Abstract

Several planar photonic crystal components topology-optimized for TE-polarized light, including 60° bends, Y-splitters, and 90° bends, have been characterized for the TM polarization. The experimental results are confirmed by finite-difference time-domain calculations. The surprising efficiency for TM-polarized light is found and paves the way for photonic crystal components suitable for both polarizations.

© 2005 Optical Society of America

1. Introduction

In 1987, Yablonovitch [1] and John [2] suggested the possibility to inhibit the propagation of photons with energy located within certain bands by creating an artificial periodicity in dielectric materials. This gave rise to the concept of the photonic bandgap (PBG) where the host material is referred to as a photonic crystal (PhC), which has the potential to lead to integrated optical devices with nanoscale features.

Components based on planar photonic crystal waveguides (PhCWs) have experienced a major development during the last years. This progress is mainly due to improvements in the fabrication techniques and the design of these devices. Recently, an optimization technique, called topology optimization [3–8], has been used to improve the performance of PhCW components. Applied to PhCW structures, it consists of a redistribution of material in a way, which maximises the transmission through the device for a given polarization. The transverse-electric (TE) polarization has been the target for this optimization method since it exhibits a large photonic bandgap in a triangular lattice of low index holes in a high index material. Though there is no nearby bandgap for the transverse-magnetic (TM) polarization, we investigated the propagation of TM-polarized light in PhCW-based components originally optimized for TE-polarized light. We found that the propagation of the TM polarization was significantly improved by the optimization for TE polarization, which makes these devices suitable for both polarizations. In this paper, we present the experimental and numerical study of the propagation of TM-polarized light in PhCW components optimized for the TE polarization. In particular, we investigated 60° and 90° bends and a Y-splitter, which are essential components to build optical integrated circuits.

2. Design and fabrication

The components have been fabricated using e-beam lithography and standard anisotropic reactive-ion etching to define the PhC structure into the 300 nm top silicon layer of a silicon-on-insulator (SOI) wafer. The PhC structure has a pitch of ʌ≈400 nm in a triangular configuration of air holes of diameter d≈290 nm. This arrangement gives rise to a large bandgap below the silica line for TE-polarized light. The waveguides were obtained by removing a single row of holes in the T-K direction of the lattice.

The topology optimization method was used to improve the propagation properties of TE-polarized light. This method is a gradient-based optimization method redistributing the material in a given area to enhance the transmission for a specific bandwidth [3,5]. A two-dimensional frequency-domain solver based on a finite element discretization is the basis of the optimization algorithm. One of the specificities of this technique is that the arrangement of material is not restricted to circular holes. The goal is finding the material distribution within certain predefined areas that will maximise the power transmitted through the component. Fig. 1 shows the scanning electron micrograph of the resulting optimized structures for a 60° bend [7], a 90° bend [6], a Y-splitter [8], and a Z-bend [3].

 

Fig. 1. Scanning electron micrograph of topology-optimized components: a) 60° bend, b) 90° bend, c) Y-splitter, and d) Z bend.

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3. Characterization

The components have been characterized with the setup illustrated in Fig. 2. The source was a broadband light emitting diode polarized with a polarizer giving an extinction ratio of more than 40 dB. The polarization of the injected light in the device under test (DUT) was selected with the polarization controller. Tapered lensed fibers enabled us to efficiently couple light in and out of the device. To increase the coupling efficiency into the PhCW, ridge waveguides tapered from 4 μm to 1 μm were used and connected before and after the PhCW. Finally, the light was measured with an optical spectrum analyser with a resolution of 10 nm.

 

Fig. 2. Experimental characterization setup for PhCW components.

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4. Results and discussion

Several components topology-optimized for TE polarization have been characterized with TM-polarized light, including a 60° bend and a Y-splitter, two key components for integrated optics. The two 60° bends (Fig. 1(a)) are separated by a straight 7ʌ long PhCW with identical ridge waveguides for in- and out- coupling. The topology optimization method has been applied to the bend region including the inner and outer parts. Fig. 3 shows the loss per bend for this component for TM-polarized light. The transmission spectrum is normalized to a straight PhCW of similar length as the device with identical ridge waveguide coupling structures. The Fig. also shows the performance of an un-optimized 60° bend with ordinary holes. Both the experimental results and the 3D FDTD (finite-difference time-domain) [9] results are shown for the two configurations. The optimized component has an average loss per bend of 0.4±0.3 dB in the range 1400–1650 nm for TM-polarized light. A slight shift of 1% in absolute wavelength was applied to the 3D FDTD spectrum to better fit the experimental data. Apart from this, the simulation curves are in agreement with the measured spectra. The topology optimization method reduced the propagation loss of TM-polarized light by ~7dB per bend for this 60° bend. Thus, the optimization technique improves the transmission through the 60° bend for TM as well as TE [7] polarization.

