Abstract

We present a novel design for a W1 (one missing row of holes) waveguide 60° bend implemented in a substrate-type InPInGaAsPInP planar photonic crystal based on a triangular array of air holes. The bend has been designed to provide high transmission over a large bandwidth. The investigated design improvement relies only on displacing holes while avoiding changing individual holes diameter in the interest of better process control (homogenous hole depth). Two-dimensional (2D) finite-element simulations were used to increase the relative transmission bandwidth from 18% to 40% of the photonic bandgap for unoptimized and optimized 60° bends, respectively. The 2D results were verified by means of rigorous three-dimensional (3D) finite-difference time-domain (FDTD) simulations. We show that excellent agreement between 2D and 3D simulations can be obtained, provided a small effective-index shift of 0.024 (0.74%) and an imaginary loss parameter (ϵ=0.014) is introduced in the 2D simulations. To demonstrate the applicability of our improved design, the bend was fabricated and measured using the endfire technique. A bending loss of 3dB is obtained for the optimized W1 waveguide bend compared to more than 8dB in the unoptimized case.

© 2008 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. K. Rauscher, "Simulation, design, and characterization of photonic crystal devices in a low vertical index contrast regime," dissertation ETH 16516, electrical engineering (ETH Zurich, 2006).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  11. S. Olivier, H. Benisty, M. Rattier, C. Weisbuch, M. Qiu, A. Karlsson, C. J. M. Smith, R. Houdré, and U. Oesterle, "Resonant and nonresonant transmission through waveguide bends in a planar photonic crystal," Appl. Phys. Lett. 79, 2514-2516 (2001).
    [CrossRef]
  12. S. Xiao and M. Qiu, "Study of transmission properties for waveguide bends by use of a circular photonic crystal," Phys. Lett. A 340, 474-479 (2005).
    [CrossRef]
  13. M. Qiu, "Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals," Appl. Phys. Lett. 81, 1163-1165 (2002).
    [CrossRef]
  14. http://wwwhome.math.utwente.nl/~hammer/oms.html.
  15. R. Wüest, F. Robin, C. Hunziker, P. Strasser, D. Erni, and H. Jäckel, "Limitations of proximity-effect corrections for electron-beam patterning of planar photonic crystals," Opt. Eng. 44, 043401 (2005).
    [CrossRef]
  16. R. Ferrini, D. Leuenberger, M. Mulot, M. Qiu, J. Moosburger, M. Kamp, A. Forchel, S. Anand, and R. Houdré, "Optical study of two-dimensional InP-based photonic crystals by internal light source technique," IEEE J. Quantum Electron. 38, 786-799 (2002).
    [CrossRef]
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  18. http://www.comsol.com.
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    [CrossRef]
  21. H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Béraud, and C. Jouanin, "Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate," Appl. Phys. Lett. 76, 532-534 (2000).
    [CrossRef]
  22. R. Ferrini, R. Houdré, H. Benisty, M. Qiu, and J. Moosburger, "Radiation losses in planar photonic crystals: two-dimensional representation of hole depth and shape by an imaginary dielectric constant," J. Opt. Soc. Am. B 20, 469-478 (2003).
    [CrossRef]
  23. R. Wüest, P. Strasser, F. Robin, D. Erni, and H. Jäckel, "Fabrication of a hard mask for InP based photonic crystals: increasing the plasma-etch selectivity of poly(methyl methacrylate) versus SiO2 and SiNx," J. Vac. Sci. Technol. B 23, 3197-3201 (2005).
    [CrossRef]
  24. R. Wüest, "Nanometer-scale technology and near-field characterization of InP-based planar photonic-crystal devices," Dissertation 17146, Electrical engineering (ETH Zurich, 2007).

2007 (1)

P. Strasser, R. Wüest, F. Robin, D. Erni, and H. Jäckel, "A detailed analysis of the influence of an ICP-RIE process on the hole depth and shape of photonic crystals in InP/InGaAsP," J. Vac. Sci. Technol. B 25, 387-393 (2007).
[CrossRef]

2006 (2)

2005 (3)

R. Wüest, P. Strasser, F. Robin, D. Erni, and H. Jäckel, "Fabrication of a hard mask for InP based photonic crystals: increasing the plasma-etch selectivity of poly(methyl methacrylate) versus SiO2 and SiNx," J. Vac. Sci. Technol. B 23, 3197-3201 (2005).
[CrossRef]

