## Energy exchange between two orthogonally polarized waves by cascading of two quasi-phase-matched quadratic processes

Optics Express, Vol. 15, Issue 21, pp. 13630-13639 (2007)

http://dx.doi.org/10.1364/OE.15.013630

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### Abstract

We demonstrate energy exchange between two orthogonally polarized optical waves as a consequence of a two-color multistep parametric interaction. The energy exchange results from cascading of two quasi-phase-matched (QPM) second-harmonic parametric processes, and it is intrinsically instantaneous. The effect is observed when both the type-I (*ooe*) second-harmonic generation process and higher QPM order type-0 (*eee*) second-harmonic generation processes are phase-matched simultaneously in a congruent periodically-poled lithium niobate crystal. The two second-harmonic generation processes share a common second-harmonic wave which couple the two cross-polarized fundamental components and facilitate an energy flow between them. We demonstrate a good agreement between the experimental data and the results of numerical simulations.

© 2007 Optical Society of America

## 1. Introduction

^{(2)}) nonlinear parametric optical processes is of fundamental interest for the study of parametric interactions in optics, and can also be used for all-optical processing applications. Of particular interest are nonlinear phase shifts and induced Kerr-like nonlinearities, as well as multi-step frequency conversion. Second-harmonic generation (SHG) or sum-frequency generation (SFG), cascaded with difference-frequency generation (DFG) in periodically poled lithium niobate (PPLN) waveguides has been widely reported as a means for frequency conversion of c-band optical channels in a high-bit-rate low noise fashion, as well as optical gating of signals. Efficient third- and fourth-harmonic generation by cascaded quasi-phase-matching (QPM) has also been demonstrated for generation of visible wavelengths from near and mid IR sources. Most of these applications require the design and fabrication of longitudinal varying QPM gratings, such as phase-reversed [1

1. M. H. Chou, K. R. Parameswaran, and M. M. Fejer, “Multiple-channel wavelength conversion by use of engineered quasi-phase-matching” Opt. Lett. **24**, 1157–1159 (1999). [CrossRef]

2. S. Zhu, Y. Zhu, and N. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science **278**, 843–846 (1997). [CrossRef]

3. A. H. Norton and C. M. de Sterke, “Aperiodic one-dimensional structures for quasi-phase matching” Opt. Express **12**, 841–846 (2004). [CrossRef] [PubMed]

4. N. G. R. Broderick, R. T. Bratfalean, T. M. Monro, D. J. Richardson, and C. M. de Sterke, “Temperature and wavelength tuning of second-, third-, and fourth-harmonic generation in a two-dimensional hexagonally poled nonlinear crystal,” J. Opt. Soc. Am. B **19**, 2263–2272 (2002). [CrossRef]

5. A. Chowdhury, C. Staus, B. F. Boland, T. F. Kuech, and L. McCaughan, “Experimental demonstration of 1535-1555-nm simultaneous optical wavelength interchange with a nonlinear photonic crystal,” Opt. Lett. **26**, 1353–1355 (2001). [CrossRef]

6. B. F. Johnston, P. Dekker, S. M. Saltiel, M. J. Withford, and Yu. S. Kivshar, “Simultaneous phase matching and interference of two second order parametric processes,” Opt. Express **14**, 11756–11765 (2006). [CrossRef] [PubMed]

## 2. Crystal design and fabrication techniques

12. M. Reich, F. Korte, C. Fallnich, H. Welling, and A. Tunnermann, “Electrode geometries for periodic poling of ferroelectric materials,” Opt. Lett. **23**, 1817–1819 (1998). [CrossRef]

13. B. F. Johnston and M. J. Withford, “Dynamics of domain inversion in LiNbO_{3} poled using topographic electrode geometries,” Appl. Phys. Lett. **86**, 262901 (2005). [CrossRef]

14. L E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO_{3},” J. Opt. Soc. Am. B **12**, 2102–2116 (1995). [CrossRef]

