## Dual-wavelength micro-resonator combining photonic crystal membrane and Fabry-Perot cavity |

Optics Express, Vol. 19, Issue 16, pp. 15255-15264 (2011)

http://dx.doi.org/10.1364/OE.19.015255

Acrobat PDF (1273 KB)

### Abstract

We propose a novel system of dual-wavelength micro-cavity based on the coupling between a photonic crystal membrane (PCM); operating at the Γ- point of the Brillouin zone, with a Fabry-Perot vertical cavity (FP). The optical coupling, which can be adjusted by the overlap between both optical modes, leads to the generation of two hybrid modes separated by a frequency difference which can be tuned using micro-opto-electromechanical structures. The proposed dual-wavelength micro-cavity is attractive for application where dual-mode behaviour is desirable as dual-lasing, frequency conversion. An analytical model, numerical (FDTD) and transfer matrix method investigations are presented.

© 2011 OSA

## 1. Introduction

1. C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. **69**(23), 3314–3317 (1992). [CrossRef] [PubMed]

4. M. S. Skolnick, T. A. Fisher, and D. M. Whittaker, “Strong coupling phenomena in quantum microcavity structures,” Semicond. Sci. Technol. **13**(7), 645–669 (1998). [CrossRef]

5. B. Ben Bakir, Ch. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli, “Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. **88**(8), 081113 (2006). [CrossRef]

6. M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser,” Opt. Express **13**(8), 2869–2880 (2005). [CrossRef] [PubMed]

7. D. Gusev, I. Soboleva, M. Martemyanov, T. Dolgova, A. Fedyanin, and O. Aktsipetrov, “Enhanced second-harmonic generation in coupled microcavities based on all-silicon photonic crystals,” Phys. Rev. B **68**(23), 233303 (2003). [CrossRef]

8. F. Tanaka, T. Takahashi, K. Morita, T. Kitada, and T. Isu, “Strong sum frequency generation in a GaAs/AlAs coupled multilayer cavity grown on a (113)B-oriented GaAs substrate,” Jpn. J. Appl. Phys. **49**(4), 04DG01 (2010). [CrossRef]

*vertical*) direction by using a multi-layer to control the coupling between PCM resonant modes and free space modes [9

9. X. Letartre, J. Mouette, J. L. Leclercq, P. R. Romeo, C. Seassal, and P. Viktorovitch, “Switching devices with spatial and spectral resolution combining photonic crystal and MOEMS structures,” J. Lightwave Technol. **21**(7), 1691–1699 (2003). [CrossRef]

10. K. Kusiaku, X. Letartre, J. L. Leclercq, P. Rojo-Romeo, C. Seassal, and P. Viktorovitch, “Multi-resonant microresonators for optical frequency conversion,” Proc. SPIE **7728**, 77280K (2010). [CrossRef]

7. D. Gusev, I. Soboleva, M. Martemyanov, T. Dolgova, A. Fedyanin, and O. Aktsipetrov, “Enhanced second-harmonic generation in coupled microcavities based on all-silicon photonic crystals,” Phys. Rev. B **68**(23), 233303 (2003). [CrossRef]

8. F. Tanaka, T. Takahashi, K. Morita, T. Kitada, and T. Isu, “Strong sum frequency generation in a GaAs/AlAs coupled multilayer cavity grown on a (113)B-oriented GaAs substrate,” Jpn. J. Appl. Phys. **49**(4), 04DG01 (2010). [CrossRef]

11. R. P. Stanley, R. Houdré, U. Oesterle, M. Ilegems, and C. Weisbuch, “Coupled semiconductor microcavities,” Appl. Phys. Lett. **65**(16), 2093–2095 (1994). [CrossRef]

12. J. F. Carlin, R. P. Stanley, P. Pellandini, U. Oesterle, and M. Ilegems, “The dual wavelength bi-vertical cavity surface-emitting laser,” Appl. Phys. Lett. **75**(7), 908–910 (1999). [CrossRef]

13. K. S. Yee, “Numerical solutions of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. **14**(3), 302–307 (1966). [CrossRef]

9. X. Letartre, J. Mouette, J. L. Leclercq, P. R. Romeo, C. Seassal, and P. Viktorovitch, “Switching devices with spatial and spectral resolution combining photonic crystal and MOEMS structures,” J. Lightwave Technol. **21**(7), 1691–1699 (2003). [CrossRef]

## 2. Dual mode micro-cavity design

_{h}) membrane with a periodic lateral pattern formed by a 2-D lattice-of holes or a 1-D lattice of slits surrounded by a lower index (n

_{l}) material.

