## Observation of continuous-wave second-harmonic generation in semiconductor waveguide directional couplers

Optics Express, Vol. 14, Issue 6, pp. 2256-2262 (2006)

http://dx.doi.org/10.1364/OE.14.002256

Acrobat PDF (102 KB)

### Abstract

We report the observation of continuous-wave second-harmonic generation in waveguide directional couplers. We employ a GaAs/AlGaAs system and observe four resonance peaks in a ~15nm spectral range, with a maximal conversion efficiency of 1.6%W^{-1}cm^{-2}. This observation is theoretically explained by the coupled-mode theory. This new configuration has the potential to open a new range of applications for nonlinear frequency conversion.

© 2006 Optical Society of America

## 1. Introduction

2. M. M. Fejer, “Nonlinear optical frequency conversion,” Phys. Today **47**, 25–31 (1994). [CrossRef]

3. J. P. Van der Ziel, “Phase-matched harmonic generation in a laminar structure with wave propagation in the plane of the layers,” Appl. Phys. Lett. **26**, 60–61 (1975). [CrossRef]

5. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. **127**, 1918–1939 (1962). [CrossRef]

8. G. L. J. A. Rikken, C. J. E. Seppen, E. G. J. Staring, and A. H. J. Venhuizen, “Efficient modal dispersion phase-matched frequency-doubling in poled polymer waveguides,” Appl. Phys. Lett. **62**, 2483–2485 (1993). [CrossRef]

9. P. K. Tien, R. Ulrich, and R. J. Martin, “Optical second harmonic generation in form of coherent Cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. **17**, 447–449 (1970). [CrossRef]

10. P. Dong and A. G. Kirk, “Nonlinear frequency conversion in waveguide directional couplers,” Phys. Rev. Lett. **93**, 133901 (2004). [CrossRef] [PubMed]

4. A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature **391**, 463–465 (1998). [CrossRef]

11. S. J. B. Yoo, C. Caneau, R. Bhat, M. A. Koza, A. Rajhel, and N. Antoniades, “Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding,” Appl. Phys. Lett. **68**, 2609–2611 (1996). [CrossRef]

10. P. Dong and A. G. Kirk, “Nonlinear frequency conversion in waveguide directional couplers,” Phys. Rev. Lett. **93**, 133901 (2004). [CrossRef] [PubMed]

18. X. G. Huang and M. R. Wang, “A novel quasi-phase-matching frequency doubling technique,” Opt. Commun. **150**, 235–238 (1998). [CrossRef]

18. X. G. Huang and M. R. Wang, “A novel quasi-phase-matching frequency doubling technique,” Opt. Commun. **150**, 235–238 (1998). [CrossRef]

10. P. Dong and A. G. Kirk, “Nonlinear frequency conversion in waveguide directional couplers,” Phys. Rev. Lett. **93**, 133901 (2004). [CrossRef] [PubMed]

**93**, 133901 (2004). [CrossRef] [PubMed]

19. G. Assanto, G. Stegeman, M. Sheik-Bahae, and E. V. Stryland, “All-optical switching devices based on large nonlinear phase shifts from second harmonic generation,” Appl. Phys. Lett., **62**, 1323–1325 (1993). [CrossRef]

20. R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons”, Phys. Rev. Lett. **93**, 113902 (2004). [CrossRef] [PubMed]

## 2. Design of experiment

_{0.9}Ga

_{0.1}As / 140nm Al

_{0.3}Ga

_{0.7}As / 300nm Al

_{0.5}Ga

_{0.5}As / 140nm Al

_{0.3}Ga

_{0.7}As / 500nm Al

_{0.9}Ga

_{0.1}As / 140nm Al

_{0.3}Ga

_{0.7}As / 300nm Al

_{0.5}Ga

_{0.5}As / 140nm Al

_{0.3}Ga

_{0.7}As / 1500nm Al

_{0.9}Ga

_{0.1}As. The Al

_{0.9}Ga

_{0.1}As layers serve as cladding and as the separating layer between the two waveguides. The Al

_{0.3}Ga

_{0.7}As/Al

_{0.5}Ga

_{0.5}As/Al

_{0.3}Ga

_{0.7}As combination acts as the guiding layer and this is a type of “M” waveguide designed for optimizing the field overlap between TE

_{2}mode at the second-harmonic frequency and TE

_{0}and TM

_{0}modes at the fundamental frequencies [21

21. Chowdhury and L. McCaughan, “Continuously phase-matched M-waveguides for second-order nonlinear upconversion,” IEEE Photon. Technol. Lett. **12**, 486–488 (2000). [CrossRef]

_{j}(z) and Bω

_{j}(z) to represent the slowly varying amplitudes in waveguides 1 and 2, respectively, the coupled wave equations are

