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Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 20 — Oct. 4, 2004
  • pp: 4922–4928
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Photonic crystal heterostructures implemented with vertical-cavity surface-emitting lasers

Gilles Guerrero, Dmitri L. Boiko, and Eli Kapon  »View Author Affiliations


Optics Express, Vol. 12, Issue 20, pp. 4922-4928 (2004)
http://dx.doi.org/10.1364/OPEX.12.004922


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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

1. Introduction

In semiconductor homostructures, consisting ideally of perfectly periodic crystals, the band structure is set by the crystal potential, and the states of charge carriers consist of periodic Bloch functions modulated by plane wave envelopes. In semiconductor heterostructures, several such homostructures are joined together, stitched by heterojunctions constituting the interfaces between the periodic domains. In each domain, the material properties (band gap, carriers effective masses, …) are fixed by the “local” crystalline structure. At the heterojunctions, the envelope functions of the wavestates are altered by reflections due to the band offsets. Semiconductor heterostructures thus provide means for controlling the envelope functions. Moreover, in semiconductor heterostructures incorporating lower-bandgap domains of dimensions comparable to the Fermi wavelength of the carriers, quantum confinement effects set in, yielding discrete energy spectra and localized envelope functions. Such semiconductor quantum structures made possible numerous fundamental studies of low-dimensional systems and form the basis for important device technologies, e.g., quantum well lasers and high mobility electron transistors [13

13. 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]

].

By analogy, PCHs consisting of PC domains joined at photonic heterojunctions of well-defined interface configurations offer exciting possibilities for tailoring photonic envelope functions. Similar to low-dimensional semiconductors, low-dimensional PCHs, e.g., photonic quantum wells, have been proposed [16–18

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

]. The quantization of the photonic band was predicted and indeed observed in the transmission spectra of photonic quantum wells in the millimeter wavelength range [14

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

]. Here, we implement the concept of the PC heterojunction and show how it can be designed to achieve photonic envelope function confinement in photonic crystal heterostructures. Using this notion, we present experimentally and theoretically the control of such confinement in two-dimensional (2D) PCHs based on arrays of phase-coupled VCSELs operating in the near-infrared region of the optical spectrum.

2. Heterojunctions and heterostructures implemented with VCSEL-crystal

A 2D PCH based on phase-coupled arrays of VCSELs is depicted in Fig.1(a). These structures represent a special class of 2D PCs incorporating laterally coupled optical resonators [19–21

19. C.-A. Berseth, G. Guerrero, E. Kapon, M. Moser, and 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.

] or waveguides (e.g., photonic crystal fibers [9

9. P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003). [CrossRef] [PubMed]

]). In this case, the electromagnetic modes propagate nearly perpendicular to the periodic index modulation such that only a small in–plane component k of the propagation vector k undergoes Bragg reflections [Fig.1(b)]. Thus, effective in-plane Bragg reflection occurs in a 2D PC of periodicity much larger than the wavelength. For structures utilizing coupled resonators, the longitudinal component k // is fixed by the cavity resonance condition. In VCSEL-based structures [Fig. 1(b)], k // also undergoes Bragg reflection along z axis in each of the distributed Bragg reflectors (DBRs), however its value is fixed across the uniform VCSEL wafer by the length of the vertical cavity and does not influence the in-plane effects we discuss here. The elements of the VCSEL PC (the pixels) are defined by patterning the reflectivity of the top DBR [15

15. 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]

] of a VCSEL wafer. Square-shaped, higher-reflectivity Au pixels surrounded by a lower-reflectivity Cr grid define the single-mode VCSEL resonators [Fig. 1(b)]. Since the round trip optical gain is low, a reflectivity modulation of the order of 1% is sufficient to define the position of the lasing microcavities.

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. 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.

3. Modeling of photonic crystal well

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.

4. Experimental results and discussion

The impact of the band offset at a PC heterojunction was investigated experimentally in VCSEL - based PCHs. A series of square - lattice PCHs ( lattice constant Λ = 6 μm ) incorporating coupled VCSELs emitting at 940 nm wavelength (the design wavelength of the vertical structure of the VCSEL wafer) were fabricated and tested. Details of the VCSEL wafer structure are given in Ref. [24

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

]. Each PCH contained 16×16 unit cells in which a 10×N (N=4 or 5) core with FF=0.69 was defined. The barrier Au pixels had widths ranging from 3 to 4 μm, corresponding to FF contrasts of 0.25 to 0.44.

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.

The measured near field patterns of the lowest-loss photonic state, lasing under pulsed electrical pumping, are shown in Fig. 4(a) for different values of the FF contrast. The observed near field patterns are characteristic of the confined |T5(00)⟩ Bloch states, comprising an envelope function modulated by a periodic “out-of-phase” supermode with maxima of intensity at the gold pixels locations [15

15. 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]

]. The envelope function is cosine-like in the core and evanescent in the PCH barrier. The evanescent tails extend more into the barrier for small FF contrast, which is expected due to the reduction in photonic band offset with decreasing FF contrast. This evolution of the envelope function is in agreement with the calculated intensity patterns presented in Fig. 4(b).

