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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 13 — Jun. 25, 2007
  • pp: 8472–8478
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InP-based compact photonic crystal directional coupler with large operation range

Patric Strasser, Ralf Flückiger, Robert Wüest, Franck Robin, and Heinz Jäckel  »View Author Affiliations


Optics Express, Vol. 15, Issue 13, pp. 8472-8478 (2007)
http://dx.doi.org/10.1364/OE.15.008472


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Abstract

We present the design, fabrication and measurement of photonic crystal directional couplers in the InP/InGaAsP/InP material system. A comprehensive analysis of the dependence of the coupling length and usable wave-length range on the diameter of the holes next to the waveguides is given. The possibility to trade-off coupling length against usable wavelength range is shown. Designs with coupling lengths as low as 52 lattice constants and with an operation range covering 16% of the bandgap width are fabricated and measured. Good agreement between optimized and measured devices is achieved.

© 2007 Optical Society of America

1. Introduction

Planar photonic crystals (PhCs) [1

1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals - Molding the flow of light (1995).

] are structures with a spatially periodic modulation of the refractive index in one, two or three dimensions. Two-dimensional PhCs are often fabricated by etching a triangular array of air holes with lattice constant a into a background semiconductor slab waveguide. Applying this concept, basic devices like W1 waveguides (one missing row of holes) in InP/InGaAsP [2

2. A. Xing, M. Davanço, D. J. Blumenthal, and E. L. Hu, “Transmission measurement of tapered single-line defect photonic crystal waveguides,” IEEE Photon. Technol. Lett. 17, 2092–2094 (2005). [CrossRef]

] and SOI [3

3. M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. l. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000). [CrossRef]

], power splitters and 60° bends [4

4. K. Rauscher, Simulation, design and characterisation of photonic crystal devices in a low vertical index contrast regime, Diss. ETH Nr. 16516, Electr. Eng. ETH Zürich, 2006.

] have been demonstrated. Parallel PhC waveguide directional couplers (DCs) [5

5. Y. Tanaka, H. Nakamura, Y. Sugimoto, N. Ikeda, K. Asakawa, and K. Inoue, “Coupling properties in a 2-D photonic crystal slab directional coupler with a triangular lattice of air holes,” IEEE J. Quantum Electron. 41, 76–84 (2005). [CrossRef]

] are key components for optical communication systems. They can be used as power splitters of any spitting ratio, and have been widely investigated, both theoretically [5–9

5. Y. Tanaka, H. Nakamura, Y. Sugimoto, N. Ikeda, K. Asakawa, and K. Inoue, “Coupling properties in a 2-D photonic crystal slab directional coupler with a triangular lattice of air holes,” IEEE J. Quantum Electron. 41, 76–84 (2005). [CrossRef]

] and experimentally [5

5. Y. Tanaka, H. Nakamura, Y. Sugimoto, N. Ikeda, K. Asakawa, and K. Inoue, “Coupling properties in a 2-D photonic crystal slab directional coupler with a triangular lattice of air holes,” IEEE J. Quantum Electron. 41, 76–84 (2005). [CrossRef]

, 10–13

10. M. Tokushima and H. Yamada, “Photonic crystal line defect waveguide directional coupler,” Electron. Lett. 37, 1454–1455 (2001). [CrossRef]

]. InP or GaAs are the materials of choice when heading for active telecommunication devices at λ=1550nm, but only few reports present DCs in these material systems. Qiu et.al. [12

12. M. Qiu, M. Mulot, M. Swillo, S. Anand, B. Jaskorzynska, A. Karlsson, M. Kamp, and A. Forchel, “Photonic crystal optical filter based on contra-directional waveguide coupling,” Appl. Phys. Lett. 83, 5121–5123 (2003). [CrossRef]

] present an asymmetric bidirectional coupler in InP. For GaAs, W3 DCs with coupling lengths (CLs) of several hundreds of periods [11

11. D. Leuenberger, R. Ferrini, L. A. Dunbar, R. Houdré, M. Kamp, and A. Forchel, “Codirectional couplers in GaAs-based planar photonic crystals,” Appl. Phys. Lett. 86, 081108 (2005). [CrossRef]

