## Broadband directional coupling in aluminum nitride nanophotonic circuits |

Optics Express, Vol. 21, Issue 6, pp. 7304-7315 (2013)

http://dx.doi.org/10.1364/OE.21.007304

Acrobat PDF (5041 KB)

### Abstract

Aluminum nitride (AlN)-on-insulator has emerged as a promising platform for the realization of linear and non-linear integrated photonic circuits. In order to efficiently route optical signals on-chip, precise control over the interaction and polarization of evanescently coupled waveguide modes is required. Here we employ nanophotonic AlN waveguides to realize directional couplers with a broad coupling bandwidth and low insertion loss. We achieve uniform splitting of incoming modes, confirmed by high extinction-ratio exceeding 33dB in integrated Mach-Zehnder Interferometers. Optimized three-waveguide couplers furthermore allow for extending the coupling bandwidth over traditional side-coupled devices by almost an order of magnitude, with variable splitting ratio. Our work illustrates the potential of AlN circuits for coupled waveguide optics, DWDM applications and integrated polarization diversity schemes.

© 2013 OSA

## 1. Introduction

1. R. Kirchain and L. Kimerling, “A roadmap for nanophotonics,” Nat. Photonics **1**(6), 303–305 (2007). [CrossRef]

2. B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. **24**(12), 4600–4615 (2006). [CrossRef]

4. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. **23**(1), 401–412 (2005). [CrossRef]

5. W. Bludau, A. Onton, and W. Heinke, “Temperature dependence of the band gap of silicon,” J. Appl. Phys. **45**(4), 1846 (1974). [CrossRef]

_{3}N

_{4}) has widely been used for the realization of CMOS compatible nanophotonic devices [6

6. A. Gondarenko, J. S. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express **17**(14), 11366–11370 (2009). [CrossRef] [PubMed]

10. Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett. **36**(17), 3398–3400 (2011). [CrossRef] [PubMed]

11. J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature **452**(7183), 72–75 (2008). [CrossRef] [PubMed]

12. B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. Bleszynski Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. **92**(10), 103125 (2008). [CrossRef]

13. Q. P. Unterreithmeier, T. Faust, and J. P. Kotthaus, “Damping of Nanomechanical Resonators,” Phys. Rev. Lett. **105**(2), 027205 (2010). [CrossRef] [PubMed]

_{3}N

_{4}also a prime candidate for opto-mechanical devices. However, the deposition of thick Si

_{3}N

_{4}films of high quality, which are required for nanophotonic waveguides at longer wavelengths, is often accompanied by large internal stress. High quality, stoichiometric silicon nitride films deposited by low pressure chemical vapour deposition (LPCVD) possess internal tensile stress with a magnitude up to 1GPa, which may lead to crack formation when grown to a thickness above a few hundred nanometers [14]. Recently, photonic devices based on GaN [15

15. 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]

16. Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’Brien, and M. D. Dawson, “GaN directional couplers for integrated quantum photonics,” Appl. Phys. Lett. **99**(16), 161119 (2011). [CrossRef]

17. C. Xiong, W. Pernice, X. Sun, C. Schuck, K. Fong, and H. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys. **14**(9), 095014 (2012). [CrossRef]

19. S. Ghosh, C. R. Doerr, and G. Piazza, “Aluminum nitride grating couplers,” Appl. Opt. **51**(17), 3763–3767 (2012). [CrossRef] [PubMed]

20. W. M. Yim, E. J. Stofko, P. J. Zanzucchi, J. I. Pankove, M. Ettenberg, and S. L. Gilbert, “Epitaxially grown AlN and its optical band gap,” J. Appl. Phys. **44**(1), 292–296(1973). [CrossRef]

21. M. H. Crawford, “LEDs for Solid-State Lighting: Performance Challenges and Recent Advances,” IEEE J. Sel. Top. Quantum Electron. **15**(4), 1028–1040 (2009). [CrossRef]

