Electro-optical switching using coupled photonic ... - OSA Publishing

Electro-optical switching using coupled photonic crystal waveguides Ahmed Sharkawy, Shouyuan Shi and Dennis W. Prather University of Delaware, Dept. of Elec.& Computer Engr., 147 Evans Hall, Newark, DE 19711 [email protected] http://www.ece.udel.edu/~dprather/index.html

Richard A. Soref Air Force Research Laboratory, Sensors Directorate, AFRL/SNHC, Hanscom AFB, MA 01731,

Abstract: We present an electro-optical switch implemented in coupled photonic crystal waveguides. The switch is proposed and analyzed using both the FDTD and PWM methods. The device is designed in a square lattice of silicon posts in air as well as in a hexagonal lattice of air holes in a silicon slab. The switching mechanism is a change in the conductance in the coupling region between the waveguides and hence modulating the coupling coefficient and eventually switching is achieved. Conductance is induced electrically by carrier injection or is induced optically by electron-hole pair generation. Low insertion loss and optical crosstalk in both the cross and bar switching states are predicted. 2002 Optical Society of America OCIS codes: (130.3120130) Integrated optics devices; (230.0230) Optical devices;(060.1810) Couplers, switches, and multiplexers; (230.2090) Electro-optical devices; (230.4110) Modulators;

References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato and S. Kawakami, "Photonic Crystals for Micro Lightwave Circuits Using Wavelength-Dependent Angular Beam Steering," Appl. Phys. Lett., 74, 1370-1372, (1999). E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and Electronics," Phys. Rev. Lett., 58, 2059-2062, (1987). S. John, "Strong Localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett., 58, 2486, (1987). D. W. Prather, A. Sharkawy and S. Shouyuan, "Photonic Crystals Design and Applications," in Handbook of Nanoscience, Engineering, and Technology, Electrical Engineering Handbook, G. J. Iafrate, S. E. Lyshevski, D. W. Brenner and W. A. Goddard III, Eds. (CRC Press, Boca Raton, FL. 2002). A. Adibi, R. K. Lee, Y. Xu, A. Yariv and A. Scherer, "Design of photonic crystal optical waveguides with single mode propagation in the photonic bandgap," Electron. Lett., 36, 1376-1378, (2000). J. D. Joannopoulos, R. D. Meade and J. N. Winn, Photonic Crystals. (Princeton, New Jersey, 1995). A. Sharkawy, S. Shi and D. W. Prather, "Multichannel Wavelength Division Multiplexing Using Photonic Crystals," Appl. Opt., 40, 2247-2252, (2001). D. Pustai, A. Sharkawy, S. Shouyuan and D. W. Prather, "Tunable Photonic Crystal Microcavities," Appl. Opt., 41, 5574-5579, (2002). M. Loncar, D. Nedeljkovic, T. Doll, J. Vuckovic, A. Scherer and T. P. Pearsall, "Waveguiding in Planar Photonic Crystals," Appl. Phys. Lett., 77, 1937-1939, (2000). M. Loncar, T. Doll, J. Vuckovic and A. Scherer, "Design and fabrication of silicon photonic crystal optical waveguides," J. Lightwave Technol., 18, 1402-1411, (2000). D. W. Prather, J. Murakowski, S. Shouyuan, S. Venkataraman, A. Sharkawy, C. Chen and D. Pustai, "High Efficiency Coupling Structure for a single Line-Defect Photonic Crystal Waveguide," Optics Letters, 27, 1601-1603, (2002). R. Stoffer, H. J. W. M. Hoekstra, R. M. D. Ridder, E. V. Groesen and F. P. H. V. Beckum, "Numerical Studies of 2D Photonic Crystals: Waveguides, Coupling Between Waveguides and Filters," Opt. Quantum Electron., 32, 947-961, (2000). C. J. M. Smith, H. Benisty, S. Olivier, M. Rattier, C. Weisbuch, T. F. Krauss, R. M. D. L. Rue, R. Houdre and U. Oseterle, "Low-Loss Channel Waveguides with Two-Dimensional Photonic Crystal Boundaries," Appl. Phys. Lett., 77, 2813-2815, (2000).