] and W1 DCs exhibiting short CLs of around 60a but only over a very narrow operation range (OR) [5

5. Y. Tanaka, H. Nakamura, Y. Sugimoto, N. Ikeda, K. Asakawa, and K. Inoue, “Coupling properties in a 2-D photonic crystal slab directional coupler with a triangular lattice of air holes,” IEEE J. Quantum Electron. 41, 76–84 (2005). [CrossRef]

] are reported. To best of our knowledge, this article presents the first systematic design and detailed experimental verification of W1-based DCs in InP, showing short CLs maintained over the whole OR. This is a mandatory feature for the fabrication of compact broad-band power splitters. Furthermore, a complete analysis of the dependence and trade-off of the CL and OR with the design is given.

Fig. 1. Dispersion diagram of a W1 waveguide (blue dashed lines) and a DC (red lines) with reduced central hole radius (Fig. 2, design B, rc=0.25a), restricted to the upper half of the photonic bandgap. The shaded area represents the area of bulk photonic bands. The quasisingle- mode region is limited by airband modes lowered in frequency and the odd mode.

The useful OR of DCs is the frequency range where (i) the splitting Δk of the modes is large and constant, and (ii) only two modes are present for the one frequency. This corresponds to the quasi-single-mode region depicted in Fig. 1). As the odd mode of the W1 waveguide lies in the middle of the PhC bandgap, it splits the PBG up into two halves. Depending on the design, quasi-single-mode regions can lie above or below the odd W1 mode. The mode splitting Δk(u) of ORs below the odd W1 mode are normally strongly dependent on the reduced frequency (u=a/λ). The upper frequency window has a rather flat Δk(u) as a function of reduced frequency, and is therefore suited for broad-band power splitters. Since our work is focused on power splitters, we chose the upper quasi-single-mode region for the further optimization of the DC. The goal of the optimization is to simultaneously achieve a large OR and a short CL.

2. Modelling

Due to the large size of the DC, full-wave 3D simulations are not feasible. The DCs are therefore investigated by means of 2D simulations. The vertical layer structure [InP cladding (300nm, n=3.17)/InGaAsP core (522nm, n=3.35)/InP substrate (n=3.17)] can be represented accurately by an effective refractive index (neff) [14

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

]. For our layer stack, neff is set to neff =3.258 at λ=1550nm as analytically computed from the vertical slab mode profile. The hole radius for the bulk PhC is fixed to r=0.31a, which proved to be a good balance between PBG width and fabrication tolerances. The DCs are simulated by the finite-element (FE) simulation tool COMSOL and the plane wave expansion (PWE) tool MPB [15

15. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis,” Opt. Express 8, 173–190 (2001). [CrossRef] [PubMed]

]. The light coupled into the adjacent waveguide is referred to as the cross state and the transmitted light is referred to as the bar state (see Fig. 5).

With FE simulations, LC is obtained by fitting the function A∙cos2(π∙x/LC), which represents the power intensity in the bar waveguide as a function of the waveguide position x [5

5. Y. Tanaka, H. Nakamura, Y. Sugimoto, N. Ikeda, K. Asakawa, and K. Inoue, “Coupling properties in a 2-D photonic crystal slab directional coupler with a triangular lattice of air holes,” IEEE J. Quantum Electron. 41, 76–84 (2005). [CrossRef]

], to the simulated power density plot of the bar state for each frequency individually. A and LC are fitting parameters. The slab waveguide dispersion is accounted for in the 2D simulations by calculating neff for each individual frequency. In contrast, with PWE simulations the CL is extracted from the k-vector splitting Δk(u) of the DC modes in the quasi-single-mode region. Each design is simulated by both simulation methods to verify the validity of the results. The OR is always determined from the PWE computations, as the FE method does not deliver accurate band edge information.

Fig. 2. (a). Schematics of the three investigated coupler designs. (b). PWE simulations of OR and minimal CL. The red segments represent the DCs with edge hole radius re=0.31a for different central hole radii. The blue segments correspond to designs with edge hole radius to re=0.33a, re=0.35a and re=0.37a for the upper, middle and lower segment of each group, respectively.