 

Fig. 3. Loss per bend (dB) for an optimized and un-optimized 60° bend for TM-polarized light (plain curves: experiments, dashed curves: 3D FDTD simulations).

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In the same way, Fig. 4 shows the loss per bend for an optimized and un-optimized 90° bend for TM-polarized light. As depicted in Fig. 1(b), the two 90° bends are separated by 7 rows with 2 or 3 missing holes. The topology optimization has been applied to a predefined domain as explained in detail in [6]. Again, the optimization technique was applied to this component for TE-polarized light and also improved significantly the performance for TM-polarized light reducing the loss per bend by ~7dB and keeping it on average below 1dB over 250 nm (0.9±0.3 dB).

Another important component investigated is a Y-splitter. It consists of a Y-junction and two 60° bends as displayed in Fig. 1(c). Fig. 5 shows the measured normalized transmission of TM-polarized light for the two output ports of the Y-splitter. The 3D FDTD results (TM polarization) are also shown for the two outports of the splitter. Even though the component was initially optimized for TE-polarized light [8], it exhibits a bandwidth of 180 nm with an average excess loss of only 1.6±0.5 dB for the TM polarization.

 

Fig. 4. Loss per bend (dB) for an optimized (plain curve) and un-optimized (dashed curve) 90° bend for TM-polarized light.

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Fig. 5. Normalized transmission (dB) for the two outports of a topology-optimized Y-splitter for TM-polarized light (black curves: experiments, red curves: 3D FDTD simulations)

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In Ref. 4, un-optimized straight and bent waveguides have been investigated with TM polarization. A broad low-loss transmission window in the range 1500–2000 nm predicted by theory has been confirmed experimentally. Propagation loss as low as 2.5±4 dB/mm around 1525 nm has been measured. The region of low loss for TM-like modes is dominated by index-guiding. Moreover, it overlaps one of the TE photonic bandgap modes. Since the components were topology optimized for a large bandwidth that exceeds the bandwidth of the lowest TE bandgap, the obtained structures favors the index-guiding properties. It would explain why TM-polarized light can be well guided in the 60° bend, the Y-splitter, and the 90° bend making them suitable for both polarizations. Table 1 summarizes the results obtained for the different components for TE and TM polarization.

Tables Icon

Table 1. Loss comparison between TE and TM polarization for different topology-optimized PhC components

On the other hand, for the Z-bend component shown in Fig. 1(d), the topology optimization method improved much more the performance of TE-polarized light [3] compared to that of TM-polarized light. The optimization method has been applied to the outer part of the two bends. Fig. 6 shows the loss per bend for this component. The optimized component (Fig. 1(d)) is compared to an un-optimized Z-bend, that is two consecutive 120 ° bends with ordinary holes. The improvement introduced by the optimization method is here of about 2dB, which is much less than for the previous components. The Z-bend is probing the photonic bandgap effect with strong reflection due to the 120° bend whereas the 60° and 90° bends and the Y-splitter have a more index-guiding-like behaviour. The guiding in the optimal 120° bend is dominated by bandgap effects and, therefore, it does not work so well for TM polarized light.

 

Fig. 6. Loss per bend (dB) for an optimized (plain curve) and un-optimized (dashed curve) Z-bend for TM-polarized light.