20. W. M. Yim, E. J. Stofko, P. J. Zanzucchi, J. I. Pankove, M. Ettenberg, and S. L. Gilbert, “Epitaxially grown AlN and its optical band gap,” J. Appl. Phys. **44**(1), 292–296(1973). [CrossRef]

## 2. Design of dual-waveguide directional couplers

### 2.1 Simulations

*w*, height

*h*and are separated by a gap

*g*. Furthermore, the sidewall is assumed to be sloped with an angle

*θ,*which is observed during the fabrication of AlN waveguides. Evanescent coupling between the waveguides causes a periodic power exchange characterised by the coupling length

*L*which is definded as the distance required for full energy tranfer. Hence, light coupled into the lower input waveguide will be fully transferred into the upper waveguide after

_{c}*L*, leading to zero output optical power in the lower output waveguide. Different splitting ratios can be obtained by selecting a coupling length smaller than

_{c}*L*.

_{c}22. H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, “Coupled-mode theory of optical waveguides,” J. Lightwave Technol. **5**(1), 16–23 (1987). [CrossRef]

*L*depends on the coupling coefficent

_{c}*κ*but can also be expressed in terms of the effective mode indices of the symmetric

*n*and antisymmetric

_{eff,even}*n*supermodes, respectively, where

_{eff,odd}*λ*is the incoming wavelength:

^{®}. The simulated geometry, presented in Fig. 1(b), consists of two parallel AlN-ridge waveguides of height

*h*= 500nm, width

*w*= 850nm, sidewall angles

*θ*= 24° and a gap

*g*= 470nm on top of a SiO

_{2}-layer. As refractive index in the telecoms C-band we chose

*n*= 2.12 and

_{AlN}*n*= 1.44. Because of the relatively thick AlN layer, this waveguide design supports both TE-like and TM-like optical modes, with both symmetric and anti-symmetric mode shape relative to the direction of propagation. For the two polarizations we calculated coupling lengths

_{SiO2}*L*= 32µm and

_{c}^{TM}*L*= 67µm, respectively. The resulting field distributions of the TM-like modes can be seen in Fig. 2(a) . The power transfer characteristics are also confirmed with full-vectorial finite-difference time-domain (FDTD) simulations using the commercial package OmniSim, as shown in Fig. 2(b).

_{c}^{TE}*L*= 32.5μm and

_{c}^{TM}*L*61.5µm, consistent with the finite-element simulations. Upon increasing the coupling length, the optical power is transferred back into the input waveguide, leading to a characteristic beating pattern in longer devices.

_{c}^{TE}=### 2.2 Experimental realization

_{2}/SiCl

_{4}/Ar inductively coupled plasma using an Oxford 100 system. By doing so, we are able to fabricate AOI devices with overall coupling loss below 12dB, corresponding to an overall transmission of up to 6%. The coupling loss consist of 5dB input and output coupling losses and propagation loss of approximately 3.5dB/cm due to residual sidewall roughness, respectively. Even though lower propagation loss has been obtained previously using a Cl

_{2}/BCl

_{3}/Ar dry etching chemistry [18

18. C. Xiong, W. H. Pernice, and H. X. Tang, “Low-loss, silicon integrated, aluminum nitride photonic circuits and their use for electro-optic signal processing,” Nano Lett. **12**(7), 3562–3568 (2012). [CrossRef] [PubMed]

23. D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Dale, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. **38**(7), 949–955 (2002). [CrossRef]

*L*in the range between 50µm and 300µm. The obtained coupling efficiencies are plotted versus

*L*for both the TE-like and the TM-like modes in Fig. 3(a) , 3(b). As can be seen, the resulting curves are well described by the sinusoidal oscillation expected for directional couplers. The data are fitted to the theoretically expected curve, yielding coupling lengths of

*L*= 33.3+/−0.2µm and

_{c}^{TM}*L*= 64+/−1.2µm for the TM-like and the TE-like mode, respectively. These measured values are in good agreement with the simulated coupling lengths of

_{c}^{TE}*L*= 32µm and

_{c}^{TM}*L*= 67µm.