Three different design strategies have been investigated as shown in Fig. 2(a). In addition to the simplest design with a homogenous hole size (A), DCs with a reduced central hole size (B) and an additionally increased edge hole size (C) are investigated.

Design A exhibits weak coupling causing a minimal CL of over 1000a. By reducing the central hole size from rc=0.31a to rc=0.13a (Fig. 2(b), red lines), the coupling strength is enhanced and the minimal CL is drastically reduced down to 34a. However, this reduction is achieved at the expense of the OR, which is decreased by a factor of 3. The decrease of the CL is visualized in the field plots of the different coupler designs (Fig. 3). In addition, the effect of increasing the holes at the outer edges of the W1 waveguides is investigated. The minimal CL can be further decreased by 23% and 13% for central hole radii of rc=0.25a and rc=0.19a, respectively, by increasing the edge hole radius re to 0.37a (Fig. 2(b), blue lines). The width of the OR itself is almost not affected by the edge hole increase but the OR is shifted towards higher frequencies. This may lead to a reduction of the OR if it is shifted into the PhC airband. Whereas the choice of the radius for the central hole is given by the trade-off between the targeted OR and CL, the reduction of the CL by enlarging the edge holes is only limited by the ability to fabricate large holes. Therefore the minimal CL for a specific application fixed by the required OR, which, in turn, specifies the central hole size rc. In a second design step, the edge hole size re can be increased to minimize the CL until the OR starts overlapping the bulk PhC modes or the technological limit for the fabrication of large holes is reached.

Fig. 3. FE simulations of the Hz field for coupler designs A and B (Fig. 2).

The design with the central hole size rc=0.19a provides CLs as short as 52a and an OR of 16% of the total bandgap width. In the remainder of this paper, we will focus on these designs with varying edge hole radius. Figure 4 presents the simulated CLs. Both simulation methods yield very similar results with a discrepancy below 4%. The variation of the CL within the OR is less than 10% for all DCs with rc=0.19a. This makes the DCs useful as broad-band power splitters at any given splitting ratio.

For instance, a 3dB power splitter using the DC with rc=0.19a and re=0.37a exhibits a total device length of only 14a (~6μm at a=435nm, λ=1550nm). For this design, the coupling ratio lies between 47% and 55% over the whole OR (~60nm bandwidth at a=435nm, λ=1550nm). Within 1dB tolerance, the same 3dB coupler design can be used to split up frequencies over the whole OR. Similar values were obtained for the other couplers with rc=0.19a. This DC length should be compared to conventional directional couplers with similar feature sizes in the same material system, such as trench waveguide with a width of 500nm and a waveguide separation of 170nm. Our FE simulations show that such a conventional coupler provides a CL of around 100μm at λ=1550nm with a ~25μm device length for the splitter realization.

Fig. 4. CL vs. reduced frequency simulated with the FE (empty blue diamonds) and PWE (filled red squares) techniques for the couplers with a central hole size rc=0.19a and different edge hole sizes. The change of the CL within the OR is below 10%.

3. Fabrication and measurements

The structures with central hole radius rc=0.19a were fabricated for experimental verification. A lattice constant of a=435nm is used. The vertical layer stack consists of an InP cladding (300nm, n=3.17), an InGaAsP core (522nm, n=3.35) and the InP substrate (n=3.17). A combination of electron beam lithography, reactive ion etching (RIE) and inductively coupled plasma-RIE etching was used for resist patterning, hard-mask etching and semiconductor etching, respectively. The processing details can be found elsewhere [16–18

16. 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]

].

A 10a long W1 waveguide is placed before the DC to allow the mode to settle. A short taper made of holes of decreasing radius is added at the beginning of the cross waveguide to suppress the reflections that occur due to mode mismatch between the DC modes and the W1 waveguide mode. The waveguides are separated immediately after the DC by means of multimode trench waveguides. The width and distance of these trench waveguides are matched to the W1 waveguides. No bend is integrated into the PhC to simplify the interpretation of the results. By means of FE simulations and measurements, we have verified that the coupling after the output in the short region where the two trench waveguides are in close proximity can be neglected. Light between the DC and the cleaved facets is guided through 3μm wide and ca. 1.5mm long deeply etched access waveguides. Figure 5 shows a scanning electron micrograph of a DC with reduced central hole size, the W1 waveguide with the taper and the access waveguides.

