Abstract

For nearly 20 years, progress in the field of photonic crystals has greatly benefited from analogies to semiconductor physics and devices. Here we implement the concept of photonic crystal heterojunction and heterostructures, analogues to the concept of the semiconductor heterostructure, and demonstrate devices based on this concept operating in the optical range of frequency spectrum. In particular, we examine the effect of confinement of the photonic envelope wavefunction in a two-dimensional photonic heterostructure quantum well implemented with quasi-periodic array of vertical-cavity surface emitting lasers (VCSELs) as a model system.

© 2004 Optical Society of America

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Appl. Phys. Lett. (3)

M. Oreinstein, et al. �??Two-dimensional phase-locked arrays of vertical-cavity semiconductor lasers by mirror reflectivity modulation,�?? Appl. Phys. Lett. 58, 804-806 (1991).
[CrossRef]

F. Qiao, C. Zhang, J. Wan, J. Zi, �??Photonic quantum-well structures: Multiple channeled filtering phenomena,�?? Appl. Phys. Lett. 77, 3698-3700 (2000).
[CrossRef]

G. Guerrero, D. L. Boiko, E. Kapon, �??Dynamics of polarization modes in photonic crystals based on arrays of vertical-cavity surface-emitting lasers,�?? Appl. Phys. Lett. 84, 3777-3779 (2004).
[CrossRef]

CLEO 2000 (1)

C.-A. Berseth, G. Guerrero, E. Kapon, M. Moser, R. Hoevel, �??Mode confinement in VCSEL-based photonic heterostructures,�?? in Conference on Lasers and Electro-Optics, CLEO 2000, OSA Technical Digest (Optical Society of America, Washington, D.C., 2000), pp 171-172, CtuA48.

Electron. Lett. (1)

W. D. Zhou, et al., �??Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature,�?? Electron. Lett. 36, 1541-1542 (2000).
[CrossRef]

IEEE Circuits & Devices (1)

L. J. Mawst, �??�??Anti�?? up the aperture,�?? IEEE Circuits & Devices 19, 34-41 (2002).
[CrossRef]

J. Appl. Phys. (1)

A. Golshani, H. Pier, E. Kapon, M. Moser, �??Photon mode localization in disordered arrays of vertical cavity surface emitting lasers,�?? J. Appl. Phys. 85, 2454-2456 (1999).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. Soc. Jap. (1)

H. Miyazaki, Y. Jimba, C.-Y. Kim, T. Watanabe, �??Defects and photonic wells in one-dimensional photonic lattices,�?? J. Phys. Soc. Jap. 65, 3842-3852 (1996).
[CrossRef]

Nature (5)

Y. Akahane, T. Asano, B.-S. Song, S. Noda, �??High-Q photonic nanocavity in a two-dimensional photonic crystal,�?? Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

T. F. Krauss, R.M. De La Rue, S. Brand, �??Two dimensional photonic-bandgap structures operating at near-infrared wavelengths,�?? Nature 383, 699-702 (1996).
[CrossRef]

Y. A. Vlasov, X.-Z. Bo, J.C. Sturm, D. J. Norris, �??On-chip natural assembly of silicon photonic bandgap crystals,�?? Nature 414, 289-293 (2001).
[CrossRef] [PubMed]

J. G. Fleming, S. Y. Lin, I. El-Kady, R. Biswas, K. M. Ho, �??All-metallic three-dimensional photonic crystals with a large infrared bandgap,�?? Nature 417, 52-55 (2002).
[CrossRef] [PubMed]

H. Pier, E. Kapon, M. Moser, �??Strain effects and phase transitions in photonic resonator crystals,�?? Nature 407, 880-882 (2000).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (2)

S. Yano, et al. �??Quantized states in single quantum well structure of photonic crystals,�?? Phys. Rev. B 63, 153316 (2001).
[CrossRef]

M. Charbonneau-Lefort, E. Istrate, M. Allard, J. Poon, E. H. Sargent, �??Photonic crystal heterostructures: Waveguiding phenomena and methods of solution in an envelope function picture,�?? Phys. Rev. B 65, 125318 (2002).
[CrossRef]

Phys. Rev. Lett. (3)

A. Mekis, et al. �??High transmission through sharp bends in photonic crystal waveguides,�?? Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

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

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

Rev. Mod. Phys. (1)

Z. I. Alferov, �??Nobel lecture: The double heterostructure concept and its applications in physics, electronics, and technology,�?? Rev. Mod. Phys. 73, 767-782 (2001).
[CrossRef]

Science (1)

P. Russell, �??Photonic crystal fibers,�?? Science 299, 358-362 (2003).
[CrossRef] [PubMed]

Zh. Eksp. Teor. Fiz. (1)

V. P. Bykov, �??Spontaneous emission in a periodic structure,�?? Zh. Eksp. Teor. Fiz. 62, 505-513 (1972).

Other (1)

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals (Princeton Press, New York, 1995).

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Figures (4)

Fig. 1.
Fig. 1.

Photonic crystal heterostructure (PCH) based on 2D photonic crystal (PC) VCSELs. (a) Schematic of the wafer structure showing the metal-patterned top DBR with a core region PC of type A and a cladding region PC of type B. The highlighted region of the heterojunction is detailed in (b): the two lattice-matched PCs differ by the size of gold pixels (top panel); the longitudinal component of the propagation vectors is fixed by the vertical cavity and the transversal components are affected by the heterojunction (bottom panel). (c) 2D Brillouin zone.

Fig. 2.
Fig. 2.

Analogy between photonic crystal and semiconductor heterojunctions: simplified band diagrams (left panels) and potential/loss profiles (right panels). (a) Photonic crystal heterojunction between two VCSEL PCs with the same lattice constant (Λ=6 μm) and fill factors of 0.69 and 0.44. (b) GaAs/AlAs heterojunction. The band offset ΔΓ at the PC heterojunction (grey area) acts as a barrier for photons and is equivalent to the potential barrier for charge carriers formed by the band misalignment at the semiconductor heterojunction.

Fig. 3.
Fig. 3.

Impact of the depth and geometry of a “photonic well” heterostructure on the confined photon states (numerical simulations). (a) Left panel: modal losses versus the FF contrast (FF=0.69 at the core) for a PCH containing 10×10 core unit cells. The dispersion curves of the states are represented by the coloured solid curves; the black solid curves indicate the dispersions of the photonic band edges. The inset shows the cross sections of the (full) photonic wavefunction for selected cases. Right panel: Near field patterns of the states indicated by the corresponding points on the dispersion curves. (b) Left panel: modal losses for three different states versus the aspect ratio of the core a/b (number of lattice periods a varies from 1 to 15 and b is fixed to 10) for a constant photonic well depth (FF contrast of 0.25). Right panel: near field patterns of the states labelled A, B and C in the left panel.

Fig. 4.
Fig. 4.

Comparison of measured and calculated features of the |T5(00)⟩ state in a PCH based on coupled VCSEL arrays. (a) Near field intensity patterns and cross sections (along the dashed white line) in lasing 16×16 VCSELs PCH with 5×10 unit cells in the core measured for three different values of the FF contrast: ΔFF=0.25, 0.35 and 0.44, from top to bottom. (b) Numerical simulation of the near field intensity patterns for the three measured structures. (c) Measured (triangles) and calculated (circles) in-plane propagation constants in the core (top) and attenuation constants in the cladding (bottom) versus the effective size parameter NFF)1/2 of cores containing N×10 unit cells, with N=4 or N=5 lattice periods. Red dashed lines show the influence of ΔFF for constant N and black lines show the impact of N for a constant ΔFF.

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