## 3. Two-color parametric cascading: theoretical approach

_{1}and Δk

_{0}, are the wave vector mismatches of the type-I (

*ooe*) and type-0 (

*eee*) frequency doubling processes. In the low depletion limit the dominant feature of this system is the effect of the relative phases of the fundamental components, which influence the second harmonic output by their mixing in Eq. (4). However, for the case where an appreciable efficiency is achieved and depletion of the fundamental is significant, energy exchange between the fundamental components and nonlinear phase-shifts from cascading can occur. The temperature detuning curves for the system of Eqs. (2)-(4) were simulated numerically for congruent lithium niobate, again using Sellmeier equations from [11]. To reflect the temperature dependence of the wave vector mismatches we express them as:

*sinc*detuning functions. For the narrower-temperature-bandwidth, type-I fundamental, energy exchange from the SH field produced by the broader-band type-0 phase matching can be seen. This is accompanied by an enhanced nonlinear phase-shift of the type-I fundamental at detunings of Δk

^{2}_{1}L≈±π, as shown in the lower left plot of Fig. 3. This is due to a larger SH field being available, produced by the broader-band type-0 SHG, compared to that of a single SHG process. This contributes to the back-conversion and phase-shifting of the narrower-band type-I fundamental. When the fundamentals are launched phase shifted by π/2 with respect to each other, as shown in the right of Fig. 3, they interfere destructively at zero detuning suppressing any SHG and energy exchange. At slight detuning we see some slight back conversion, but due to the suppressed SH field this is small compared to the in-phase case, and the nonlinear phase-shift while, changing in a different manner across the detuning, is of much lower magnitude. The π/2 phase shifted case is however useful for inducing parametric back conversion for the case where the magnitudes of the fundamental components are different. In this case the stronger fundamental prevails and energy from the strong fundamental couples into the weaker fundamental via the second harmonic field. This is facilitated by the weaker fundamental being in-phase with the SH field allowing for difference frequency mixing. Shown on the left of Fig. 4 is the case for fundamental components launched with power ratio of 7:3 (

*e*:

*o*). We see the weaker o-wave experiences an increase in power at zero detuning. Shown on the right of Fig. 4 is the relative gain of the

*o*-wave at zero detuning (Δ

*k*=0) for a variety of ratios of the fundamental power in the

*o*and

*e*components, but for a fixed net power (equivalent to a value of 2 in the above graphs). This is shown for a variety of nonlinear efficiencies of the parent SHG processes, which in practice is explored by using longer crystals, higher laser peak power or higher material nonlinearities. These simulated results are presented in this fashion so as to correspond to our experimental case, where the ratio of power in the orthogonal polarization components was controlled by rotating a half-wave-plate with respect the crystal axes.

## 4. Experiment

_{4}laser operating on the 1064.5 nm line with a 10 kHz repetition rate, 20 ns pulses and ~1 kW peak power. Wave-plates were used to control the laser polarization, and a Glan prism was used to resolve the polarization components after frequency conversion in the PPLN. The quarter-wave-plate was inserted when

*π*/2 phase shift between the two fundamental components was investigated, and was aligned on the axes of the lithium niobate sample. The half-wave-plate was used to control the relative magnitudes of the two fundamental components. For low power measurements at the fundamental wavelength, a Pellin-Brocca prism was used to separate the second harmonic. Calorimetric power meters and photo diodes were used to monitor the average output power and pulse shapes respectively.

^{2}relations, and the two phase-matchings exhibit very similar peak efficiencies, allowing for a robust comparison with the numerical simulations above.

## 5. Results

*e*:

*o*polarization components, while leaving the QWP aligned on the crystal axes to maintain a 90° phase between them.

*e*:

*o*) is shown on the right of Fig. 9 and shows a good agreement with our numerical simulations. The peak relative parametric gain for various ratios of fundamental components is shown on the right, along with the calculated relation for the case of 6% SH efficiency shown in Fig. 4.

