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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 19 — Sep. 17, 2007
  • pp: 12443–12449
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Ultimate vertical Fabry-Perot cavity based on single-layer photonic crystal mirrors

S. Boutami, B. Benbakir, X. Letartre, J.L. Leclercq, P. Regreny, and P. Viktorovitch  »View Author Affiliations


Optics Express, Vol. 15, Issue 19, pp. 12443-12449 (2007)
http://dx.doi.org/10.1364/OE.15.012443


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Abstract

Vertical Fabry Perot cavities (VFPC) have been extensively studied, especially for the realization of vertical-cavity surface emitting lasers (VCSELs). They are traditionally composed of two Distributed Bragg Reflectors (DBR) which reflectivity has to be sufficient in order to obtain highly resonant cavity, which is particularly necessary for laser emission in VCSELs. As a consequence, DBRs consist generally in very thick layer stacks. In this paper, we demonstrate the smallest conceivable high Q vertical Fabry-Perot cavity, using ultra-thin and highly-efficient photonic crystal slab mirrors instead of conventional DBRs, which enable moreover a control of the polarization.

© 2007 Optical Society of America

1. Introduction

VFPCs have been intensively developed because they offer several advantages such as small size, very directive output beam, and collective fabrication. They are generally composed of two semiconductor DBRs, which reflectivity and bandwidth for a given number of pairs depend on the index contrast between dielectric materials. Because of epitaxial growth constraints, the pairs of materials that can be used are limited, and refractive index contrasts obtained are generally very low [1

1. A. Karim, S. Björlin, J. Piprek, and J.E. Bowers, “Long-wavelength vertical-cavity lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 6, 1244–1253 (2000). [CrossRef]

5

5. A. Syrbu, A. Mircea, A. Mereuta, A. Caliman, C.A. Berseth, G. Suruceanu, V. Iakovlev, M. Achtenhagen, A. Rudra, and E. Kapon, “1.5-mW Single-Mode operation of wafer-fused 1550nm VCSELs,” IEEE Photon. Technol. Lett. 16, 1230–1232 (2004). [CrossRef]

]. For example, in the 1.55µm wavelength range, a DBR composed of InP/InGaAsP (index ratio 3,17/3,45) would require more than 50 pairs to provide a reflectivity of 99.9%, which results in a 12µm thick mirror, with a stop-band of 50nm.

A novel class of highly efficient and broadband mirrors have been recently proposed using single-layer high transverse-index contrast photonic crystal mirrors (PCM) [6

6. C.F.R. Mateus, M.C.Y. Huang, L. Chen, C.J. Chang-Hasnain, and Y. Suzuki, “Broadband mirror (1.12–1.62µm) using single-layer sub-wavelength grating,” IEEE Photon. Technol. Lett. 16, 1676–1678 (2004). [CrossRef]

9

9. A.E. Willner, “All mirrors are not created equal,” Nature Photon. 1, 87–88 (2007). [CrossRef]

]. These single-layer PCM are able to provide very efficient and broadband reflectivity with a very small thickness. Their operation differs from the usual operation of PC. Indeed, in most of photonic crystal (PC)-based devices, PCs are used in their photonic band-gap regime (microcavities) [10

10. E. Yablonovitch, “Inhibited spontaneous emission in solid - state physics and electronics,” Phys. Rev. Lett. E 58, 2059–2062 (1987). [CrossRef]

,11

11. E. Yablonovitch, T.J. Gmitter, and K.M. Leung, “Photonic bandgap structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295–2298 (1991). [CrossRef] [PubMed]

]. However, the virtue of PCs is not to provide only photonic band gaps, allowing efficient trapping of photons, but also photonic band edges with low curvature, which result in guided-mode with low group velocity. When excited above the light line, these slow Bloch modes suffer from out-coupling losses because of their coupling with radiated modes [12

12. Y. Ding and R. Magnusson, “Use of nondegenerate resonant leaky modes to fashion diverse optical spectra,” Opt. Express 12, 1885–1891 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-9-1885 [CrossRef] [PubMed]

]. This coupling, which appears as an important drawback for the development of Photonic Integrated Circuits (PICs) based on waveguiding PC structures, has however proved to be very useful for the realization of very efficient PCM layers [6

