design of optical waveguide polarizer using photonic band gap

Design of optical waveguide polarizer using photonic band gap

Ravindra K. Sinha and Yogita Kalra TIFAC-Center of Relevance and Excellence in Fiber Optics and Optical Communications

Department of Applied Physics, Delhi College of Engineering, (Faculty of Technology, University of Delhi)

Bawana Road, Delhi –110 042, India [email protected],[email protected]

Abstract: A new design of optical waveguide polarizer based on photonic band gap has been presented. A numerical approach based on the finite difference time domain method has been used to analyze and design photonic band gap polarizer. The performance of the device is investigated in terms of degree of polarization and transmittance. Polarizer action is achieved by engineering the defect modes in photonic band gap structures.

©2006 Optical Society of America

OCIS codes: (230.0230) Optical devices ;( 130.3120) Integrated optics devices ;( 230.5440) Polarization-sensitive devices

References and links

1. P.R.Villeneuve and M.Piche, “Photonic band gaps in two-dimensional square and hexagonal lattices,” Phys. Rev. B 46, 4969-4972 (1992)

2. P.R.Villeneuve and M.Piche, “Photonic band gaps in two-dimensional square lattices-square and circular rods,” Phys. Rev. B 46, 4973-4975 ( 1992)

3. M.Qiu and S.He, “Large complete band gap in two-dimensional photonic crystals with elliptic air holes,” Phys. Rev. B 60, 10610-10612 (1999)

4. M. Qiu, “Band gap effects in asymmetric photonic crystal slabs,” Phys. Rev. B 66, 33103- 1 – 33103-3 (2002)

5. Yogita Nagpal and R.K.Sinha, “Modeling of photonic band gap directional couplers,” Microwave and Opt. Technol. Lett. 43, 47-50 (2004)

6. M. Bayindir and E. Ozbay, “Band dropping via coupled photonic crystal waveguides,” Opt. Express 10, 1279-1284 (2002)

7. M. Kamp, T. Happ, S. Mahnkopf, G. Duan, S. Anand and A. Forhel, “Semiconductor photonic crystals for optoelectronics,” Physica E 21, 802-808 (2004)

8. E.A. Camargo, Harold M. H. Chong and Richard M. De La Rue, “Four port coupled channel-guide device based on 2D photonic crystal structure,” Photonics and Nanostructures – Fundamentals and Applications 2, 227-213 (2004 )

9. V. Rinnerbauer, J, Schermer and K.Hingerl, “Polarization Splitting based on planar photonic crystals,” Proceedings of ECOC 2004 We2.1.3

10. T. Niemi, L. H. Frandsen, K.K. Hede, A. Harporth,P.I.Boreland M.Kristenen, “Wavelength –DivisionDemultiplexing Using Photonic Crystal Waveguides,” Photonics Technol. Lett.18, 226- 228, 2006

11. L.Wu., M .Mazillu, J.f Gallet, T.F.Krauss, A.Jugessur and R.M. De La Rue, “Planar photonic crystal polarization splitter,” Opt. Lett. 29,1620-1622 ( 2004)

12. Y.Ohtera, T.Sato, T.Kawashima, T. Tamamura and S.Kawakami, “Photonic Crystal Polarization Splitter,” Electron. Lett. 35, 1271-1272 (1999)

13. Samir K. Mondal and Bethanie J.H. Stadler, “Novel designs for integrating YIG/Air photonic crystal slab polarizers with waveguide faraday rotators,” Photonics Technol. Lett. 17,127-129 (2005)

14. M. Yokoyama and Susumu Noda, “ Polarization control of two dimensional photonic crystal laser having square lattice structure,” J. Quantum Electron. 39,1074-1080 (2003)

#73038 - $15.00 USD Received 14 July 2006; accepted 16 October 2006

(C) 2006 OSA 30 October 2006 / Vol. 14, No. 22 / OPTICS EXPRESS 10790

mailto:dr rk [email protected]