S. Xiao and M. Qiu, "Study of transmission properties for waveguide bends by use of a circular photonic crystal," Phys. Lett. A 340, 474-479 (2005).
[CrossRef]

R. Wüest, F. Robin, C. Hunziker, P. Strasser, D. Erni, and H. Jäckel, "Limitations of proximity-effect corrections for electron-beam patterning of planar photonic crystals," Opt. Eng. 44, 043401 (2005).
[CrossRef]

2004 (2)

B. Miao, C. Chen, S. Shi, J. Murakowski, and D. W. Prather, "High-efficiency broadband transmission through a double-60 bend in a planar photonic crystal single-line defect waveguide," IEEE Photonics Technol. Lett. 16, 2469-2471 (2004).
[CrossRef]

L. H. Frandsen, A. Harpøth, P. I. Borel, M. Kristensen, J. S. Jensen, and O. Sigmund, "Broadband photonic crystal waveguide 60° bend obtained utilizing topology optimization," Opt. Express 12, 5916-5921 (2004).
[CrossRef] [PubMed]

2003 (1)

2002 (4)

T. Baba, "Light transmission in photonic bandgap waveguides and photonic band crystals," Proc. SPIE 4870, 265-271 (2002).

A. Chutinan, M. Okano, and S. Noda, "Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 80, 1698-1700 (2002).
[CrossRef]

M. Qiu, "Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals," Appl. Phys. Lett. 81, 1163-1165 (2002).
[CrossRef]

R. Ferrini, D. Leuenberger, M. Mulot, M. Qiu, J. Moosburger, M. Kamp, A. Forchel, S. Anand, and R. Houdré, "Optical study of two-dimensional InP-based photonic crystals by internal light source technique," IEEE J. Quantum Electron. 38, 786-799 (2002).
[CrossRef]

2001 (3)

2000 (1)

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Béraud, and C. Jouanin, "Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate," Appl. Phys. Lett. 76, 532-534 (2000).
[CrossRef]

1987 (2)

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]

Appl. Phys. Lett. (4)

S. Olivier, H. Benisty, M. Rattier, C. Weisbuch, M. Qiu, A. Karlsson, C. J. M. Smith, R. Houdré, and U. Oesterle, "Resonant and nonresonant transmission through waveguide bends in a planar photonic crystal," Appl. Phys. Lett. 79, 2514-2516 (2001).
[CrossRef]

M. Qiu, "Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals," Appl. Phys. Lett. 81, 1163-1165 (2002).
[CrossRef]

A. Chutinan, M. Okano, and S. Noda, "Wider bandwidth with high transmission through waveguide bends in two-dimensional photonic crystal slabs," Appl. Phys. Lett. 80, 1698-1700 (2002).
[CrossRef]

H. Benisty, D. Labilloy, C. Weisbuch, C. J. M. Smith, T. F. Krauss, D. Cassagne, A. Béraud, and C. Jouanin, "Radiation losses of waveguide-based two-dimensional photonic crystals: positive role of the substrate," Appl. Phys. Lett. 76, 532-534 (2000).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. Ferrini, D. Leuenberger, M. Mulot, M. Qiu, J. Moosburger, M. Kamp, A. Forchel, S. Anand, and R. Houdré, "Optical study of two-dimensional InP-based photonic crystals by internal light source technique," IEEE J. Quantum Electron. 38, 786-799 (2002).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

B. Miao, C. Chen, S. Shi, J. Murakowski, and D. W. Prather, "High-efficiency broadband transmission through a double-60 bend in a planar photonic crystal single-line defect waveguide," IEEE Photonics Technol. Lett. 16, 2469-2471 (2004).
[CrossRef]

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

J. Vac. Sci. Technol. B (2)

R. Wüest, P. Strasser, F. Robin, D. Erni, and H. Jäckel, "Fabrication of a hard mask for InP based photonic crystals: increasing the plasma-etch selectivity of poly(methyl methacrylate) versus SiO2 and SiNx," J. Vac. Sci. Technol. B 23, 3197-3201 (2005).
[CrossRef]

P. Strasser, R. Wüest, F. Robin, D. Erni, and H. Jäckel, "A detailed analysis of the influence of an ICP-RIE process on the hole depth and shape of photonic crystals in InP/InGaAsP," J. Vac. Sci. Technol. B 25, 387-393 (2007).
[CrossRef]

Opt. Eng. (1)

R. Wüest, F. Robin, C. Hunziker, P. Strasser, D. Erni, and H. Jäckel, "Limitations of proximity-effect corrections for electron-beam patterning of planar photonic crystals," Opt. Eng. 44, 043401 (2005).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Lett. A (1)

S. Xiao and M. Qiu, "Study of transmission properties for waveguide bends by use of a circular photonic crystal," Phys. Lett. A 340, 474-479 (2005).
[CrossRef]

Phys. Rev. Lett. (2)

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]

Proc. SPIE (1)

T. Baba, "Light transmission in photonic bandgap waveguides and photonic band crystals," Proc. SPIE 4870, 265-271 (2002).

