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TM pass polarizers using resonant coupling between ITO thin film lossy modes and dielectric waveguide modes
Optics Communications 291 (2013) 247–252
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Discussion
Integrated optic TE/TM pass polarizers using resonant coupling between ITO thin film lossy modes and dielectric waveguide modes Anil Kumar a, V.K. Sharma b, D. Kumar c, A. Kapoor a,n a
Department of Electronic Science, University of Delhi, South Campus, Benito Juarez Road, New Delhi-110021, India Keshav Mahavidyalaya, University of Delhi, Delhi-110034, India c Krishna Institute of Engineering and Technology, Ghaziabad, U.P., India b
a r t i c l e i n f o
abstract
Article history: Received 6 August 2012 Received in revised form 1 October 2012 Accepted 17 October 2012 Available online 1 November 2012
The resonant coupling between the lossless dielectric waveguide modes and the lossy modes supported by the absorbing indium–tin oxide (ITO) film is analyzed theoretically. It is observed that by changing the thickness of an ITO cladding layer placed above the planar dielectric waveguide, the TE or TM propagating modes may be selectively attenuated. This polarization effect can be used to design a TE or TM pass polarizer. Further it is also proposed that an electro-optic buffer layer inserted between the waveguide and ITO film can be used to design a high extinction ratio integrated optic polarizer at wavelength of 1.3 mm. A polarizer (both TE and TM pass) with extinction ratio of about 254 dB and insertion loss of about 10 dB can be easily designed for a 1 mm of its length. & 2012 Elsevier B.V. All rights reserved.
Keywords: ITO thin film Lossy modes Resonant coupling Electro-optic buffer Polarizer
1. Introduction At present the transparent conductive oxide films and in particular the indium–tin oxide (ITO) thin films find their application mainly in liquid crystal displays, flat panel displays, organic LEDs and solar cells. Their role in integrated optic components is yet to be explored. Since ITO is a transparent conductive oxide and is chemically stable, it offers new technological opportunities in sensing applications. Like another metal clad sensors, these sensors are also based on surface plasmon resonance supported by ITO thin films [1–4]. Surface plasmons are the longitudinal charge density waves, which propagate at the interface of two media with real part of their respective dielectric constants having opposite signs. These SP waves can be excited by p-polarized incident light under the conditions of attenuated total internal reflection using a prism. The excitation of SPs corresponds to an attenuation of reflected light intensity of surface plasmon resonance curve at a critical angle. These resonance effects occur for wavelength in the range of 1.8 to 2.5 mm. This range is not useful for optical communication applications.
n
Corresponding author. Tel.: þ91 9350571397; fax: þ91 11 24110606. E-mail addresses: [email protected] (A. Kumar), [email protected] (V.K. Sharma), [email protected] (D. Kumar), [email protected] (A. Kapoor). 0030-4018/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2012.10.022
However in visible range and at the optical communication wavelengths (1.3 and 1.5 mm) the ITO films have large real part of index and smaller imaginary part. Therefore, the ITO layers are expected to support the lossy modes at these wavelengths. We will show that ITO clad dielectric planar waveguides exhibit many interesting properties due to coupling between the lossless mode of the guiding layer and the lossy modes supported by the ITO cladding. Here we propose the use of thin ITO films as a TE or TM pass polarizer at communication wavelength 1.3 mm. Effect of a birefringent buffer layer on the efficiency of the polarizer is also discussed. There are many ways to produce a waveguide polarizer, e.g., using selective attenuation in metal cladding or cut off effects in waveguide [5–12]. A metal-clad optical waveguide is suitable for mode polarization filter because the ohmic losses of TM guided modes are much larger than that of TE modes. If a thin low index dielectric film (buffer layer) is sandwiched between the guide and the metal, then the absorption of TM mode is further enhanced and that of TE is reduced at a suitably chosen buffer thickness. The dielectric layer is called a buffer layer because it relaxes the metal’s influence on the preferred guided TE mode [5–10]. As a consequence, either the TM guided mode of the waveguide is completely absorbed or its power is substantially reduced, but the TE mode propagates through the interaction region with essentially no attenuation. These structures however, cannot produce a TM pass polarizer. Other polarizers use the birefringent polymer
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over layers on the waveguide or the electro-optic effect in polymer layers to split the TE and TM modes [13,14]. Semiconductor clad waveguide polarizers have also been proposed [15,16]. By varying the thickness of semiconductor cladding layer deposited on a planar dielectric waveguide, the TE or TM propagating modes may be selectively attenuated. This polarization effect is due to the coupling between the lossless modes of the dielectric waveguides and the lossy modes supported by silicon cladding layer. But these structures suffer from a relatively high insertion loss and have low extinction ratio (defined later). In this paper, we investigate theoretically the attenuation characteristics of the ITO clad glass optical waveguide by exact numerical method. The thin film transfer-matrix formulation is used as the primary tool for the multilayer waveguide analysis which forms the dispersion equation of the waveguide structure consisting of any combination of lossless and lossy (ITO) layers. The guided mode propagation constants of the structure correspond to the zeros of dispersion the equation. We show that ITO clad optical waveguides possess unique properties which arise from the effect of periodic coupling between lossless mode of dielectric waveguide and the lossy modes supported by the thin ITO films. There are regions of selected high and low attenuation for different polarization modes (TE or TM) of the propagating light at wavelength of 1.3 mm. Such a structure can be used as TE or TM pass polarizer. However, it is observed that the efficiency of the polarizer so formed is not very high. The efficiency of the polarizer is high if the attenuation of the preferred (pass polarization) mode is very small and that of the other polarization is quite large. We propose that insertion of an electro-optic dielectric layer (buffer layer) between the waveguide and ITO film can significantly improve the efficiency of the polarizer. This mechanism is discussed in detail.
eN ¼3.57, op ¼1.89 1015 rad/s, t ¼6.34 10 15 s/rad, s0 ¼ 0.49, o0 ¼5.61 1015 rad/s, and g ¼9.72 1013. This model will be used henceforward for the further analysis. The relative permittivity (which is 2.4172þ0.1849j at l ¼1.3 mm for ITO) can also be expressed in terms of complex refractive index as n ¼ e1=2 ¼ n þ jk ¼ 1:5558þ 0:0594 j
ð2Þ
where n and k are the real and imaginary parts of the refractive index, respectively. The cover (air), substrate and dielectric guide layers are lossless and are given by real permittivity. The modes of the waveguide shown in Fig. 1 are characterized by a complex propagation constant given as jkz ¼ a þjb. Where a is the absorption loss in the waveguide structure and b/k0 is the mode effective refractive index (k0 ¼2p/l). The complex propagation constant of this multilayer waveguide is obtained by solving the complex eigenvalue equation which is derived by using transfer matrix method [19–21]. The method is presented in Appendix A.