_{c}^{TE}### 2.3 MZI with directional couplers

*P*and

_{max}*P*, and calculated the extinction ratio defined as the logarithmic ratio of these powers for different wavelengths. This quantity is a good measure for the accuracy of the beam splitter since it is sensitive to small deviations from the perfect splitting ratio as shown in Fig. 4(c). As

_{min}*P*and

_{max}*P*occur at different wavelengths and the extinction ratio is defined at one wavelength, the maximal transmitted power

_{min}*P*corresponding to a measured minima

_{max}*P*extracted by interpolation using the transmission envelope as depicted in Fig. 4(b).

_{min}*w =*810nm,

*h =*500nm,

*g =*360nm and θ = 11° were used, measured from high-resolution SEM images. The resulting dispersion of the coupling length with intercept

*L*= 24.9µm and slope

_{c,0}*m*= −0.068 is in good agreement with the simulated dispersion with

*L*= 24.9µm and

_{c,0}*m*= −0.078.While we achieve high extinction ratio on the available wavelengths where destructive interference occurs, even higher values may be possible by designing MZIs with larger path difference and thus a finer sampling rate.

## 3. Beamsplitter model: theory and simulations

*L*to coupling length

*L*, the desired splitting ratio depends in particular on the accurate choice of

_{c}*L*. All this is a result of operating the coupler at an inconvenient point of the energy exchange, since the conversion efficiency varies linearly around this point. For example, for a directional coupler operated as a 50:50 splitter the following relation for the conversion efficiency

*η*holds:

*ΔL/L*denotes a small deviation of

_{c}*L/L*from the operating point

_{c}*L/L*Hence even small deviations from the right design length result in a deterioration of the device performance. To avoid this problem, an alternative beam splitter design has been proposed [24

_{c}= 1/2.24. P. Ganguly, J. C. Biswas, S. Das, and S. K. Lahiri, “A three-waveguide polarization independent power splitter on lithium niobate substrate,” Opt. Commun. **168**(5-6), 349–354 (1999). [CrossRef]

*g = g’*. Due to symmetry, this design always transfers light coming from the left middle input port equally to the outer two ports, independent on the interaction length, the wavelength and the excited mode. Improper choice of the length

*L*then results in insertion loss, rather than deviation from the 50/50 splitting ratio. However, the original design is not capable of splitting light in an arbitrary ratio.

*g*and

*g’*. Since the outer two waveguides are far apart from each other they can be considered to be uncoupled in first order approximation. In this case, phase-mismatch can be neglected because all three waveguides support the same mode profile and the self-coupling terms are small in comparison with the cross-coupling terms. The latter assumption is necessary and cannot be avoided by redefining the effective mode indices because the middle waveguide is coupled to both the outer ones, leading to a self-coupling term of approximately twice the size of the ones of the outer waveguides. Using these assumptions and labeling the coupling coefficients

*κ*and

*κ’*CMT leads to the following linear differential equation:

*z*, the solution of this equation is the matrix exponential of the above coupling matrix. By diagonalizing this matrix, the solution can be calculated explicitly:

*t = κ’/κ*denotes the coupling ratio and

*A*), then the power transfer to the outer waveguides leads to a power splitting ratio of:

_{0}= C_{0}= 0*L*and

*L*. Hence, by adjusting the two gaps appropriately this device can be used as a beam splitter of arbitrary splitting ratio. It should be noted that although the power ratio in the two outer waveguides does not depend on the interaction length, the total transferred power does. However, in contrast to the directional couplers described in the previous section, the device presented here is operated at the point at which the conversion efficiency just varies quadratically with respect to small deviations, which is the point where all the power is transferred. Hence, the functionality does not crucially depend on either the interaction or the coupling length.