6. C.F.R. Mateus, M.C.Y. Huang, L. Chen, C.J. Chang-Hasnain, and Y. Suzuki, “Broadband mirror (1.12–1.62µm) using single-layer sub-wavelength grating,” IEEE Photon. Technol. Lett. 16, 1676–1678 (2004). [CrossRef]

8

8. S. Boutami, B. BenBakir, H. Hattori, X. Letartre, J.L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2D photonic crystal reflectors with controllable polarization dependence,” IEEE Photon. Technol. Lett. 18, 835–837 (2006). [CrossRef]

,12

12. Y. Ding and R. Magnusson, “Use of nondegenerate resonant leaky modes to fashion diverse optical spectra,” Opt. Express 12, 1885–1891 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-9-1885 [CrossRef] [PubMed]

]. In addition to vertical compactness, PCMs present additional assets, like the introduction of polarization effects in the optical response, depending on the type of lattice used [7

7. V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. Fan, “Angular and polarization properties of a photonic crystal slab mirror,” Opt. Express 12, 1575–1582 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-8-1575 [CrossRef] [PubMed]

,8

8. S. Boutami, B. BenBakir, H. Hattori, X. Letartre, J.L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2D photonic crystal reflectors with controllable polarization dependence,” IEEE Photon. Technol. Lett. 18, 835–837 (2006). [CrossRef]

].

Recently, it has been proposed a novel VCSEL at 850nm, composed of a bottom conventional DBR, and a hybrid top mirror associating a high-index contrast grating (HCG: one dimensional PCM) and a conventional DBR. The authors have shown that the use of the HCG allowed for a reduced total thickness of the top mirror [13

13. C.Y. Huang, Y. Zhou, and C.J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nature Photon. 1, 119–122 (2007). [CrossRef]

]. In our group, we have reported a more compact VCSEL at 1.55µm, combining a bottom conventional DBR with a top single-layer PCM, showing that the PCM could provide sufficient reflectivity for laser emission, without the assistance of a DBR [14

14. S. Boutami, B. Benbakir, P. Regreny, J.L. Leclercq, and P. Viktorovitch, “Compact 1.55 µm room-temperature optically pumped VCSEL using Photonic crystal mirror,” IEEE Electron. Lett. 43, 282–283 (2007). [CrossRef]

]. In this letter, we go further by demonstrating the smallest conceivable high-Q VFPC, in the 1.3–1.55µm. It consists in a half-wavelength thick air VFPC, embedded between two single-layer PCMs. It requires only three epitaxial layers (one for the cavity and two for both PCMs). The total epitaxial thickness is reduced by a factor of 50 compared to traditional DBR-based VFPC. Figure 1 shows a schematic of the designed PCM-based VFPC, compared with an equivalent conventional DBR-based VFPC.

Fig. 1. Schematic representation of (a) a DBR-based VFPC and (b) a PCM-based VFPC.

2. Design

The reflectivity resonances in PCMs arise from the coupling of external radiation to the Bloch guided modes in the structures, whenever there is a good matching between the in-plane component of the wave vector of the incident wave and the wave vector of the guided modes. Photons of the Bloch guided modes are then reemitted in phase with the incident wave, which leads to a reflection.

A specific feature of a PCM, compared to a DBR with a finite number of pairs, is that the reflectivity achieved at the PCM mode wavelength is 100%. However, this is true only for an infinite grating illuminated by a plane wave. In real devices, the lateral size of the illuminated area is limited, and the efficiency of the PCM is controlled by the lateral escape rate of the wave-guided mode out of the illuminated area, where it cannot interfere anymore with the incident beam. This escape rate can be considered as a loss mechanism for PCMs, and should therefore be minimized in order to obtain efficient PCMs with a limited lateral size. This is achieved by exploiting extremes of the dispersion characteristics of high index contrast PC, like the Γ-point (normal incidence), where the group velocity tends to zero [8

8. S. Boutami, B. BenBakir, H. Hattori, X. Letartre, J.L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2D photonic crystal reflectors with controllable polarization dependence,” IEEE Photon. Technol. Lett. 18, 835–837 (2006). [CrossRef]

]. A larger part of wave-guided photons can thus couple back to radiated mode before being laterally inserted into the membrane. We focused on InP/air -based PCs, since they are very attractive for the development of optical devices operating in the 1.3µm–1.55µm range, and they provide large index contrast (3,17/1).