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5. Conclusion

In conclusion, we have shown that it is possible to obtain PhCW components working for both TE and TM polarizations using the topology optimization method. This method reduced loss by rearranging the material in some definite regions of different components bringing it, for TM-polarized light, to 0.4±0.3 dB per bend for the 60° bend, to 0.8±0.3 dB per bend for the 90° bend, and to 1.6±0.5 dB for the Y-splitter, over a bandwidth of more than 150 nm. This technique is increasing the performance of the index-guiding region for the TM-polarized light. Interestingly, the topology optimized parts of the structures resemble ridge waveguide structures as intuitively might have been expected, since it previously has been demonstrated that straight and sharply bent single-mode ridge waveguides can display very low losses [10]. Hence, our result demonstrates the reliability of the topology optimization method because it proposes, in these cases, simple and intuitive optimized designs. On the other hand, in the case of the sharp Z bend TM and TE polarized light does not give similar results as this structure is probing deeper into the PBG area due to its shape. The topology optimization method showed that the periodic arrangement of circular air holes in the bending and splitting regions of the component is not the preferred solution to guide the light.

Acknowledgments

This work was supported in part by the Danish Technical Research Council through the research programs ‘Planar Integrated PBG Elements’ (PIPE) and ‘Designing bandgap materials and structures with optimized dynamic properties’.

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 . P. I. Borel, A. Harp∅th, L. H. Frandsen, M. Kristensen, P. Shi, J. S. Jensen, and O. Sigmund , “ Topology optimization and fabrication of photonic crystal structures ,” Opt. Express 12 , 1996 – 2001 ( 2004 ), .http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1996 . [CrossRef]   [PubMed]  

4 . P. I. Borel, L. H. Frandsen, M Thorhauge, A. Harp∅th, Y. X. Zhuang, and M. Kristensen , “ Efficient propagation of TM polarized light in photonic crystal components exhibiting band gaps for TE polarized light ,” Opt. Express 11 , 1757 – 1762 ( 2003 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1757 . [CrossRef]   [PubMed]  

5 . J. S. Jensen and O. Sigmund , “ Topology optimization of photonic crystal structures: A hight bandwidth low loss T-junction waveguide ,” J. Opt. Soc. Am. B 22 , 1191 – 1198 ( 2005 ). [CrossRef]  

6 . J. S. Jensen, O. Sigmund, L. H. Frandsen, P. I. Borel, A. Harp∅th, and M. Kristensen , “ Topology design and fabrication of an efficient double 90° photonic crystal waveguide bend ,” IEEE Photonics Technol. Lett. 17 , 1202 – 1204 ( 2005 ). [CrossRef]  

7 . L. H. Frandsen, A. Harp∅th, 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 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5916 . [CrossRef]   [PubMed]  

8 . P. I. Borel, L. H. Frandsen, A. Harp∅th, M. Kristensen, J. S. Jensen, and O. Sigmund , “ Topology optimised broadband photonic crystal Y-splitter ,” Electron. Lett. 41 , 69 – 71 ( 2005 ). [CrossRef]  

9 . A. Lavrinenko, P. I. Borel, L. H. Frandsen, M. Thorhauge, A. Harp∅th, M. Kristensen, and T. Niemi , “ Comprehensive FDTD modelling of photonic crystal waveguide components ,” Opt. Express 12 , 234 – 248 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-234 . [CrossRef]   [PubMed]  

10 . Y. A. Vlasov and S. J. McNab , “ Losses in single-mode silicon-on-insulator strip waveguides and bends ,” Opt. Express 12 , 1622 – 1631 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1622 . [CrossRef]   [PubMed]  