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Received August 15, 2002; Revised September 20, 2002

7 October 2002 / Vol. 10, No. 20 / OPTICS EXPRESS 1048

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M. Bayindir, B. Temmelkuran and E. Ozbay, "Propagation of Photons by Hopping: A Waveguiding Mechanism Through Localized Coupled Cavities in Three-Dimensional Photonic Crystals," Phys. Rev. B, 61, R11855-R11858, (2000). M. Bayindir and E. Ozbay, "Heavy photons at coupled-cavity waveguide band edges in a three-dimensional photonic crystal," Phys. Rev. B, 62, R2247-R2250, (2000). M. Loncar, J. Vuckovic and A. Scherer, "Methods for controlling positions of guided modes of photoniccrystal waveguides," J. Opt. Soc. Am. B-Optical Physics, 18, 1362-1368, (2001). S. Fan, P. R. Villeneuve, J. D. Joannopoulos, B. E. Little and H. A. Haus, "High Efficiency Channel drop filter with Absorption-Induced On/Off Switching and Modulation." USA, 2000. M. Plihal and A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Phys. Rev. B, 44, 8565-8571, (1991). D. Hermann, M. Frank and K. Busch, "Photonic Band Structure Computations," Opt. Express, 8, 167-172, (2001). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-1-167. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, Second Edition. (Boston, MA: Artech House, 2000). L. L. Liou and A. Crespo, "Dielectric Optical waveguide coupling analysis using two-dimensional finite difference in time-domain simulations," Microwave and optical Technology Letters, 26, 234-237, (2000). S. Boscolo, M. Midiro and C. G. Someda, "Coupling and Decoupling of Electromagnetic Waves in Parallel 2-D Photonic Crystal Waveguides," IEEE J. Quant. Electron., 38, 47-53, (2002). O. Painter, J. Vuckovic and A. Scherer, "Defect modes of a two-dimensional photonic crystal in an optically think dielectric slab," J. opt. Soc. Am. B, 16, 275-285, (1999). 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). A. Yariv and P. Yeh, Optical waves in Crystals. (New York: John Wiley & Sons, 1984). M. L. Povinelli, S. G. Johnson, J. Fan and J. D. Joannopoulos, "Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap," Phys. Rev. B, 64, 753131-753138, (2001). S. G. Johnson, S. Fan, P. R. Villeneuve and J. D. Joannopoulos, "Guided modes in photonic crystal slabs," Phys. Rev. B, 60, 5751-5758, (1999). R. A. Soref and B. E. Little, "Proposed N-Wavelength M-Fiber WDM crossconnect switch using Active Microring Resonators," IEEE Photon. Technol. Lett., 10, 1121-1123, (1998). M. Koshiba, "Wavelength Division Multiplexing and Demultiplexing with Photonic Crystal Waveguide couplers," J. Lightwave Technol., 19, 1970-1975, (2001). S. M. Sze, Physics of Semiconductor Devices, 2nd ed: John Wiley & Sons Inc., 1981). R. A. Soref and B. R. Bennett, "Electrooptical effects in silicon," IEEE J. Quantum Electron., QE-23, 123129, (1987). A. Chutinan and S. Noda, "Waveguides and waveguide bends in two-dimensional photonic crystal slabs," Phys. Rev. B, 62, 4488-4492, (2000). S. Fan, S. G. Johnson and J. D. Joannopoulos, "Waveguide branches in photonic crystals," J. Opt. Soc. Am. B, 18, 162-165, (2001).