^{TE2}

_{2ω}is the mode-coupling coefficient of the directional coupler for the second harmonic [15], η includes the product of the nonlinear optical coefficient and the overlap integral of the fundamental and the second harmonic waves, and Δk = k

^{TE2}

_{2ω}- k

^{TE0}

_{ω}- k

^{TM0}

_{2ω}is the phase mismatch (k is the wave number). The mode-coupling coefficients indicate how rapidly the power in the first waveguide is transferred to the second waveguide. The first terms in the right-hand sides of the above equations describe the coupling effect of the directional coupler and the second terms in the right-hand sides result from the nonlinear effects. Under the non-depletion assumption which implies that the presence of the second harmonic does not influence the motion of the fundamental wave, the amplitudes for the fundamental wave oscillate between the two waveguides:

^{TE0}

_{ω}and κ

^{TM0}

_{ω}are the coupling coefficients of TE

_{0}and TM

_{0}modes at the fundamental frequency, c

_{1}and c

_{2}are two constants depending on how much power is coupled into the individual waveguides from free space. In our experiment, we align the input polarization of the fundamental wave at 45 degrees with respect to the waveguide y-direction, by which the input power is divided equally in TE mode and TM mode. Because the modal fields for TE

_{0}and TM

_{0}do not differ very much, it is reasonable to assume that the power ratio coupled in the first to the second waveguide are identical for TE

_{0}and TM

_{0}. This results in identical constants c

_{1}and c

_{2}for TE

_{0}and TM

_{0}modes.

## 3. Experimental results and discussions

22. T. Reed and A. P. Knights, *Silicon photonics* (John Wiley & Sons Inc.,2004). [CrossRef]

^{-1}for TE input and ~2.71 cm

^{-1}for TM input, both at a 1550nm wavelength. We were unable to measure the waveguide loss of the TE

_{2}mode at the second-harmonic frequency.

**93**, 133901 (2004). [CrossRef] [PubMed]

13. K. Moutzouris, S. V. Rao, M. Ebrahimzadeh, A. De Rossi, M. Calligaro, V. Ortiz, and V. Berger, “Second-harmonic generation through optimized modal phase matching in semiconductor waveguides,” Appl. Phys. Lett. **83**, 620–622 (2003). [CrossRef]

13. K. Moutzouris, S. V. Rao, M. Ebrahimzadeh, A. De Rossi, M. Calligaro, V. Ortiz, and V. Berger, “Second-harmonic generation through optimized modal phase matching in semiconductor waveguides,” Appl. Phys. Lett. **83**, 620–622 (2003). [CrossRef]

8. G. L. J. A. Rikken, C. J. E. Seppen, E. G. J. Staring, and A. H. J. Venhuizen, “Efficient modal dispersion phase-matched frequency-doubling in poled polymer waveguides,” Appl. Phys. Lett. **62**, 2483–2485 (1993). [CrossRef]

^{TE0}

_{ω}+ κ

^{TM0}

_{ω}+ Δk = -κ

^{TE2}

_{2ω}, (κ

^{TE0}

_{ω}- κ

^{TM0}

_{ω}+ Δk = -κ

^{TE2}

_{2ω}, -(κ

^{TE0}

_{ω}- κ

^{TM0}

_{ω}+ Δk = -κ

^{TE2}

_{2ω}and (κ

^{TE0}

_{ω}+ κ

^{TM0}

_{ω}+ Δk = -κ

^{TE2}

_{2ω}, respectively. At the first resonance, for example, the coupling coefficients are calculated as ~0.04 μm

^{-1}for TE

_{0}and TM

_{0}pump and ~0.02 μm

^{-1}for TE

_{2}SHG, which implies that the power of the fundamental wave exchanges between the two waveguides about one hundred times. The relative peak values of the four resonances can be changed by modifying the position of input beam, as shown in Fig. 2, where the three curves were obtained with different locations of input beam. This occurs because variation of the input position modifies the power ratio coupled into the first and the second waveguide, and therefore modifies the value of c

_{1}and c

_{2}in Eq. (2). This imprecision could be avoided in future by the fabrication of a more complex waveguide device with a single input waveguide connected to the coupled waveguides with a controlled splitting ratio. By optimizing the 1573nm resonance, we achieved a maximum measured SHG power of 50nW with a 90mW input power. The SHG power as a function of input power was then measured and plotted in Fig. 3. The fitting to the slope results in a value of 2.0 on a log-log plot. This confirms the quadratic dependence of the SHG power on the pumping power. By measuring the transmitted power of the fundamental wave, we estimated that the average internal pumping power for the TE and TM is P

_{TE}≈ 5mW and P

_{TM}≈5mW. After taking into account the numerical aperture of the collecting lens (0.65) and the facet reflectivity for the second harmonic (0.6), we estimate that only 20% of the generated SHG was collected [14