References

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  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. P. I. Borel, A. Harp∅th, L. H. Frandsen, M. Kristensen, P. Shi, J. S. Jensen, and O. Sigmund , “ Topology optimization and fabrication of photonic crystal structures ,” Opt. Express   12 , 1996 – 2001 ( 2004 ), .http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1996 .
    [CrossRef] [PubMed]
  4. P. I. Borel, L. H. Frandsen, M Thorhauge, A. Harp∅th, Y. X. Zhuang, and M. Kristensen , “ Efficient propagation of TM polarized light in photonic crystal components exhibiting band gaps for TE polarized light ,” Opt. Express   11 , 1757 – 1762 ( 2003 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1757 .
    [CrossRef] [PubMed]
  5. J. S. Jensen and O. Sigmund , “ Topology optimization of photonic crystal structures: A hight bandwidth low loss T-junction waveguide ,” J. Opt. Soc. Am. B   22 , 1191 – 1198 ( 2005 ).
    [CrossRef]
  6. J. S. Jensen, O. Sigmund, L. H. Frandsen, P. I. Borel, A. Harp∅th, and M. Kristensen , “ Topology design and fabrication of an efficient double 90° photonic crystal waveguide bend ,” IEEE Photonics Technol. Lett.   17 , 1202 – 1204 ( 2005 ).
    [CrossRef]
  7. L. H. Frandsen, A. Harp∅th, 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 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5916 .
    [CrossRef] [PubMed]
  8. P. I. Borel, L. H. Frandsen, A. Harp∅th, M. Kristensen, J. S. Jensen, and O. Sigmund , “ Topology optimised broadband photonic crystal Y-splitter ,” Electron. Lett.   41 , 69 – 71 ( 2005 ).
    [CrossRef]
  9. A. Lavrinenko, P. I. Borel, L. H. Frandsen, M. Thorhauge, A. Harp∅th, M. Kristensen, and T. Niemi , “ Comprehensive FDTD modelling of photonic crystal waveguide components ,” Opt. Express   12 , 234 – 248 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-234 .
    [CrossRef] [PubMed]
  10. Y. A. Vlasov and S. J. McNab , “ Losses in single-mode silicon-on-insulator strip waveguides and bends ,” Opt. Express   12 , 1622 – 1631 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1622 .
    [CrossRef] [PubMed]

2005 (3)

J. S. Jensen, O. Sigmund, L. H. Frandsen, P. I. Borel, A. Harp∅th, and M. Kristensen , “ Topology design and fabrication of an efficient double 90° photonic crystal waveguide bend ,” IEEE Photonics Technol. Lett.   17 , 1202 – 1204 ( 2005 ).
[CrossRef]

P. I. Borel, L. H. Frandsen, A. Harp∅th, M. Kristensen, J. S. Jensen, and O. Sigmund , “ Topology optimised broadband photonic crystal Y-splitter ,” Electron. Lett.   41 , 69 – 71 ( 2005 ).
[CrossRef]

J. S. Jensen and O. Sigmund , “ Topology optimization of photonic crystal structures: A hight bandwidth low loss T-junction waveguide ,” J. Opt. Soc. Am. B   22 , 1191 – 1198 ( 2005 ).
[CrossRef]

2004 (4)

2003 (1)

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]

Borel, P. I.

J. S. Jensen, O. Sigmund, L. H. Frandsen, P. I. Borel, A. Harp∅th, and M. Kristensen , “ Topology design and fabrication of an efficient double 90° photonic crystal waveguide bend ,” IEEE Photonics Technol. Lett.   17 , 1202 – 1204 ( 2005 ).
[CrossRef]

P. I. Borel, L. H. Frandsen, A. Harp∅th, M. Kristensen, J. S. Jensen, and O. Sigmund , “ Topology optimised broadband photonic crystal Y-splitter ,” Electron. Lett.   41 , 69 – 71 ( 2005 ).
[CrossRef]

A. Lavrinenko, P. I. Borel, L. H. Frandsen, M. Thorhauge, A. Harp∅th, M. Kristensen, and T. Niemi , “ Comprehensive FDTD modelling of photonic crystal waveguide components ,” Opt. Express   12 , 234 – 248 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-234 .
[CrossRef] [PubMed]

L. H. Frandsen, A. Harp∅th, 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 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5916 .
[CrossRef] [PubMed]

P. I. Borel, A. Harp∅th, L. H. Frandsen, M. Kristensen, P. Shi, J. S. Jensen, and O. Sigmund , “ Topology optimization and fabrication of photonic crystal structures ,” Opt. Express   12 , 1996 – 2001 ( 2004 ), .http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1996 .
[CrossRef] [PubMed]

P. I. Borel, L. H. Frandsen, M Thorhauge, A. Harp∅th, Y. X. Zhuang, and M. Kristensen , “ Efficient propagation of TM polarized light in photonic crystal components exhibiting band gaps for TE polarized light ,” Opt. Express   11 , 1757 – 1762 ( 2003 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1757 .
[CrossRef] [PubMed]

Frandsen, L. H.