3. Solution of the eigenvalue equation for ITO clad waveguides The lossy multilayer waveguide structure shown in Fig. 1 is analyzed at a wavelength of 1.3 mm. For ITO films the index is given by Eqs. (1) and (2) while for other layers the index is same as shown in Fig. 1. The waveguide considered is a single mode potassium ion exchange glass waveguide in microscopic glass slides with guide thickness of 4 mm (sufficient to support TE0 and TM0 modes). The complex eigenvalue equation describing the structure is exactly solved numerically by Muller’s method [22].
4. Results and discussion 2. ITO clad waveguide A four-layer ITO clad waveguide is shown in Fig. 1. It consists of a thin layer of ITO deposited on a thin layer lossless dielectric waveguide. The cover (air) and substrate layers are assumed to be semi-infinite. The layers are characterized by their relative permittivity. The ITO layer absorbs light and is thus characterized by a complex value of relative permittivity. The oscillatory model represents the dielectric constant of ITO film more accurately (as compared to Drude model) because it also considers the dielectric behavior of the ITO film. The value of dielectric constant calculated using this model provides very good agreement with the experimentally determined values for ITO films deposited at room temperature [18]. Therefore the dielectric constant of the ITO can be expressed as [17]
eðoÞ ¼ e1
o2p s o2 þ 2 0 0 o2 þi o=t o0 o2 igo
Let us first consider the waveguide structure without the buffer layer as shown in Fig. 1. Figs. 2 and 3 show, respectively, the variation of TE and TM modes in their mode effective index and the attenuation as the ITO film thickness is varied. Wavelength used is 1.3 mm. The glass waveguide supports only the fundamental TE0 and TM0 modes, however as the thickness of the ITO layer is increased the number of modes supported by the composite structure increase and are confined mainly in ITO layer. The attenuation results for both the polarizations show a damped oscillatory behavior as the ITO layer thickness is
ð1Þ
where eN is the high frequency dielectric constant, t is the electronic scattering time and op is the plasma frequency. It is an oscillator model whose variables are: s0 (oscillator strength), o0 (oscillator resonance frequency) and g (oscillator damping constant). The parameters used are:
Fig. 1. Schematic cross section of four layers ITO clad waveguide.
Fig. 2. TE and TM mode effective index as a function of ITO film thickness.
A. Kumar et al. / Optics Communications 291 (2013) 247–252
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Fig. 4. Schematic cross section of five layers waveguide with birefringent buffer layer.
Fig. 3. TE and TM mode attenuation constant versus ITO film thickness.
increased. These oscillations are due to coupling between the zeroth-order mode propagating in the glass waveguide and various orders of modes supported by the ITO layer. As the ITO layer thickness is increased each successive maximum on the attenuation curve represents a point where the ITO layer is supporting a successively higher order mode as shown in Fig. 3. The first peak in TE curve represents the attenuation due to coupling of waveguide mode to the TE0 mode supported by the ITO film, second peak represents the attenuation due to coupling of waveguide mode to the lossy TE1 mode of ITO film. The guided mode now does not couple to TE0 lossy mode of ITO layer due to mode effective refractive indices mismatch. The next peak represents the attenuation due to the coupling of guided mode to lossy TE2 mode of ITO film and so on. Similarly, peaks in TM curve, represents the attenuation due to coupling of guided TM0 mode to the successively higher order lossy modes supported by the ITO film. Since the attenuation peaks appear at different ITO thicknesses both TE and TM pass polarizers can be designed by selecting its thickness appropriately. The attenuation coefficient (aTM for TM modes and aTE for TE modes) in dB/cm is obtained after multiplying the imaginary part of mode effective index by 2k0 105 log10 ðeÞ. The first peak for TM mode loss 580.3 dB/cm appears at 0.593 mm thickness of ITO film. TE attenuation at this thickness is 398.9 dB/cm. Similarly the first TE mode maximum (loss is 504.2 dB/cm) occurs at 0.485 mm and TM loss is 440.7 dB/cm at this thickness. However, the difference between the TM loss (580.3 dB/cm) and TE (398.9 dB/cm) losses at 0.593 mm and TE losses (504.2 dB/cm) and TM losses (440.7 dB/cm) at 0.485 mm is not very large and hence the extinction ratio for TM pass or TE pass polarizer will not be large and the insertion losses will be quite high. The extinction ratio for the TM pass polarizer is defined as (aTE– aTM) length of polarizer and its insertion loss is aTM length of polarizer. We propose that a dielectric birefringent layer can be used to increase the extinction ratio. We will also show that it also reduces the insertion losses. As a result an efficient polarizer (both TE pass and TM pass) can be produced.