Other (5)

R. Wüest, "Nanometer-scale technology and near-field characterization of InP-based planar photonic-crystal devices," Dissertation 17146, Electrical engineering (ETH Zurich, 2007).

K. Rauscher, "Simulation, design, and characterization of photonic crystal devices in a low vertical index contrast regime," dissertation ETH 16516, electrical engineering (ETH Zurich, 2006).

http://www.comsol.com.

http://wwwhome.math.utwente.nl/~hammer/oms.html.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals--Molding the Flow of Light (Princeton U. Press, 1995).

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Figures (7)

Fig. 1
Fig. 1

Dispersion diagram of a W1 waveguide with r = 0.33 a calculated in 2D with the plane wave expansion method [17] with a frequency-dependent n eff ( λ ) . The PBG extends from u = 0.229 0.318 . For single-mode operation, the frequency range above the odd mode (A, u = 0.270 0.309 ) has a larger bandwidth than the frequency range below (B, u = 0.234 0.258 ).

Fig. 2
Fig. 2

Power transmission for the unoptimized bend computed by the 2D FE method. The gray regions in the transmission spectrum indicate the single-mode frequency range (B) below and (A) above the odd mode. High transmission in B can be achieved at the expense of a narrow 3 dB bandwidth that spans from u = 0.239 0.255 (18% of the PBG, arrow). Outside the single-mode frequency ranges A and B, the simulation results are not meaningful owing to the long-range beatings between the modes, which makes the result dependant on the detector position.

Fig. 3
Fig. 3

Labeling of the holes in the bending region. Only the location of the two black holes at the apex of the bend are parameterized within the optimizer. The arrows indicate the definition of the positive directions for the displacement values in Fig. 4. The dashed circles indicate the position of holes 1 and 2 after the optimization. The background shows the field plot ( H z ) of the optimized bend at u = 0.294 . The power-density integration areas for the simulations are indicated by the rectangles.

Fig. 4
Fig. 4

(a) 3 dB bandwidth as a function of the hole shifts Δ x 1 and Δ x 2 . A large range of shifts (bright region) allows for maximal power transmission and large bandwidth ( Δ u > 0.036 , corresponding to 40% of the PBG). Each darker level step represents a bandwidth reduction of Δ u = 0.02 . The plot for the 1.5 dB bandwidth looks very similar. (b) Maximal transmitted power within the upper single-mode window A as a function of the hole shift Δ x 1 and Δ x 2 . Each darker level step represents a power level reduction of T = 2 % . The circles indicate the optimized position ( Δ x 1 = 0.15 a and Δ x 2 = 0.80 a ).

Fig. 5
Fig. 5

Power transmission of the optimized bend computed with the 2D FE method. Hole 1 is displaced by Δ x 1 = 0.15 a and hole 2 by Δ x 2 = 0.80 a along the symmetry axis of the bend. The frequency range for high transmission is shifted above the odd mode, and the 3 dB bandwidth has increased from 18% to 40% of the PBG. Outside the single-mode frequency ranges A and B, the simulation results are not meaningful owing to the long-range beatings between the modes, which makes the result dependent on the detector position.

Fig. 6
Fig. 6

Simulated power transmission spectra for the bend implemented with r = 0.36 a . The gray region indicates the single-mode frequency range A ( u = 0.281 0.325 ) . A loss term ϵ = 0.014 and effective-index shift δ n = 0.024 ( 0.74 % ) are introduced in the 2D simulation to optimally match the 3D simulations. As the area-integration method for the transmission calculation fails for a simulation including losses, power flux detectors are used at the input and output, and the transmission is calculated according to T = P out P in . As the reflections are low, the result is believed to be accurate within the single-mode transmission window.

Fig. 7
Fig. 7

Measured transmitted power through optimized and unoptimized bends in comparison with a reference W 1 waveguide of the same length. The gray region indicates the single-mode frequency range above the odd mode ( u = 0.281 0.325 ) . An increase of about 5 dB has been achieved by the optimization. The optimized bend retains a device loss of 3 dB .

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