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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 15 — Jul. 28, 2003
  • pp: 1799–1808
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Analysis of hybrid photonic crystal vertical cavity surface emitting lasers

Haroldo T. Hattori, Xavier Letartre, Christian Seassal, Pedro Rojo-Romeo, Jean L. Leclercq, and Pierre Viktorovitch  »View Author Affiliations


Optics Express, Vol. 11, Issue 15, pp. 1799-1808 (2003)
http://dx.doi.org/10.1364/OE.11.001799


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Abstract

Vertical resonators with a top mirror constituted of 1D photonic crystal membrane on top of a Bragg stack are investigated in this paper. These structures allow the fabrication of compact vertical-cavity surface-emitting lasers, which can be designed, in addition, for in-plane emission. With this hybrid approach, fabrication problems related to both classical VCSEL and Photonic Crystal lasers may be significantly relaxed, given that a full Bragg stack is replaced by a single photonic crystal membrane and that the Photonic Crystal is not formed in the active gain layer.

© 2003 Optical Society of America

1. Introduction

We have recently proposed [7

7. X. Letartre, J. Mouette, J. L. Leclercq, P. Rojo-Romeo, C. Seassal, and P. Viktorovitch, “Switching devices with spatial and spectral resolution combining photonic crystal and MOEMS structures,” J. Light. Technol. (to be published).

] a major extension of planar technology through exploitation of the third (‘vertical’) dimension by using a multi-layered approach, where the lateral high index contrast patterning of layers could be combined with the vertical 1D high index contrast patterning: it is here more appropriate to think in terms of ‘2.5 dimensional’ photonic structures in which an interplay between guided confined photons and photons propagating through the planar layer structure occurs. A simple illustration of this approach is the use of a plain Photonic Crystal Membrane (PCM) as a wavelength selective transmitter / reflector: when light is shined on a PCM in an out-of-plane (normal or oblique) direction, sharp resonances in the reflectivity spectrum can be observed [8

8. V. N. Astratov, I. S. Culshaw, R. M. Stevenson, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Resonant coupling of near-infrared radiation to photonic band structure waveguides,” J. Light. Technol. 17, 2050–2057 (1999). [CrossRef]

]. These resonances arise from the coupling of external radiation to the 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. More recently, Pottage et al. [9

9. J. M. Pottage, E. Silvestre, and P. St. J. Russell, “Vertical-cavity surface emitting resonances in photonic crystals,” J. Opt. Soc. Am. A 18, 442–447 (2001). [CrossRef]

] have shown that photonic crystal membranes can exhibit vertical resonances in its reflectivity spectrum. Tibuleac and co-workers [10

10. S. Tibuleac and R. Magnusson, “Diffractive narrow-band transmission filter based on guided-mode resonance effects in thin-film multilayers,” IEEE Photon. Technol. Lett. 9, 464–466 (1997). [CrossRef]

] have proposed an accurate description of the optical behavior of dielectric multi-layered structures with infinite lateral size, under normal incidence, with some of the dielectric layers being patterned laterally, thus forming a one dimensional (1D) diffraction grating. Very recently, Sooh and co-workers [11

11. W. Sooh, M. F. Yannick, O. Solgaard, and S. Fan, “Displacement sensitive photonic crystal structures based on guided resonance in photonic crystal,” Appl. Phys. Lett. 82, 1999–2001 (2003). [CrossRef]

] have proposed a theoretical study of two suspended and tunable 2D PCM with infinite lateral size, to be used for various types of micro-mechanically tunable optical devices. In our above mentioned contribution [7

7. X. Letartre, J. Mouette, J. L. Leclercq, P. Rojo-Romeo, C. Seassal, and P. Viktorovitch, “Switching devices with spatial and spectral resolution combining photonic crystal and MOEMS structures,” J. Light. Technol. (to be published).

