## Phase matching using Bragg reflection waveguides for monolithic nonlinear optics applications

Optics Express, Vol. 14, Issue 3, pp. 1243-1252 (2006)

http://dx.doi.org/10.1364/OE.14.001243

Acrobat PDF (159 KB)

### Abstract

A novel design to achieve phase matching between modes of a vertical distributed Bragg reflector waveguide and those of a conventional total internal reflection waveguide is reported for the first time. The device design and structure lend themselves to monolithic integration with active devices using well developed photonic fabrication technologies. Due to the lack of any modulation of the optical properties in the direction of propagation, the device promises very low insertion loss. This property together with the large overlap integral between the interacting fields dramatically enhances the conversion efficiency. The phase matching bandwidth, tunability and dimensions of these structures make them excellent contenders to harness optical nonlinearities in compact, low insertion loss monolithically integrable devices.

© 2006 Optical Society of America

## 1. Introduction

02. J. B. Khurgin, E. Rosencher, and Y. J. Ding, “Analysis of all-semiconductor intracavity optical parametric oscillators,” J. Opt. Soc. Am. B **15**, 1726–1734 (1998). [CrossRef]

*k*

_{2ω}= 2

*k*which leads to the condition that requires the effective indices of both waves to be equal in order for perfect phase matching to occur, namely

_{ω}*n*=

_{2ω}*n*. The difficulty of achieving this in semiconductors is usually most severe while operating near the bandgap resonances where dispersion prevents such condition from naturally taking place. Various means have been devised to overcome this problem; form birefringence [3

_{ω}03. A. Fiore, S. Janz, L. Delobel, P. van der Meer, P. Bravetti, V. Berger, and E. Rosencher, “Second-harmonic generation at λ= 1.6 μm in AlGaAs/Al2O3 waveguides using birefringence phase matching,” Appl. Phys. Lett. **72**, 2942–2945 (1998). [CrossRef]

04. A. S. Helmy, D. C. Hutchings, T. C. Kleckner, J. H. Marsh, A. C. Bryce, J. M. Arnold, C. R. Stanley, J. S. Aitchison, C. T. A. Brown, K. Moutzouris, and M. Ebrahimzadeh, “Quasi phase matching in GaAs-AlAs superlattice waveguides via bandgap tuning using quantum well intermixing,” Opt. Lett. **25**, 1370–1373 (2000). [CrossRef]

05. R. Haidar, N. Forget, and E. Rosencher, “Optical parametric oscillation in micro-cavities based on isotropic semiconductors: a theoretical study,” IEEE J. Quantum Electron. **39**, 569–576 (2003). [CrossRef]

06. D. Faccio, F. Bragheri, and M. Cherchi, “Optical Bloch-mode-induced quasi phase matching of quadratic interactions in one-dimensional photonic crystals,” J. Opt. Soc. Am. B **21**, 296–301 (2004). [CrossRef]

04. A. S. Helmy, D. C. Hutchings, T. C. Kleckner, J. H. Marsh, A. C. Bryce, J. M. Arnold, C. R. Stanley, J. S. Aitchison, C. T. A. Brown, K. Moutzouris, and M. Ebrahimzadeh, “Quasi phase matching in GaAs-AlAs superlattice waveguides via bandgap tuning using quantum well intermixing,” Opt. Lett. **25**, 1370–1373 (2000). [CrossRef]

07. K. L. Vodopyanov, O. Levi, P.S. Kuo, T.J. Pinguet, J.S. Harris, M.M. Fejer, B. Gerard, L. Becouarn, and E. Lallier “Optical parametric oscillation in quasi-phase-matched GaAs,” Opt. Lett. **29**, 1912–1914, (2004). [CrossRef] [PubMed]

08. A. S. Helmy and Brian R. West “Phase Matching using Bragg Reflector Waveguides,” IEEE LEOS Annual Meeting, Sydney , (2005). [CrossRef]

*n*=

_{2ω}*n*. A discussion of this technique will be presented in Section 5 followed by a study of the tuning behavior in Section 6.