Fig. 5. SEM micrograph of a typical fabricated coupler. A W1 waveguide is preceding the DC and a short taper in the cross waveguide suppresses reflections between the W1 and the DC.

The device characterization is performed by the endfire technique. Light from an off-chip tunable laser sources covering the 1470nm to 1630nm wavelength range, which corresponds to a reduced-frequency range of u=0.267 to 0.297 for a=435nm. Light is coupled into the chip facet by a lensed fiber. At the exit the light is collected by a microscope objective and measured by an InGaAs detector.

Of each coupler design, couplers of 5 different lengths (10a, 20a, 30a, 40a and 50a) were fabricated. The transmission through the bar and cross states was recorded sequentially without moving the input fiber. A spectral tuning resolution of λ=0.5nm was chosen for the tunable sources, and the raw measurements were averaged over a sliding window of 5nm to eliminate the Fabry-Pérot (FP) fringes arising due to the the presence of a parasitic FP cavity between the coupler and the cleaved facets. The measured transmission power (P) was normalized for each measurement and frequency according to P(u)bar/cross,norm.=P(u)bar/cross/(P(u)bar+P(u)cross). This normalization makes the measurement independent of the incoupling efficiency and the waveguides loss. For each frequency, the CL was extracted by fitting the normalized power vs. device length curves with A∙cos2(π∙x/LC) and A∙sin2(π∙x/LC) for the bar and the cross state, respectively. As norm for the fitting, the mean least square distance (RMS) over all 10 measurement points was taken. The fitting error is in average around 5%. Although substrate type PhC waveguides by necessity operate above the substrate light line, and hence are intrinsically lossy, in practice losses stem primarily from out of plane scattering induce by fabrication imperfections. To estimate the losses of a DC, we refer to the measured reference W1 waveguides as an upper limit for the loss. The W1 waveguide loss is ~160dB/mm within the OR of the DCs as determined by the cutback method. Therefore the above mentioned 3dB power splitter shows only an additional propagation loss of 1dB.

Fig. 6. (a). Fitting of the measured normalized transmitted power for the bar (red filled squares) and cross (empty blue diamonds) states vs. device length. rc=0.19a, re=0.31a and u=0.271. (b). Comparison of the PWE simulation (dashed blue line) and measurements (red line) of the CL for the DCs with rc=0.19a.

The measured CLs are presented in Fig. 6 for DCs with rc=0.19a and re=0.31a to re=0.37a, together with the PWE simulations. The measured CLs amount to 60a to 70a and are between 8a and 12a higher than the corresponding PWE simulations. The slight increase of the CL with frequency is reproduced in the measurement. A further significant reduction in CL at a given frequency can be achieved by enlarging the edge holes.

The observed mismatch in the CL between simulations and measurements of around 10a can be explained by a slight variation in the fabricated hole size. The deviation of the fabricated hole diameter from the targeted value was evaluated by SEM micrographs, and is summarized in Table 1, second row. To understand the impact of hole-size deviations on the CL, we performed a sensitivity analysis using PWE simulations, for each hole type separately. This analysis was performed by varying the hole diameter around the target value and extracting the change of CL depending on the hole diameter deviation (ΔCL/Δ%). The contribution of the central hole size is the most significant with 1.6a/% hole size variation in the CL, as these holes are most strongly interacting to the light mode. The crystal hole size, however, has a minor impact of just 0.2a/% hole size variation, as the mode is mostly shielded from these holes by the edge holes. Comparing the deviation of the fabricated hole size to the target hole size, a total 15a increase in the CL has to be expected from fabrication imperfections, superior to the observed value of 8a to 12a. It should however be considered that real holes are in general not perfectly cylindrical but of conical shape [18

18. 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]

]. The light mode therefore experiences a smaller effective hole size than measured from top-view SEM micrographs, which thus mitigates the change in CL, especially caused by the central holes.