5. Summary

We have shown that the concepts of heterojunctions and heterostructures developed for semiconductors can be implemented with photonic crystal heterostructures. By joining several periodic photonic crystal domains at photonic heterojunctions of well-defined photonic band offsets, it is possible to control the characteristics of the photonic envelope functions and thus achieve new means for controlling photonic states in quasi periodic media. Particular PCHs implemented with 2D arrays of coupled VCSELs were employed to illustrate the use of this concept in achieving confinement of lasing modes in VCSEL-based PCHs. These concepts should stimulate further development of novel PCHs for control of photon propagation and confinement.

References and links

1.

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

2.

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

3.

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

4.

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

5.

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

6.

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

7.

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

8.

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

9.

P. Russell, “Photonic crystal fibers,” Science 299, 358–362 (2003). [CrossRef] [PubMed]

10.

E. Yablonovitch, “Photonic band-gap structures,” J. Opt. Soc. Am. B 10, 283–295 (1993). [CrossRef]

11.

V. P. Bykov, “Spontaneous emission in a periodic structure,” Zh. Eksp. Teor. Fiz. 62, 505–513 (1972).

12.

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

13.

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]

14.

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

15.

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]

16.

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

17.

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

18.

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

19.

C.-A. Berseth, G. Guerrero, E. Kapon, M. Moser, and 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.

20.

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

21.

L. J. Mawst, ““Anti” up the aperture,” IEEE Circuits & Devices 19, 34–41 (2002). [CrossRef]

22.

D. L Boiko, G. Guerrero, and E. Kapon, “Polarization Bloch waves in photonic crystals based on vertical cavity surface emitting laser arrays,” Opt. Express 12, 2597–2602 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-12-2597. [CrossRef] [PubMed]

23.

E. Kapon, J. Katz, and A. Yariv, “Supermode analysis of phase-locked arrays of semiconductor-lasers,” Opt. Lett. 9, 125–127 (1984); E. Kapon, ibid. 9, 318 (1984). [CrossRef] [PubMed]

24.

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

25.

G. Guerrero, D. L. Boiko, and 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]

OCIS Codes
(140.3290) Lasers and laser optics : Laser arrays
(250.7260) Optoelectronics : Vertical cavity surface emitting lasers

ToC Category:
Research Papers

History
Original Manuscript: August 16, 2004
Revised Manuscript: September 16, 2004
Published: October 4, 2004

Citation
Gilles Guerrero, Dmitri Boiko, and Eli Kapon, "Photonic crystal heterostructures implemented with vertical-cavity surface-emitting lasers," Opt. Express 12, 4922-4928 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-20-4922


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References

  1. J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals (Princeton Press, New York, 1995).
  2. E. Yablonovitch, �??Inhibited spontaneous emission in solid-state physics and electronics,�?? Phys. Rev. Lett. 58, 2059�??2062 (1987). [CrossRef] [PubMed]
  3. S. John, �??Strong localization of photons in certain disordered dielectric superlattices,�?? Phys. Rev. Lett. 58, 2486-2489 (1987). [CrossRef] [PubMed]
  4. 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]
  5. 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]
  6. 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]
  7. A. Mekis, et al. �??High transmission through sharp bends in photonic crystal waveguides,�?? Phys. Rev. Lett. 77, 3787-3790 (1996). [CrossRef] [PubMed]
  8. W. D. Zhou, et al., �??Electrically injected single-defect photonic bandgap surface-emitting laser at room temperature,�?? Electron. Lett. 36, 1541-1542 (2000). [CrossRef]
  9. P. Russell, �??Photonic crystal fibers,�?? Science 299, 358-362 (2003). [CrossRef] [PubMed]
  10. E. Yablonovitch, �??Photonic band-gap structures,�?? J. Opt. Soc. Am. B 10, 283-295 (1993). [CrossRef]
  11. V. P. Bykov, �??Spontaneous emission in a periodic structure,�?? Zh. Eksp. Teor. Fiz. 62, 505-513 (1972).
  12. 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]
  13. 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]
  14. S. Yano, et al. �??Quantized states in single quantum well structure of photonic crystals,�?? Phys. Rev. B 63, 153316 (2001). [CrossRef]
  15. 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]
  16. 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]
  17. F. Qiao, C. Zhang, J. Wan, J. Zi, �??Photonic quantum-well structures: Multiple channeled filtering phenomena,�?? Appl. Phys. Lett. 77, 3698-3700 (2000). [CrossRef]
  18. 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]
  19. 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.
  20. H. Pier, E. Kapon, M. Moser, �??Strain effects and phase transitions in photonic resonator crystals,�?? Nature 407, 880-882 (2000). [CrossRef] [PubMed]
  21. L. J. Mawst, �??�??Anti�?? up the aperture,�?? IEEE Circuits & Devices 19, 34-41 (2002). [CrossRef]
  22. D. L Boiko, G. Guerrero, E. Kapon, �??Polarization Bloch waves in photonic crystals based on vertical cavity surface emitting laser arrays,�?? Opt. Express 12, 2597-2602 (2004), <a href=" http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-12-2597.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-12-2597</a> [CrossRef] [PubMed]
  23. E. Kapon , J. Katz, A. Yariv, �??Supermode analysis of phase-locked arrays of semiconductor-lasers,�?? Opt. Lett. 9, 125-127 (1984); E. Kapon, ibid. 9, 318 (1984). [CrossRef] [PubMed]
  24. 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]
  25. 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]

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