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1. Introduction

Photonic Crystals (PhCs), also known as Photonic Band Gap (PBG) structures are artificially engineered periodic structures in which refractive index modulation gives rise to stop bands for electromagnetic waves within a certain frequency window [1-4]. As a result, these structures can be used to confine, route, suppress, localize, split, disperse, and filter electromagnetic waves .Hence, in recent years, PBG structures have attracted significant attention and many novel applications of such materials have been proposed. The optical properties of photonic crystals such as light localization; high dispersion and anisotropy depend on the structural parameters such as the depth of modulation of refractive index, period of modulation and lattice type of the modulation. In other words we can control the properties of PhCs by adjusting these design parameters and thus obtain extensive freedom in designing application specific optical devices. One of the unique properties of PhC structures is the polarization sensitivity exhibited by these structures which has been used to design various polarization sensitive devices such as polarization splitters, polarizers, lasers, etc [5-14]. In this paper, the polarization sensitivity of PhC structures as well as the complete photonic band gaps in PhC structures has been capitalized to design PhC optical waveguide polarizer. Polarizer is one of the basic elements in optics, which selectively transmits one state of polarization and blocks the other state of polarization by using the properties of absorption, reflection and refraction. Earlier polarizers that have been reported utilize pseudo band gaps in PhC structures.

Since PBG structures allow strong control over the propagation of light, some of the most exciting applications of these structures are based on the functionalities through the incorporation of defects in periodic lattice leading to the design of PhC heterostructure. Defects influence the photonic band structure of the PhC and can result in the in the flow or confinement of light along particular pathways in the crystal and this property of the PBG structures has been exploited to design PBG polarizer in this paper.

In this paper we envisage the existence of photonic band gap (PBG) as well as complete photonic band gap (CPBG) in PhC heterostructure to design a novel PBG polarizer. An input waveguide is created in which the light of both TE and TM polarization can be guided due to the CPBG effect which is followed by creation of defect waveguide which possess the band gap for only one sate of polarization where as guides the other state of polarization in the output waveguide leading to formation of PBG polarizer. The photonic band gap computations have been carried out using the plane wave expansion (PWE) method and the light wave propagation in the proposed PBG polarizer has been modeled using the finite difference time domain (FDTD) method.

2. Design parameters and numerical analysis

The PBG structure considered to design a PBG polarizer is composed of triangular lattice of air holes in silicon (Si) (n = 3.42) with lattice constant a = 0.79 μm with normalized air hole radius r/a = 0.48. The design parameters are chosen to obtain a maximum range of complete photonic band gap. The photonic band diagrams for transverse electric (TE) and transverse magnetic (TM) polarizations for the PBG structure have been obtained using the PWE method are shown in Figs. 1(a) and 1(b). As evident from the band diagrams, the PBG structure exhibits complete photonic band gap (CPBG) for normalized frequency range 0.45244 ≤ a/λ ≤ 0.53077.



TM mode TE mode

(a) (b)

Fig. 1. (a) Band Diagram for the PBG structure composed of triangular lattice of air holes with r/a = 0.48 in Si for TM mode. (b) Band Diagram for the PBG structure composed of triangular lattice of air holes with r/a = 0.48 in Si for TE mode

An input PBG waveguide is formed by creating linear defect waveguide by removing one row of air holes. Since the considered PBG structure possesses the complete photonic band gap, light of both TE and TM polarization in the wavelength range 1.41 ≤ λ ≤ 1.67 can be guided in this structure.

Now to design a PBG polarizer we have to design a PhC heterostructure in such a way that the light of one polarization is blocked while the light of another polarization is allowed to pass, so that at the output end wavelength of one state of polarization is obtained. And this property of the sensitivity of the photonic band gaps to the polarization of light can be used to design PBG polarizer. So after the input waveguide, modifications are made in the PBG structure such that it exhibits a band gap for either of the two polarizations.