5. Effect of birefringent buffer layer on guided modes Let us now consider the effect of a birefringent buffer layer inserted between the ITO film and the guiding layer as shown in Fig. 4. The buffer can be chosen as an electro-optic controlled birefringent polymer film. Polymers have been widely used in integrated optics because they have excellent waveguiding
properties [23,24]. Moreover, their optical properties can be tailored (e.g., by doping various dyes). The birefringence of this layer can be induced and controlled precisely by electrical poling technique [25–27]. Since ITO is a conducting material, it can be used as a contact for poling as well as a cladding layer. Another advantage of using polymer buffer layer is that, there are a large number of polymers with refractive index ranging from 1.4 to 1.7 [28]. So, depending upon the poling direction we can have either nTE 4nTM or nTM 4nTE, where nTE is the buffer index for TE polarization and nTM for TM polarization [26]. Birefringence of more than 0.03 can easily be achieved in polymer films. We will now show that such a birefringent buffer layer increases the extinction ratio and decreases the insertion losses of the ITO clad polarizers. The efficiency of the polarizer can be maximized by optimizing the thicknesses of ITO and the buffer layers and the index of buffer layer. The refractive index of ITO film is larger than that of the waveguide and therefore the modes are always lossy (leaky). For the devices without buffer, the peaks appear when there is phase matching between the guided mode and lossy mode supported by ITO film. The role of the buffer is two-fold. First, if the buffer index is higher than the waveguide and lower than the real part of index of ITO film, say, for TE (or TM) mode, then a better phase matching takes place and a larger portion of TE (or TM) guided mode energy is transferred to the lossy ITO film. So, basically the high index buffer provides the perfect enhanced phase matching or resonant phase matching between the guided mode and lossy mode of ITO film. Second, for other polarizers, say, TM (or TE) mode, if the buffer index (because of birefringence) is smaller than the waveguide index (1.521) the waveguide structure will support a guided mode. However small losses will be there because of lossy ITO film and there will be no phase matching between the guiding mode and the lossy mode supported by ITO film. To fully utilize the phase matching effect, the thickness and index of buffer layer must be precisely controlled. The variation of attenuation and effective mode index as a function of buffer thickness is shown in Figs. 5 and 6 respectively for the TE mode. We have taken nTE ¼1.55 and nTM ¼1.52 for buffer. Fig. 5 shows variation for two different values of ITO thickness. It is clear from Fig. 5 that for 2 mm thick ITO film, there is a sharp peak at buffer thickness of 1 mm. The loss at this thickness is 2640 dB/cm for TE polarization. The corresponding loss for TM polarization it is 100 dB/cm (not shown in Fig. 5). Therefore for a polarizer of length 1 mm, the polarization extinction ratio for the clad section of TM pass polarizer is 254 dB and the excess insertion loss is 10 dB. The reason for high TE mode attenuation at 1 mm buffer thickness is that the high index buffer layer introduces an additional mode which is strongly coupled to both the lossy ITO film and the waveguide and enhances waveguide and ITO film mode coupling. There is another peak at around 3 mm buffer thickness but attenuation is not equally high, because as the buffer thickness is increased, the induced additional mode starts confining to this layer and coupling becomes weak. Another plot in Fig. 5 is shown for 1.8 mm thick ITO film. It has similar behavior with different peak positions and attenuation values. The index
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Fig. 5. TE mode attenuation as a function buffer thickness at ITO film thicknesses. (a) 2.0 mm, (b) 1.8 mm.
Fig. 6. TE mode effective index as a function buffer thickness at ITO film thicknesses. (a) 2.0 mm, (b) 1.8 mm.
matching also depends on the ITO film thickness. The mode coupling can be best analyzed using field plots. Figs. 7 and 8 show the absolute value of the Ey field component of TE0 mode plotted as a function of the waveguide cross section with 1.12 and 1 mm buffer thicknesses and ITO film thicknesses of 1.8 and 2.0 mm, respectively. Comparison of Figs. 7 and 8 indicates that the field confinement for TE0 mode in ITO film is better for 2 mm thick ITO film at optimized buffer thickness. In Fig. 8, the field plot for TM0 mode is also shown. Clearly there is no resonant coupling (strong field confinement) for the TM0 mode in ITO film and most of the energy is confined to the waveguide. In our next design, we will show that using the same principle (of having high index buffer for phase matching) we can design a TE polarization pass polarizer. But, now we have nTM ¼ 1.55 and nTE ¼1.52. The attenuation and effective index variation as a function of buffer thickness are shown for TM polarization in Figs. 9 and 10, respectively. The behavior of curves is similar as that of the curves for TE polarization. The first strong peak appears at buffer thickness of 1.12 mm and ITO thickness of 2 mm. The TM mode loss at this thickness is 2530 dB/cm. The corresponding loss for TE mode is 89 dB/cm. Therefore, for a 1 mm long polarizer, the polarization extinction ratio for the clad section of TE pass polarizer is 244 dB and the excess insertion loss is 8.9 dB. The field plots for TM0 and TE0 mode of this polarizer is shown in Fig. 11. It is evident from Fig. 11 that most of the TM0 is
Fig. 8. TE0 and TM0 mode field distribution for a TM0 pass polarizer. (ITO thickness¼ 2.0 mm and buffer thickness ¼1.0 mm).
Fig. 7. TE0 mode field distribution for the multilayer structure with buffer. (ITO thickness ¼1.8 mm and buffer thickness ¼ 1.12 mm).
A. Kumar et al. / Optics Communications 291 (2013) 247–252
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Fig. 11. TE0 and TM0 mode field distribution for a TE0 pass polarizer. (ITO thickness¼ 2.0 mm and buffer thickness ¼1.12 mm).
Fig. 9. TM mode attenuation as a function buffer thickness at ITO film thickness ¼ 2.0 mm.
dipoles, which is frozen in by cooling down in the presence of the field below Tg, thereby inducing permanent birefringence. It can be precisely controlled by controlling the amplitude of applied electric field. The conducting ITO film deposited on polymer buffer can be used as one of the electrodes for poling.