_{c}*L*does not affect the splitting ratio, the dispersion of

_{c}*t*has to be taken into account. Because

*t*is the ratio of coupling coefficients of two almost equal structures differing only in the gap size, one may expect that

*t*is less affected by dispersion than

*L*. We confirmed this expectation by evaluating the dispersion curve numerically with COMSOL. We calculated the effective mode indices of a structure like in Fig. 1(b) for different gap sizes and different wavelengths. Using Eq. (1), the corresponding coupling coefficients can be obtained from the different mode indices of the symmetric and antisymmetric supermodes. An exemplary result is shown in Fig. 5(b).

_{c}*t*changes only slightly from 2.12 to 1.94, corresponding to splitting ratios of 68%:32% to 66%:34%, across a wavelength interval of over 120nm. Therefore the design is only weakly sensitive to fabrication imperfections.

^{2}## 4. Three-waveguide beamsplitter: experimental results

### 4.1 Implementation of a 50:50 splitter

*A*), the extinction ratio

_{0}= C_{0}= 0*R*of the middle output port can then be derived as a function of the absorption coefficient

_{e}*α*and the path difference

*d*:

*d =*500µm and the approximate propagation loss of 3.5dB/cm in our waveguides are plugged into the formula above, giving a maximal extinction ratio of around 37dB, close to the maximum value measured experimentally.

*w =*810nm, height

*h*= 500nm, sidewall angles

*θ*= 11° and gaps

*g =*460nm. In contrast to the theoretical results presented above,

*R*shows non-negligible dispersion. The observed residual dispersion is due to a small width difference between the outer the middle waveguide as a result of fabrication errors. This in turn leads to a phase mismatch between the coupled modes and thus reduced maximal conversion efficiency. We note, however, that the results are plotted on a logarithmic scale and thus the deviation from the ideal behavior is still very small.

_{e}### 4.2 Implementation of a 66:33 splitter

*A*0). Eventually, the following expression for the extinction ratio can be derived:

_{0}= C_{0}=*t*denotes the wavelength-dependent ratio of the coupling coefficients,

*α*is the absorption coefficient and

*d*the path difference. Due to different propagation losses in the two different long arms of the device, the perfect splitting ratio is shifted from 66:33 (corresponding to

*t*2) to slightly larger values. If one assumes a path difference

^{2}=*d*= 500µm and propagation losses of 3.5dB/cm, the above formula yields the divergence at

*t*= 2.17 corresponding to a power ratio of 68:32.

^{2}*w*= 1µm, height

*h*= 500nm, sidewall angles

*θ*= 11° and gap sizes of

*g*= 470nm and

*g’*= 540nm. The high values of over 30dB close to

*λ*= 1530nm correspond to an excellent 66:33 splitting ratio. Again, the observed 20dB and 30dB bandwidths of approximately 18nm and 30nm are much broader than the ones obtained with directional couplers, at least by a factor of 2-3. Deviations from the theoretical curve are due to non-uniformities and residual dispersion of the Y-splitter.

## 5. Conclusions

## Acknowledgments

## References and links

1. | R. Kirchain and L. Kimerling, “A roadmap for nanophotonics,” Nat. Photonics |

2. | B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol. |

3. | R. Soref, “The past, present and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron. |

4. | W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. |

5. | W. Bludau, A. Onton, and W. Heinke, “Temperature dependence of the band gap of silicon,” J. Appl. Phys. |

6. | A. Gondarenko, J. S. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express |

7. | E. S. Hosseini, S. Yegnanarayanan, A. H. Atabaki, M. Soltani, and A. Adibi, “High quality planar silicon nitride microdisk resonators for integrated photonics in the visible wavelength range,” Opt. Express |