To, obtain such a structure we create a linear defect waveguide in the photonic crystal structure after the input waveguide by changing the radius of the air holes in one row, which is followed by an output waveguide formed by removing one row of the air holes. Figure 2 shows the schematic diagram of the PBG polarizer.

Fig. 2. Schematic view of the PBG polarizer

The radius of the air holes in the linear defect waveguide has been chosen to be 0.12a. The dispersion relations for the defect waveguide for TE and TM polarizations shown in Figs. 3(a) and 3(b) respectively ,which indicate that a PBG is introduced for TM polarization in the



range 0.49273 ≤ a/λ ≤ 0.528, however no such band gap is observed for TE polarization. From the dispersion relation for TE polarization in Fig. 3(b), it is evident that the guided mode exists for this structure in the region where the PBG is observed for TM polarization. Hence, if at the input end light of both TE and TM polarization is launched in the input waveguide then light of TE polarization should be guided in the defect waveguide whereas the light of TM polarization should be blocked because of the photonic band gap.

(a) (b)

Fig. 3. (a) Dispersion diagrams for the defect waveguide for TM polarization. (b) Dispersion diagram for the defect waveguide for TE polarization

The FDTD method has been used to simulate light propagation in the proposed PBG polarizer. The simulation results have been shown in Fig. 4(a) and 4(b) for λ = 1.55µm for TM and TE polarization respectively.

TM mode TE mode

(a) (b)

Fig. 4. (a) Snapshots of the PBG polarizer for TM mode at 1.55 μm. (b) Snapshots of the PBG polarizer for TE mode at 1.55 μm

The simulations exhibit if at the input end light of both TE and TM polarization of the allowed operational range is launched in the input waveguide then at output end, light of only TE polarization is obtained as expected from the dispersion relations.

The proposed polarizer is operational in the range 0.49273 ≤ a/λ ≤ 0.528 providing a large bandwidth of 90nm, where bandwidth is defined as the difference of the maximum and minimum operational wavelengths.

The performance of a polarizer is conventionally characterized by the degree of polarization P which is defined as

TE TM

TE TM

I IP

I I

−=

+ (1)



where TE

I (TM

I ) is the intensity of the outgoing TE(TM) component which is obtained as

one for the entire operational range. The transmittance T of a polarizer is defined here as the ratio of the intensity of the TE

mode

)(

)(

inTE

outTE

I

IT = (2)

where in and out stand for the incident and outgoing waves, respectively. The transmittance T is obtained to be 0.5 for TE mode for the PBG polarizer for the entire operational range.

Further, by tailoring the radius of the defect rods in PhC heterostructure, PBG polarizer can be designed for the desired wavelength range depending upon the defect bands introduced because of the defects.

Similarly, PBG polarizer can be designed in the PhC composed of dielectric columns in air in honeycomb lattice which satisfies the band gap requirements. PBG polarizer in such a structure has its own advantages and disadvantages. PBG polarizer in this structure provides higher transmittance with degree of polarization as one but the operational range is very narrow and hence becomes highly wavelength specific.

3. Conclusion

A new design of ultra compact PBG polarizer by utilizing the different photonic band gaps for TE and TM polarization exhibited by PhC structures has been proposed. Further by tailoring the radius of the defect rods, we can design the PBG polarizer for the required wavelength range with degree of polarization equal to one leading to formation of ultra compact PBG super polarizer.

Acknowledgments

The authors gratefully acknowledge the (i) financial support provided by All India Council of Technical Education, Government of India for the R& D project “Propagation Characteristics of Photonic Crystal Fibers and Waveguides for Telecom and Sensing Applications” and (ii) initiatives towards establishment of “TIFAC-Center of Relevance and Excellence in Fiber Optics and Optical Communications at Delhi College of Engineering, Delhi” through “Mission REACH” program of Technology Vision-2020, Government of India.



design of optical waveguide polarizer using photonic band gap

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