], we have analyzed the effect of the limited lateral size of the device and proposed a simple modeling approach derived from the coupled mode theory [12

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

,13

13. A. Yariv, Optical Electronics in Modern Communications (Oxford, New York, NY1997).

] and based on the transfer matrix method (TMM), allowing a very fast simulation of the reflectivity / transmission spectral characteristics of any stack of photonic crystal slabs: it was demonstrated that the optical characteristics are, to a large extent, controlled by the coupling rate (time constant τc) of guided and radiated modes through the periodic corrugation and by the in-plane lateral escape rate (time constant τg) of the guided photons out of the corrugated membrane illuminated area; in particular, the lateral escape of photons should be considered as a loss mechanism in devices specifically designed for “vertical” operation. The reflectivity bandwith (Δωp) of the PCM alone is approximately given by Δωp=1/τc+1/τg. The ability of high index contrast PC to slow down photons, allows a very good control over the lateral escape losses and results in very compact devices: this is achieved especially at high symmetry points (or extreme points) of the dispersion characteristics, where the group velocity approaches zero and guided modes are stationary; we showed that, in these conditions, the relevant parameter is the second derivative at the extreme point, which should be made the smallest possible, for the most efficient lateral confinement of guided modes interacting with radiated modes.

2. Design of the vertical patterning of the multi-layered structure

The basic structure is illustrated in Fig. 1. For the PCM, we choose an optical thickness which is an integer N of half of its resonant wavelength (λp) corresponding to the coupling between radiated modes and the PCM under normal incidence (λp is defined when the PCM is immersed in air, without the rest of the laser structure). In these conditions, the PCM behaves like a reflector whose spectral response exhibits a Gaussian shape, with a frequency bandwidth on the order of 1/τc, when lateral losses are negligible. For the rest of the paper N=2 : this choice will be justified later when further details of the PCM design are provided. The Bragg stack is constituted of four pairs of quarter wavelength air/semiconductor layers. The intermediate section in between the PCM and Bragg stack includes an air gap and a semiconductor active layer, which is meant to host the gain material (e.g., quantum heterostructures such as quantum wells, dots, etc.).

Fig. 1. Basic laser structure

TMM is now used to complete the design of the vertical patterning of the device, which does not include yet any gain material in the active layer : for that purpose the transmission spectrum of the structure is determined as shown in [7

7. X. Letartre, J. Mouette, J. L. Leclercq, P. Rojo-Romeo, C. Seassal, and P. Viktorovitch, “Switching devices with spatial and spectral resolution combining photonic crystal and MOEMS structures,” J. Light. Technol. (to be published).

], and, in addition, the field distribution of the “vertical” radiated modes can be obtained for each wavelength. The material in the semiconductor layers is assumed to be Indium Phosphide (InP). In all cases, light is incident from the semiconductor substrate, which is assumed to be infinite for calculation purposes. The design aims at obtaining a strong “vertical” resonance, i.e., a strong build-up of vertical radiated photons. This is achieved at, or close to, the resonance wavelength λp of the PCM and corresponds to phase conditions for constructive vertical interference. Also, the structure should be defined in such a way that the electric field is maximized in the active region, for an efficient operation of the laser. Based on these criteria, a maximum photon build-up, for the simple case where lateral losses are negligible, can be obtained when the operation wavelength λ coincides with λp and for h 2=3λp/4 (or also λp/4 : we have chosen a three quarters wave thickness for h 2 in order to prevent any significant evanescent coupling of the gain material into the resonant guided modes in the PCM) and nInPh3=λp/2, where nInP is the refractive index of InP. τC is assumed to be, for example, 0.3 ps (2πτcc/λp=Qc≅365, c is the speed of light in free space): this choice corresponds to a reflectivity bandwidth for the PCM (Δωp) significantly larger than the bandwidth of the resonance of the laser structure (Δωr). In the spectral response of the phase of the reflected field, it is observed a fast variation of phase near resonance. Based on the spectral width of this phase change, it is possible to estimate the bandwidth of resonance, Δωr. The resonance lifetime is then defined as τr=1/Δωr. An extra index ‘o’ is added to τr, to indicate the maximum value of τr, situation that occurs when the PCM presents no losses (in this case, τr=τro). The vertical field distribution in the laser structure is shown in Fig. 2(a) at resonance (in this case, the resonance wavelength of the laser structure (λr) coincides with λp). The field in the active membrane is strongly enhanced (factor 300) within respect to the incident field in the substrate: this enhancement corresponds to a quality factor Qro of the resonance in the order of 1.2×106, which gives τro=1 ns (2πτroc/λp=Qro). No transmission of photons is possible across the structure at and around the resonance : this results from the fact that the PCM behaves like a perfect reflector for λ=λp (in absence of lateral losses); in these specific conditions, the lifetime of the resonance τro is essentially controlled by the escape rate of photons across the Bragg stack. If the air gap is slightly de-tuned (2% decrease in the air gap thickness), a resonance is still observed, but λr is shifted toward a neighboring wavelength which meets vertical phase matching conditions; the PCM does not behave anymore as a perfect reflector, and transmission of photons is now allowed across the structure at and around the resonance, as shown in Fig. 2(b). The lifetime of the resonance is reduced since photons can also escape across the PCM: this results, accordingly, in a reduction of the field in the active layer at the operation wavelength corresponding to the shifted resonant wavelength.