Fig. 2. (a) RCWA calculations of the PCM reflectivity (h=250nm, a=1.10µm, f=65%) for normal incidence, as a function of wavelength, for TE and TM polarizations; (b) Dispersion curves around Γ of TE and TM modes of the crystal responsible for the reflection characteristics.

Fig. 3. Reflectivity of the PCM as a function of air filling factor and wavelength for (a) TE polarization and (b) TM polarization.

In order to evaluate the impact of the limited lateral size of the PCM on its efficiency, we performed 3D FDTD calculations of the PCM reflectivity for the TE2 mode of interest, as a function of the lateral size of the incident Gaussian beam (Fig. 4).

Fig. 4. Reflectivity of the 1D PCM for the TE2 mode, as a function of the lateral size of the incident beam (3D-FDTD simulations).

As expected, the efficiency of the PCM increases with the illuminated surface area. The lateral losses decrease, as a combined result of a decrease of the mean group velocity of waveguided photons (due to the reduction of the incident beam angular components around the Γ-point) and an increase of the interacting area between the wave-guided and the incident mode. The reflectivity can be as high as desired, provided that the illuminated surface area is sufficient. As an example, the PCM reflectivity is superior to 99.9% for a 10µm-wide illuminated area (Fig. 4).

For PCM-based VFPC, the Q-factor of the cavity mode is therefore given by the lateral size of PCMs.

3. Fabrication and characterization

The fabricated PCM-VFPC is based on an InP/InGaAs heterostructure, which consists of successive InP/InGaAs layers epitaxially grown on an InP substrate by MBE deposition technique. The InGaAs layers are meant to be sacrificial. The PCM has been fabricated using electron-beam lithography, and Reactive Ion Etching transfer. The air gap cavities have been achieved by wet selective chemical etching, followed by CO2 critical point drying technique [17

17. J.L. Leclercq, P. Rojo-Romeo, C. Seassal, J. Mouette, X. Letartre, and P. Viktorovitch, “3D structuring of multilayer suspended membranes including 2D photonic crystal structures,” J. Vac. Sci. Technol. B 21, 2903–2906 (2003).

]. The sidewall angle of the RIE etching is 86.5°. Therefore, the air filling factors of the top and bottom PCM are respectively 70% and 60%, which is suitable regarding the simulation tolerances (from 55% to 75%). Figure 5 shows the scanning electron microscope (SEM) top views of the fabricated VFPC structure. The lateral size of PCMs is 30µm

Fig. 5. SEM views of the fabricated PCM-based VFPC

The reflectance of the structure was characterized using an incident beam provided by a monomode fiber coupled to the device using a lens collimator (waist diameter of 10µm). The excitation light was provided by a large band light source combining superluminescent light emitting diodes and an erbium-doped fiber amplifier. This source was connected to the collimator through a 50/50 directional coupler, followed by a polarizer and a section of polarization maintaining fiber. The reflected beam was collected back by the collimator, separated on the directional coupler, and analyzed by a spectrum analyzer.

Experimental characterizations for TE polarization, shown in Fig. 6(a), exhibit two resonant modes around 1,375 µm. They correspond to different Fabry-Perot lateral orders, due to the finite size of the device. The fundamental mode is on the longer wavelength side (lower energy).

Quality factor of the resonance as high as 3000 has been achieved (FWHM≅0.45nm around 1.4um) for the fundamental mode. Given the large lateral size of PCMs (30µm), the Q-factor of the intrinsic cavity mode excited by the incident probe beam should be up to 30 000, as predicted by FDTD calculations for perfectly identical PCMs. The difference between theoretical and experimental Q-factor is due to the different filling factors between the top and bottom PCMs, which results in a slight spectral shift of the TE2 mode between the mirrors. At the FP resonant wavelength, PCMs reflectivities can therefore not be both optimal. The experimental Q-factor of 3000 has been confirmed by FDTD calculations performed with the parameters of the fabricated structure.

For TM polarization, the resonant wavelength is be located around 1.32µm, due to a slight phase shift at the reflection on the PCM for this polarization. As the PCMs TM reflectivity at this wavelength is very low (Fig. 3(b)), the resonance observed for this polarization is therefore very weak (Fig. 6(b)).

