 31, 2013

Published: November 7, 2013

**Citation**

Adrián J. Torregrosa, Haroldo Maestre, and Juan Capmany, "Towards a versatile active wavelength converter for all-optical networks based on quasi-phase matched intra-cavity difference-frequency generation," Opt. Express **21**, 27933-27945 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-23-27933

Sort: Year | Journal | Reset

### References

- S. J. B. Yoo, “Wavelength conversion technologies for WDM network applications,” J. Lightwave Technol.14(6), 955–966 (1996). [CrossRef]
- J. M. Yates and M. P. Rumsewicz, “Wavelength converters in dynamically reconfigurable WDM networks,” IEEE Commun. Surv. Tutor.2(2), 2–15 (1999).
- K. C. Lee and V. Li, “A wavelength-convertible optical network,” J. Lightwave Technol.11(5), 962–970 (1993). [CrossRef]
- H. S. Hamza and J. S. Deogun, “WDM optical interconnects: A balanced design approach,” IEEE/ACM Trans. Netw.15(6), 1565–1578 (2007). [CrossRef]
- X. Qin and Y. Yang, “Multicast connection capacity of WDM switching networks with limited wavelength conversion,” IEEE/ACM Trans. Netw.12(3), 526–538 (2004). [CrossRef]
- J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between Light Waves in a Nonlinear Dielectric,” Phys. Rev. Lett.127, 1918–1939 (1962).
- M. H. Chou, J. Hauden, M. A. Arbore, and M. M. Fejer, “1.5-microm-band wavelength conversion based on difference-frequency generation in LiNbO3 waveguides with integrated coupling structures,” Opt. Lett.23(13), 1004–1006 (1998). [CrossRef] [PubMed]
- For general aspects of fiber optics communications see G. P. Agrawal, Fiber Optic Communication Systems (John Wiley & Sons, 2002).
- S. Walklin and J. Conradi, “Multilevel Signaling for Increasing the Reach of 10 Gb/s Lightwave Systems,” J. Lightwave Technol.17(11), 2235–2248 (1999). [CrossRef]
- R. Muñoz, R. Martínez, and R. Casellas, “Challenges for GMPLS lightpath provisioning in transparent optical networks: Wavelength constraints in routing and signaling,” IEEE Commun. Mag.47(8), 26–34 (2009). [CrossRef]
- S. A. Payne, L. L. Chase, H. W. Newkirk, L. K. Smith, and W. F. Krupke, “LiCaA1F6:Cr3+: A Promising New Solid-state Laser Material,” IEEE J. Quantum Electron.24(11), 2243–2252 (1988). [CrossRef]
- A. E. Siegman, “Laser injection locking,” in Lasers (University Science Book, 1986), pp. 1129–1170.
- M. Tsunekane, M. Ihara, N. Taguchi, and H. Inaba, “Analysis and design of widely tunable diode-pumped Cr:LiSAF lasers with external grating feedback,” IEEE J. Quantum Electron.34(7), 1288–1296 (1998). [CrossRef]
- H. Maestre, A. J. Torregrosa, and J. Capmany, “Intracavity Cr3+:LiCAF + PPSLT optical parametric oscillator with self-injection-locked pump wave,” Laser Phys. Lett.10(3), 035806 (2013). [CrossRef]
- D. S. Hum and M. M. Fejer, “Quasi-phasematching,” C. R. Phys.8(2), 180–198 (2007). [CrossRef]
- C. R. Fernández-Pousa and J. Capmany, “Dammann grating design of domain-engineered lithium niobate for Equalized wavelength conversion grids,” IEEE Photon. Technol. Lett.17(5), 1037–1039 (2005). [CrossRef]
- N. O’Brien, M. Missey, P. Powers, V. Dominic, and K. L. Schepler, “Electro-optic spectral tuning in a continuous-wave, asymmetric-duty-cycle, periodically poled LiNbO3 optical parametric oscillator,” Opt. Lett.24(23), 1750–1752 (1999). [CrossRef] [PubMed]
- A. J. Torregrosa, H. Maestre, C. R. Fernández-Pousa, and J. Capmany, “Electro-Optic Reconfiguration of Quasi-Phase Matching in a Dammann Domain Grating for WDM Applications”, Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference 1–9, 1790–1791 (2008). [CrossRef]
- M. H. Chou, K. R. Parameswaran, M. M. Fejer, and I. Brener, “Multiple-channel wavelength conversion by use of engineered quasi-phase-matching structures in LiNbO3 waveguides,” Opt. Lett.24(16), 1157–1159 (1999). [CrossRef] [PubMed]
- R. G. Smith, “Theory of intracavity optical second-harmonic generation,” IEEE J. Quantum Electron.6(4), 215–223 (1970). [CrossRef]
- J. Capmany, J. A. Pereda, V. Bermúdez, D. Callejo, and E. Diéguez, “Laser frequency converter for continuous-wave tunable Ti:sapphire lasers,” Appl. Phys. Lett.79(12), 1751–1753 (2001). [CrossRef]
- U. Demirbas, D. Li, J. R. Birge, A. Sennaroglu, G. S. Petrich, L. A. Kolodziejski, F. X. Kaertner, and J. G. Fujimoto, “Low-cost, single-mode diode-pumped Cr:colquiriite lasers,” Opt. Express17(16), 14374–14388 (2009). [CrossRef] [PubMed]
- G. D. Boyd and D. A. Kleinman, “Parametric interaction of focused gaussian light beams,” J. Appl. Phys.39(8), 3597–3641 (1968). [CrossRef]
- W. P. Risk, “Modeling of longitudinally pumped solid-state lasers exhibiting reabsorption losses,” J. Opt. Soc. Am. B5(7), 1412–1423 (1988). [CrossRef]
- I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, “Linear and nonlinear optical properties of MgO:LiTaO3,” Appl. Phys. B96(2-3), 423–432 (2009). [CrossRef]
- H. Maestre, A. J. Torregrosa, C. R. Fernández-Pousa, J. A. Pereda, and J. Capmany, “Widely tuneable dual-wavelength operation of a highly doped erbium fiber laser based on diffraction gratings,” IEEE J. Quantum Electron.47, 1238–1243 (2011).
- R. L. Sutherland, D. G. McLean, and S. Kirkpatrick, Handbook of Nonlinear Optics, 2nd ed. (Dekker, 2003).
- A. Bruner, D. Eger, M. B. Oron, P. Blau, M. Katz, and S. Ruschin, “Temperature-dependent Sellmeier equation for the refractive index of stoichiometric lithium tantalate,” Opt. Lett.28(3), 194–196 (2003). [CrossRef] [PubMed]
- M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-Phase-Matched Second Harmonic Generation: Tuning and Tolerances,” IEEE J. Quantum Electron.28(11), 2631–2654 (1992). [CrossRef]
- M. H. Chou, I. Brener, K. R. Parameswaran, and M. M. Fejer, “Stability and Bandwidth Enhancement of Difference Frequency Generation (DFG)-based wavelength conversion by pump detuning,” Elec. Lett.35(12), 978–980 (1999). [CrossRef]
- Telecommunication Standardization Sector of International Telecommunication Union, Recommendation ITU-T G.694.1, “Spectral grids for WDM applications: DWDM frequency grid” (2002).
- SNLO nonlinear optics code available from A. V. Smith, Sandia National Laboratories, Albuquerque, NM 87185–1423.

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.