Coming back to the case of a tuned structure (that is for h 2=3λp/4), we examine now the impact of the lateral losses. It is illustrated in Fig. 3(a) where the field in the active layer is plotted versus the lateral escape time in the PCM, τg. It is observed that if τg<τro, the field decreases sharply; this is expected since the lifetime of the resonance τr coincides now withτg, and the lateral losses in the PCM prevent the build-up of photons fed into the active layer across the Bragg stack. A plot of τr versus τg is presented in Fig. 3(b). For low values of τg (less than 80 ps), it is noticed that τrτg. Further increasing τg (implying reduction of lateral losses), makesτr slowly converge to τro, case in which the linewidth of the structure is limited by losses in the Bragg layers.

Fig. 2. Electric field distribution (based upon TMM) at resonance for no lateral losses. In case (a), h 2=3λp/4 and in (b), h 2=2.94λp/4.

One has to remark that TMM should be considered as a preliminary design tool for the final laser structure, which cannot be fully described at this stage of the design procedure. In an actual laser device, light is generated internally and, in case of quantum heterostructures, the radiation pattern is quite different from a plane wave : in any case, for example, the electric field distribution provided by TMM cannot be considered as the actual field distribution in the laser device. However, TMM has given a fast access to vertical patterning of the structure and provided preliminary basic information about how the electric field will build up in the active layer (information which can be used to determine the optimum position of the quantum well, wire or dot gain material) and, importantly, on key factors which control the lifetime of the resonance in the multi-layered structure: these factors can be summarized in terms of the escape rates of photons (vertical radiated modes) across the Bragg stack and PCM reflector and the lateral losses of guided modes in the PCM escaping out from the beam area before having a chance to be coupled back to the radiated vertical modes.

3. Design of the PCM

Fig. 3. Electric field in the active layer (based upon TMM) at resonance versus lateral escape time(a). Resonance lifetime as a function of lateral escape time (b).

Without loss of generality, our analysis is restricted to one dimensional Photonic Crystals: this is motivated by the need of relaxing simulation and modeling constraints. Moreover, the principal conclusions can be derived from this simpler case. In this case, it is assumed that the structure is infinite in the y direction, leading to no significant variation of the electromagnetic fields in this direction [13

13. A. Yariv, Optical Electronics in Modern Communications (Oxford, New York, NY1997).

]. Therefore, two dimensional finite-difference time-domain method (2D FDTD) can be used to analyze this structure, which is far less time consuming than 3D FDTD. The initial design of the PCM is based upon FDTD analysis.

In the PCM design, three parameters need to be defined: the lattice constant (Λ), the filling factor (FF) and the PCM thickness (h 1). In order to begin with the PCM design, Λ is “arbitrarily” set to 1 µm; this initial value will be modified later when the whole designed structure will be re-scaled to operate at λ=1550 nm. The lateral size of the PCM structure is set to about 30 µm, in such a way that it includes several grating periods in the x direction. Absorbing layers are placed at the boundaries of the computation area in the FDTD simulation and the membrane is embedded in air (without the rest of the laser structure). The source is a Gaussian waveform with spot size diameter (D) of about 20 µm. Line detectors are placed behind and in front of the PCM in order to evaluate its reflectivity and transmission. Whenever spectral information is necessary (for example, to calculate the reflectivity spectrum of the PCM), the temporal variation of the source is made Gaussian, otherwise it is assumed to be sinusoidal. Several PCMs are analyzed with different filling factors (FF).