Fig. 6. Experimental reflectivity spectrum of the PCM-based VFPC for (a) TE polarization and (b) TM polarization

4. Conclusion

We have demonstrated the most compact high-Q VFPC realized ever, combining two single-layer PCMs. The experimental Q-factor of resonance is 3000, for a 30 µm-wide structure. It could be raised to 30 000 if improving the fabrication process. Moreover, as has been explained in this paper, there is no theoretical limit for improving the selectivity of the cavity. Indeed, by increasing the lateral size of the device, one can increase the PCM reflectivity, thus the quality factor of the resonance, while keeping the same vertical compactness.

Experimental characterizations have shown a shorter wavelength lateral order mode, due to the finite size of the device. The mode spacing between the fundamental and the first order mode is inversely proportional to the lateral size of the device. Increasing this lateral size, for achieving better PCM reflectivity and thus better Q-factor, would bring closer these two modes. This can be one drawback of PCM-VFPC, especially for filters or VCSELs applications. One way to overcome this problem could be to gradually modify the lateral filling factors of PCM, in order to confine the PCM band edge Bloch mode by Photonic bandgap [18

18. F. Bordas, M.J. Steel, C. Seassal, and A. Rahmani, “Confinement of band-edge modes in a photonic crystal slab,” Opt. Express (to be published). [PubMed]

]. One could so achieve laterally compact VFPC with high Q-factor and large lateral modes spacing.

Besides, it has also been shown that the use of PCMs enable polarization sensitivity. Experimental characterizations have shown a high-Q resonance only for TE polarization. A single PCM layer can behave as a mirror and a polarizer in the same time. However, polarization free VFPCs can also be obtained, using 2D photonic crystals for example [7.8]. PCMs can thus provide considerable benefits for the realization of ultra-compact and polarization controlled surface-normal devices, such as filters, detectors, LEDs, or VCSELs. They can in principle be extended to any operation wavelength, by applying a scale factor to the geometrical dimensions of the crystals, provided that materials absorption remains low.

Moreover, a very interesting and original feature of PCM-based VFPCs lies in the fact that the resonant mode is a hybrid mode which is partly radiated (into the air-cavity) and partly guided (into the PCMs). The guided component of the resonant mode allows potentially a coupling of the energy from PCMs to conventional ridge waveguides, enabling thus a 3-dimensional selective optical communication between two levels. This device can therefore be considered also as a key component in the prospect of future multi-level planar Photonic Integrated Circuits.

Acknowledgments

This work was partly developed into the frame of 6th PCRD “ePiXnet” European network of excellence. The authors would like to thank Dr. P. Regreny at INL for providing MBE heterostructures.

References and links

1.

A. Karim, S. Björlin, J. Piprek, and J.E. Bowers, “Long-wavelength vertical-cavity lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 6, 1244–1253 (2000). [CrossRef]

2.

S. Nakagawa, E. Hall, G. Almuneau, J.K. Kim, D.A. Buell, H. Kroemer, and L.A. Coldren, “1.55µm InP lattice matched VCSELs with AlGaAsSb-AlAsSb DBRs,” IEEE J. Sel.Top. Quantum Electron. 7, 224–230 (2001). [CrossRef]

3.

M. Ortsiefer, S. Baydar, K. Windhorn, G. Böhm, J. Rosskopf, R. Shau, E. Rönneberg, W. Hofmann, and M.C. Amann, “2.5-mW Single-Mode Operation of 1.55µm buried Tunnel Junction VCSELs,” IEEE Photon. Technol. Lett. 17, 1596–1598 (2005). [CrossRef]

4.

J. Boucart, R. Pathak, D. Zhang, M. Beaudoin, P. Kner, D. Sun, R.J. Stone, R.F. Nabiev, and W. Yuen, “Long wavelength MEMS tunable VCSEL with InP-InAlGaAs bottom DBR,” IEEE Photon. Technol. Lett. 15, 1186–1188 (2003). [CrossRef]

5.

A. Syrbu, A. Mircea, A. Mereuta, A. Caliman, C.A. Berseth, G. Suruceanu, V. Iakovlev, M. Achtenhagen, A. Rudra, and E. Kapon, “1.5-mW Single-Mode operation of wafer-fused 1550nm VCSELs,” IEEE Photon. Technol. Lett. 16, 1230–1232 (2004). [CrossRef]

6.

