Theoretical study of polymeric metal clad optical waveguide polarizer

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Optics & Laser Technology 37 (2005) 397–401 www.elsevier.com/locate/optlastec

Theoretical study of polymeric metal clad optical waveguide polarizer Dharmendra Kumar, V.K. Sharma, K.N. Tripathi Department of Electronic Science, University of Delhi South Campus, Benito Juarez Road, New Delhi 110021, India Received 30 January 2004; received in revised form 8 May 2004; accepted 2 June 2004 Available online 13 August 2004

Abstract Planar optical waveguides consisting of thin dielectric films and buffer layers with metal cladding have been investigated theoretically. A computer program was written to calculate the exact zeroes of complex eigenvalue equation for TE and TM modes in multilayer metal clad waveguide polarizer. Numerical results and illustrations are given for Polycarbonate waveguide with other polymers as buffer and Al, Ag and Au as cladding metals at 0:6238 mm. It is also shown that, using thin (finite) films of metal produce more efficient polarizers as compared to semi-infinite metal films. Effect of low index buffer layer on attenuation of TM/TE modes is also investigated. r 2004 Elsevier Ltd. All rights reserved. Keywords: Integrated optics; Optical waveguide polarizer; Complex refractive index

1. Introduction Polymers have attracted great interest for photonic components in optical communication and optical sensing that enable unique functions without sacrificing high performance [1–3]. Advanced planar polymer technologies are suitable in every respect. Polymeric materials permit the mass production of low-cost highperformance circuit on many planar substrates (like Glass, Si and InP) [4]. In addition they provide the possibility for a much higher degree of ruggedness. In contrast to the inorganic material (like LiNbO3 ), the Electro-Optic (EO) polymers have also been investigated due to their advantages such as, large optical nonlinearity coefficients, fast response, low dielectric constants, simple fabrication process and easy fabrication of multilayer structure [4]. Further, material properties can be tailored for specific applications. Polymers are important class of materials for advance sensor photonics [4]. In particular, Polycarbonate (PC) has high transparency (more than 89%), ease of processing and high physical, chemical, mechanical and thermal stabiCorresponding author.

E-mail address: [email protected] (D. Kumar). 0030-3992/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2004.06.003

lity and are mechanically strong and can therefore be profitably used in many Integrated Optic (IO) devices [5,6]. Polycarbonate films have extensively been studied and its use in mode polarization filter for IO has already been reported [5]. However, a more compatible polarizer can be designed if we use metal clad optical waveguides. A dielectric film (buffer) layer is sandwiched between the waveguide (PC) layer and the metal outer layer. The surface plasmon waves supported by the metal surface, being of TM type, interact only with the TM-guided mode through the evanescent fields in the cover region between them. As a consequence, either the TM-guided mode of dielectric film is completely absorbed or its power is substantially reduced, but TE mode propagates through the interaction region essentially with no attenuation. This large TM-to-TE loss ratio can be used to produce a polarization filter for IO [7–9]. In the case of mode filter, it is necessary to obtain a sufficient extinction ratio without introducing a significant loss in the transmitted light. A TM-guided mode exhibits an absorption peak as a function of thickness of the low index buffer layer in the multilayer structure shown in Fig. 1. The purpose of this paper is to investigate attenuation characteristics of the polymeric multilayer metal clad optical waveguides by exact

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The total multilayer system for Fig. 1 is given by the matrix product of the two characteristic matrices.   m11 m12 ¼ M 1
M2 : M¼ m21 m22 Once the characteristic matrix of a multilayer structure is known, we can easily get the eigenvalue equation or dispersion equation for TE polarization [11] Fig. 1. A metal clad film waveguide structure.

f ðkz Þ ¼ iðgs m11 þ gc m22 Þ  m21 þ gc gs m12 ¼ 0; where

numerical method. The dependence of attenuation constant on buffer layer thickness, its refractive index and different cladding metals are presented. It is also observed that for an efficient design of a polarizer, a thick layer of material is not required and the configuration in Fig. 1 is modified by taking finite thickness of the metal layer (Fig. 7). This results in a more efficient and high extinction ratio polarizer. The thin film transfer matrix formulation [10,11] is used as the primary tool for the multilayer waveguide analysis. The thin film transfer matrix theory can easily form the dispersion equation of a multilayer waveguide consisting of any combination of lossless and lossy (dielectric and metal) layers. The guided mode propagation constants of the structure correspond to the zero of the equation.