## 6. Discussions

18. Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, “Broadband efficient second harmonic generation in media with a short-range order,” Appl. Phys. Lett. **91**, 011101 (2007). [CrossRef]

## 7. Conclusions

*o*and

*e*polarizations do not become an overriding factor. The advantage of the proposed interaction is its instantaneous character due to the nonlinearities involved being of the second order. Similar schemes for the parametric energy exchange are possible due to two beam coupling [19

19. P. Yeh, “Photorefractive two-beam coupling in cubic crystals,” J. Opt. Soc. Am. B , **4**, 1382–1386 (1987). [CrossRef]

## Acknowledgments

## References and links

1. | M. H. Chou, K. R. Parameswaran, and M. M. Fejer, “Multiple-channel wavelength conversion by use of engineered quasi-phase-matching” Opt. Lett. |

2. | S. Zhu, Y. Zhu, and N. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science |

3. | A. H. Norton and C. M. de Sterke, “Aperiodic one-dimensional structures for quasi-phase matching” Opt. Express |

4. | N. G. R. Broderick, R. T. Bratfalean, T. M. Monro, D. J. Richardson, and C. M. de Sterke, “Temperature and wavelength tuning of second-, third-, and fourth-harmonic generation in a two-dimensional hexagonally poled nonlinear crystal,” J. Opt. Soc. Am. B |

5. | A. Chowdhury, C. Staus, B. F. Boland, T. F. Kuech, and L. McCaughan, “Experimental demonstration of 1535-1555-nm simultaneous optical wavelength interchange with a nonlinear photonic crystal,” Opt. Lett. |

6. | B. F. Johnston, P. Dekker, S. M. Saltiel, M. J. Withford, and Yu. S. Kivshar, “Simultaneous phase matching and interference of two second order parametric processes,” Opt. Express |

7. | G. Assanto, G. Stegeman, M. Sheik-Bahae, and E. Van Stryland, “All optical switching devices based on large nonlinear phase-shifts from second harmonic generation,” App. Phys. Lett. |

8. | G. Assanto, I. Torelli, and S. Trillo, “All-optical processing by means of vectorial interactions in 2 |

9. | S. Saltiel and Y. Deyanova, “Polarization switching as a result of cascading to simultaneously phase-matched quadratic processes,” Opt. Lett , |

10. | P. Vidakovic, D. J. Lovering, J. A. Levenson, J. Webjrn, and P. S. J. Russell, “Large nonlinear phase shift owing to cascaded χ |

11. | G. G. Gurzadian, V. G. Dmitriev, and D. N. Nikogosian, |

12. | M. Reich, F. Korte, C. Fallnich, H. Welling, and A. Tunnermann, “Electrode geometries for periodic poling of ferroelectric materials,” Opt. Lett. |

13. | B. F. Johnston and M. J. Withford, “Dynamics of domain inversion in LiNbO |

14. | L E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, “Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO |

15. | S. M. Saltiel, A. A. Sukhorukov, and Yu S Kivshar, “Multistep parametric processes in nonlinear optics,” Prog. Opt. |

16. | R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, “Self-focusing and self-defocusing by cascaded 2 |

17. | G. I. Petrov, O. Albert, J. Etchepare, and S. M. Saltiel, “Cross-polarized wave generation by effective cubic nonlinear optical interaction,” Opt. Lett. |

18. | Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, “Broadband efficient second harmonic generation in media with a short-range order,” Appl. Phys. Lett. |

19. | P. Yeh, “Photorefractive two-beam coupling in cubic crystals,” J. Opt. Soc. Am. B , |

**OCIS Codes**

(190.4360) Nonlinear optics : Nonlinear optics, devices

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: August 17, 2007

Revised Manuscript: September 27, 2007

Manuscript Accepted: September 28, 2007

Published: October 3, 2007

**Citation**

Benjamin F. Johnston, Peter Dekker, Solomon M. Saltiel, Yuri S. Kivshar, and Michael J. Withford, "Energy exchange between two orthogonally polarized waves by cascading of two quasi-phase-matched quadratic processes," Opt. Express **15**, 13630-13639 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-21-13630

