## Quasi-phase-matched second harmonic generation in silicon nitride ring resonators controlled by static electric field |

Optics Express, Vol. 21, Issue 26, pp. 32690-32698 (2013)

http://dx.doi.org/10.1364/OE.21.032690

Acrobat PDF (1784 KB)

### Abstract

Actively-controlled second harmonic generation in a silicon nitride ring resonator is proposed and simulated. The ring was designed to resonate at both pump and second harmonic wavelengths and quasi-phase-matched frequency conversion is induced by a periodic static electric field generated by voltage applied to electrodes arranged along the ring. Nonlinear propagation simulations were undertaken and an efficiency of −21.67 dB was calculated for 60 mW of pump power at 1550 nm and for a 30V applied voltage, which compares favorably with demonstrated all-optical second harmonic generation in integrated microresonators. Transient effects were also evaluated. The proposed design can be exploited for the construction of electro-optical devices based on nonlinear effects in CMOS compatible circuits.

© 2013 Optical Society of America

## 1. Introduction

1. M. Lipson, “Guiding, modulating, and emitting light on silicon-challenges and opportunities,” J. Lightwave Technol. **23**(12), 4222–4238 (2005). [CrossRef]

2. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature **431**(7012), 1081–1084 (2004). [CrossRef] [PubMed]

3. M. Krause, H. Renner, and E. Brinkmeyer, “Silicon Raman amplifiers with ring-resonator-enhanced pump power,” IEEE J. Sel. Top. Quantum Electron. **16**(1), 216–225 (2010). [CrossRef]

4. M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature **441**(7096), 960–963 (2006). [CrossRef] [PubMed]

5. S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics **1**(5), 293–296 (2007). [CrossRef]

6. D. A. B. Miller, “Optical interconnects to silicon,” IEEE J. Sel. Top. Quantum Electron. **6**(6), 1312–1317 (2000). [CrossRef]

7. D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics **7**(8), 597–607 (2013). [CrossRef]

8. M. Lipson, “Compact electro-optic modulators on a silicon chip,” IEEE J. Sel. Top. Quantum Electron. **12**(6), 1520–1526 (2006). [CrossRef]

1. M. Lipson, “Guiding, modulating, and emitting light on silicon-challenges and opportunities,” J. Lightwave Technol. **23**(12), 4222–4238 (2005). [CrossRef]

9. J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics **4**(1), 37–40 (2010). [CrossRef]

13. C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express **19**(11), 10462–10470 (2011). [CrossRef] [PubMed]

14. J. L. O’Brien, “Exploiting entanglement,” Science **330**(6004), 588–589 (2010). [CrossRef]

16. J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. **104**(15), 153901 (2010). [CrossRef] [PubMed]

20. A. Dutt, K. Luke, S. Manipatruni, A. L. Gaeta, P. Nussensveig, and M. Lipson, “Observation of on-chip optical squeezing,” in *The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting,* OSA Technical Digest (online) (Optical Society of America, 2013), paper M6.67.

9. J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics **4**(1), 37–40 (2010). [CrossRef]

10. A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express **16**(7), 4881–4887 (2008). [CrossRef] [PubMed]

12. J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express **19**(12), 11415–11421 (2011). [CrossRef] [PubMed]

13. C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express **19**(11), 10462–10470 (2011). [CrossRef] [PubMed]

23. R. Kashyap, “Phase-matched periodic electric-field-second-harmonic generation in optical fibers,” J. Opt. Soc. Am. B **6**(3), 313–328 (1989). [CrossRef]

24. R. E. P. de Oliveira, M. Lipson, and C. J. S. de Matos, “Electrically controlled silicon nitride ring resonator for quasi-phase matched second-harmonic generation,” in *Conference on Lasers and Electro-Optics 2012*, OSA Technical Digest (online) (Optical Society of America, 2012), paper CF3M.5. [CrossRef]

## 2. Ring resonator design

*κ*. The remaining light fraction is transmitted with a coefficient

*t*such that

*κ*

^{2}+

*t*

^{2}= 1. The light coupling is described bywhere

*j*is the square root of −1,

*E*

_{i1}and

*E*

_{i2}are the light electric fields in the bus waveguide and inside the ring, respectively, that are incident in the coupling region, and

*E*

_{t1}and

*E*

_{t2}refer to the respective electric fields that are transmitted through this region, as shown in Fig. 1.