1. Introduction Optical components that permit the miniaturization of an application specific optical integrated circuit (ASPIC) to a scale comparable to the wavelength of light are a good candidate for next generation high density optical interconnects and integration. In recent years, there has been a growing effort in the realization of active and passive photonic crystals (PhCs) as optical components and circuits [1], which can be integrated monolithically on a single chip. In 1987 E. Yablonovitch [2] and S. John [3], proposed the idea that a periodic dielectric structure can posses the property of a band gap for a certain regions in the frequency spectrum, in much the same way as an electronic band gap exists in semiconductor materials. Two and three-dimensional photonic crystals have been explored both theoretically [4-8], and experimentally [9-11]. In particular two-dimensional photonic crystals have been studied extensively since they are relatively easier to fabricate for the optical regime. Twodimensional photonic crystals were used to provide in-plane confinement for in-plane propagation. As an example, planar waveguides [12, 13] as well as coupled-cavity waveguides [14, 15] have been used to efficiently guide electromagnetic waves through a line defect or a chain of coupled cavities, respectively, in a PhC. To this end, a single line defect introduced to a photonic crystal resembled a waveguide, for which careful design of waveguide parameters such as width and thickness, number of propagating modes can be controlled [16]. Electro-optical switches are key components of such photonic integrated circuits, yet only one proposal for implementing such switches--a resonator device--has appeared in the #1581 - $15.00 US

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literature [17]. In this paper we present the conception, numerical analysis of a PhC channelwaveguided 2 x 2 directional coupler switch that utilizes electrically or optically induced loss (conductivity) in the coupling region between two coupled waveguides. To our knowledge, this is the first PhC directional coupler switch that has been proposed and analyzed. The organization of this paper is as follows. In section 2 we explain in detail the design procedure for two-single mode waveguides brought into close proximity to form a directional coupler, for both cases of silicon pillars in air background as well as perforated silicon slab, we also calculate the modal propagation constant of the eigenmodes of the coupled waveguide system, which we shall use to estimate the frequency dependant coupling coefficient and hence the coupling length necessary to design our switch. In section 3, we briefly discuss the switching approach we used, and in section 4 we present the numerical analysis of the electrooptical switch. In section 5 we present the FDTD results obtained for the proposed switch implementations, and finally in section 7 we present our concluding remarks. 2. Design procedure When two PhC waveguides are brought in close proximity of each other they form what is known in the literature as a directional coupler, shown in Fig.1. Under suitable conditions, an electromagnetic lightwave launched into one of the waveguides can couple completely into the nearby waveguide. Once the wave has crossed over, the wave couples back into the first guide so that the power is exchanged continuously as often as the length between the two waveguides permits. However, complete exchange of optical power is only possible between modes that have equal phase velocities or, equal propagation constants. More specifically, the propagation constants must be equal for each guide in isolation. Equality of propagation constants, also known as phase synchronization, occurs naturally when the two waveguides are identical. In that case all the guided modes of both waveguides are in phase synchronism and can couple to each other at all wavelengths. Directional Coupler

Port 3

Port 4 Waveguide

2

Waveguide

1

y Port 2

Port 1

x

Coupling Length Lc

Fig. 1.Coupled Photonic Crystal Waveguided (CPhCW) system consisting of two closely coupled PBG waveguides separated by two PBG layers of length Lc. system formed using a periodic array of silicon pillars arranged in square lattice.

We begin with a structure composed of two single mode waveguides placed in close proximity of each other, as the one shown in Fig. 1. This structure is no longer a single mode device, which can be seen clearly if both waveguides were fused together into one wider waveguide that is no longer single mode waveguide. Instead, it now has two eigenmode solutions, an even (symmetric) and an odd (anti-symmetric) mode, which have slightly different propagation constants and hence they propagate at different velocities. In order to