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### References

- M. H. Chou, K. R. Parameswaran, and M. M. Fejer, "Multiple-channel wavelength conversion by use of engineered quasi-phase-matching," Opt. Lett. 24, 1157-1159 (1999). [CrossRef]
- S. Zhu, Y. Zhu, and N. Ming, "Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice," Science 278, 843-846 (1997). [CrossRef]
- A. H. Norton and C. M. de Sterke, "Aperiodic one-dimensional structures for quasi-phase matching," Opt. Express 12, 841-846 (2004). [CrossRef] [PubMed]
- N. G. R. Broderick, R. T. Bratfalean, T. M. Monro, D. J. Richardson, and C. M. de Sterke, "Temperature and wavelength tuning of second-, third-, and fourth-harmonic generation in a two-dimensional hexagonally poled nonlinear crystal," J. Opt. Soc. Am. B 19, 2263-2272 (2002). [CrossRef]
- A. Chowdhury, C. Staus, B. F. Boland, T. F. Kuech, and L. McCaughan, "Experimental demonstration of 1535-1555-nm simultaneous optical wavelength interchange with a nonlinear photonic crystal," Opt. Lett. 26, 1353-1355 (2001). [CrossRef]
- B. F. Johnston, P. Dekker, S. M. Saltiel, M. J. Withford, and Yu. S. Kivshar, "Simultaneous phase matching and interference of two second order parametric processes," Opt. Express 14, 11756-11765 (2006). [CrossRef] [PubMed]
- G. Assanto, G. Stegeman, M. Sheik-Bahae, E. Van Stryland, "All optical switching devices based on large nonlinear phase-shifts from second harmonic generation," App. Phys. Lett. 62, 1324-1326 (1993). [CrossRef]
- G. Assanto, I. Torelli, and S. Trillo, "All-optical processing by means of vectorial interactions in 2nd-order cascading -novel approaches," Opt. Lett. 19, 1720-1722 (1994). [CrossRef] [PubMed]
- S. Saltiel and Y. Deyanova, "Polarization switching as a result of cascading to simultaneously phase-matched quadratic processes," Opt. Lett, 24, 1296-1298 (1999). [CrossRef]
- P. Vidakovic, D. J. Lovering, J. A. Levenson, J. Webjrn, and P. S. J. Russell, "Large nonlinear phase shift owing to cascaded ?(2) in quasi-phase-matched bulk LiNbO3," Opt. Lett. 22, 277-279 (1997). [CrossRef]
- G. G. Gurzadian, V. G. Dmitriev, and D. N. Nikogosian, Handbook of Nonlinear Optical Crystals, 3rd ed., Vol. 64 of Springer Series in Optical Sciences (Springer-Verlag, New York, 1999).
- M. Reich, F. Korte, C. Fallnich, H. Welling, and A. Tunnermann, "Electrode geometries for periodic poling of ferroelectric materials," Opt. Lett. 23, 1817-1819 (1998). [CrossRef]
- B. F. Johnston and M. J. Withford, "Dynamics of domain inversion in LiNbO3 poled using topographic electrode geometries," Appl. Phys. Lett. 86, 262901 (2005). [CrossRef]
- L. E. Myers, R. C. Eckardt, M. M. Fejer, R. L. Byer, W. R. Bosenberg, and J. W. Pierce, "Quasi-phase-matched optical parametric oscillators in bulk periodically poled LiNbO3," J. Opt. Soc. Am. B 12, 2102-2116 (1995). [CrossRef]
- S. M. Saltiel, A. A. Sukhorukov, and YuS Kivshar, "Multistep parametric processes in nonlinear optics," Prog. Opt. 47, 1-73 (2005). [CrossRef]
- R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, "Self-focusing and self-defocusing by cascaded 2nd-order effects in KTP," Opt. Lett. 17, 28-30 (1992). [CrossRef] [PubMed]
- G. I. Petrov, O. Albert, J. Etchepare, and S. M. Saltiel, "Cross-polarized wave generation by effective cubic nonlinear optical interaction," Opt. Lett. 26, 355-357 (2001). [CrossRef]
- Y. Sheng, J. Dou, B. Ma, B. Cheng, and D. Zhang, "Broadband efficient second harmonic generation in media with a short-range order," Appl. Phys. Lett. 91, 011101 (2007). [CrossRef]
- P. Yeh, "Photorefractive two-beam coupling in cubic crystals," J. Opt. Soc. Am. B, 4, 1382-1386 (1987). [CrossRef]

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