For a given FF, the effect of h 1 is investigated. Starting from a small initial value, h 1 is increased systematically in FDTD analysis. The reflectivity spectrum of the PCM changes from a Fano shape to a Gaussian shape (for a half wavelength optical thickness in an effective index approximation). Further increasing the thickness, it changes again into a Fano shape and later on back to a Gaussian shape. At this point, the PCM has an effective full wavelength optical thickness. This procedure to determine h 1 is repeated for different filling factors. The aim is to choose parameters in such a way that the PCM’s reflectivity peak is maximized. In order to provide a better understanding of the designed structures, band diagrams are generated by MIT’s photonic bands software [14

14. S. G. Johnson and J. D. Joannopoulos, “Bloch-iterative frequency domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173 (2000), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173. [CrossRef]

]. Based upon band diagrams, we can observe that the second derivative at Γ point is quite low for FF=50% and even lower for FF=60%. However, FF=50% provides higher reflectivity than FF=60%, as revealed by FDTD analysis. That is due to the fact that although for FF=60%, the guided waves in the PCM look to be more stationary, the coupling of energy to these modes is worse, which leads to lower reflectivity. Therefore, FF=50% is chosen for the final design. Its band diagram is illustrated in Fig. 4(a), where the Γ point corresponds to a wave vector k=0, while the X point orresponds to a wave vector k=πâx, with âx being the unit vector in the x direction. In this band diagram, mode 1 is chosen because it provides the largest reflectivity, while mode 2 cannot couple efficiently with the incoming vertical waves. After choosing a filling factor of 50%, the whole structure is re-scaled for operation close to λ=1550 nm, in this case, the period (Λ) and the thickness (h 1) are set to 1200 nm and 670 nm, respectively. For the final designed structure, the peak reflectivity is greater than 97% and the linewidth Δλ is about 80 nm, as illustrated in Fig. 4(b). Based upon the reflectivity spectrum, we obtain τc=0.016 ps (Qc≈19.6) and, based upon the band diagram, we obtain τg=2.2 ps (τg≈D2/4α and Qg=2πτgc/λr≈2700) clearly demonstrating that τcτg for a good operation of this surface emitting device. Using these parameters, we have obtained (using TMM) the field distribution at resonance in the multi-layered structure, as shown in Fig. 4(c): the buildup of photons in PCM is clearly observed.

4. FDTD simulations of the multi-layered laser structures.

Absorbing boundary layers are placed in the boundaries of the computation area of the FDTD simulation. A point detector is positioned close to the upper edge of the air gap (in respect to z direction) and in the middle of the structure within respect to x axis. In order to obtain the spectrum of the radiated light, a Gaussian temporal pulse is emitted by this source and by using fast-Fourier transform algorithms it is possible to analyze the spectral behavior of the structure.

Fig. 4. Band diagram (a) and reflectivity spectrum (b) for the designed PCM. Electric field distribution, at resonance, for the laser structure (c).

Fig. 5. Electric field spectrum at a point in the air gap (a). Electric field distribution at resonance for h 2=3λp/4(b).

For the “perfectly” tuned device, both Bragg reflector and PCM are strongly reflective and, in an ideal situation, would not allow photons to be radiated to free space. However, due to finite losses of the PCM, some photons are allowed to be radiated to free space while others escape laterally. In this case, as the lateral escape time is small compared with the vertical one, photons can reach the edges of the PCM and be partially reflected back. The main peak in the electric field spectrum represents the fundamental lateral mode in the PCM. This perfectly tuned situation is the most favorable for in-plane emission, since it is difficult to emit light vertically and the easiest way for photons to escape laterally.