6. Conclusion
Fig. 10. TM mode effective index as a function buffer thickness at ITO film thickness ¼2.0 mm.
confined to the ITO film. The TE0 mode is largely confined to the waveguide region. The extinction ratio and the insertion losses can be further improved if the birefringence is increased (i.e., if nTE can be reduced). Although the analysis of the multilayer waveguide in this paper is purely theoretical, it is easy to realize these polarizers experimentally. The waveguide represents the ion-exchanged glass waveguide which have been fabricated with excellent control over the waveguide parameters (depth and index) [29,30]. Polymer buffer layers can be easily deposited on the glass waveguides [25,30]. They are easily processed so that the films can be applied by spin coating or dip coating on large waveguide surfaces [25,27,31]. A large but precisely controlled birefringence can be induced in the polymers by ‘poling’ technique [25,27]. In poling process the polymer film heated upto its glass transition temperature Tg, it brought in strong electric field. The interaction of the field causes an alignment of molecular
We have theoretically studied the modes of the lossy ITO film clad optical waveguide at l ¼ 1.3 mm. It is shown that optical waveguides clad with lossy ITO films exhibit a damped oscillatory behavior in their attenuation characteristics. This is due to the periodic coupling between the lossy modes in ITO film and the lossless mode supported by the waveguide. The effect of an electro-optic (birefringent) buffer layer is also studied. It is shown that birefringent buffer layer can largely change the attenuation characteristics of both TE and TM modes. We demonstrate that both TE and TM pass polarizer with high extinction ratio and small insertion loss can be designed by suitably choosing the buffer index and its birefringence and thickness. The polarizer efficiency is also shown to dependent on the ITO film thickness. The result of this study may lead to applications in designing very short length and highly efficient TM or TE mode pass polarizers, which are essential for integrated photonics applications. In addition, such waveguide structures may find their application in modulation and switching devices.
Acknowledgment The authors are thankful to University Grants Commission (UGC) New Delhi, India for providing financial support.
Appendix: A. A1. Transfer Matrix Method Transfer matrix method (TMM) is used to find eigenmode in an arbitrary layer slab waveguide structure. Transfer matrix of each layer is calculated, and eigenvalues of the effective refractive indices are found by solving eigenfunctions numerically. The method is presented below and the dispersion equations are obtained. Consider a non-magnetic multilayer structure as shown in Fig. 1. The z-axis is the direction of the light propagation.
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Every layer is characterized by its thickness d and its complex refractive index ni. For TE mode propagation in þz-direction in the th layer, the field components are as follows: ðA1Þ Ei ¼ yEyi ðxÞexp jwtjgz Hi ¼ ½xHxi ðxÞ þ zHzi ðxÞexp jwtjgz
ðA2Þ
where Ei and Hi are electric and magnetic fields respectively in the th layer, x, y, z are unit vectors along x, y, z directions. g ¼ko (NR jNI)¼(b ja) is complex propagation constant with b and a being the phase and attenuation constants, respectively. NR and NI are real and imaginary parts of mode effective index and ko ¼2p/lo, lo being the free space wavelength. The relation between the electric fields in the substrate and the cover can be deduced by applying the appropriate boundary conditions at each interface. This results in the following matrix equation: " # " # Eys Eyc dEys ¼ M 1 M 2 M 3 M r dEyc dx
¼
m11
m12
m21
m22
!"
Eyc
#
dx
ðA3Þ
dEyc dx
where Mi ¼
coski di
k1i sinki di
ki sinki di
coski di
! i ¼ 1,2,3,. . .,r
ðA4Þ
are the transfer matrices for all the r layers having thickness di and qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ki ¼ ko n2i g2 ðA5Þ The fields in substrate and cover must vanish at infinity, so: Eys ðxÞ ¼ As egs x
ðA6Þ
Eyc ðxÞ ¼ Bc egc ðxxg þ 1 Þ
ðA7Þ
where ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r r gs ¼ g2 k20 n2s and gc ¼ g2 k20 n2c
ðA8Þ
Eqs. (6) and (7) in conjuction with Eq. (3) yield the dispersion equation: ðA9Þ FðgÞ ¼ j gs m11 þ gc m22 m21 þ gs gc m12 ¼ 0 The same procedure can be followed for TM modes. The transfer matrices and the dispersion equation now become: 0 1 n2 kii sinki di coski di B C M i ¼ @ ki ðA10Þ A sinki di coski di n2 i
g g gg F g ¼ j 2s m11 þ 2c m22 m21 þ 2s c2 m12 ¼ 0 ns nc ns nc
ðA11Þ
The dispersion equations are solved using Muller iteration method. The multiple roots are found using deflation and root polishing.