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calculate the coupling length necessary for a certain wavelength to completely cross over from first waveguide to second waveguide, the frequency dependant propagation constant of the even and odd modes must be defined first, also known as the modal dispersion relation of the system of coupled waveguides. In order to determine this relation a computational unit cell shown in the bottom right corner of Fig. 2a is used since the structure is periodic. For our numerical experiments we consider first a directional coupler built using two single mode 2DPhC waveguides, obtained by removing a row from a square lattice of infinitely long dielectric rods in air background. The design parameters for the photonic crystal are as follows: the dielectric rods have a dielectric constant ε r = 11.56 and a radius r = 0.2a . Where a is the lattice constant of the crystal. Using these values the structure was found to have a complete band gap in the spectral range 0.23 ≤ a λ ≤ 0.41 for TM polarization (magnetic filed in plane). The structure shown in Fig.2 (a) can be numerically analyzed using either plane wave expansion method [18] (PWM), or finite difference time domain (FDTD) method [19, 20] with periodic boundary conditions. The result of either method is a modal dispersion diagram for the eigenmodes of the structure, from which we will be able to extract the modal propagation constants and hence calculate the coupling length necessary for full transmission of the optical power from one waveguide to a nearby waveguide. Here we will briefly explain each method as well as discuss the results, starting with a super-cell shown in Fig. 2(a) by the dashed region, PWM was used to numerically compute the Bloch propagation constants for a plane wave propagating through the super-cell. The dispersion diagram obtained using PWM is shown in Fig. 2(a). On the other hand, if the FDTD method was to be used, a set of normalized propagation constants in the range ( 0 < β 2π a < 0.35 ) with an interval ∆β = 0.01 × 2π / a will be used. In order to categorize the odd and the even modes, excitations of a TM-even mode and a TM-odd mode were launched [21], from which it was found that eigenmodes with lower frequencies belongs to the even mode, while the higher frequencies belongs to the odd mode. The dispersion diagram is then plotted over the same one previously obtained from the PWM from which we can see that they overlap for a great extent, as shown in Fig. 2(a). We will only focus our attention to the modal dispersion curves within the band gap of the structure ( 0.23 ≤ a λ ≤ 0.41) , as shown in Fig. 2(b). From the dispersion curves of both odd and even modes obtained previously we can calculate the length necessary for the signal launched in waveguide 1 to completely transfer to waveguide 2 using the following procedure; for a specific frequency, find the corresponding values of the normalized modal Bloch phase constants, for the even and the odd eigenmodes. The length required for full transmission can be then calculated using [22].

Lc =

π

( βe − β o )

.

(1)

As an example for the device shown in Fig.2 (a) and for a wavelength of 1550 nm a = 542.5 nm , r = 108.5 nm . From Fig.2 (b) we can find the propagation

( a λ = 0.35 )

constant of the odd and even modes to be

(β

e

(β

0

= 2π × 0.1977 a = 2.357 ×106 m −1 ) and

= 2π × 0.2154 a = = 2.568 × 106 m −1 ) from which we can calculate the full transmission

length as, Lc = π ( 2.568 − 2.357 ) × 106 = 14.88 µ m = 14.88µ m 0.5425 µ m = 28a = 9.6λ.

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(2)



0.4 FDTD PWM

0.3 0.2 x Supercell

0.1 0 0

Normalized frequency (a/λ)

0.5

0.45


0.5

y 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Propagation constant (β 2π/a) (a)

0.4 0.3 0.2 x 0.1 0

Supercell 0

y 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Propagation constant (β 2π/a) (c)

0.3

Odd mode Even mode

Even mode 0.28 Odd mode



Which means that complete transmission from one waveguide to the other requires only ten wavelengths to occur, which makes such a theory viable for high density photonic integrated circuit applications.