14. R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. **61**(9), 1022–1024 (1992). [CrossRef]

_{0}located at the Γ-point of the Brillouin zone above the light line. Such pseudo-guided resonant Bloch mode can interact with optical beams, normal to the PCM. If a resonant “vertical” FP cavity mode is provided at the same frequency f

_{0}, optical coupling can occur between both modes, leading to a splitting into two “new” resonant frequencies at f

_{1}and f

_{2}as illustrated in Fig. 2 . The coupling strength depends on the overlap between the FP and PCM mode field profiles. This phenomenon can be seen as a photon-photon “strong coupling” interaction, by analogy with the well-known atom-photon or exciton-photon ones (Rabi oscillations) [2

2. A. Armitage, M. S. Skolnick, V. N. Astratov, D. M. Whittaker, G. Panzarini, L. C. Andreani, T. A. Fisher, J. S. Roberts, A. V. Kavokin, M. A. Kaliteevski, and M. R. Vladimirova, “Optically induced splitting of bright excitonic states in coupled quantum microcavities,” Phys. Rev. B **57**(23), 14877–14881 (1998). [CrossRef]

3. G. Panzarini, L. Andreani, A. Armitage, D. Baxter, M. Skolnick, V. Astratov, J. Roberts, A. Kavokin, M. Vladimirova, and M. Kaliteevski, “Exciton-light coupling in single and coupled semiconductor microcavities: polariton dispersion and polarization splitting,” Phys. Rev. B **59**(7), 5082–5089 (1999). [CrossRef]

_{2}). In order to develop tunable dual-λ cavity, the lower index medium could be air gaps. In this latter case, electro-mechanical actuation can be used to tune the mode splitting Δf [9

9. X. Letartre, J. Mouette, J. L. Leclercq, P. R. Romeo, C. Seassal, and P. Viktorovitch, “Switching devices with spatial and spectral resolution combining photonic crystal and MOEMS structures,” J. Lightwave Technol. **21**(7), 1691–1699 (2003). [CrossRef]

## 3. Coupled mode theory modelling

_{0}(the PCM thickness) and optical index n

_{0}(the “mean” refractive index of the PCM) [9

**21**(7), 1691–1699 (2003). [CrossRef]

_{.}The proposed dual-wavelength micro-cavity is therefore equivalent to a resonator inserted in a FP cavity as showed in Fig. 1(b). We assume the PCM, thus the resonator, supports only one mode in the frequency range of interest. Using coupled mode theory [15

15. C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add–drop filters,” IEEE J. Quantum Electron. **35**(9), 1322–1331 (1999). [CrossRef]

*ω*is the resonant frequency of the PCM mode, 1/τ

_{0}_{c}its decay rate due to out of plane losses, 1/τ

_{0}a time constant accounting for any other type of optical losses (absorption, lateral losses). C

_{+i}(C

_{–i}) is the incoming (outgoing) wave as defined in Fig. 1(b). K = √1/τ

_{c}is the coupling factor and θ

_{1}(θ

_{2}) its dephasing associated with the forward (backward) propagating wave. Δθ = |θ

_{1}- θ

_{2}| is zero (π) for symmetric (anti-symmetric) PCM mode [9

**21**(7), 1691–1699 (2003). [CrossRef]

_{0}e

^{jωt}represents a monochromatic time dependent excitation source.

_{0}will be supposed negligible compared to 1/τ

_{c}. To give a physical insight, and for the sake of simplicity, we start by considering r(λ), the reflection coefficient of the two mirrors enclosing the FP cavity, real, positive and constant. The PCM is located at the mid-thickness of the FP cavity (d

_{1}= d

_{2}= d). The relation between the in-coming (C

_{+i}) and out-going (C

_{-i}) fields at the PCM resonator is therefore simply given by Eq. (2) as their dephasing is caused only by the round-trip propagation of the wave through the layer of thickness d

_{i}:Then, from Eqs. (1) and (2) and for symmetric PCM mode, the output signal amplitude spectrum is found to take form: Figure 3 features a s(λ) normalized spectrum of λ

_{0}and 1.5λ

_{0}optically thick cavities and a PCM resonator of Q

_{c}= 5000 quality factor. It demonstrates that coupling occurs only when the FP cavity thickness is an integer number of the resonance wavelength (pλ

_{0}). In this case C

_{i}and C

_{-i}constructively interfere at the centre of the cavity, resulting in an even FP mode profile with respect to the PCM middle plan. Conversely, for an anti-symmetric PCM mode scheme, we obtain dual-wavelength resonance only in the case of half-wavelength ((2p + 1/2)λ

_{0}) cavity. If we consider now a negative reflectivity, then the above observations are simply reversed between even and odd PCM mode schemes. These observations are consistent with the fact that the coupling strength is linked to the overlap integral between the FP and PCM field distributions.