References [1] S. Szunerits, X. Castel, R. Boukherroub, Journal of Physical Chemistry C 112 (2008) 15813. [2] S. Franzen, Journal of Physical Chemistry C 112 (2008) 6027. [3] C. Phodes, et al., Journal of Applied Physics 100 (2006) 054905. [4] M.D. Losego, et al., Journal of Applied Physics 106 (2009) 024903. [5] V.K. Sharma, Anil Kumar, A. Kapoor, Journal of Optical Communication 284 (2011) 1815. [6] I.V. IL’ ichev, N.V. Toguzov, A.V. Shamray, Technical Physics Letters 35 (2009) 9831. [7] C.H. Chen, L. Wang, Japanese Journal of Applied Physics 39 (2000) 4130. [8] W. Johnstone, G. Stewart, T. Hart, B. Culshaw, Journal of Lightwave Technology 8 (1990) 538. [9] M.A. Sletten, M.A. Seshadri, Journal of Applied Physics 70 (1991) 574. [10] C. Ma, S. Liu, Journal of the Optical Society of America A 7 (1990) 1577. [11] P.S. Davids, B.A. Block, K.C. Cadien, Optics Express 13 (2005) 7063. [12] G. Li, A. Xu, Journal of Lightwave Technology 26 (2008) 1234. [13] A. Morand, C.S. Perez, P. Bench, S. Tedjini, IEEE Photonics Technology Letters 10 (1998) 1599. [14] M.C. Oh, S.S. Lee, S.Y. Shin, W.Y. Hwang, J.J. Kim, Electronics Letters 32 (1996) 324. [15] R.F. Carson, T.E. Batchman, Applied Optics 29 (1990) 2769. [16] M.P. Khodr, J.J. Sluss, T.E. Batchman, IEE Proceedings Optoelectronics 142 (1995) 183. [17] I.D. Villar, et al., Journal of Lightwave Technology 28 (2010) 3351. [18] S. Laure, N. Kaiser, A. Zoller, R. Gotzelmann, H. Lauth, H. Bernitzki, Thin Solid Films 335 (1998) 1. [19] J. Chilwell, I. Hodgkinson, Journal of the Optical Society of America A 1 (1984) 742. [20] H. Kogelnik, in: T. Tamir (Ed.), Guided Wave Optoelectronics, Springer-Verlag, 1998. [21] M. Born, E. Wolf, Principles of Optics, sixth ed., Cambridge Univ. Press, 1980. [22] S.D. Conte, Elementary Numerical Analysis: An Algorithm Approach, Mc-Graw Hill, New York, 1972. [23] L. Eldada, Journal of Quantum Electronics 6 (2000) 54. [24] A. Yeniag, et al., Journal of Lightwave Technology 22 (1) (2004) 154. [25] L.A. Hornak, Polymers for Lightwave and Integrated Optics, Marcel Dekker, 1992. [26] W.H.G. Horsthuis, G.J.M. Krijnen, Applied Physics Letters 55 (1989) 616. [27] E.V. Tomme, P.P.V. Daele, R.G. Baets, P.E. Lagasse, IEEE Journal of Quantum Electronics 27 (1991) 778. [28] J. Bicerano, Prediction of Polymer Properties, Marcel Dekkar, 1993. [29] S.I. Najafi (Ed.), Introduction to Glass Integrated Optics, Artech House, London, 1992. [30] D. Kumar, V.K. Sharma, K.N. Tripathi, Optical Engineering 45 (5) (2006) 054601. [31] G.K. Singh, V.K. Sharma, A. Kapoor, K.N. Tripathi, Optical and Laser Technology 33 (2001) 455.
Contents lists available at SciVerse ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Discussion
Integrated optic TE/TM pass polarizers using resonant coupling between ITO thin film lossy modes and dielectric waveguide modes Anil Kumar a, V.K. Sharma b, D. Kumar c, A. Kapoor a,n a
Department of Electronic Science, University of Delhi, South Campus, Benito Juarez Road, New Delhi-110021, India Keshav Mahavidyalaya, University of Delhi, Delhi-110034, India c Krishna Institute of Engineering and Technology, Ghaziabad, U.P., India b
a r t i c l e i n f o
abstract
Article history: Received 6 August 2012 Received in revised form 1 October 2012 Accepted 17 October 2012 Available online 1 November 2012
The resonant coupling between the lossless dielectric waveguide modes and the lossy modes supported by the absorbing indium–tin oxide (ITO) film is analyzed theoretically. It is observed that by changing the thickness of an ITO cladding layer placed above the planar dielectric waveguide, the TE or TM propagating modes may be selectively attenuated. This polarization effect can be used to design a TE or TM pass polarizer. Further it is also proposed that an electro-optic buffer layer inserted between the waveguide and ITO film can be used to design a high extinction ratio integrated optic polarizer at wavelength of 1.3 mm. A polarizer (both TE and TM pass) with extinction ratio of about 254 dB and insertion loss of about 10 dB can be easily designed for a 1 mm of its length. & 2012 Elsevier B.V. All rights reserved.
Keywords: ITO thin film Lossy modes Resonant coupling Electro-optic buffer Polarizer
1. Introduction At present the transparent conductive oxide films and in particular the indium–tin oxide (ITO) thin films find their application mainly in liquid crystal displays, flat panel displays, organic LEDs and solar cells. Their role in integrated optic components is yet to be explored. Since ITO is a transparent conductive oxide and is chemically stable, it offers new technological opportunities in sensing applications. Like another metal clad sensors, these sensors are also based on surface plasmon resonance supported by ITO thin films [1–4]. Surface plasmons are the longitudinal charge density waves, which propagate at the interface of two media with real part of their respective dielectric constants having opposite signs. These SP waves can be excited by p-polarized incident light under the conditions of attenuated total internal reflection using a prism. The excitation of SPs corresponds to an attenuation of reflected light intensity of surface plasmon resonance curve at a critical angle. These resonance effects occur for wavelength in the range of 1.8 to 2.5 mm. This range is not useful for optical communication applications.