14. S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, and M. Calligaro, “Continuous-wave second harmonic generation in modal phase matched semiconductor waveguides,” Appl. Phys. Lett. **84**, 2974–2976 (2004). [CrossRef]

_{SHG}/(4P

_{TE}P

_{TM}L

^{2}) =~1.6% W

^{-1}cm

^{-2}(for a detailed analysis of this estimation, we refer to Ref. [14

14. S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, and M. Calligaro, “Continuous-wave second harmonic generation in modal phase matched semiconductor waveguides,” Appl. Phys. Lett. **84**, 2974–2976 (2004). [CrossRef]

_{2}mode at the second harmonic frequency is expected to be very high, which limits the effective conversion length. Another reason is that the pump power is distributed into the two waveguides, which actually reduce the effective power in each individual waveguide. Further optimization, therefore, can include improving the coupling efficiency, reducing the leaky loss of SHG mode, optimizing the modal overlap between the fundamental wave and SHG, and choosing an appropriate interaction length.

## 4. Conclusion

23. K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, “Practical quantum cryptography based on 2-photon interferometry,” Phys. Rev. Lett. **69**, 1293–1296 (1992). [CrossRef] [PubMed]

^{-1}cm

^{-2}is obtained experimentally. To our knowledge, this phenomenon has not been shown in bulk materials or single waveguides.

## References and Links

1. | R. W. Boyd, |

2. | M. M. Fejer, “Nonlinear optical frequency conversion,” Phys. Today |

3. | J. P. Van der Ziel, “Phase-matched harmonic generation in a laminar structure with wave propagation in the plane of the layers,” Appl. Phys. Lett. |

4. | A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, “Phase matching using an isotropic nonlinear optical material,” Nature |

5. | J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. |

6. | V. Berger, “Nonlinear photonic crystals,” Phys. Rev. Lett. |

7. | M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation-tuning and tolerance,” IEEE J. Quantum Electron. |

8. | G. L. J. A. Rikken, C. J. E. Seppen, E. G. J. Staring, and A. H. J. Venhuizen, “Efficient modal dispersion phase-matched frequency-doubling in poled polymer waveguides,” Appl. Phys. Lett. |

9. | P. K. Tien, R. Ulrich, and R. J. Martin, “Optical second harmonic generation in form of coherent Cerenkov radiation from a thin-film waveguide,” Appl. Phys. Lett. |

10. | P. Dong and A. G. Kirk, “Nonlinear frequency conversion in waveguide directional couplers,” Phys. Rev. Lett. |

11. | S. J. B. Yoo, C. Caneau, R. Bhat, M. A. Koza, A. Rajhel, and N. Antoniades, “Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding,” Appl. Phys. Lett. |

12. | T. Skauli, “Measurement of the nonlinear coefficient of orientation-patterned GaAs and demonstration of highly efficient second-harmonic generation,” Opt. Lett. |

13. | K. Moutzouris, S. V. Rao, M. Ebrahimzadeh, A. De Rossi, M. Calligaro, V. Ortiz, and V. Berger, “Second-harmonic generation through optimized modal phase matching in semiconductor waveguides,” Appl. Phys. Lett. |

14. | S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, and M. Calligaro, “Continuous-wave second harmonic generation in modal phase matched semiconductor waveguides,” Appl. Phys. Lett. |

15. | A. Yariv, |

16. | A. A. Maier, “Coupled modes phase matching and synchronous non-linear wave interaction in coupled waveguides,” Kvantovaya Elektronika |

17. | S. I. Bozhevol’nyi, K. S. Buritskii, E. M. Zolotov, and V. Chernykh, Sov. Tech. Phys. Lett.7, 278 (1981). |

18. | X. G. Huang and M. R. Wang, “A novel quasi-phase-matching frequency doubling technique,” Opt. Commun. |

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

20. | R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons”, Phys. Rev. Lett. |

21. | Chowdhury and L. McCaughan, “Continuously phase-matched M-waveguides for second-order nonlinear upconversion,” IEEE Photon. Technol. Lett. |

22. | T. Reed and A. P. Knights, |

23. | K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, “Practical quantum cryptography based on 2-photon interferometry,” Phys. Rev. Lett. |

24. | D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature, |

**OCIS Codes**

(130.4310) Integrated optics : Nonlinear

(190.2620) Nonlinear optics : Harmonic generation and mixing

(190.4360) Nonlinear optics : Nonlinear optics, devices

(190.5970) Nonlinear optics : Semiconductor nonlinear optics including MQW

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: January 17, 2006

Revised Manuscript: March 14, 2006

Manuscript Accepted: March 14, 2006

Published: March 20, 2006

**Citation**

Po Dong, Jeremy Upham, Aju Jugessur, and Andrew G. Kirk, "Observation of continuous-wave second-harmonic generation in semiconductor waveguide directional couplers," Opt. Express **14**, 2256-2262 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-6-2256