_{ω}## 2. Features of Bragg reflection waveguides

09. P. Yeh and A. Yariv, “Bragg reflection waveguides,” Opt. Commun. **19**, 427–430 (1976). [CrossRef]

11. S. R. A. Dods, “Bragg reflection waveguides,” J. Opt. Soc. Am. A , **6**, 1465–1475 (1989). [CrossRef]

12. E. Simova and I. Golub, “Polarization splitter/combiner in high index contrast reflector waveguides,” Opt. Express **11**, 3425–3430 (2003). [CrossRef] [PubMed]

13. A. Mizrahi and L. Schächter, “Bragg reflection waveguides with a matching layer,” Opt. Express **12**, 3156–3170 (2004). [CrossRef] [PubMed]

14. C. Wätcher, F. Lederer, L. Leine, U. Trutschel, and M. Mann, “Nonlinear Bragg reflection waveguide,” J. Appl. Phys. **71**, 3688–3692 (1992). [CrossRef]

15. P. M. Lambkin and K. A. Shore, “Nonlinear semiconductor Bragg reflection waveguide structures,” IEEE J. Quantum Eletron. **27**, 824–828 (1991). [CrossRef]

09. P. Yeh and A. Yariv, “Bragg reflection waveguides,” Opt. Commun. **19**, 427–430 (1976). [CrossRef]

_{0.24}G

_{0.76}aAs, sandwiched in a Bragg stack made of alternating layers of Al

_{0.3}G

_{0.7}aAs and Al

_{0.5}G

_{0.5}aAs. As can be expected, the zero-order TIR modal index is lower than that of the core index by a factor of 2 %. In contrast, when the BRW mode of the same waveguide is examined, it is easy to observe that at any given wavelength, its effective index is lower than the core index and those of the cladding by at least 12 %. This property can then result in the BRW mode index, at a wavelength close to the core material bandgap, being equal to that of the zero-order TIR mode, at a wavelength further away than the material bandgap, as can be seen in Fig. 2. This property of BRWs has been observed previously and is documented but has not been used for the purpose of phase matching, to the best of our knowledge. Such waveguides can hence be used to provide guiding for the SH wavelength. It is worth noting that we have studied the material dispersion in this optical system experimentally using recent grating assisted measurements which lead to improved resolution to the existing measurements, and hence we have a reasonable handle on the refractive index values within this operating regime [16]. In the next section we shall present the waveguiding condition for BR waveguides.

## 3. Waveguiding condition for Bragg reflection waveguides

*y*direction, the electric field propagating in the waveguide seen in Fig. 1 can be written as,

*k*is the wave vector in the waveguide transverse direction.

_{x}09. P. Yeh and A. Yariv, “Bragg reflection waveguides,” Opt. Commun. **19**, 427–430 (1976). [CrossRef]

*k*,

_{1x}*k*are the transverse wave vectors in both stack layers. In the special case of quarter-wavelength stack, the waveguiding condition then becomes [9

_{2x}09. P. Yeh and A. Yariv, “Bragg reflection waveguides,” Opt. Commun. **19**, 427–430 (1976). [CrossRef]

*∂*/

*∂x*) at the interfaces of the core with both claddings to satisfy the necessary guiding condition for a bound mode. By designing the structure using quarter-wavelength stacks in the claddings we ensure that we operate right at the center of the stop band of the Bragg stack. This Bloch wave vector

*K*is in the form,

*κ*determines the exponential decay/growth of the BR mode envelope into the claddings, and will be at a maximum in the center of the forbidden gap with a sign appropriate for field decay, which is described as follows for the quarter-wavelength claddings [17],

_{i}*β*, group velocity dispersion, and mode shapes afforded by BRWs is substantial. The mode shapes of these waveguides have also been studied recently [13

13. A. Mizrahi and L. Schächter, “Bragg reflection waveguides with a matching layer,” Opt. Express **12**, 3156–3170 (2004). [CrossRef] [PubMed]

*d*and

_{1}*d*prior to the design. In our case of quarter-wavelength claddings both thicknesses are defined as per Eq. (3), and hence can be expressed as a function of the propagation constant and the wave vector of their respective layer. This enables their determination after solving for the propagation constant

_{2}*β*. Therefore there is no need for prior knowledge of

*d*and

_{1}*d*when using the method described here since we inherently set their contribution (

_{2}*k*) to be π/2. In the section that follows we shall simultaneously solve the waveguiding condition of both the TIR and BRW modes for a given waveguides in order to fulfill the condition

_{i}d_{i}*n*=

_{2ω}*n*.