In order to make the device to further emit light vertically, two options are possible: first, the Bragg reflectivity can be made smaller, to the extent where the escape rate across it becomes larger than the lateral escape of photons in the PCM; second, keeping the Bragg reflector unchanged, the device can be slightly de-tuned as explained in the TMM section, thus reducing the reflectivity of the PCM (while shifting the resonance wavelength for phase matching requirements) and promoting further escaping of photons in the vertical direction across the PCM reflector at the expense of lateral insertion. This can be achieved by moving, via electrostatic actuation, judiciously chosen semiconductor layers of the multi-layered structures (either within the Bragg stack to reduce its reflectivity for the first option, or in the region where the vertical field is strong, for the second option). Figure 6(a) shows the spectrum for the case in which the air gap is reduced by 2%. The resonant peak (λr) is shifted to 1527 nm and the quality factor (Qr) is reduced to 1500. Fig. 6(b) shows the electric field distribution in the laser structure, at resonance, for cw excitation. It can be noticed that, although the field enhancement in the laser device has decreased, there is more light being radiated out of the device compared with the electric field in the active region. Note also that the envelope of the field distribution shows that the field presents a smaller lateral extension, which indicates that most of the photons are emitted vertically before they can reach the edges of the PCM: therefore they do not have a chance to be reflected at the boundaries. A power analysis of the FDTD simulation indicates that the ratio of the radiated power to the power lost laterally is about twenty (20). Further increasing the air gap thickness leads to lower Q values and to lower buildup of electric field in the active region, what is not desirable.

Fig. 6. Electric field spectrum at a point in the air gap (a). Electric field distribution at resonance for h 2=2.94λp/4.

In any case it is clear that minimizing lateral losses is essential for an improved operation of the device in that more freedom will be left for operation in the different above described regimes. In that respect, making use of a two dimensional (2D) PCM should be more favorable, since one can expect to achieve a more efficient lateral confinement of photons than with a 1D PCM.

Typical micro-cavities embedded in two Bragg mirrors have quality factors in the range of 2000 and 10000. Moreover, these mirrors have reflectivities in the range of 97% and 100%. These values are comparable with those obtained in our hybrid PCSEL design.

5. Summary

In summary, we have presented a hybrid version of a laser which combines a photonic crystal membrane and a Bragg stack. The proposed approach results in compact devices with relaxed technological constraints and versatile functionality. For example, via micro-opto-electro-mechanical actuation, not only the wavelength can be changed, but also the direction (vertical or in-plane) where most of the photons will be emitted. Also, multiple emission of different wavelengths can be achieved by using photonic crystals with different lattice constants in the same wafer. Devices based on similar concepts may find applications in switches, tunable filters, etc.

References and links

1.

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

2.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987). [CrossRef] [PubMed]

3.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’ Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999). [CrossRef] [PubMed]

4.

C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Holinger, E. Jalaguier, S. Pocas, and B. Aspar, “InP 2D photonic crystal microlasers on silicon wafer: room temperature operation at 1.55 µm,” Electron. Lett. 37, 764–765 (2001). [CrossRef]

5.

T. Baba, N. Fukaya, and J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–655 (1999). [CrossRef]

6.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop filters in photonic crystals,” Opt. Express 3, 4 (1998), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-1-4. [CrossRef] [PubMed]

7.

X. Letartre, J. Mouette, J. L. Leclercq, P. Rojo-Romeo, C. Seassal, and P. Viktorovitch, “Switching devices with spatial and spectral resolution combining photonic crystal and MOEMS structures,” J. Light. Technol. (to be published).

8.

V. N. Astratov, I. S. Culshaw, R. M. Stevenson, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Resonant coupling of near-infrared radiation to photonic band structure waveguides,” J. Light. Technol. 17, 2050–2057 (1999). [CrossRef]

9.

J. M. Pottage, E. Silvestre, and P. St. J. Russell, “Vertical-cavity surface emitting resonances in photonic crystals,” J. Opt. Soc. Am. A 18, 442–447 (2001). [CrossRef]

10.

S. Tibuleac and R. Magnusson, “Diffractive narrow-band transmission filter based on guided-mode resonance effects in thin-film multilayers,” IEEE Photon. Technol. Lett. 9, 464–466 (1997). [CrossRef]

11.