n
Corresponding author. Tel.: þ91 9350571397; fax: þ91 11 24110606. E-mail addresses: [email protected] (A. Kumar), [email protected] (V.K. Sharma), [email protected] (D. Kumar), [email protected] (A. Kapoor). 0030-4018/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2012.10.022
However in visible range and at the optical communication wavelengths (1.3 and 1.5 mm) the ITO films have large real part of index and smaller imaginary part. Therefore, the ITO layers are expected to support the lossy modes at these wavelengths. We will show that ITO clad dielectric planar waveguides exhibit many interesting properties due to coupling between the lossless mode of the guiding layer and the lossy modes supported by the ITO cladding. Here we propose the use of thin ITO films as a TE or TM pass polarizer at communication wavelength 1.3 mm. Effect of a birefringent buffer layer on the efficiency of the polarizer is also discussed. There are many ways to produce a waveguide polarizer, e.g., using selective attenuation in metal cladding or cut off effects in waveguide [5–12]. A metal-clad optical waveguide is suitable for mode polarization filter because the ohmic losses of TM guided modes are much larger than that of TE modes. If a thin low index dielectric film (buffer layer) is sandwiched between the guide and the metal, then the absorption of TM mode is further enhanced and that of TE is reduced at a suitably chosen buffer thickness. The dielectric layer is called a buffer layer because it relaxes the metal’s influence on the preferred guided TE mode [5–10]. As a consequence, either the TM guided mode of the waveguide is completely absorbed or its power is substantially reduced, but the TE mode propagates through the interaction region with essentially no attenuation. These structures however, cannot produce a TM pass polarizer. Other polarizers use the birefringent polymer
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over layers on the waveguide or the electro-optic effect in polymer layers to split the TE and TM modes [13,14]. Semiconductor clad waveguide polarizers have also been proposed [15,16]. By varying the thickness of semiconductor cladding layer deposited on a planar dielectric waveguide, the TE or TM propagating modes may be selectively attenuated. This polarization effect is due to the coupling between the lossless modes of the dielectric waveguides and the lossy modes supported by silicon cladding layer. But these structures suffer from a relatively high insertion loss and have low extinction ratio (defined later). In this paper, we investigate theoretically the attenuation characteristics of the ITO clad glass optical waveguide by exact numerical method. The thin film transfer-matrix formulation is used as the primary tool for the multilayer waveguide analysis which forms the dispersion equation of the waveguide structure consisting of any combination of lossless and lossy (ITO) layers. The guided mode propagation constants of the structure correspond to the zeros of dispersion the equation. We show that ITO clad optical waveguides possess unique properties which arise from the effect of periodic coupling between lossless mode of dielectric waveguide and the lossy modes supported by the thin ITO films. There are regions of selected high and low attenuation for different polarization modes (TE or TM) of the propagating light at wavelength of 1.3 mm. Such a structure can be used as TE or TM pass polarizer. However, it is observed that the efficiency of the polarizer so formed is not very high. The efficiency of the polarizer is high if the attenuation of the preferred (pass polarization) mode is very small and that of the other polarization is quite large. We propose that insertion of an electro-optic dielectric layer (buffer layer) between the waveguide and ITO film can significantly improve the efficiency of the polarizer. This mechanism is discussed in detail.
eN ¼3.57, op ¼1.89 1015 rad/s, t ¼6.34 10 15 s/rad, s0 ¼ 0.49, o0 ¼5.61 1015 rad/s, and g ¼9.72 1013. This model will be used henceforward for the further analysis. The relative permittivity (which is 2.4172þ0.1849j at l ¼1.3 mm for ITO) can also be expressed in terms of complex refractive index as n ¼ e1=2 ¼ n þ jk ¼ 1:5558þ 0:0594 j
ð2Þ
where n and k are the real and imaginary parts of the refractive index, respectively. The cover (air), substrate and dielectric guide layers are lossless and are given by real permittivity. The modes of the waveguide shown in Fig. 1 are characterized by a complex propagation constant given as jkz ¼ a þjb. Where a is the absorption loss in the waveguide structure and b/k0 is the mode effective refractive index (k0 ¼2p/l). The complex propagation constant of this multilayer waveguide is obtained by solving the complex eigenvalue equation which is derived by using transfer matrix method [19–21]. The method is presented in Appendix A.
3. Solution of the eigenvalue equation for ITO clad waveguides The lossy multilayer waveguide structure shown in Fig. 1 is analyzed at a wavelength of 1.3 mm. For ITO films the index is given by Eqs. (1) and (2) while for other layers the index is same as shown in Fig. 1. The waveguide considered is a single mode potassium ion exchange glass waveguide in microscopic glass slides with guide thickness of 4 mm (sufficient to support TE0 and TM0 modes). The complex eigenvalue equation describing the structure is exactly solved numerically by Muller’s method [22].
4. Results and discussion 2. ITO clad waveguide A four-layer ITO clad waveguide is shown in Fig. 1. It consists of a thin layer of ITO deposited on a thin layer lossless dielectric waveguide. The cover (air) and substrate layers are assumed to be semi-infinite. The layers are characterized by their relative permittivity. The ITO layer absorbs light and is thus characterized by a complex value of relative permittivity. The oscillatory model represents the dielectric constant of ITO film more accurately (as compared to Drude model) because it also considers the dielectric behavior of the ITO film. The value of dielectric constant calculated using this model provides very good agreement with the experimentally determined values for ITO films deposited at room temperature [18]. Therefore the dielectric constant of the ITO can be expressed as [17]
eðoÞ ¼ e1
o2p s o2 þ 2 0 0 o2 þi o=t o0 o2 igo
Let us first consider the waveguide structure without the buffer layer as shown in Fig. 1. Figs. 2 and 3 show, respectively, the variation of TE and TM modes in their mode effective index and the attenuation as the ITO film thickness is varied. Wavelength used is 1.3 mm. The glass waveguide supports only the fundamental TE0 and TM0 modes, however as the thickness of the ITO layer is increased the number of modes supported by the composite structure increase and are confined mainly in ITO layer. The attenuation results for both the polarizations show a damped oscillatory behavior as the ITO layer thickness is
ð1Þ
where eN is the high frequency dielectric constant, t is the electronic scattering time and op is the plasma frequency. It is an oscillator model whose variables are: s0 (oscillator strength), o0 (oscillator resonance frequency) and g (oscillator damping constant). The parameters used are:
Fig. 1. Schematic cross section of four layers ITO clad waveguide.
Fig. 2. TE and TM mode effective index as a function of ITO film thickness.
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Fig. 4. Schematic cross section of five layers waveguide with birefringent buffer layer.
Fig. 3. TE and TM mode attenuation constant versus ITO film thickness.