8. | K. Fong, W. Pernice, M. Li, and H. Tang, “High Q optomechanical resonators in silicon nitride nanophotonic circuits,” Appl. Phys. Lett. |

9. | M.-C. Tien, J. F. Bauters, M. J. R. Heck, D. T. Spencer, D. J. Blumenthal, and J. E. Bowers, “Ultra-high quality factor planar Si3N4 ring resonators on Si substrates,” Opt. Express |

10. | Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett. |

11. | J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature |

12. | B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. Bleszynski Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett. |

13. | Q. P. Unterreithmeier, T. Faust, and J. P. Kotthaus, “Damping of Nanomechanical Resonators,” Phys. Rev. Lett. |

14. | B. Bhushan, Springer Handbook of Nanotechnology. (second ed.)Springer-Verlag, Heidelberg (2007). |

15. | 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 |

16. | Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’Brien, and M. D. Dawson, “GaN directional couplers for integrated quantum photonics,” Appl. Phys. Lett. |

17. | C. Xiong, W. Pernice, X. Sun, C. Schuck, K. Fong, and H. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys. |

18. | C. Xiong, W. H. Pernice, and H. X. Tang, “Low-loss, silicon integrated, aluminum nitride photonic circuits and their use for electro-optic signal processing,” Nano Lett. |

19. | S. Ghosh, C. R. Doerr, and G. Piazza, “Aluminum nitride grating couplers,” Appl. Opt. |

20. | W. M. Yim, E. J. Stofko, P. J. Zanzucchi, J. I. Pankove, M. Ettenberg, and S. L. Gilbert, “Epitaxially grown AlN and its optical band gap,” J. Appl. Phys. |

21. | M. H. Crawford, “LEDs for Solid-State Lighting: Performance Challenges and Recent Advances,” IEEE J. Sel. Top. Quantum Electron. |

22. | H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, “Coupled-mode theory of optical waveguides,” J. Lightwave Technol. |

23. | D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Dale, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. |

24. | P. Ganguly, J. C. Biswas, S. Das, and S. K. Lahiri, “A three-waveguide polarization independent power splitter on lithium niobate substrate,” Opt. Commun. |

**OCIS Codes**

(130.3120) Integrated optics : Integrated optics devices

(160.1050) Materials : Acousto-optical materials

(160.6000) Materials : Semiconductor materials

(230.5750) Optical devices : Resonators

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: January 14, 2013

Revised Manuscript: March 7, 2013

Manuscript Accepted: March 7, 2013

Published: March 15, 2013

**Citation**

Matthias Stegmaier and Wolfram H. P. Pernice, "Broadband directional coupling in aluminum nitride nanophotonic circuits," Opt. Express **21**, 7304-7315 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-6-7304

