Dikdörtgen kesitli dielektrik dalga kılavuzları için adyabatik mod yaklaşımı
Adiabatic mode approach for dielectric rectangular waveguides
- Tez No: 22070
- Danışmanlar: PROF. DR. ERCAN TOPUZ
- Tez Türü: Yüksek Lisans
- Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
- Anahtar Kelimeler: Adyabatik mod yaklaşımı, Dielektrik dalga kılavuzu, İletişim sistemleri, Adiabatic mode approach, Dielectric waveguide, Communication systems
- Yıl: 1992
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: Belirtilmemiş.
Özet
ÖZET Bu tezde, dikdörtgen kesitli dielektrik dalga kılavuzlarının, adyabatik mod yaklaşıklığı adı verilen yöntemle analizi için bir formülasyon geliştirilmiş ve yöntem integre optikte kullanılan tipten homojen dielektrikli bazı dalga kılavuzlarında ûzdegerlerin belirlenmesine uygulanmıştır. Bu analiz neticesinde elde edilen sayısal sonuçlar, literatürde daha önce farklı bir sayısal yöntemle elde edilen sonuçlarla karşılaştırılarak, adyabatik mod yaklaşıklığının geçerli olduğu parametre bölgesi ve doğruluk derecesi belirlenmiştir. s. Tezin ikinci bölümünde; dikdörtgen kesitli dielektrik dalga kılavuzlarındaki özçözümlerin elde edilmesi için kullanılmış olan çeşitli yaklaşık yöntemler tanıtılmıştır. Üçüncü bölümde, adyabatik mod yaklaşımı kullanılarak ödevin ana konusunu içeren temel bağıntılar elde edilmiş ve bilgisayar analizine uygun bir algoritma geliştirilmiştir. Dördüncü bölümde, analiz için önerilen algoritma ve programda kullanılan alt programlar ile işlevleri açıklanmış ve uygulama örnekleri verilmiştir, elde edilen sonuçlar daha önce çeşitli yöntemlerle bulunmuş olan sonuçlarla karşılaştırılarak, geçerlik dereceleri irdelenmiştir.
Özet (Çeviri)
SUMMARY ADIABATIC MODE APPROACH FOR DIELECTRIC RECTANGULAR WAVEGUIDES A jO.^ X 2 Q Figure 1. Dielectric rectangular waveguide In this thesis, the dielectric waveguide shown in the figure 1 was analyzed using the“Adiabatic Mode”approach. Various forms of rectangular dielectric waveguides are utilized in optical integrated circuits and hence their analysis has been of interest since the pioneering works of Goell and Marcatilli in 1966. Here we present a numerical implementation of the adiabatic mode approach and compose results with the results given in the literature. -v-In section 1 we introduce the problem and outline the scope of this work. Section 2 is devoted to a survey of the existing literature. Special attention is given to methods based on“Approximate expansion in cartesien coordinates”(Marcatilli, 1969),“Expansion in circular harmonics”(Goell, 1969),“The effective refractive index method”(Knox and Toulios, 1970) Goell' s approach differs from the other two in that it describes a computer analysis of the propagation characteristic of a rectangular wavequide which does not suffer from intervening approximations and hence is in principle an exact numerical solution of the scalarized problem. The analysis is based on an expansion of the electromagnetic field in terms of a series of circular harmonics. That is, Bessel and modified Bessel functions multiplied by trigonometric functions. The electric and magnetic fields inside the wavequide core are matched to those outside the core at appropriate points on the boundary to yield equations. Which are then solved on a computer for the propagation constants and field configurations of the various modes. That paper presents the results of the computations in the form of curves of the propagation constants and as computer generated mode patterns. The propagation curves are presented in a form which makes them refractive index independent as long as the difference of the index of the core and the surrounding medium is small, the case which applies to integrated optics. In addition to those for small index difference, it also gives results for larger index differences such as might be encountered for microwave applications. In his paper entitled“Dielectric Rectangular Wavequide and Directional Coupler for Integrated Optics”, Marcatilli studies the transmission properties of a dielectric rod with rectangular cross section, surrounded by several dielectrics of smaller refractive indices. Several guiding structures such as the burried strip which can be obtained from this generic geometry by proper choice of the dielectric properties of the surrounding media. After making some simplifying assumptions, he solved Maxwell's equations in closed form and found that, because of total internal reflection, the guide supports two types of hybrid modes which are essentially TEM modes polarized at right angles. Their attenuations are comperable to that of a plane wave traveling in the material of which the rod is made. -yi-If the refractive indices are ohoosen properly, the quide can support only the fundamental modes of each family with any aspect ratio of the quide cross section. By adding thin lossy layers, the quide can be made to support only one of the modes if part of surrounding dielectrics is made a low impedance medium. Finally, he determined the coupling between parallel rods, of slightly different sizes and dielectrics and showed that at wavelengths arround are micron, 3-dB directional couplers could be realized with typically a few hundred microns coupling length and with separations which are about the same as the oross-seotional dimensions of the individual guides. In section three, we develop an entirely different approach which can be used to analyze the propagation characteristics of dielectric waveguides under quite general conditions. Since we reguire slow variation of the parameters of the guiding structure in one judiciously chosen direction and introduce an adiabatic type approximation to simplify the problem we have coined this technique as the adiabatic mode approach. In the adiabatic mode approach, first we can use symmetry consideration to reduce the problem to an equivalent one determined by assumming a PEC (Perfect Electric Conductor) or a PMC (Perfect Magnetic Conductor) along the semiaxes x* 0 and y i 0. For the group of modes for what identical (either PEC or PMC) boundary conditions apply on both semiaxes one can make use at the additional symmetry and reduce the problem to the first octant as depicted in the figure 2. We will begin by considering the problem under the assumption of the stated higher degree of symmetry and for defruitener concentrate in the modes for which Ez vanishes in 0=0 and t»0 = arctg (b/a) (1) [i.e. that PEC s are place along x > 0 and o] The boundary conditions can them be expressed as; Ey, Hy Ez, Hz oontinous at x=a <J>e(0,<Jlo) (2) Ez, Ep= 0 at 0=O,<|)a (0o=artog (b/a) (3) -^yii-6v üv A F -B F' PKi2 Ki E0=i.Cosu { (12) fiV Cüp. - A G +B G' pK22 K2 we0nı2v Ö -A F+B F' Kl2P Ki Hp=i.Cosu { (13) <ûe0n22V B A G-B G" K22p K2 (û£0ni2 BV A F'-B F Ki Kx2p HlK-Sin^ { (14) toe0n22 BV -A G'+B G K2 K22p where upper and lover equations are valid for p i p0 and pi p0 respectively and prime indicates derivative with respect to the argument [i.e. Ki.p and K2.p in F and G, respectively]. Eigenvalue equation results from continuity of the tangential fields (i.e. y directed fields) at p= po(0) -x-
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