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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 18 — Sep. 6, 2004
  • pp: 4269–4274
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Design and analysis of anti-resonant reflecting photonic crystal VCSEL lasers

Hairong Liu, Min Yan, Ping Shum, H. Ghafouri-Shiraz, and Deming Liu  »View Author Affiliations


Optics Express, Vol. 12, Issue 18, pp. 4269-4274 (2004)
http://dx.doi.org/10.1364/OPEX.12.004269


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Abstract

Anti-resonant reflecting photonic crystal structure is employed in vertical cavity surface emitting lasers (VCSELs) to achieve photon confinement in lateral direction. Such a design is promising in supporting large-aperture single-mode emission. In the configuration, hexagonal arrays of high-index cylinders which run vertically in the cladding region are introduced in the VCSEL’s top DBR (p-DBR) mirror region. The transverse modal property of the proposed structure, especially leakage loss, has been theoretically investigated. An optimum design for the minimum radiation loss while maintaining single-mode operation has been discussed in this paper.

© 2004 Optical Society of America

1. Introduction

Index-guiding photonic crystal (PC) waveguide has recently been applied in VCSEL design to get single-fundamental-mode operation by Dae-Sung Song et al. [4

4. D. S. Song, S.H. Kim, H.G. Park, C.K. Kim, and Y.H. Lee, “Single-fundamental-mode photonic-crystal vertical-cavity surface-emitting lasers”, Appl. Phys.Lett. 80 , 3901–3903 (2002). [CrossRef]

]. The microstructured waveguide incorporated has a holey cladding structure and a solid core. This kind of VCSEL is expected to provide good single-mode operation. However, the single mode operation can be provided only if the ratio of the hole diameter to the hole-to-hole distance stays smaller than a certain value. This threshold value could be very small if index contrast involved is relatively high, which would make fabrication a difficult process. Though partial etching of the air holes would be a solution to this problem [5–6

5. A. J. Danner, J. J. Raffery, and N. Yokouchi etc., “Transverse modes of photonic crystal vertical-cavity lasers”, Appl. Phys. Lett. 84, 1031–1033 (2004). [CrossRef]

], it may be a difficult controlling process during fabrication.

In this paper, we propose an alternative design. In top DBR mirror region, a hexagonal array of high-index cylinders is introduced in the cladding region. These high-index cylinders are tuned in dimension to strongly reflect light back to the core region. We refer to this design as anti-resonant reflecting photonic crystal vertical cavity surface emitting lasers (ARPC-VCSEL). In contrast to a positive-index waveguide, the ARPC-VCSEL can operate with only a fundamental mode even cylinder dimension is relatively big compared to cylinder-to-cylinder distance, since high order modes suffer excessively large loss in this structure.

2. Design of anti-resonant reflecting PC-VCSEL

The proposed ARPC-VCSEL is shown in Fig. 1(a). As stated in reference (Fig. 2 in Ref. 3

3. D. Zhou and L. J. Mawst, “High-power single-mode antiresonant reflecting optical waveguide-type vertical-cavity surface-emitting lasers,” IEEE J. Quantum. Electron. 38, 1599–1605 (2002). [CrossRef]

), one proper way to get the cylindrical ARROW structure is by chemically etching a thin GaAs-GaInP spacer layer. Following by regrowth process, the high- and low-index ring reflectors can be defined. Our proposed APRC-VCSEL can be realized exactly in the same way. That is, the GaAs-GaInP spacer layer is selectively etched with a photomask whose pattern matches the array of high index cylinders. The places where the spacer layer remains (an array of circular regions in this case) are responsible for the formation of high index cylinders after Hadley’s effective index modeling [7

7. G. R. Hardley, “Effective index model for vertical-cavity surface-emitting lasers,” Opt. Lett. 20, 1483–1485 (1995). [CrossRef]

]. After our proposed structure is converted to Hardley’s effective index model [2

2. L. J. Mawst, ““anti” up the aperture,” IEEE circuits & devices magazine 19 , 34–41 (2003). [CrossRef]

][7

7. G. R. Hardley, “Effective index model for vertical-cavity surface-emitting lasers,” Opt. Lett. 20, 1483–1485 (1995). [CrossRef]

] , the waveguide adopted in our proposed VCSEL can be schematically shown in Fig. 1(b). Background region is of lower index. Black regions represent high-index rods that run along the waveguide’s axial direction. As the average index of cladding is higher than that of core, index-guiding is dismissed in such waveguide. In fact, PC formed by the hexagonal array of rods in cladding region reflects light strongly at certain wavelength ranges. Such light confinement in low-index core region is attributed to Bragg reflections at cylinder boundaries along any propagation direction in the entire transverse plane [8