2. Transfer matrix method for analysis of multilayer systems The transfer matrix analysis provides an easy formulation of the multilayer problem [10,11]. In this method each layer is characterized by a 2
2 matrix, " # i cosðkj hi Þ kj sinðk j hj Þ Mj ¼ : ikj sinðkj hj Þ cosðkj hj Þ In our case j ¼ 1; 2; 3. pffiffiffiffiffiffiffi i ¼ 1 and kj ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n2j k20  k2z ;

where k0 ¼ 2p l and nj and kz ðb  iaÞ are complex refractive index and complex propagation constant respectively and hj ¼ thickness of the jth layer. a is the attenuation coefficient (dB/cm) of the guided mode and l is the wavelength of light (in our study l ¼ 0:6328 mm).This wavelength was chosen for two reasons first, we would realize the polarizer at this wavelength and secondly, these guides find their use in many biological/chemical sensors operating at 0:6328 mm.

gs ¼ ðk2z  n2s k20 Þ ¼ k2s gc ¼ ðk2z  n2c k20 Þ ¼ k2c : Similar expression can be obtained for TM polarization.

3. Solution of dispersion equation The relation has been solved numerically using Muller iteration method [12]. This method was chosen because it does not require the evaluation of any derivative of the dispersion relation. It has been found that this method converges fairly rapidly to the solution and computation time is small. 3.1. Effect of buffer layer The materials used for buffer layer calculations are the polymers Poly(tetrafluoroethylene), Poly(trifluoroethyl Acrylate), Poly(vinylisobutyl ether) and PMMA with refractive indices 1.35, 1.407, 1.4507 and 1.49, respectively. These polymers have the solvents different from that of Polycarbonate (waveguide) and therefore can be deposited on it. The thickness of these films can easily be controlled by controlling the spinner speed [13]. The effect of the variation of the buffer layer thickness on guided modes supported by this guide are examined for the metals Al, Ag, and Au with refractive indices 1:2  j7, 0:065  j4 and 0:14  j3:5 respectively. For a free space wavelength l ¼ 0:6328 mm (which corresponds to He–Ne laser), the plots of the attenuation coefficient (a) versus the buffer layer thickness h2 are shown in Figs. 2–5 for TM0 and TE0 modes. TE losses decay monotonically as h2 increases. The TM loss is higher than TE when h2 ¼ 0. As h2 increases, loss increases several orders of magnitude (for TM) and then decreases sharply. The absorption maxima appearing in Figs. 2–5 for different buffer layer materials result from strong coupling between the normal guided mode in layer 1 (through buffer) and lossy surface plasmon wave supported by metal buffer layer interface for TM waves. For TE modes there is no such coupling. It can also be seen that buffer thickness increases as its index increases for all the metals. Further it is observed that as the

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10000 PC/1.49/Metal(Al/Ag/Au)

PC/1.407/Metal(Al/Ag/Au) AlTM

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AuTE

AlTE

AgTE

AuTE

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1 0.01

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Fig. 4. Attenuation coefficient vs thickness of buffer layer for semiinfinite metal. The buffer layer is poly(trifluoroethyl acrylate) ðRI ¼ 1:407Þ.

Fig. 2. Attenuation coefficient vs thickness of buffer layer for semiinfinite metal. The buffer layer is PMMA ðRI ¼ 1:49Þ. AlTM

PC/1.4507/Metal(Al/Ag/Au)

1000 AlTM

PC/1.35/Metal(Al/Ag/Au) AuTM Loss(dB/cm)

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AlTE

AgTE

AuTE 10

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AgTE

0.01

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1

1

Buffer Thickness (µm)

Fig. 3. Attenuation coefficient vs thickness of buffer layer for semiinfinite metal. The buffer layer is poly(tetrafluoroethylene) ðRI ¼ 1:35Þ.

magnitude of the real part of the complex refractive permittivity increases, the critical buffer layer thickness (where absorption for TM mode is maximum) decreases. Plot of buffer critical buffer layer thickness as a function of its index for different metals is shown in Fig. 6. The index of the buffer layer was varied from 1.35 to 1.485 in steps of 0.005 and for every index of buffer, its critical thickness (where the absorption loss for TM mode is maximum) was selected. Thickness of the buffer layer increases exponentially as its index increases for all metals. 3.2. Variation of metal thickness In Fig. 1, the metal layer is considered to be semiinfinite. To consider the effect of metal thickness, the

Fig. 5. Attenuation coefficient vs thickness of buffer layer for semiinfinite metal. The buffer layer is poly(vinylisobutyl ether) ðRI ¼ 1:4507Þ.