*θ*, accumulated by light after one ring round trip, is a multiple of 2

*π*,where

*n*is the guided mode effective refractive index,

_{eff}*λ*is the light vacuum wavelength,

*R*is the ring radius and

*m*is a natural number. When light at a given wavelength is resonant, its intensity inside the ring builds up and, at the steady state, is increased relative to the launched intensity. This enhancement can be calculated via the build-up factor,

*B*, for a lossless ring through [21]

*n*in Eq. (2) is not a constant and, therefore, these wavelengths do not necessarily match ring resonances simultaneously, requiring the adjustment of the waveguide cross section (which tunes waveguide dispersion) and of the ring dimensions. The pump and second harmonic

_{eff}*n*were numerically obtained using the software COMSOL Multiphysics, in which quasi-TE propagation modes inside the ring were calculated in a 2D axisymmetric model. Figure 2 shows the transverse electric field intensity distribution inside the ring waveguide cross section for the fundamental mode at 1550 nm. Arrows indicate the optical electric field direction. Quasi-TE optical modes are chosen because their electric field is collinear with the static electric field, improving the nonlinearities and simplifying the third-order nonlinear susceptibility tensor; the dispersion curve was calculated by sweeping the wavelength and taking into account both silicon nitride [25

_{eff}25. H. R. Philipp, “Optical properties of silicon nitride,” J. Electrochem. Soc. **120**(2), 295–300 (1973). [CrossRef]

^{2}= 0.008 at 1550 nm and κ

^{2}= 0.0004 at 775 nm, and in build up factors of ~500 (Q factor of ~10

^{5}) at 1550 nm and ~10,000 (Q factor of ~5 × 10

^{6}) at 775 nm. The normalized build-up factor spectra for both the pump and second harmonic are shown in Fig. 3; the nonlinearity induced resonance shifts are also indicated and are explained in the next section.

*k*

_{0}wavenumber. To achieve quasi phase matching, this wavenumber must satisfy the momentum conservation equation

*k*

_{0}

*= 2k*

_{1}

*-k*

_{2}, where

*k*

_{1}and

*k*

_{2}are the pump and second harmonic wavenumbers, respectively.

## 3. Optical nonlinearity model, simulations and results

27. R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. **18**(7), 1062–1072 (1982). [CrossRef]

**E**(

*r,φ,z*) is written as the product of a longitudinal propagating field along the ring,

**A**(

*φ*), and a perpendicular modal field, Ψ(

*r,z*),where the

*φ*direction is the direction of light propagation inside the ring, while

*r*and

*z*denote the ring waveguide transverse directions. The guided optical power for a given mode is given bywhere

*ε*is the vacuum electric permittivity,

_{0}*c*is the speed of light and |

**F|**

^{2}is the squared optical electric field modulus integrated over the cross section:

*E*

_{t}_{1}and

*E*

_{t}_{2}, with the

*E*

_{t}_{2}fields then used as the initial conditions for the next nonlinear propagation round trip. By iteration, it is then possible to calculate both second harmonic generation and transient effects, including resonance drifts towards longer wavelengths due to the nonlinearity-induced phase shifts caused by self- and cross-phase modulation.

*ϕ*

_{NL}, wherewith the resonance drift,

*Δλ*, can be calculated by

28. K. Padmaraju, J. Chan, L. Chen, M. Lipson, and K. Bergman, “Thermal stabilization of a microring modulator using feedback control,” Opt. Express **20**(27), 27999–28008 (2012). [CrossRef] [PubMed]

12. J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express **19**(12), 11415–11421 (2011). [CrossRef] [PubMed]

13. C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express **19**(11), 10462–10470 (2011). [CrossRef] [PubMed]

*W*in the parametric down-conversion process through the relation proposed by Mitchell [29

29. M. W. Mitchell, “Parametric down-conversion from a wave-equation approach: Geometry and absolute brightness,” Phys. Rev. A **79**(4), 043835 (2009). [CrossRef]

*is the effective angular frequency linewidth of the 1550 nm filter, or in this case the ring resonance linewidth,*

_{eff}*P*

_{775}is the pump power at 775nm and

*Q*is the second harmonic generation efficiency defined as

_{SHG}*Q*

_{SHG}= P_{775}/(

*P*

_{1550})

^{2}. Based on the ring resonance linewidth and the intracavity powers with 30V applied voltage to calculate

*Q*, an output down-converted rate of

_{SHG}*W*= 5.3x10

^{6}photon pairs per second per input pump power is expected. This process can generate both squeezed and entangled states, which can be used in quantum based integrated devices where the flux of photon pairs is controlled by the applied voltage.