C.F.R. Mateus, M.C.Y. Huang, L. Chen, C.J. Chang-Hasnain, and Y. Suzuki, “Broadband mirror (1.12–1.62µm) using single-layer sub-wavelength grating,” IEEE Photon. Technol. Lett. 16, 1676–1678 (2004). [CrossRef]

7.

V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, and S. Fan, “Angular and polarization properties of a photonic crystal slab mirror,” Opt. Express 12, 1575–1582 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-8-1575 [CrossRef] [PubMed]

8.

S. Boutami, B. BenBakir, H. Hattori, X. Letartre, J.L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, “Broadband and compact 2D photonic crystal reflectors with controllable polarization dependence,” IEEE Photon. Technol. Lett. 18, 835–837 (2006). [CrossRef]

9.

A.E. Willner, “All mirrors are not created equal,” Nature Photon. 1, 87–88 (2007). [CrossRef]

10.

E. Yablonovitch, “Inhibited spontaneous emission in solid - state physics and electronics,” Phys. Rev. Lett. E 58, 2059–2062 (1987). [CrossRef]

11.

E. Yablonovitch, T.J. Gmitter, and K.M. Leung, “Photonic bandgap structure: the face-centered-cubic case employing nonspherical atoms,” Phys. Rev. Lett. 67, 2295–2298 (1991). [CrossRef] [PubMed]

12.

Y. Ding and R. Magnusson, “Use of nondegenerate resonant leaky modes to fashion diverse optical spectra,” Opt. Express 12, 1885–1891 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-9-1885 [CrossRef] [PubMed]

13.

C.Y. Huang, Y. Zhou, and C.J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nature Photon. 1, 119–122 (2007). [CrossRef]

14.

S. Boutami, B. Benbakir, P. Regreny, J.L. Leclercq, and P. Viktorovitch, “Compact 1.55 µm room-temperature optically pumped VCSEL using Photonic crystal mirror,” IEEE Electron. Lett. 43, 282–283 (2007). [CrossRef]

15.

S. Boutami, B. Benbakir, X. Letartre, J.L. Leclercq, P. Rojo-Romeo, M. Garrigues, P. Viktorovitch, I. Sagnes, L. Legratiet, and M. Strassner, “Highly selective and compact tunable Fabry-Perot filter associating photonic crystal and MOEMS,” Opt. Express 14, 3129–3137 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-8-3129 [CrossRef] [PubMed]

16.

M. G. Moharam and T.K. Gaylord, “Rigorous coupled-wave analysis of planar grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981). [CrossRef]

17.

J.L. Leclercq, P. Rojo-Romeo, C. Seassal, J. Mouette, X. Letartre, and P. Viktorovitch, “3D structuring of multilayer suspended membranes including 2D photonic crystal structures,” J. Vac. Sci. Technol. B 21, 2903–2906 (2003).

18.

F. Bordas, M.J. Steel, C. Seassal, and A. Rahmani, “Confinement of band-edge modes in a photonic crystal slab,” Opt. Express (to be published). [PubMed]

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(050.2230) Diffraction and gratings : Fabry-Perot
(130.3120) Integrated optics : Integrated optics devices
(220.4000) Optical design and fabrication : Microstructure fabrication
(250.5300) Optoelectronics : Photonic integrated circuits

ToC Category:
Integrated Optics

History
Original Manuscript: May 30, 2007
Revised Manuscript: July 19, 2007
Manuscript Accepted: July 20, 2007
Published: September 14, 2007

Citation
S. Boutami, B. Benbakir, X. Letartre, J. L. Leclercq, P. Regreny, and P. Viktorovitch, "Ultimate vertical Fabry-Perot cavity based on single-layer photonic crystal mirrors," Opt. Express 15, 12443-12449 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-19-12443