0.4

0.26

0.35

0.24

0.3 0.25 0

βo

0.22

βe

0.05 0.1 0.15 0.2 0.25 0.3 0.35 Propagation constant (β 2π/a) (b)

0.2 0

βe

βo

0.05 0.1 0.15 0.2 0.25 0.3 0.35 Propagation constant (β 2π/a) (d)

Fig. 2 (a) Dispersion diagram for the structure shown in Fig.1 obtained using both PWM and FDTD methods. Two solutions corresponding to the eigenmodes (odd and even) exists within the band gap (0.23 85 % for σ > 105 Ω-1cm-1 and T(Port3) >90 % for σ < 102 Ω-1cm-1. At σ = 10 Ω-1cm-1, the predicted crosstalks are: Forward CT= P(2)/P(3) = -22.2 dB, Backward CT= P(4)/P(3) =-23 dB, while for σ = 3 x 105 Ω-1cm-1, Forward CT=P(3)/P(2) = -32.2 dB, Backward CT= P(4)/P(2) = -36.9 dB.

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σ = 102 (Ω .cm)-1

12

σ = 103 (Ω .cm)-1

1

1

12 0.9

a 9

0.9

b

0.8

0.8

9

0.7

0.7

6

0.5

0.6 µm

µm

0.6

0.5

6

0.4

Cross state

3

0

1

2

3

4

0.4

0.3

0.3 3

0.2

0.2

0.1 5

6

0.1

7

0

1

2

3

µm

4

5

6

7

σ = 5 x 103 (Ω .cm)-1

σ = 104 (Ω .cm)-1

1

12

0.9

d

0.8

9

1

12

0.9

c

0.8

9

0.7

0.7

0.5

6

0.6 µm

µm

0.6

0.5

6

0.4

0.4

0.3 3

0.2

0.3

Bar state

3

0.1 0

1

2

4

3

0

µm

5

6

7

0.2 0.1

0

0 0

1

2

3

µm

4

5

6

7

µm

Fig. 6 Four snapshots for FDTD simulations of 2x2 electro-optical switch formed in a perforated slab of air holes arranged on a hexagonal photonic crystal lattice.

Optical Output Power (Normalized to Input)

1 Port 3 1

Port 2

0.1

0.01

1E-3

1E-4

Port 4

1E-5 1

10 100 103 104 105 Conductivity of CPhCW in the coupling region (Ω. Cm)-1

106

Fig. 7 Calculated switching characteristics of Fig. 3 crossbar switch (perforated slab case).

The switching response shown in Fig. 5 and Fig. 7 show that there is a minimum value for the output optical power at various ports for a specific value of conductivity (σ = 0.1 Ω-1cm-1) for the silicon pillars case and (σ = 104 Ω-1cm-1) for the perforated slab case, at this transient #1581 - $15.00 US

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value the optical power launched at the input port will be absorbed in the coupling region between the two waveguides and the device suffer high attenuation coefficient α in the coupling region. An increase or decrease in the conductivity will redirect the optical power to either bar- or cross-states respectively. This behavior was previously discussed in by Soref and Bennett [31]. The Fig.-1 and 3 devices are intended to be interconnected and cascaded in the forward direction into an N x N optical cross-connect network. In this case further optimization to crosstalk can be achieved by minimizing the reflections at the waveguide bends. Techniques for enhancing transmission through waveguide bends and hence reducing reflections include, broadband [24, 32], and narrowband [13, 33] techniques. 6. Acknowledgments The authors would like to thank the reviewers for their very constructive and insightful comments. The authors would also like to thank Emphotonics.com for providing the FDTD and PWM tools (EMP), which were used in the simulation and design of the work, presented in this article. 7. Summary We have presented simulation results on a novel, compact, 2D-PhCwaveguided 2 x 2 directional coupler switch controlled by optical loss induced in the dielectric posts as well as perforated slab between the parallel line defects. Using the FDTD method on a 1.55 µm device, we predict low insertion loss and crosstalk below -23 dB in both switching states although the required change in conductance is large in this non-optimized switch. We are presently exploring improved switch designs that produce "complete" switching with smaller ∆σ.

Fig. 8 (171KB) Movie 2x2 cross bar PhC switch (silicon pillars) in OFF state.

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Fig. 9 (253KB) Movie 2x2 cross bar PhC switch (silicon pillars) in ON state.

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