P. I. Borel, L. H. Frandsen, A. Harp∅th, M. Kristensen, J. S. Jensen, and O. Sigmund , “ Topology optimised broadband photonic crystal Y-splitter ,” Electron. Lett.   41 , 69 – 71 ( 2005 ).
[CrossRef]

J. S. Jensen, O. Sigmund, L. H. Frandsen, P. I. Borel, A. Harp∅th, and M. Kristensen , “ Topology design and fabrication of an efficient double 90° photonic crystal waveguide bend ,” IEEE Photonics Technol. Lett.   17 , 1202 – 1204 ( 2005 ).
[CrossRef]

A. Lavrinenko, P. I. Borel, L. H. Frandsen, M. Thorhauge, A. Harp∅th, M. Kristensen, and T. Niemi , “ Comprehensive FDTD modelling of photonic crystal waveguide components ,” Opt. Express   12 , 234 – 248 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-234 .
[CrossRef] [PubMed]

P. I. Borel, A. Harp∅th, L. H. Frandsen, M. Kristensen, P. Shi, J. S. Jensen, and O. Sigmund , “ Topology optimization and fabrication of photonic crystal structures ,” Opt. Express   12 , 1996 – 2001 ( 2004 ), .http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1996 .
[CrossRef] [PubMed]

L. H. Frandsen, A. Harp∅th, 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 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5916 .
[CrossRef] [PubMed]

P. I. Borel, L. H. Frandsen, M Thorhauge, A. Harp∅th, Y. X. Zhuang, and M. Kristensen , “ Efficient propagation of TM polarized light in photonic crystal components exhibiting band gaps for TE polarized light ,” Opt. Express   11 , 1757 – 1762 ( 2003 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1757 .
[CrossRef] [PubMed]

HarpØth, A.

P. I. Borel, L. H. Frandsen, A. Harp∅th, M. Kristensen, J. S. Jensen, and O. Sigmund , “ Topology optimised broadband photonic crystal Y-splitter ,” Electron. Lett.   41 , 69 – 71 ( 2005 ).
[CrossRef]

J. S. Jensen, O. Sigmund, L. H. Frandsen, P. I. Borel, A. Harp∅th, and M. Kristensen , “ Topology design and fabrication of an efficient double 90° photonic crystal waveguide bend ,” IEEE Photonics Technol. Lett.   17 , 1202 – 1204 ( 2005 ).
[CrossRef]

A. Lavrinenko, P. I. Borel, L. H. Frandsen, M. Thorhauge, A. Harp∅th, M. Kristensen, and T. Niemi , “ Comprehensive FDTD modelling of photonic crystal waveguide components ,” Opt. Express   12 , 234 – 248 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-234 .
[CrossRef] [PubMed]

L. H. Frandsen, A. Harp∅th, 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 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5916 .
[CrossRef] [PubMed]

P. I. Borel, A. Harp∅th, L. H. Frandsen, M. Kristensen, P. Shi, J. S. Jensen, and O. Sigmund , “ Topology optimization and fabrication of photonic crystal structures ,” Opt. Express   12 , 1996 – 2001 ( 2004 ), .http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1996 .
[CrossRef] [PubMed]

P. I. Borel, L. H. Frandsen, M Thorhauge, A. Harp∅th, Y. X. Zhuang, and M. Kristensen , “ Efficient propagation of TM polarized light in photonic crystal components exhibiting band gaps for TE polarized light ,” Opt. Express   11 , 1757 – 1762 ( 2003 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1757 .
[CrossRef] [PubMed]

Jensen, J. S.

John, S.

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

Kristensen, M.

J. S. Jensen, O. Sigmund, L. H. Frandsen, P. I. Borel, A. Harp∅th, and M. Kristensen , “ Topology design and fabrication of an efficient double 90° photonic crystal waveguide bend ,” IEEE Photonics Technol. Lett.   17 , 1202 – 1204 ( 2005 ).
[CrossRef]

P. I. Borel, L. H. Frandsen, A. Harp∅th, M. Kristensen, J. S. Jensen, and O. Sigmund , “ Topology optimised broadband photonic crystal Y-splitter ,” Electron. Lett.   41 , 69 – 71 ( 2005 ).
[CrossRef]

A. Lavrinenko, P. I. Borel, L. H. Frandsen, M. Thorhauge, A. Harp∅th, M. Kristensen, and T. Niemi , “ Comprehensive FDTD modelling of photonic crystal waveguide components ,” Opt. Express   12 , 234 – 248 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-234 .
[CrossRef] [PubMed]