8. N. M. Litchiniser, A. K. Abeeluck, C. Headley, and B. J. Eggtleton, “Antiresonant r eflecting photonic crystal optical waveguides,” Opt. Lett. 27, 1592–1594 (2002). [CrossRef]

]. Photonic bandgap (PBG) is another explanation for the Bragg reflection mentioned here [9

9. A. K. Abeeluck, N. M. Litchinister, C. Headley, and B. J. Eggleton, “Analysis of spectral characteristics of photonic bandgap waveguides,” Opt. Express 10, 1320–1333 (2002). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1320. [CrossRef] [PubMed]

].

The cross section of the ARPC-VCSEL is shown in the Fig. 1(c). d is the diameter of the high index cylinders and Λ is the pitch of the cladding PC. In our design, the effective refractive indices of cylinder ncylinder (black areas) and core (or the background region, white areas) ncore are assumed to be 3.35 and 3.3, respectively. Λ is chosen at 7.36μm , and diameter of the cylinder d 3.31μm. The emission wavelength is 0.98 μm. The core diameter is roughly 2Λ =14.7μm , which is considered very big.

Fig. 1. (a) Schematic of anti-resonant reflecting photonic crystal VCSEL. (b) Waveguide incorporated in ARRP -VCSEL after Hardley model. (c) Cross section of the ARRP -VCSEL, the black regions represent high index cylinders.

3. Results and discussions

Table 1. Mode effective refractive index for the first four modes

table-icon
View This Table

Fig. 2. Transverse electric field of: (a) HE11y mode; (b) TE 01 mode; (c) TM 01 mode; (d) HE 21 mode. (e) is for Ey field of HE11y mode and (f) for Ey field of TE 01 mode.

Jl(kexd2)=0
(1)

where kex is the transverse component of the wavevector κ in high index regions. If we assume neffncore , the peak-loss wavelength points can then be predicted by the following expression

d·πλncylinder2ncore2=roots(Jl)
(2)

where roots(Jl ) means the roots of Bessel function of order l.

Fig. 3. The modal loss of HE 11 (dotted line) and TE 01 (solid line) modes with the change of the wavelength.

Another method for loss peaks prediction is to employ the PBG theory. PBG-map for photonic crystal cladding depicted in Fig. 1 has been calculated by using the plane wave expansion (PWE) method. Fig. 4 shows the gap-map obtained in the coordinate of neff versus of wavelength λ. Shaded regions are PBG gap regions, within which no propagating mode is supported by the cladding structure. As a result the light is rejected back to the core region.

Fig. 4. Map of phtonics bandgaps found for cladding photonic crystal structure.

4. Conclusions

References and links

1.

Y. A. Wu, G. S. Li, R. F. Nabiev, K. D. Choquette, C. Caneau, and C. J. Chang-Haisnain, “Single-mode, passive antiguide vertical cavity surface emitting laser,” IEEE J. Sel. Top . Quantum Electron .. 1, 629–637 (1995). [CrossRef]

2.

L. J. Mawst, ““anti” up the aperture,” IEEE circuits & devices magazine 19 , 34–41 (2003). [CrossRef]

3.

D. Zhou and L. J. Mawst, “High-power single-mode antiresonant reflecting optical waveguide-type vertical-cavity surface-emitting lasers,” IEEE J. Quantum. Electron. 38, 1599–1605 (2002). [CrossRef]

4.

D. S. Song, S.H. Kim, H.G. Park, C.K. Kim, and Y.H. Lee, “Single-fundamental-mode photonic-crystal vertical-cavity surface-emitting lasers”, Appl. Phys.Lett. 80 , 3901–3903 (2002). [CrossRef]

5.

A. J. Danner, J. J. Raffery, and N. Yokouchi etc., “Transverse modes of photonic crystal vertical-cavity lasers”, Appl. Phys. Lett. 84, 1031–1033 (2004). [CrossRef]

6.

D. S. Song, Y. J. Lee, H.W. Choi, and Y.H. Lee, “Polarized-controlled, single-transverse-mode, photonic-crystal, vertical-cavity, surface-emitting lasers”, Appl. Phys. Lett. 82,3 182–3184 (2003). [CrossRef]

7.

G. R. Hardley, “Effective index model for vertical-cavity surface-emitting lasers,” Opt. Lett. 20, 1483–1485 (1995). [CrossRef]

8.

N. M. Litchiniser, A. K. Abeeluck, C. Headley, and B. J. Eggtleton, “Antiresonant r eflecting photonic crystal optical waveguides,” Opt. Lett. 27, 1592–1594 (2002). [CrossRef]

9.