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### References

- R. W. Boyd, Nonlinear Optics (Academic Press Inc., 2003).
- M. M. Fejer, "Nonlinear optical frequency conversion," Phys. Today 47, 25-31 (1994). [CrossRef]
- J. P. Van der Ziel, "Phase-matched harmonic generation in a laminar structure with wave propagation in the plane of the layers," Appl. Phys. Lett. 26, 60-61 (1975). [CrossRef]
- A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, "Phase matching using an isotropic nonlinear optical material," Nature 391, 463-465 (1998). [CrossRef]
- J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, "Interactions between light waves in a nonlinear dielectric," Phys. Rev. 127, 1918-1939 (1962). [CrossRef]
- V. Berger, "Nonlinear photonic crystals," Phys. Rev. Lett. 81, 4136-4139 (1998). [CrossRef]
- M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, "Quasi-phase-matched second harmonic generation-tuning and tolerance," IEEE J. Quantum Electron. 28, 2631-2654 (1992). [CrossRef]
- G. L. J. A. Rikken, C. J. E. Seppen, E. G. J. Staring, and A. H. J. Venhuizen, "Efficient modal dispersion phase-matched frequency-doubling in poled polymer waveguides," Appl. Phys. Lett. 62, 2483-2485 (1993). [CrossRef]
- P. K. Tien, R. Ulrich, and R. J. Martin, "Optical second harmonic generation in form of coherent Cerenkov radiation from a thin-film waveguide," Appl. Phys. Lett. 17, 447-449 (1970). [CrossRef]
- P. Dong, and A. G. Kirk, "Nonlinear frequency conversion in waveguide directional couplers," Phys. Rev. Lett. 93,133901 (2004). [CrossRef] [PubMed]
- S. J. B. Yoo, C. Caneau, R. Bhat, M. A. Koza, A. Rajhel, and N. Antoniades, "Wavelength conversion by difference frequency generation in AlGaAs waveguides with periodic domain inversion achieved by wafer bonding," Appl. Phys. Lett. 68, 2609-2611 (1996). [CrossRef]
- T. Skauli, "Measurement of the nonlinear coefficient of orientation-patterned GaAs and demonstration of highly efficient second-harmonic generation," Opt. Lett. 27, 628-630 (2002). [CrossRef]
- K. Moutzouris, S. V. Rao, M. Ebrahimzadeh, A. De Rossi, M. Calligaro, V. Ortiz, and V. Berger, "Second-harmonic generation through optimized modal phase matching in semiconductor waveguides," Appl. Phys. Lett. 83, 620-622 (2003). [CrossRef]
- S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, and M. Calligaro, "Continuous-wave second harmonic generation in modal phase matched semiconductor waveguides," Appl. Phys. Lett. 84, 2974-2976 (2004). [CrossRef]
- A. Yariv, Optical Electronics in Modern Communications (Oxford University Press, 1997).
- A. A. Maier, "Coupled modes phase matching and synchronous non-linear wave interaction in coupled waveguides," Kvantovaya Elektronika 7, 1596-1598 (1980).
- S. I. Bozhevol’nyi, K. S. Buritskii, E. M. Zolotov, and V. Chernykh, Sov. Tech. Phys. Lett. 7, 278 (1981).
- X. G. Huang and M. R. Wang, "A novel quasi-phase-matching frequency doubling technique," Opt. Commun. 150, 235-238 (1998). [CrossRef]
- G. Assanto, G. Stegeman, M. Sheik-Bahae, and E. V. Stryland, "All-optical switching devices based on large nonlinear phase shifts from second harmonic generation," Appl. Phys. Lett., 62, 1323-1325 (1993). [CrossRef]
- R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, "Observation of discrete quadratic solitons", Phys. Rev. Lett. 93, 113902 (2004). [CrossRef] [PubMed]
- Chowdhury, and L. McCaughan, "Continuously phase-matched M-waveguides for second-order nonlinear upconversion," IEEE Photon. Technol. Lett. 12, 486-488 (2000). [CrossRef]
- T. Reed, and A. P. Knights, Silicon photonics (John Wiley & Sons Inc., 2004). [CrossRef]
- K. Ekert, J. G. Rarity, P. R. Tapster, and G. M. Palma, "Practical quantum cryptography based on 2-photon interferometry," Phys. Rev. Lett. 69, 1293-1296 (1992). [CrossRef] [PubMed]
- D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, "Experimental quantum teleportation," Nature, 390, 575-579 (1997). [CrossRef]

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