Table 1. Comparison between target and fabricated hole sizes and impact on the CL by means of PWE simulations.

table-icon
View This Table

In summary, we have presented the full cycle of design, fabrication and measurement of DCs in the InP/InGaAsP/InP low-refractive-index-contrast system. New designs with increased holes size at the outer edges of the waveguides and a smaller central hole radius have been proposed to maintain the OR of the coupler while dramatically reducing the CL. A comprehensive analysis of the different DC designs demonstrated the dependence of the CL and the OR on the edge and central hole size. Short CLs as low as 52a with a large OR were obtained in simulations for DCs with rc=0.19a, and the flat dependence of the CL on the reduced frequency makes these design suitable for the use as a power splitter over a broad frequency range. These proposed designs have been fabricated and characterized. Good agreement between simulations and verifying measurements has been achieved. The relatively high propagation losses observed in the InP/InGaAsP/InP system could be reduced by switching to an airbridge-type membrane material system. We believe that the coupling length reduction can be achieved with an analogous topology in membranes, due to the strong similarities in the dispersion relations of DCs in both material systems. A slightly larger CL was measured compared to simulations, which can be attributed to fabrication variations, as confirmed by a sensitivity analysis. Even shorter coupling lengths could be achieved by trading-off the OR. The CLs of PhC-based DCs are significantly (~4x) shorter than for conventional directional couplers.

Acknowledgments

This work was carried out in the framework of the Swiss National Science Foundation program NCCR Quantum Photonics. Devices were fabricated at the FIRST Center of Micro- and Nanoscience of the ETH Zurich in the framework of the Nanostructuring platform of the European ePiXnet network of excellence on photonic integrated circuits. The authors would like to acknowledge O. Homan, E. Gini and M. Ebnöther (FIRST) for technical support.

References and links

1.

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals - Molding the flow of light (1995).

2.

A. Xing, M. Davanço, D. J. Blumenthal, and E. L. Hu, “Transmission measurement of tapered single-line defect photonic crystal waveguides,” IEEE Photon. Technol. Lett. 17, 2092–2094 (2005). [CrossRef]

3.

M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. l. Scherer, and T. P. Pearsall, “Waveguiding in planar photonic crystals,” Appl. Phys. Lett. 77, 1937–1939 (2000). [CrossRef]

4.

K. Rauscher, Simulation, design and characterisation of photonic crystal devices in a low vertical index contrast regime, Diss. ETH Nr. 16516, Electr. Eng. ETH Zürich, 2006.

5.

Y. Tanaka, H. Nakamura, Y. Sugimoto, N. Ikeda, K. Asakawa, and K. Inoue, “Coupling properties in a 2-D photonic crystal slab directional coupler with a triangular lattice of air holes,” IEEE J. Quantum Electron. 41, 76–84 (2005). [CrossRef]

6.

M. Koshiba, “Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers,” J. Lightwave Technol. 19, 1970–1975 (2001). [CrossRef]

7.

A. Sharkawy, S. Shi, and D. W. Prather, “Electro-optical switching using coupled photonic crystal waveguides,” Opt. Express 10, 1048–1059 (2002). [PubMed]

8.

S. Boscolo, M. Midrio, and C. G. Someda, “Coupling and decoupling of electromagnetic waves in parallel 2D photonic crystal waveguides,” IEEE J. Quantum Electron. 38, 47–53 (2002). [CrossRef]

9.

A. Martinez, F. Cuesta, and J. Marti, “Ultrashort 2-D photonic crystal directional couplers,” IEEE Photon. Technol. Lett. 15, 694–696 (2003). [CrossRef]

10.

M. Tokushima and H. Yamada, “Photonic crystal line defect waveguide directional coupler,” Electron. Lett. 37, 1454–1455 (2001). [CrossRef]

11.

D. Leuenberger, R. Ferrini, L. A. Dunbar, R. Houdré, M. Kamp, and A. Forchel, “Codirectional couplers in GaAs-based planar photonic crystals,” Appl. Phys. Lett. 86, 081108 (2005). [CrossRef]

12.

M. Qiu, M. Mulot, M. Swillo, S. Anand, B. Jaskorzynska, A. Karlsson, M. Kamp, and A. Forchel, “Photonic crystal optical filter based on contra-directional waveguide coupling,” Appl. Phys. Lett. 83, 5121–5123 (2003). [CrossRef]

13.