_{ω}## 4. Simultaneously solving for TIR and BRW waveguiding conditions

18. J. Chilwell and I. Hodgkinson, “Thin-film field-transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguides,” J. Opt. Soc. Am. A **1**, 742–753 (1984) [CrossRef]

18. J. Chilwell and I. Hodgkinson, “Thin-film field-transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguides,” J. Opt. Soc. Am. A **1**, 742–753 (1984) [CrossRef]

*M*are defined as,

_{j}*c*,

*μ*,

_{o}*ε*,

_{o}*n*,

_{eff}*d*,

_{j}*n*,

_{j}*k*are the speed of light, vacuum permeability, vacuum permittivity, effective modal index, thickness, refractive index and propagation constant in

_{jx}*x*direction of layer

*j*respectively. The modal dispersion function can be written as,

_{c}and γ

_{s}are the γ parameter for the top cladding and substrate of the layers respectively. For lossless bound modes the modal dispersion function is imaginary [18

18. J. Chilwell and I. Hodgkinson, “Thin-film field-transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguides,” J. Opt. Soc. Am. A **1**, 742–753 (1984) [CrossRef]

*χ*(

_{M}*n*) = 0 is solved for the structure studied. However in order to preserve self consistency,

_{eff}*χ*(

_{M}*n*) needs to be solved simultaneously with Eq. (5) to obtain the SH and fundamental modes with an identical propagation constant. For demonstration, the solutions from both Eq. are plotted graphically and the intersection point represents the solution as shown in Fig. 3 for the device parameters discussed below.

_{eff}_{0.3}G

_{0.7}aAs layer, while the quarter-wavelength Bragg stacks on either side are made of alternating Al

_{0 2}G

_{0.8}aAs and Al

_{0.4}G

_{0.6}aAs. For demonstration purposes both Eqs. (5) and (13) are solved and presented here graphically. As can be seen in Fig. 3, the propagation constant of both modes match at a core thickness of 310 nm. The respective modes are then calculated and plotted, as shown in Fig. 4, where the 45% of the TE mode of the fundamental at 1550 nm is spatially centered in the core of the structure overlapping with 23 % of the SH field which is the TM BR mode at 775 nm. The effective index of these guides coincided at a value of 3.2236 for this structure.

## 5. Discussion

*ω*,

*P*(

^{2ω}*x*) =

*ε*

_{0}

*d*(

*x*)[

*E*(

^{ω}*x*)]

^{2}, and the field of SH mode,

*E*(

^{2ω}*x*), where

*d*(

*x*) is the effective nonlinear coefficient [19

19. J. Khurgin, “Improvement of frequency-conversion efficiency in waveguides with rotationally twinned layers,” Opt. Lett , **13**, 603–605 (1988). [CrossRef] [PubMed]

*E*(

^{2ω}*x*) goes out of phase from [

*E*(

^{ω}*x*)]

^{2}. One intuitive route to maximize the fields’ overlap is to maximize the core confinement. In this case the confinement is ~ 45 % and that of the SH is ~ 23 %, which is considerable for an initial design without exhaustive optimization. However it is imperative to take into account that the case presented here is generic, without a thorough optimization procedure for mere proof of principle. BRWs provide extensive degrees of design freedom to control the field decay in the cladding, modal shapes, overlap and dispersion. Hence they hold tremendous potential for maximizing the overlap and hence the conversion efficiency. For the case studied here the conversion efficiency is comparable to those of modal phase matching [19