_{0}optical length cavity and denote ω’ the new resonance frequencies. We assume that the photons lifetime in the resonator is much longer than their round- trip propagation time through the cavity FP alone, that is Q

_{c}= ω

_{0}τ

_{c}/2>>pπ. We finally presume r≈1 and ε = (ω’- ω

_{0})/ω

_{0}<<1. Hence, using the first order Taylor expansion of α, we derive from Eq. (3) the transmission maxima ω’(Eq. (4)). It shows that the transmission spectrum of the dual-λ cavity exhibits two symmetrically shifted peaks from ω

_{0}as expected. It demonstrates besides that Δω depends on both the FP field intensity at the center of the cavity (through p parameter) and on the PCM quality factor (Q

_{c}).It is worth noticing that the splitting Δω is only observable in the strong coupling regime i.e. when Δω/ω

_{0}≥ 1/Q

_{FP}, where Q

_{FP}= 2pπ/(1-R) is the FP cavity quality factor. Here R = r

^{2}denotes the intensity reflection coefficient of the FP mirror. Therefore, mirrors with higher reflectivity are required for smaller targeted splitting. Hence for a given PCM of quality factor Q

_{c}and a dual-λ cavity system of pλ optical thickness (Fig. 1), there is a minimum reflectivity value R

_{0}(Eq. (5)) for the mirrors (Fig. 1) to be met, below which a dual-λ output is impossible.At this step, we may distinguish two situations: Q

_{c}<Q

_{FP}and Q

_{c}>Q

_{FP}. In the first case, the splitting is still observable as the strong coupling regime condition (Eq. (5)) is always verified. In the second case, the strong coupling regime requires a minimum of reflectivity (R

_{0}) as defined in Eq. (5). For instance, for a cavity of optical thickness 2λ

_{0}and Q

_{c}= 5.10

^{3}, R

_{0}is thus equal to ~0.929. Figure 4 shows the output signal amplitude spectrum derived from Eq. (3) for different values of R, where a dual mode spectrum is obtained only with R≥R

_{0}.

_{1}(resp: λ

_{2}) the lower resonance wavelength(resp: the upper). Under condition given by Eq. (5), λ

_{1}and λ

_{2}, as well as their quality factor, variations are plotted in Fig. 5 as a function of the half-cavity thickness (d) and for Q

_{c}= 5.10

^{3}. It shows that Δλ = |λ

_{1}- λ

_{2}| reaches a minimum, namely the anti-crossing point, for λ

_{0}optically thick cavity.

_{FP}with only 2% shift of the cavity thickness from its anti-crossing value (Fig. 5). This configuration is an interesting way to reduce the out of plane losses of a PCM modes operating above the light line and has been previously exploited for low threshold vertical emitting laser [5

5. B. Ben Bakir, Ch. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli, “Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. **88**(8), 081113 (2006). [CrossRef]

_{0}. They can destroy the dual-λ behavior in the worst case (1/2πτ

_{0}>Δf), otherwise, the Q factor of both modes will be limited compared to an ideal structure. Besides, it is a matter of technology to realize such dual-λ cavity with controlled geometrical parameters as the period, the filling factor, the thickness of the PCM and its position in the cavity that determine the coupling condition.

## 4. Numerical validation

**21**(7), 1691–1699 (2003). [CrossRef]

^{−8}, are added at the top and bottom of the simulation domain along the vertical direction.

_{h}= 3.17) enclosed in a lower index material (n

_{l}= 1.45) corresponding respectively to an InP membrane and a silica cladding medium. The PCM thickness is h = 0.57µm, its period 0.95µm and the filling factor 50%. Figure 6 illustrates the wavelength-dependent reflectance feature for TE polarization (that is, the E-field vector is along the slits axis). The resonance wavelength is λ

_{0}= 1541.6 nm and the mode profile is symmetric with respect to the PCM middle plane (Fig. 6(b)). Using TMM-CMT method, we determine Q

_{c}as well as the mean refractive optical index of the PCM. We obtain Q

_{c}~4.10

^{4}with a mean refractive index n

_{0}~2.71. The PCM is thus a wavelength optically thick membrane. To fulfill the condition given by Eq. (5), we design a Bragg reflector composed of 4 quarter-wave stacks of n

_{1}= 1.45 and n

_{2}= 3.45 refractive index layers. For a plane wave at normal incidence, the intensity reflectivity is higher than 0.99 in the range [1.35µm - 1.97µm].