## 4. Conclusions

## Acknowledgments

## References and links

1. | M. Lipson, “Guiding, modulating, and emitting light on silicon-challenges and opportunities,” J. Lightwave Technol. |

2. | V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature |

3. | M. Krause, H. Renner, and E. Brinkmeyer, “Silicon Raman amplifiers with ring-resonator-enhanced pump power,” IEEE J. Sel. Top. Quantum Electron. |

4. | M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature |

5. | S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics |

6. | D. A. B. Miller, “Optical interconnects to silicon,” IEEE J. Sel. Top. Quantum Electron. |

7. | D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics |

8. | M. Lipson, “Compact electro-optic modulators on a silicon chip,” IEEE J. Sel. Top. Quantum Electron. |

9. | J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics |

10. | A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express |

11. | K. Ikeda, R. E. Saperstein, N. Alic, and Y. Fainman, “Thermal and Kerr nonlinear properties of plasma-deposited silicon nitride/ silicon dioxide waveguides,” Opt. Express |

12. | J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express |

13. | C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express |

14. | J. L. O’Brien, “Exploiting entanglement,” Science |

15. | N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett. |

16. | J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett. |

17. | R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett. |

18. | S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A |

19. | S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. |

20. | A. Dutt, K. Luke, S. Manipatruni, A. L. Gaeta, P. Nussensveig, and M. Lipson, “Observation of on-chip optical squeezing,” in |

21. | D. G. Rabus, |

22. | R. W. Boyd, |

23. | R. Kashyap, “Phase-matched periodic electric-field-second-harmonic generation in optical fibers,” J. Opt. Soc. Am. B |

24. | R. E. P. de Oliveira, M. Lipson, and C. J. S. de Matos, “Electrically controlled silicon nitride ring resonator for quasi-phase matched second-harmonic generation,” in |

25. | H. R. Philipp, “Optical properties of silicon nitride,” J. Electrochem. Soc. |

26. | M. Bass, |

27. | R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. |

28. | K. Padmaraju, J. Chan, L. Chen, M. Lipson, and K. Bergman, “Thermal stabilization of a microring modulator using feedback control,” Opt. Express |

29. | M. W. Mitchell, “Parametric down-conversion from a wave-equation approach: Geometry and absolute brightness,” Phys. Rev. A |

**OCIS Codes**

(190.2620) Nonlinear optics : Harmonic generation and mixing

(250.4390) Optoelectronics : Nonlinear optics, integrated optics

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: November 18, 2013

Revised Manuscript: December 19, 2013

Manuscript Accepted: December 19, 2013

Published: December 24, 2013

**Citation**

Rafael E. P. de Oliveira and Christiano J. S. de Matos, "Quasi-phase-matched second harmonic generation in silicon nitride ring resonators controlled by static electric field," Opt. Express **21**, 32690-32698 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-26-32690