configuration is slightly modified as shown in Fig. 7. The configuration studied is Glass/PC/Poly(trifluoroethyl Acrylate)/Metal (Al, Ag, Au)/Air. It has been observed that for a particular critical thickness of metal, the attenuation coefficient (a) is maximum. The attenuation coefficient as a function of metal thickness is shown in Fig. 8. For Ag, a is maximum between 0.035 to 0:045 mm. After 0:045 mm the attenuation decreases. For Al films, maximum attenuation occurs around 0:015 mm and for Au films maximum attenuation occurs at 0.055–0:065 mm. If the thickness of Au or Al is increased further, a decreases slightly and then attains a constant value. In all the above calculations, the thickness of the buffer layer is chosen as the critical thickness (where TM losses are maximum) for semiinfinite films (Fig. 1). For all the metals it has been observed that choosing the critical metal thickness, loss

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0.24 0.22 0.20

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Fig. 8. Attenuation coefficient vs metal layer thickness.

0.06 0.04 1.36

1.38

1.40

1.42 1.44 Index (Buffer)

1.46

1.48

1.50

Fig. 6. Critical buffer thickness vs buffer index.

exact numerical method. Since, polymers have low cost and ease of fabrication (index can be tailored), we have chosen waveguide and buffer as polymer materials in our study. The result obtained can be used to fabricate all polymeric high performance TE pass optical waveguide polarizer. We have also shown that to design an efficient polarizer, thin finite metal films can produce better extinction ratio (aTM =aTE ). The studied waveguide structure can also be used for designing an absorption modulator by using buffer layer of electrooptic material in which sufficient extinction ratio can be obtained by a small change in the refractive index difference between the buffer and the waveguide.

Acknowledgements Fig. 7. A metal clad film waveguide with finite metal thickness.

(for TM) is larger as compare to semi-infinite metal clad configuration of Fig. 1. As the metal thickness exceeds the critical thickness, the value of a approaches that value, when metal was considered semi-infinite. The increase in attenuation for thin metal films is due to coupling between the surface plasmon waves associated with each boundary (air and polymer buffer layer). However, attenuation for TE modes remains same as that for semi-infinite configuration. This increased value of TM to TE attenuation ratio (the extinction coefficient) can be used to produce a more efficient polarizer.

4. Conclusion The attenuation characteristics of a multilayer metal clad polymeric optical waveguides are examined by

The authors wish to acknowledge University Grants Commission, New Delhi, India, (vide Letter No. F.1420/2003(SR)) for financial assistance.

References [1] Lee SS, Shin SY. Polymeric digital optical switch incorporating linear branch with modified coupling region. Electron Lett 1995;35:1245–6. [2] Oh MC, Shin SY. Poling induced waveguide polarizers in electrooptic polymers. IEEE Photonics Technol Lett 1996;8:375–7. [3] Lavers CR, Itoh K, Wu SC, Murabayashi M, Mauchline I, Stewart G, Stout T. Planar optical waveguide for sensing application. Sensors Actuators B 2000;69:89–95. [4] Eldada L, Shacklette LW. Advances in polymer integrated optics. IEEE J Sel Top Quantum Electron 2000;6:54–68. [5] Singh GK, Sharma VK, Kapoor A, Tripathi KN. Four layer polymeric mode polarization filter for integrated optics. Opt Laser Technol 2001;33:455–9. [6] Booth BL.. In: Hallmark LA, editor. Polymer for lightwave and integrated optics. New York: Marcel Dekker; 1992. p. 231–66.

ARTICLE IN PRESS D. Kumar et al. / Optics & Laser Technology 37 (2005) 397–401 [7] Walpita LM. Solution for planar optical waveguide equation by selecting zero elements of a characteristics matrix. Opt Soc Am A 1985;2:595–602. [8] Tong Y, Yizun W. Theoretical study of metal clad optical waveguide polarizer. IEEE J Quantum Electron 1989;25:1209–13. [9] Sletter MA, Seshadri SR. Thick metal surface polarization polarizer for a planar optical waveguide. J Opt Soc Am A 1990;7:1174–84. [10] ChillWell J, Hodgkinson I. Thin films fields transfer matrix theory of planar multilayer waveguide and reflection from prism loaded waveguides. J Opt Soc Am A 1984;1:742–53.

401

[11] Anemogiannis E, Glytsis EN. Multilayer waveguides: efficient numerical analysis of general structures. J Lightwave Technol 1992;10:1344–51. [12] Conte SD, Elementary numerical analysis: an algorithm approach. New York: McGraw Hill; 1972. p. 120. [13] Watanable T, Hikita M, Amano M, Shuto Y. Vertically stacked coupler and serially grafted waveguide: hybrid waveguide structure formed using an electro-optic polymer. J Appl Phys 1998;83(2):639–49.