19. J. Khurgin, “Improvement of frequency-conversion efficiency in waveguides with rotationally twinned layers,” Opt. Lett , **13**, 603–605 (1988). [CrossRef] [PubMed]

20. 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]

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

20. 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]

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

22. N. Yokouchi, A. J. Danner, and K. D. Choquette, “Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron. , **9**, 1439–1447 (2003). [CrossRef]

03. A. Fiore, S. Janz, L. Delobel, P. van der Meer, P. Bravetti, V. Berger, and E. Rosencher, “Second-harmonic generation at λ= 1.6 μm in AlGaAs/Al2O3 waveguides using birefringence phase matching,” Appl. Phys. Lett. **72**, 2942–2945 (1998). [CrossRef]

04. A. S. Helmy, D. C. Hutchings, T. C. Kleckner, J. H. Marsh, A. C. Bryce, J. M. Arnold, C. R. Stanley, J. S. Aitchison, C. T. A. Brown, K. Moutzouris, and M. Ebrahimzadeh, “Quasi phase matching in GaAs-AlAs superlattice waveguides via bandgap tuning using quantum well intermixing,” Opt. Lett. **25**, 1370–1373 (2000). [CrossRef]

20. 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]

## 6. Tuning

*p-i-n*doped structure where the intrinsic layer overlaps chiefly with the core. Hence the refractive index of the core waveguide can be tuned using current or potential [8

08. A. S. Helmy and Brian R. West “Phase Matching using Bragg Reflector Waveguides,” IEEE LEOS Annual Meeting, Sydney , (2005). [CrossRef]

_{0.3}G

_{0.7}As. In this plot it is assumed that the refractive index change is caused by a change in the bandgap; however the effect is the same if current or other effects are used for tuning. One of the attractive features of using BRWs is that the waveguide dispersion can be tailored to minimise the mismatch with that of the TIR mode at the fundamental; however this entails using BR stacks that are much more complex than the quarter-wavelength plate used here, and hence will be presented elsewhere. Although thermal tuning is also possible, it is of less practical use in compound semiconductors, as more effective means are available for tuning, including electro optic and carrier tuning.

- No patterning along the direction of propagation and hence have the potential to possess low optical losses in comparison with other quasi-phase matching designs. However it must be noted that Fresnel and modal phase matching share this advantage with our technique.
- Gain can be provided in structures through carrier injection via electrical pumping. The electrical pumping is readily available in such structures due to the work which has been carried out developing vertical cavity surface emitting lasers.
- The structure lends itself to be grown along side active and passive photonic devices for monolithic integration.

## 7. Conclusions

## Acknowledgments

## References and links

01. | C. B. Ebert, L. A. Eyres, M. M. Fejer, and J. H. Harris, “GaAs/Ge/GaAs sublattice reversal epitaxy and its application to nonlinear optical devices,” J. Cryst. Growth |

02. | J. B. Khurgin, E. Rosencher, and Y. J. Ding, “Analysis of all-semiconductor intracavity optical parametric oscillators,” J. Opt. Soc. Am. B |

03. | A. Fiore, S. Janz, L. Delobel, P. van der Meer, P. Bravetti, V. Berger, and E. Rosencher, “Second-harmonic generation at λ= 1.6 μm in AlGaAs/Al2O3 waveguides using birefringence phase matching,” Appl. Phys. Lett. |

04. | A. S. Helmy, D. C. Hutchings, T. C. Kleckner, J. H. Marsh, A. C. Bryce, J. M. Arnold, C. R. Stanley, J. S. Aitchison, C. T. A. Brown, K. Moutzouris, and M. Ebrahimzadeh, “Quasi phase matching in GaAs-AlAs superlattice waveguides via bandgap tuning using quantum well intermixing,” Opt. Lett. |

05. | R. Haidar, N. Forget, and E. Rosencher, “Optical parametric oscillation in micro-cavities based on isotropic semiconductors: a theoretical study,” IEEE J. Quantum Electron. |

06. | D. Faccio, F. Bragheri, and M. Cherchi, “Optical Bloch-mode-induced quasi phase matching of quadratic interactions in one-dimensional photonic crystals,” J. Opt. Soc. Am. B |