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### References

- M. Lipson, “Guiding, modulating, and emitting light on silicon-challenges and opportunities,” J. Lightwave Technol.23(12), 4222–4238 (2005). [CrossRef]
- V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature431(7012), 1081–1084 (2004). [CrossRef] [PubMed]
- M. Krause, H. Renner, and E. Brinkmeyer, “Silicon Raman amplifiers with ring-resonator-enhanced pump power,” IEEE J. Sel. Top. Quantum Electron.16(1), 216–225 (2010). [CrossRef]
- M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature441(7096), 960–963 (2006). [CrossRef] [PubMed]
- S. F. Preble, Q. Xu, and M. Lipson, “Changing the colour of light in a silicon resonator,” Nat. Photonics1(5), 293–296 (2007). [CrossRef]
- D. A. B. Miller, “Optical interconnects to silicon,” IEEE J. Sel. Top. Quantum Electron.6(6), 1312–1317 (2000). [CrossRef]
- D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photonics7(8), 597–607 (2013). [CrossRef]
- M. Lipson, “Compact electro-optic modulators on a silicon chip,” IEEE J. Sel. Top. Quantum Electron.12(6), 1520–1526 (2006). [CrossRef]
- J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics4(1), 37–40 (2010). [CrossRef]
- A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express16(7), 4881–4887 (2008). [CrossRef] [PubMed]
- K. Ikeda, R. E. Saperstein, N. Alic, and Y. Fainman, “Thermal and Kerr nonlinear properties of plasma-deposited silicon nitride/ silicon dioxide waveguides,” Opt. Express16(17), 12987–12994 (2008). [CrossRef] [PubMed]
- J. S. Levy, M. A. Foster, A. L. Gaeta, and M. Lipson, “Harmonic generation in silicon nitride ring resonators,” Opt. Express19(12), 11415–11421 (2011). [CrossRef] [PubMed]
- C. Xiong, W. Pernice, K. K. Ryu, C. Schuck, K. Y. Fong, T. Palacios, and H. X. Tang, “Integrated GaN photonic circuits on silicon (100) for second harmonic generation,” Opt. Express19(11), 10462–10470 (2011). [CrossRef] [PubMed]
- J. L. O’Brien, “Exploiting entanglement,” Science330(6004), 588–589 (2010). [CrossRef]
- N. B. Grosse, W. P. Bowen, K. McKenzie, and P. K. Lam, “Harmonic entanglement with second-order nonlinearity,” Phys. Rev. Lett.96, 63601 (2006).
- J. U. Fürst, D. V. Strekalov, D. Elser, M. Lassen, U. L. Andersen, C. Marquardt, and G. Leuchs, “Naturally phase-matched second-harmonic generation in a whispering-gallery-mode resonator,” Phys. Rev. Lett.104(15), 153901 (2010). [CrossRef] [PubMed]
- R. Paschotta, M. Collett, P. Kürz, K. Fiedler, H. A. Bachor, and J. Mlynek, “Bright squeezed light from a singly resonant frequency doubler,” Phys. Rev. Lett.72(24), 3807–3810 (1994). [CrossRef] [PubMed]
- S. F. Pereira, M. Xiao, H. J. Kimble, and J. L. Hall, “Generation of squeezed light by intracavity frequency doubling,” Phys. Rev. A38(9), 4931–4934 (1988). [CrossRef] [PubMed]
- S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys.77(2), 513–577 (2005). [CrossRef]
- A. Dutt, K. Luke, S. Manipatruni, A. L. Gaeta, P. Nussensveig, and M. Lipson, “Observation of on-chip optical squeezing,” in The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting, OSA Technical Digest (online) (Optical Society of America, 2013), paper M6.67.
- D. G. Rabus, Integrated Ring Resonators. The Compendium (Springer, 2007).
- R. W. Boyd, Nonlinear Optics (Academic, 2003), Chap. 2.
- R. Kashyap, “Phase-matched periodic electric-field-second-harmonic generation in optical fibers,” J. Opt. Soc. Am. B6(3), 313–328 (1989). [CrossRef]
- R. E. P. de Oliveira, M. Lipson, and C. J. S. de Matos, “Electrically controlled silicon nitride ring resonator for quasi-phase matched second-harmonic generation,” in Conference on Lasers and Electro-Optics 2012, OSA Technical Digest (online) (Optical Society of America, 2012), paper CF3M.5. [CrossRef]
- H. R. Philipp, “Optical properties of silicon nitride,” J. Electrochem. Soc.120(2), 295–300 (1973). [CrossRef]
- M. Bass, Handbook of Optics Volume II, Measurements and Properties (McGraw-Hill, 1995), Chap. 3.
- R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron.18(7), 1062–1072 (1982). [CrossRef]
- K. Padmaraju, J. Chan, L. Chen, M. Lipson, and K. Bergman, “Thermal stabilization of a microring modulator using feedback control,” Opt. Express20(27), 27999–28008 (2012). [CrossRef] [PubMed]
- M. W. Mitchell, “Parametric down-conversion from a wave-equation approach: Geometry and absolute brightness,” Phys. Rev. A79(4), 043835 (2009). [CrossRef]

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