W. Sooh, M. F. Yannick, O. Solgaard, and S. Fan, “Displacement sensitive photonic crystal structures based on guided resonance in photonic crystal,” Appl. Phys. Lett. 82, 1999–2001 (2003). [CrossRef]

12.

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

13.

A. Yariv, Optical Electronics in Modern Communications (Oxford, New York, NY1997).

14.

S. G. Johnson and J. D. Joannopoulos, “Bloch-iterative frequency domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173 (2000), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173. [CrossRef]

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(140.2020) Lasers and laser optics : Diode lasers

ToC Category:
Research Papers

History
Original Manuscript: May 27, 2003
Revised Manuscript: July 23, 2003
Published: July 28, 2003

Citation
Haroldo Hattori, Xavier Letartre, Christian Seassal, Pedro Rojo-Romeo, Jean Leclercq, and Pierre Viktorovitch, "Analysis of hybrid photonic crystal vertical cavity surface emitting lasers," Opt. Express 11, 1799-1808 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-15-1799


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References

  1. E. Yablonovitch, �??Inhibited spontaneous emission in solid-state physics and electronics,�?? Phys. Rev. Lett. 58, 2059-2062 (1987). [CrossRef] [PubMed]
  2. S. John, �??Strong localization of photons in certain disordered dielectric superlattices,�?? Phys. Rev. Lett. 58, 2486-2489 (1987). [CrossRef] [PubMed]
  3. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O�?? Brien, P. D. Dapkus, and I. Kim, �??Two-dimensional photonic band-gap defect mode laser,�?? Science 284, 1819-1821 (1999). [CrossRef] [PubMed]
  4. C. Monat, C. Seassal, X. Letartre, P. Viktorovitch, P. Regreny, M. Gendry, P. Rojo-Romeo, G. Holinger, E. Jalaguier, S. Pocas, and B. Aspar, �??InP 2D photonic crystal microlasers on silicon wafer: room temperature operation at 1.55 m,�?? Electron. Lett. 37, 764-765 (2001). [CrossRef]
  5. T. Baba, N. Fukaya, J. Yonekura, �??Observation of light propagation in photonic crystal optical waveguides with bends,�?? Electron. Lett. 35, 654-655 (1999). [CrossRef]
  6. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, H. A. Haus, �??Channel drop filters in photonic crystals,�?? Opt. Express 3, 4 (1998), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-1-4">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-1-4</a>. [CrossRef] [PubMed]
  7. X. Letartre, J. Mouette, J. L. Leclercq, P. Rojo-Romeo, C. Seassal, P. Viktorovitch, �??Switching devices with spatial and spectral resolution combining photonic crystal and MOEMS structures,�?? J. Light. Technol. (to be published).
  8. V. N. Astratov, I. S. Culshaw, R. M. Stevenson, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, �??Resonant coupling of near-infrared radiation to photonic band structure waveguides,�?? J. Light. Technol. 17, 2050-2057 (1999). [CrossRef]
  9. J. M. Pottage, E. Silvestre, and P. St. J. Russell, �??Vertical-cavity surface emitting resonances in photonic crystals,�?? J. Opt. Soc. Am. A 18, 442-447 (2001). [CrossRef]
  10. S. Tibuleac and R. Magnusson, �??Diffractive narrow-band transmission filter based on guided-mode resonance effects in thin-film multilayers,�?? IEEE Photon. Technol. Lett. 9, 464-466 (1997). [CrossRef]
  11. W. Sooh, M. F. Yannick, O. Solgaard, and S. Fan, �??Displacement sensitive photonic crystal structures based on guided resonance in photonic crystal,�?? Appl. Phys. Lett. 82, 1999-2001 (2003). [CrossRef]
  12. C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos, �??Coupling of modes analysis of resonant channel add-drop filters,�?? IEEE J. Quan. Electron. 35, 1322-1331 (1999). [CrossRef]
  13. A. Yariv, Optical Electronics in Modern Communications (Oxford, New York, NY 1997).
  14. S. G. Johnson, and J. D. Joannopoulos, �??Bloch-iterative frequency domain methods for Maxwell�??s equations in a planewave basis,�?? Opt. Express 8, 173 (2000), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-3-173</a>. [CrossRef]

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