increased. These oscillations are due to coupling between the zeroth-order mode propagating in the glass waveguide and various orders of modes supported by the ITO layer. As the ITO layer thickness is increased each successive maximum on the attenuation curve represents a point where the ITO layer is supporting a successively higher order mode as shown in Fig. 3. The first peak in TE curve represents the attenuation due to coupling of waveguide mode to the TE0 mode supported by the ITO film, second peak represents the attenuation due to coupling of waveguide mode to the lossy TE1 mode of ITO film. The guided mode now does not couple to TE0 lossy mode of ITO layer due to mode effective refractive indices mismatch. The next peak represents the attenuation due to the coupling of guided mode to lossy TE2 mode of ITO film and so on. Similarly, peaks in TM curve, represents the attenuation due to coupling of guided TM0 mode to the successively higher order lossy modes supported by the ITO film. Since the attenuation peaks appear at different ITO thicknesses both TE and TM pass polarizers can be designed by selecting its thickness appropriately. The attenuation coefficient (aTM for TM modes and aTE for TE modes) in dB/cm is obtained after multiplying the imaginary part of mode effective index by 2k0 105 log10 ðeÞ. The first peak for TM mode loss 580.3 dB/cm appears at 0.593 mm thickness of ITO film. TE attenuation at this thickness is 398.9 dB/cm. Similarly the first TE mode maximum (loss is 504.2 dB/cm) occurs at 0.485 mm and TM loss is 440.7 dB/cm at this thickness. However, the difference between the TM loss (580.3 dB/cm) and TE (398.9 dB/cm) losses at 0.593 mm and TE losses (504.2 dB/cm) and TM losses (440.7 dB/cm) at 0.485 mm is not very large and hence the extinction ratio for TM pass or TE pass polarizer will not be large and the insertion losses will be quite high. The extinction ratio for the TM pass polarizer is defined as (aTE– aTM) length of polarizer and its insertion loss is aTM length of polarizer. We propose that a dielectric birefringent layer can be used to increase the extinction ratio. We will also show that it also reduces the insertion losses. As a result an efficient polarizer (both TE pass and TM pass) can be produced.
5. Effect of birefringent buffer layer on guided modes Let us now consider the effect of a birefringent buffer layer inserted between the ITO film and the guiding layer as shown in Fig. 4. The buffer can be chosen as an electro-optic controlled birefringent polymer film. Polymers have been widely used in integrated optics because they have excellent waveguiding
properties [23,24]. Moreover, their optical properties can be tailored (e.g., by doping various dyes). The birefringence of this layer can be induced and controlled precisely by electrical poling technique [25–27]. Since ITO is a conducting material, it can be used as a contact for poling as well as a cladding layer. Another advantage of using polymer buffer layer is that, there are a large number of polymers with refractive index ranging from 1.4 to 1.7 [28]. So, depending upon the poling direction we can have either nTE 4nTM or nTM 4nTE, where nTE is the buffer index for TE polarization and nTM for TM polarization [26]. Birefringence of more than 0.03 can easily be achieved in polymer films. We will now show that such a birefringent buffer layer increases the extinction ratio and decreases the insertion losses of the ITO clad polarizers. The efficiency of the polarizer can be maximized by optimizing the thicknesses of ITO and the buffer layers and the index of buffer layer. The refractive index of ITO film is larger than that of the waveguide and therefore the modes are always lossy (leaky). For the devices without buffer, the peaks appear when there is phase matching between the guided mode and lossy mode supported by ITO film. The role of the buffer is two-fold. First, if the buffer index is higher than the waveguide and lower than the real part of index of ITO film, say, for TE (or TM) mode, then a better phase matching takes place and a larger portion of TE (or TM) guided mode energy is transferred to the lossy ITO film. So, basically the high index buffer provides the perfect enhanced phase matching or resonant phase matching between the guided mode and lossy mode of ITO film. Second, for other polarizers, say, TM (or TE) mode, if the buffer index (because of birefringence) is smaller than the waveguide index (1.521) the waveguide structure will support a guided mode. However small losses will be there because of lossy ITO film and there will be no phase matching between the guiding mode and the lossy mode supported by ITO film. To fully utilize the phase matching effect, the thickness and index of buffer layer must be precisely controlled. The variation of attenuation and effective mode index as a function of buffer thickness is shown in Figs. 5 and 6 respectively for the TE mode. We have taken nTE ¼1.55 and nTM ¼1.52 for buffer. Fig. 5 shows variation for two different values of ITO thickness. It is clear from Fig. 5 that for 2 mm thick ITO film, there is a sharp peak at buffer thickness of 1 mm. The loss at this thickness is 2640 dB/cm for TE polarization. The corresponding loss for TM polarization it is 100 dB/cm (not shown in Fig. 5). Therefore for a polarizer of length 1 mm, the polarization extinction ratio for the clad section of TM pass polarizer is 254 dB and the excess insertion loss is 10 dB. The reason for high TE mode attenuation at 1 mm buffer thickness is that the high index buffer layer introduces an additional mode which is strongly coupled to both the lossy ITO film and the waveguide and enhances waveguide and ITO film mode coupling. There is another peak at around 3 mm buffer thickness but attenuation is not equally high, because as the buffer thickness is increased, the induced additional mode starts confining to this layer and coupling becomes weak. Another plot in Fig. 5 is shown for 1.8 mm thick ITO film. It has similar behavior with different peak positions and attenuation values. The index
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Fig. 5. TE mode attenuation as a function buffer thickness at ITO film thicknesses. (a) 2.0 mm, (b) 1.8 mm.
Fig. 6. TE mode effective index as a function buffer thickness at ITO film thicknesses. (a) 2.0 mm, (b) 1.8 mm.
matching also depends on the ITO film thickness. The mode coupling can be best analyzed using field plots. Figs. 7 and 8 show the absolute value of the Ey field component of TE0 mode plotted as a function of the waveguide cross section with 1.12 and 1 mm buffer thicknesses and ITO film thicknesses of 1.8 and 2.0 mm, respectively. Comparison of Figs. 7 and 8 indicates that the field confinement for TE0 mode in ITO film is better for 2 mm thick ITO film at optimized buffer thickness. In Fig. 8, the field plot for TM0 mode is also shown. Clearly there is no resonant coupling (strong field confinement) for the TM0 mode in ITO film and most of the energy is confined to the waveguide. In our next design, we will show that using the same principle (of having high index buffer for phase matching) we can design a TE polarization pass polarizer. But, now we have nTM ¼ 1.55 and nTE ¼1.52. The attenuation and effective index variation as a function of buffer thickness are shown for TM polarization in Figs. 9 and 10, respectively. The behavior of curves is similar as that of the curves for TE polarization. The first strong peak appears at buffer thickness of 1.12 mm and ITO thickness of 2 mm. The TM mode loss at this thickness is 2530 dB/cm. The corresponding loss for TE mode is 89 dB/cm. Therefore, for a 1 mm long polarizer, the polarization extinction ratio for the clad section of TE pass polarizer is 244 dB and the excess insertion loss is 8.9 dB. The field plots for TM0 and TE0 mode of this polarizer is shown in Fig. 11. It is evident from Fig. 11 that most of the TM0 is
Fig. 8. TE0 and TM0 mode field distribution for a TM0 pass polarizer. (ITO thickness¼ 2.0 mm and buffer thickness ¼1.0 mm).