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### References

- R. Kirchain and L. Kimerling, “A roadmap for nanophotonics,” Nat. Photonics1(6), 303–305 (2007). [CrossRef]
- B. Jalali and S. Fathpour, “Silicon photonics,” J. Lightwave Technol.24(12), 4600–4615 (2006). [CrossRef]
- R. Soref, “The past, present and future of silicon photonics,” IEEE J. Sel. Top. Quantum Electron.12(6), 1678–1687 (2006). [CrossRef]
- W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol.23(1), 401–412 (2005). [CrossRef]
- W. Bludau, A. Onton, and W. Heinke, “Temperature dependence of the band gap of silicon,” J. Appl. Phys.45(4), 1846 (1974). [CrossRef]
- A. Gondarenko, J. S. Levy, and M. Lipson, “High confinement micron-scale silicon nitride high Q ring resonator,” Opt. Express17(14), 11366–11370 (2009). [CrossRef] [PubMed]
- E. S. Hosseini, S. Yegnanarayanan, A. H. Atabaki, M. Soltani, and A. Adibi, “High quality planar silicon nitride microdisk resonators for integrated photonics in the visible wavelength range,” Opt. Express17(17), 14543–14551 (2009). [CrossRef] [PubMed]
- K. Fong, W. Pernice, M. Li, and H. Tang, “High Q optomechanical resonators in silicon nitride nanophotonic circuits,” Appl. Phys. Lett.97(7), 073112 (2010). [CrossRef]
- M.-C. Tien, J. F. Bauters, M. J. R. Heck, D. T. Spencer, D. J. Blumenthal, and J. E. Bowers, “Ultra-high quality factor planar Si3N4 ring resonators on Si substrates,” Opt. Express19(14), 13551–13556 (2011). [CrossRef] [PubMed]
- Y. Okawachi, K. Saha, J. S. Levy, Y. H. Wen, M. Lipson, and A. L. Gaeta, “Octave-spanning frequency comb generation in a silicon nitride chip,” Opt. Lett.36(17), 3398–3400 (2011). [CrossRef] [PubMed]
- J. D. Thompson, B. M. Zwickl, A. M. Jayich, F. Marquardt, S. M. Girvin, and J. G. Harris, “Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane,” Nature452(7183), 72–75 (2008). [CrossRef] [PubMed]
- B. M. Zwickl, W. E. Shanks, A. M. Jayich, C. Yang, A. C. Bleszynski Jayich, J. D. Thompson, and J. G. E. Harris, “High quality mechanical and optical properties of commercial silicon nitride membranes,” Appl. Phys. Lett.92(10), 103125 (2008). [CrossRef]
- Q. P. Unterreithmeier, T. Faust, and J. P. Kotthaus, “Damping of Nanomechanical Resonators,” Phys. Rev. Lett.105(2), 027205 (2010). [CrossRef] [PubMed]
- B. Bhushan, Springer Handbook of Nanotechnology. (second ed.)Springer-Verlag, Heidelberg (2007).
- 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]
- Y. Zhang, L. McKnight, E. Engin, I. M. Watson, M. J. Cryan, E. Gu, M. G. Thompson, S. Calvez, J. L. O’Brien, and M. D. Dawson, “GaN directional couplers for integrated quantum photonics,” Appl. Phys. Lett.99(16), 161119 (2011). [CrossRef]
- C. Xiong, W. Pernice, X. Sun, C. Schuck, K. Fong, and H. Tang, “Aluminum nitride as a new material for chip-scale optomechanics and nonlinear optics,” New J. Phys.14(9), 095014 (2012). [CrossRef]
- C. Xiong, W. H. Pernice, and H. X. Tang, “Low-loss, silicon integrated, aluminum nitride photonic circuits and their use for electro-optic signal processing,” Nano Lett.12(7), 3562–3568 (2012). [CrossRef] [PubMed]
- S. Ghosh, C. R. Doerr, and G. Piazza, “Aluminum nitride grating couplers,” Appl. Opt.51(17), 3763–3767 (2012). [CrossRef] [PubMed]
- W. M. Yim, E. J. Stofko, P. J. Zanzucchi, J. I. Pankove, M. Ettenberg, and S. L. Gilbert, “Epitaxially grown AlN and its optical band gap,” J. Appl. Phys.44(1), 292–296(1973). [CrossRef]
- M. H. Crawford, “LEDs for Solid-State Lighting: Performance Challenges and Recent Advances,” IEEE J. Sel. Top. Quantum Electron.15(4), 1028–1040 (2009). [CrossRef]
- H. A. Haus, W. P. Huang, S. Kawakami, and N. A. Whitaker, “Coupled-mode theory of optical waveguides,” J. Lightwave Technol.5(1), 16–23 (1987). [CrossRef]
- D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. Van Dale, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron.38(7), 949–955 (2002). [CrossRef]
- P. Ganguly, J. C. Biswas, S. Das, and S. K. Lahiri, “A three-waveguide polarization independent power splitter on lithium niobate substrate,” Opt. Commun.168(5-6), 349–354 (1999). [CrossRef]

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