07. | K. L. Vodopyanov, O. Levi, P.S. Kuo, T.J. Pinguet, J.S. Harris, M.M. Fejer, B. Gerard, L. Becouarn, and E. Lallier “Optical parametric oscillation in quasi-phase-matched GaAs,” Opt. Lett. |

08. | A. S. Helmy and Brian R. West “Phase Matching using Bragg Reflector Waveguides,” IEEE LEOS Annual Meeting, Sydney , (2005). [CrossRef] |

09. | P. Yeh and A. Yariv, “Bragg reflection waveguides,” Opt. Commun. |

10. | P. Yeh, A. Yariv, and C Hong “Electromagnetic propagation in periodic stratified media: I. General Theory,” J. Appl. Phys. , |

11. | S. R. A. Dods, “Bragg reflection waveguides,” J. Opt. Soc. Am. A , |

12. | E. Simova and I. Golub, “Polarization splitter/combiner in high index contrast reflector waveguides,” Opt. Express |

13. | A. Mizrahi and L. Schächter, “Bragg reflection waveguides with a matching layer,” Opt. Express |

14. | C. Wätcher, F. Lederer, L. Leine, U. Trutschel, and M. Mann, “Nonlinear Bragg reflection waveguide,” J. Appl. Phys. |

15. | P. M. Lambkin and K. A. Shore, “Nonlinear semiconductor Bragg reflection waveguide structures,” IEEE J. Quantum Eletron. |

16. | T. C. Kleckner, A. S. Helmy, K. Zeaiter, D. C. Hutchings, and J. S. Aitchison, “Dispersion and Modulation of the Linear Optical Properties of GaAs/AlAs Superlattices Waveguides using Quantum Well Intermixing,” IEEE J. Quantum Eletron. (Accepted). |

17. | P. Yeh, |

18. | J. Chilwell and I. Hodgkinson, “Thin-film field-transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguides,” J. Opt. Soc. Am. A |

19. | J. Khurgin, “Improvement of frequency-conversion efficiency in waveguides with rotationally twinned layers,” Opt. Lett , |

20. | 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. |

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

22. | N. Yokouchi, A. J. Danner, and K. D. Choquette, “Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers,” IEEE J. Sel. Top. Quantum Electron. , |

**OCIS Codes**

(130.3120) Integrated optics : Integrated optics devices

(190.2620) Nonlinear optics : Harmonic generation and mixing

(190.4390) Nonlinear optics : Nonlinear optics, integrated optics

(230.1480) Optical devices : Bragg reflectors

(230.7370) Optical devices : Waveguides

**ToC Category:**

Optical Devices

**History**

Original Manuscript: December 21, 2005

Revised Manuscript: January 30, 2006

Manuscript Accepted: January 31, 2006

**Citation**

A. S. Helmy, "Phase matching using Bragg reflection waveguides for monolithic nonlinear optics applications," Opt. Express **14**, 1243-1252 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-3-1243