Fig. 7. TE0 mode field distribution for the multilayer structure with buffer. (ITO thickness ¼1.8 mm and buffer thickness ¼ 1.12 mm).
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Fig. 11. TE0 and TM0 mode field distribution for a TE0 pass polarizer. (ITO thickness¼ 2.0 mm and buffer thickness ¼1.12 mm).
Fig. 9. TM mode attenuation as a function buffer thickness at ITO film thickness ¼ 2.0 mm.
dipoles, which is frozen in by cooling down in the presence of the field below Tg, thereby inducing permanent birefringence. It can be precisely controlled by controlling the amplitude of applied electric field. The conducting ITO film deposited on polymer buffer can be used as one of the electrodes for poling.
6. Conclusion
Fig. 10. TM mode effective index as a function buffer thickness at ITO film thickness ¼2.0 mm.
confined to the ITO film. The TE0 mode is largely confined to the waveguide region. The extinction ratio and the insertion losses can be further improved if the birefringence is increased (i.e., if nTE can be reduced). Although the analysis of the multilayer waveguide in this paper is purely theoretical, it is easy to realize these polarizers experimentally. The waveguide represents the ion-exchanged glass waveguide which have been fabricated with excellent control over the waveguide parameters (depth and index) [29,30]. Polymer buffer layers can be easily deposited on the glass waveguides [25,30]. They are easily processed so that the films can be applied by spin coating or dip coating on large waveguide surfaces [25,27,31]. A large but precisely controlled birefringence can be induced in the polymers by ‘poling’ technique [25,27]. In poling process the polymer film heated upto its glass transition temperature Tg, it brought in strong electric field. The interaction of the field causes an alignment of molecular
We have theoretically studied the modes of the lossy ITO film clad optical waveguide at l ¼ 1.3 mm. It is shown that optical waveguides clad with lossy ITO films exhibit a damped oscillatory behavior in their attenuation characteristics. This is due to the periodic coupling between the lossy modes in ITO film and the lossless mode supported by the waveguide. The effect of an electro-optic (birefringent) buffer layer is also studied. It is shown that birefringent buffer layer can largely change the attenuation characteristics of both TE and TM modes. We demonstrate that both TE and TM pass polarizer with high extinction ratio and small insertion loss can be designed by suitably choosing the buffer index and its birefringence and thickness. The polarizer efficiency is also shown to dependent on the ITO film thickness. The result of this study may lead to applications in designing very short length and highly efficient TM or TE mode pass polarizers, which are essential for integrated photonics applications. In addition, such waveguide structures may find their application in modulation and switching devices.
Acknowledgment The authors are thankful to University Grants Commission (UGC) New Delhi, India for providing financial support.
Appendix: A. A1. Transfer Matrix Method Transfer matrix method (TMM) is used to find eigenmode in an arbitrary layer slab waveguide structure. Transfer matrix of each layer is calculated, and eigenvalues of the effective refractive indices are found by solving eigenfunctions numerically. The method is presented below and the dispersion equations are obtained. Consider a non-magnetic multilayer structure as shown in Fig. 1. The z-axis is the direction of the light propagation.
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Every layer is characterized by its thickness d and its complex refractive index ni. For TE mode propagation in þz-direction in the th layer, the field components are as follows: ðA1Þ Ei ¼ yEyi ðxÞexp jwtjgz Hi ¼ ½xHxi ðxÞ þ zHzi ðxÞexp jwtjgz
ðA2Þ
where Ei and Hi are electric and magnetic fields respectively in the th layer, x, y, z are unit vectors along x, y, z directions. g ¼ko (NR jNI)¼(b ja) is complex propagation constant with b and a being the phase and attenuation constants, respectively. NR and NI are real and imaginary parts of mode effective index and ko ¼2p/lo, lo being the free space wavelength. The relation between the electric fields in the substrate and the cover can be deduced by applying the appropriate boundary conditions at each interface. This results in the following matrix equation: " # " # Eys Eyc dEys ¼ M 1 M 2 M 3 M r dEyc dx
¼
m11
m12
m21
m22
!"
Eyc
#
dx
ðA3Þ
dEyc dx
where Mi ¼
coski di
k1i sinki di
ki sinki di
coski di
! i ¼ 1,2,3,. . .,r
ðA4Þ
are the transfer matrices for all the r layers having thickness di and qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ki ¼ ko n2i g2 ðA5Þ The fields in substrate and cover must vanish at infinity, so: Eys ðxÞ ¼ As egs x
ðA6Þ
Eyc ðxÞ ¼ Bc egc ðxxg þ 1 Þ
ðA7Þ
where ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r r gs ¼ g2 k20 n2s and gc ¼ g2 k20 n2c
ðA8Þ
Eqs. (6) and (7) in conjuction with Eq. (3) yield the dispersion equation: ðA9Þ FðgÞ ¼ j gs m11 þ gc m22 m21 þ gs gc m12 ¼ 0 The same procedure can be followed for TM modes. The transfer matrices and the dispersion equation now become: 0 1 n2 kii sinki di coski di B C M i ¼ @ ki ðA10Þ A sinki di coski di n2 i
g g gg F g ¼ j 2s m11 þ 2c m22 m21 þ 2s c2 m12 ¼ 0 ns nc ns nc
ðA11Þ
The dispersion equations are solved using Muller iteration method. The multiple roots are found using deflation and root polishing.
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