_{0}denotes the spacer thickness at the anti-crossing point. The splitting is in the range [0.4THz, 1.2THz]. The minimum frequency difference (Δf) is obtained for 2.5 λ

_{0}optically thick cavity at the anti-crossing point, with two modes (λ

_{1}= 1539.6 nm and λ

_{2}= 1542.9 nm) of same spectral purity (Q~8000).

_{0}) at the anti-crossing point, which is due to the approximations of the TMM-CMT method. Let us point out that the variations in FDTD simulation come from numerical fluctuations when computing the resonance wavelength and the corresponding Q factor. They mainly appear for high Q resonant modes because of a limited spectral resolution.

_{0}, are shown in Fig. 8 . They are clearly linear combinations of PCM and FP modes.

*artificial*” periodicity in the vertical direction. The structure is thus composed of periodic sequence of dual-λ cavities, separated by a sufficient amount of background (air) to avoid coupling between vertical adjacent structures, hence insuring modes localization in a single cavity. However, notice that this approach induces unfortunately not only bands folding but also the onset, in the band diagram, of some spurious modes, due to the artificial vertical periodicity. However, considerations about the symmetry and/or the field confinement allows for distinguishing the “real” modes of the dual-λ cavity.

_{g}(v

_{g}= ∂ω/∂k), which illustrates how the energy flows along the propagation direction. The larger curvature of the PCM mode dispersion characteristic curvature at point B, unlike at point A, results therefore in higher lateral escape rate of photons at the former point.

## 5. Conclusion

## Acknowledgments

## References and links

1. | C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. |

2. | A. Armitage, M. S. Skolnick, V. N. Astratov, D. M. Whittaker, G. Panzarini, L. C. Andreani, T. A. Fisher, J. S. Roberts, A. V. Kavokin, M. A. Kaliteevski, and M. R. Vladimirova, “Optically induced splitting of bright excitonic states in coupled quantum microcavities,” Phys. Rev. B |

3. | G. Panzarini, L. Andreani, A. Armitage, D. Baxter, M. Skolnick, V. Astratov, J. Roberts, A. Kavokin, M. Vladimirova, and M. Kaliteevski, “Exciton-light coupling in single and coupled semiconductor microcavities: polariton dispersion and polarization splitting,” Phys. Rev. B |

4. | M. S. Skolnick, T. A. Fisher, and D. M. Whittaker, “Strong coupling phenomena in quantum microcavity structures,” Semicond. Sci. Technol. |

5. | B. Ben Bakir, Ch. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli, “Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. |

6. | M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser,” Opt. Express |

7. | D. Gusev, I. Soboleva, M. Martemyanov, T. Dolgova, A. Fedyanin, and O. Aktsipetrov, “Enhanced second-harmonic generation in coupled microcavities based on all-silicon photonic crystals,” Phys. Rev. B |

8. | F. Tanaka, T. Takahashi, K. Morita, T. Kitada, and T. Isu, “Strong sum frequency generation in a GaAs/AlAs coupled multilayer cavity grown on a (113)B-oriented GaAs substrate,” Jpn. J. Appl. Phys. |

9. | X. Letartre, J. Mouette, J. L. Leclercq, P. R. Romeo, C. Seassal, and P. Viktorovitch, “Switching devices with spatial and spectral resolution combining photonic crystal and MOEMS structures,” J. Lightwave Technol. |

10. | K. Kusiaku, X. Letartre, J. L. Leclercq, P. Rojo-Romeo, C. Seassal, and P. Viktorovitch, “Multi-resonant microresonators for optical frequency conversion,” Proc. SPIE |

11. | R. P. Stanley, R. Houdré, U. Oesterle, M. Ilegems, and C. Weisbuch, “Coupled semiconductor microcavities,” Appl. Phys. Lett. |

12. | J. F. Carlin, R. P. Stanley, P. Pellandini, U. Oesterle, and M. Ilegems, “The dual wavelength bi-vertical cavity surface-emitting laser,” Appl. Phys. Lett. |

13. | K. S. Yee, “Numerical solutions of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. |