Sort: Year | Journal | Reset

### References

- C. B. Ebert, L. A. Eyres, M. M. Fejer, J. H. Harris, "GaAs/Ge/GaAs sublattice reversal epitaxy and its application to nonlinear optical devices," J. Cryst. Growth 227, 183-192 (1999).
- J. B. Khurgin, E. Rosencher, Y. J. Ding, "Analysis of all-semiconductor intracavity optical parametric oscillators," J. Opt. Soc. Am. B 15, 1726-1734 (1998). [CrossRef]
- A. Fiore, S. Janz, L. Delobel, P. van der Meer, P. Bravetti, V. Berger, and E. Rosencher, "Second-harmonic generation at λ= 1.6 µm in AlGaAs/Al2O3 waveguides using birefringence phase matching," Appl. Phys. Lett. 72, 2942-2945 (1998). [CrossRef]
- A. S. Helmy, D. C. Hutchings, T. C. Kleckner, J. H. Marsh, A. C. Bryce, J. M. Arnold, C. R. Stanley, and J. S. Aitchison, C. T. A. Brown, K. Moutzouris and M. Ebrahimzadeh, "Quasi phase matching in GaAs-AlAs superlattice waveguides via bandgap tuning using quantum well intermixing," Opt. Lett. 25, 1370-1373 (2000). [CrossRef]
- R. Haidar, N. Forget, E. Rosencher, "Optical parametric oscillation in micro-cavities based on isotropic semiconductors: a theoretical study," IEEE J. Quantum Electron. 39, 569-576 (2003). [CrossRef]
- D. Faccio, F. Bragheri, M. Cherchi, "Optical Bloch-mode-induced quasi phase matching of quadratic interactions in one-dimensional photonic crystals," J. Opt. Soc. Am. B 21, 296-301 (2004). [CrossRef]
- K. L. Vodopyanov, O. Levi, P.S. Kuo, T.J. Pinguet, J.S. Harris, M.M. Fejer, B. Gerard, L. Becouarn, E. Lallier "Optical parametric oscillation in quasi-phase-matched GaAs," Opt. Lett. 29, 1912-1914, (2004). [CrossRef] [PubMed]
- A. S. Helmy, BrianR. West "Phase Matching using Bragg Reflector Waveguides," IEEE LEOS Annual Meeting, Sydney, (2005). [CrossRef]
- P. Yeh, A. Yariv, " Bragg reflection waveguides," Opt. Commun. 19, 427-430 (1976). [CrossRef]
- P. Yeh, A. Yariv, C Hong "Electromagnetic propagation in periodic stratified media: I. General Theory," J. Appl. Phys., 67, 423-438 (1977).
- S. R. A. Dods, "Bragg reflection waveguides," J. Opt. Soc. Am. A, 6, 1465-1475 (1989). [CrossRef]
- E. Simova, I. Golub, "Polarization splitter/combiner in high index contrast reflector waveguides," Opt. Express 11, 3425-3430 (2003). [CrossRef] [PubMed]
- A. Mizrahi, L. Schächter, "Bragg reflection waveguides with a matching layer," Opt. Express 12, 3156-3170 (2004). [CrossRef] [PubMed]
- C. Wätcher, F. Lederer, L. Leine, U. Trutschel, M. Mann, " Nonlinear Bragg reflection waveguide," J. Appl. Phys. 71, 3688-3692 (1992). [CrossRef]
- P. M. Lambkin, K. A. Shore, "Nonlinear semiconductor Bragg reflection waveguide structures," IEEE J. Quantum Eletron. 27, 824-828 (1991). [CrossRef]
- T. C. Kleckner, A. S. Helmy, K. Zeaiter, D. C. Hutchings, J. S. Aitchison, "Dispersion and Modulation of the Linear Optical Properties of GaAs/AlAs Superlattices Waveguides using Quantum Well Intermixing," IEEE J. Quantum Eletron. (Accepted).
- P. Yeh, Optical Waves in layered media, (Wiley, 1988).
- J. Chilwell, I. Hodgkinson, "Thin-film field-transfer matrix theory of planar multilayer waveguides and reflection from prism-loaded waveguides," J. Opt. Soc. Am. A 1, 742-753 (1984) [CrossRef]
- J. Khurgin, "Improvement of frequency-conversion efficiency in waveguides with rotationally twinned layers," Opt. Lett, 13, 603-605 (1988). [CrossRef] [PubMed]
- S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, M. Calligaro, "Continuous-wave second-harmonic generation in modal phase matched semiconductor waveguides," Appl. Phys. Lett. 84,2974-2976 (2004). [CrossRef]
- P. Dong, A. G. Kirk, "Nonlinear frequency conversion in waveguide directional couplers," Phys. Rev. Lett. 93,133901 (2004). [CrossRef] [PubMed]
- N. Yokouchi, A. J. Danner, K. D. Choquette, "Two-dimensional photonic crystal confined vertical-cavity surface-emitting lasers," IEEE J. Sel. Top. Quantum Electron., 9, 1439-1447 (2003). [CrossRef]

## 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.