L. H. Frandsen, A. Harp∅th, 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 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5916 .
[CrossRef] [PubMed]

P. I. Borel, A. Harp∅th, L. H. Frandsen, M. Kristensen, P. Shi, J. S. Jensen, and O. Sigmund , “ Topology optimization and fabrication of photonic crystal structures ,” Opt. Express   12 , 1996 – 2001 ( 2004 ), .http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1996 .
[CrossRef] [PubMed]

P. I. Borel, L. H. Frandsen, M Thorhauge, A. Harp∅th, Y. X. Zhuang, and M. Kristensen , “ Efficient propagation of TM polarized light in photonic crystal components exhibiting band gaps for TE polarized light ,” Opt. Express   11 , 1757 – 1762 ( 2003 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1757 .
[CrossRef] [PubMed]

Lavrinenko, A.

McNab, S. J.

Niemi, T.

Shi, P.

Sigmund, O.

Thorhauge, M

Thorhauge, M.

Vlasov, Y. A.

Yablonovitch, E.

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

Zhuang, Y. X.

Electron. Lett. (1)

P. I. Borel, L. H. Frandsen, A. Harp∅th, M. Kristensen, J. S. Jensen, and O. Sigmund , “ Topology optimised broadband photonic crystal Y-splitter ,” Electron. Lett.   41 , 69 – 71 ( 2005 ).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

J. S. Jensen, O. Sigmund, L. H. Frandsen, P. I. Borel, A. Harp∅th, and M. Kristensen , “ Topology design and fabrication of an efficient double 90° photonic crystal waveguide bend ,” IEEE Photonics Technol. Lett.   17 , 1202 – 1204 ( 2005 ).
[CrossRef]

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

Opt. Express (5)

P. I. Borel, L. H. Frandsen, M Thorhauge, A. Harp∅th, Y. X. Zhuang, and M. Kristensen , “ Efficient propagation of TM polarized light in photonic crystal components exhibiting band gaps for TE polarized light ,” Opt. Express   11 , 1757 – 1762 ( 2003 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-15-1757 .
[CrossRef] [PubMed]

A. Lavrinenko, P. I. Borel, L. H. Frandsen, M. Thorhauge, A. Harp∅th, M. Kristensen, and T. Niemi , “ Comprehensive FDTD modelling of photonic crystal waveguide components ,” Opt. Express   12 , 234 – 248 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-2-234 .
[CrossRef] [PubMed]

Y. A. Vlasov and S. J. McNab , “ Losses in single-mode silicon-on-insulator strip waveguides and bends ,” Opt. Express   12 , 1622 – 1631 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1622 .
[CrossRef] [PubMed]

P. I. Borel, A. Harp∅th, L. H. Frandsen, M. Kristensen, P. Shi, J. S. Jensen, and O. Sigmund , “ Topology optimization and fabrication of photonic crystal structures ,” Opt. Express   12 , 1996 – 2001 ( 2004 ), .http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-9-1996 .
[CrossRef] [PubMed]

L. H. Frandsen, A. Harp∅th, 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 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-24-5916 .
[CrossRef] [PubMed]

Phys. Rev. Lett (1)

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

Phys. Rev. Lett. (1)

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

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Figures (6)

Fig. 1.
Fig. 1.

Scanning electron micrograph of topology-optimized components: a) 60° bend, b) 90° bend, c) Y-splitter, and d) Z bend.

Fig. 2.
Fig. 2.

Experimental characterization setup for PhCW components.

Fig. 3.
Fig. 3.

Loss per bend (dB) for an optimized and un-optimized 60° bend for TM-polarized light (plain curves: experiments, dashed curves: 3D FDTD simulations).

Fig. 4.
Fig. 4.

Loss per bend (dB) for an optimized (plain curve) and un-optimized (dashed curve) 90° bend for TM-polarized light.

Fig. 5.
Fig. 5.

Normalized transmission (dB) for the two outports of a topology-optimized Y-splitter for TM-polarized light (black curves: experiments, red curves: 3D FDTD simulations)

Fig. 6.
Fig. 6.

Loss per bend (dB) for an optimized (plain curve) and un-optimized (dashed curve) Z-bend for TM-polarized light.

Tables (1)

Tables Icon

Table 1. Loss comparison between TE and TM polarization for different topology-optimized PhC components

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