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References

  1. A. Karim, S. Björlin, J. Piprek, J.E. Bowers, "Long-wavelength vertical-cavity lasers and amplifiers," IEEE J. Sel. Top. Quantum Electron. 6, 1244-1253 (2000).Q1 [CrossRef]
  2. S. Nakagawa, E. Hall, G. Almuneau, J.K. Kim, D.A. Buell, H. Kroemer, L.A. Coldren, "1.55µm InP lattice matched VCSELs with AlGaAsSb-AlAsSb DBRs," IEEE J. Sel. Top. Quantum Electron. 7, 224-230 (2001).Q2 [CrossRef]
  3. M. Ortsiefer, S. Baydar, K. Windhorn, G. Böhm, J. Rosskopf, R. Shau, E. Rönneberg, W. Hofmann, M.C. Amann, "2.5-mW Single-Mode Operation of 1.55µm buried Tunnel Junction VCSELs," IEEE Photon. Technol. Lett. 17, 1596-1598 (2005). [CrossRef]
  4. J. Boucart, R. Pathak, D. Zhang, M. Beaudoin, P. Kner, D. Sun, R.J. Stone, R.F. Nabiev, W. Yuen, "Long wavelength MEMS tunable VCSEL with InP-InAlGaAs bottom DBR," IEEE Photon. Technol. Lett. 15, 1186-1188 (2003). [CrossRef]
  5. A. Syrbu, A. Mircea, A. Mereuta, A. Caliman, C.A. Berseth, G. Suruceanu, V. Iakovlev, M. Achtenhagen, A. Rudra, E. Kapon, "1.5-mW Single-Mode operation of wafer-fused 1550nm VCSELs," IEEE Photon. Technol. Lett. 16, 1230-1232 (2004). [CrossRef]
  6. C.F.R. Mateus, M.C.Y. Huang, L. Chen, C.J. Chang-Hasnain, Y. Suzuki, "Broadband mirror (1.12-1.62μm) using single-layer sub-wavelength grating," IEEE Photon. Technol. Lett. 16, 1676-1678 (2004). [CrossRef]
  7. V. Lousse, W. Suh, O. Kilic, S. Kim, O. Solgaard, S. Fan, "Angular and polarization properties of a photonic crystal slab mirror," Opt. Express 12, 1575-1582 (2004). http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-8-1575 [CrossRef] [PubMed]
  8. S. Boutami, B. BenBakir, H. Hattori, X. Letartre, J.L. Leclercq, P. Rojo-Romeo, M. Garrigues, C. Seassal, P. Viktorovitch, "Broadband and compact 2D photonic crystal reflectors with controllable polarization dependence," IEEE Photon. Technol. Lett. 18, 835-837 (2006). [CrossRef]
  9. A.E. Willner, "All mirrors are not created equal," Nature Photon. 1,87-88 (2007).Q3 [CrossRef]
  10. E. Yablonovitch, "Inhibited spontaneous emission in solid - state physics and electronics," Phys. Rev. Lett. E 58, 2059-2062 (1987).Q4 [CrossRef]
  11. E. Yablonovitch, T.J. Gmitter, K.M. Leung, "Photonic bandgap structure: the face-centered-cubic case employing nonspherical atoms," Phys. Rev. Lett. 67, 2295-2298 (1991). [CrossRef] [PubMed]
  12. Y. Ding, R. Magnusson, "Use of nondegenerate resonant leaky modes to fashion diverse optical spectra," Opt. Express 12, 1885-1891 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-9-1885 [CrossRef] [PubMed]
  13. C.Y. Huang, Y. Zhou, C.J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nature Photon. 1, 119-122 (2007).Q5 [CrossRef]
  14. S. Boutami, B. Benbakir, P. Regreny, J.L. Leclercq, P. Viktorovitch, "Compact 1.55 µm room-temperature optically pumped VCSEL using Photonic crystal mirror," IEEE Electron. Lett. 43, 282-283 (2007).Q6 [CrossRef]
  15. S. Boutami, B. Benbakir, X. Letartre, J.L. Leclercq, P. Rojo-Romeo, M. Garrigues, P. Viktorovitch, I. Sagnes, L. Legratiet, M. Strassner, "Highly selective and compact tunable Fabry-Perot filter associating photonic crystal and MOEMS," Opt. Express 14, 3129-3137 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-8-3129 [CrossRef] [PubMed]
  16. M. G. Moharam, T.K. Gaylord, "Rigorous coupled-wave analysis of planar grating diffraction," J. Opt. Soc. Am. 71, 811-818 (1981). [CrossRef]
  17. J.L. Leclercq, P. Rojo-Romeo, C. Seassal, J. Mouette, X. Letartre, P. Viktorovitch, "3D structuring of multilayer suspended membranes including 2D photonic crystal structures," J. Vac. Sci. Technol. B 21, 2903-2906 (2003).
  18. F. Bordas, M.J. Steel, C. Seassal, A. Rahmani, "Confinement of band-edge modes in a photonic crystal slab," Opt. Express (to be published). [PubMed]

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