M. Thorhauge, L. H. Frandsen, and P. I. Borel, “Efficient photonic crystal directional couplers,” Opt. Lett. 28, 1525–1527 (2003). [CrossRef] [PubMed]

14.

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

15.

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis,” Opt. Express 8, 173–190 (2001). [CrossRef] [PubMed]

16.

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]

17.

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]

18.

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]

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(230.3120) Optical devices : Integrated optics devices

ToC Category:
Integrated Optics

History
Original Manuscript: May 16, 2007
Revised Manuscript: June 11, 2007
Manuscript Accepted: June 11, 2007
Published: June 22, 2007

Citation
Patric Strasser, Ralf Flückiger, Robert Wüest, Franck Robin, and Heinz Jäckel, "InP-based compact photonic crystal directional coupler with large operation range," Opt. Express 15, 8472-8478 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-13-8472


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References

  1. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals - Molding the flow of light (1995).
  2. A. Xing, M. Davanço, D. J. Blumenthal, and E. L. Hu, "Transmission measurement of tapered single-line defect photonic crystal waveguides," IEEE Photon. Technol. Lett. 17, 2092-2094 (2005). [CrossRef]
  3. M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. l. Scherer, and T. P. Pearsall, "Waveguiding in planar photonic crystals," Appl. Phys. Lett. 77, 1937-1939 (2000). [CrossRef]
  4. K. Rauscher, Simulation, design and characterisation of photonic crystal devices in a low vertical index contrast regime, Diss. ETH Nr. 16516, Electr. Eng. ETH Zürich, 2006.
  5. Y. Tanaka, H. Nakamura, Y. Sugimoto, N. Ikeda, K. Asakawa, and K. Inoue, "Coupling properties in a 2-D photonic crystal slab directional coupler with a triangular lattice of air holes," IEEE J. Quantum Electron. 41, 76-84 (2005). [CrossRef]
  6. M. Koshiba, "Wavelength division multiplexing and demultiplexing with photonic crystal waveguide couplers," J. Lightwave Technol. 19, 1970-1975 (2001). [CrossRef]
  7. A. Sharkawy, S. Shi, and D. W. Prather, "Electro-optical switching using coupled photonic crystal waveguides," Opt. Express 10, 1048-1059 (2002). [PubMed]
  8. S. Boscolo, M. Midrio, and C. G. Someda, "Coupling and decoupling of electromagnetic waves in parallel 2D photonic crystal waveguides," IEEE J. Quantum Electron. 38, 47 - 53 (2002). [CrossRef]
  9. A. Martinez, F. Cuesta, and J. Marti, "Ultrashort 2-D photonic crystal directional couplers," IEEE Photon. Technol. Lett. 15, 694-696 (2003). [CrossRef]
  10. M. Tokushima and H. Yamada, "Photonic crystal line defect waveguide directional coupler," Electron. Lett. 37, 1454 - 1455 (2001). [CrossRef]
  11. D. Leuenberger, R. Ferrini, L. A. Dunbar, R. Houdré, M. Kamp, and A. Forchel, "Codirectional couplers in GaAs-based planar photonic crystals," Appl. Phys. Lett. 86, 081108 (2005). [CrossRef]
  12. M. Qiu, M. Mulot, M. Swillo, S. Anand, B. Jaskorzynska, A. Karlsson, M. Kamp, and A. Forchel, "Photonic crystal optical filter based on contra-directional waveguide coupling," Appl. Phys. Lett. 83, 5121-5123 (2003). [CrossRef]
  13. M. Thorhauge, L. H. Frandsen, and P. I. Borel, "Efficient photonic crystal directional couplers," Opt. Lett. 28, 1525-1527 (2003). [CrossRef] [PubMed]
  14. M. Qiu, "Effective index method for heterostructure-slab-waveguide-based two-dimensional photonic crystals," Appl. Phys. Lett. 81, 1163-1165 (2002). [CrossRef]
  15. S. G. Johnson, and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001). [CrossRef] [PubMed]
  16. 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]
  17. 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]
  18. 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]

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