14. | R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. |

15. | C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add–drop filters,” IEEE J. Quantum Electron. |

**OCIS Codes**

(140.3945) Lasers and laser optics : Microcavities

(350.4238) Other areas of optics : Nanophotonics and photonic crystals

(230.7405) Optical devices : Wavelength conversion devices

**ToC Category:**

Photonic Crystals

**History**

Original Manuscript: June 3, 2011

Revised Manuscript: July 9, 2011

Manuscript Accepted: July 9, 2011

Published: July 25, 2011

**Citation**

Koku Kusiaku, Ounsi El Daif, Jean-Louis Leclercq, Pedro Rojo-Romeo, Christian Seassal, Pierre Viktorovitch, Taha Benyattou, and Xavier Letartre, "Dual-wavelength micro-resonator combining photonic crystal membrane and Fabry-Perot cavity," Opt. Express **19**, 15255-15264 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-16-15255

Sort: Year | Journal | Reset

### References

- C. Weisbuch, M. Nishioka, A. Ishikawa, and Y. Arakawa, “Observation of the coupled exciton-photon mode splitting in a semiconductor quantum microcavity,” Phys. Rev. Lett. 69(23), 3314–3317 (1992). [CrossRef] [PubMed]
- A. Armitage, M. S. Skolnick, V. N. Astratov, D. M. Whittaker, G. Panzarini, L. C. Andreani, T. A. Fisher, J. S. Roberts, A. V. Kavokin, M. A. Kaliteevski, and M. R. Vladimirova, “Optically induced splitting of bright excitonic states in coupled quantum microcavities,” Phys. Rev. B 57(23), 14877–14881 (1998). [CrossRef]
- G. Panzarini, L. Andreani, A. Armitage, D. Baxter, M. Skolnick, V. Astratov, J. Roberts, A. Kavokin, M. Vladimirova, and M. Kaliteevski, “Exciton-light coupling in single and coupled semiconductor microcavities: polariton dispersion and polarization splitting,” Phys. Rev. B 59(7), 5082–5089 (1999). [CrossRef]
- M. S. Skolnick, T. A. Fisher, and D. M. Whittaker, “Strong coupling phenomena in quantum microcavity structures,” Semicond. Sci. Technol. 13(7), 645–669 (1998). [CrossRef]
- B. Ben Bakir, Ch. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli, “Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. 88(8), 081113 (2006). [CrossRef]
- M. Yokoyama and S. Noda, “Finite-difference time-domain simulation of two-dimensional photonic crystal surface-emitting laser,” Opt. Express 13(8), 2869–2880 (2005). [CrossRef] [PubMed]
- D. Gusev, I. Soboleva, M. Martemyanov, T. Dolgova, A. Fedyanin, and O. Aktsipetrov, “Enhanced second-harmonic generation in coupled microcavities based on all-silicon photonic crystals,” Phys. Rev. B 68(23), 233303 (2003). [CrossRef]
- F. Tanaka, T. Takahashi, K. Morita, T. Kitada, and T. Isu, “Strong sum frequency generation in a GaAs/AlAs coupled multilayer cavity grown on a (113)B-oriented GaAs substrate,” Jpn. J. Appl. Phys. 49(4), 04DG01 (2010). [CrossRef]
- X. Letartre, J. Mouette, J. L. Leclercq, P. R. Romeo, C. Seassal, and P. Viktorovitch, “Switching devices with spatial and spectral resolution combining photonic crystal and MOEMS structures,” J. Lightwave Technol. 21(7), 1691–1699 (2003). [CrossRef]
- K. Kusiaku, X. Letartre, J. L. Leclercq, P. Rojo-Romeo, C. Seassal, and P. Viktorovitch, “Multi-resonant microresonators for optical frequency conversion,” Proc. SPIE 7728, 77280K (2010). [CrossRef]
- R. P. Stanley, R. Houdré, U. Oesterle, M. Ilegems, and C. Weisbuch, “Coupled semiconductor microcavities,” Appl. Phys. Lett. 65(16), 2093–2095 (1994). [CrossRef]
- J. F. Carlin, R. P. Stanley, P. Pellandini, U. Oesterle, and M. Ilegems, “The dual wavelength bi-vertical cavity surface-emitting laser,” Appl. Phys. Lett. 75(7), 908–910 (1999). [CrossRef]
- K. S. Yee, “Numerical solutions of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antenn. Propag. 14(3), 302–307 (1966). [CrossRef]
- R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992). [CrossRef]
- C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add–drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999). [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.