A. K. Abeeluck, N. M. Litchinister, C. Headley, and B. J. Eggleton, “Analysis of spectral characteristics of photonic bandgap waveguides,” Opt. Express 10, 1320–1333 (2002). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1320. [CrossRef] [PubMed]

10.

T.P. White, B.T. Kuhlmey, and R.C. McPhedram, etc., “Multipole method for microstructured optical fibers, I. Formulation,” J. Opt. Soc. Am. B. 19, 2322–2330 (2002). [CrossRef]

11.

T.P. White, R.C. McPhedran, and C. M. D. Sterke, “Resonance and scattering in microstructured optical fibers,” Opt. Lett. 27, 1977–1979 (2002). [CrossRef]

12.

N. M. Litchinister and S. C. Dunn, etc., “Resonances in microstructured optical waveguides,” Opt. Express 11 , 1243–1251 (2003). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1243. [CrossRef]

OCIS Codes
(140.3570) Lasers and laser optics : Lasers, single-mode
(140.5960) Lasers and laser optics : Semiconductor lasers

ToC Category:
Research Papers

History
Original Manuscript: July 7, 2004
Revised Manuscript: August 27, 2004
Published: September 6, 2004

Citation
Hairong Liu, Min Yan, Ping Shum, H. Ghafouri-Shiraz, and Deming Liu, "Design and analysis of anti-resonant reflecting photonic crystal VCSEL lasers," Opt. Express 12, 4269-4274 (2004)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-12-18-4269


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References

  1. Y. A. Wu, G. S. Li, R. F. Nabiev, K. D. Choquette, C, Caneau, and C. J. Chang-Haisnain, �??Single-mode, passive antiguide vertical cavity surface emitting laser,�?? IEEE J. Sel. Top. Quantum Electron.. 1, 629-637 (1995). [CrossRef]
  2. L. J. Mawst, �?? �??anti�?? up the aperture,�?? IEEE circuits & devices magazine 19, 34-41 (2003). [CrossRef]
  3. D. Zhou and L. J. Mawst, �??High-power single-mode antiresonant reflecting optical waveguide-type vertical-cavity surface-emitting lasers,�?? IEEE J. Quantum. Electron. 38, 1599-1605 (2002). [CrossRef]
  4. D. S. Song, S.H. Kim, H.G. Park, C.K. Kim and Y.H. Lee, �??Single-fundamental-mode photonic-crystal vertical-cavity surface-emitting lasers�??, Appl. Phys. Lett. 80, 3901-3903 (2002). [CrossRef]
  5. A. J. Danner, J. J. Raffery, N. Yokouchi etc., �??Transverse modes of photonic crystal vertical-cavity lasers�??, Appl. Phys. Lett. 84, 1031-1033 (2004). [CrossRef]
  6. D. S. Song, Y. J. Lee,H.W. Choi, and Y.H. Lee, �??Polarized-controlled, single-transverse-mode, photonic-crystal, vertical-cavity, surface-emitting lasers�??, Appl. Phys. Lett. 82, 3182-3184 (2003). [CrossRef]
  7. G. R. Hardley, �??Effective index model for vertical-cavity surface-emitting lasers,�?? Opt. Lett. 20, 1483- 1485 (1995). [CrossRef]
  8. N. M. Litchiniser, A. K. Abeeluck, C. Headley and B. J. Eggtleton, �??Antiresonant reflecting photonic crystal optical waveguides,�?? Opt. Lett. 27, 1592-1594 (2002). [CrossRef]
  9. A. K. Abeeluck, N. M.Litchinister, C. Headley, and B. J. Eggleton, �??Analysis of spectral characteristics of photonic bandgap waveguides,�?? Opt. Express 10, 1320-1333 (2002) <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1320">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-23-1320</a> [CrossRef] [PubMed]
  10. T.P.White, B.T.Kuhlmey, R.C.McPhedram, etc., �?? Multipole method for microstructured optical fibers, I. Formulation,�?? J. Opt. Soc. Am. B. 19, 2322-2330 (2002). [CrossRef]
  11. T.P.White, R.C.McPhedran, and C. M. D. Sterke, �??Resonance and scattering in microstructured optical fibers,�?? Opt. Lett. 27, 1977-1979 (2002). [CrossRef]
  12. N. M. Litchinister, S. C. Dunn, etc., �??Resonances in microstructured optical waveguides,�?? Opt. Express 11, 1243-1251 (2003). <a href= "http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1243">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-10-1243</a>. [CrossRef]

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