IEEE JOURNAL OF QUANTUM ELECTRONICS.VOL.QE-22,NO.6.JUNE 1986 959 Coupling Characteristics of Two Rectangular Dielectric Waveguides Laid in Different Layers KAZUHITO MATSUMURA,MEMBER,IEEE,AND YOSHIRO TOMABECHI,MEMBER,IEEE Abstract-The coupling characteristic of rectangular dielectric waveguides which lay in different,parallel layers and one waveguide crossed over the other one are studied.Step-like approximation and the variational method are used for calculating the coupling coefficient which varies with axial distance z.Electromagnetic field expression for the dielectric waveguide mode of rectangular cross section is newly in- troduced and used.Calculated coupling characteristics are compared OWG-F with experimental results carried on 50 GHz band.The principle of crossed waveguides leads us to the new design concept of"multilay- ered integrated circuit." 1.INTRODUCTION TN recent years much research has been directed towards Fig.I.Coupled rectangular dielectric waveguide and their coordinate sys- Ithe use of dielectric waveguide (DWG)for the milli- tems. meter,submillimeter and optical wave transmission.To realize millimeter through optical wavelength integrated circuits,several ideas for the waveguiding mechanism and tems.Each guide lays in different layers (parallel to x-z circuit component have been proposed [1]-[4]. plane)and are separated by a distance d in the y-direction. The projection of the guides axes in the x-z plane makes The coupling mechanism of dielectric waveguides has been analyzed [5]and the results applied to the design of small angle 0.This dielectric waveguide structure is a typ- directional couplers [6],[7].Relating to these applica- ical model of circuit elements or waveguide components in the multilayered integrated circuit.In this paper,we tions,couplings of nonparallel dielectric waveguide have also discussed [8],[9]. assume that the each dielectric waveguide supports only one fundamental mode. In most of the previous work,the axes of the coupled dielectric waveguides are coplanar. In this paper,we treat the coupling mechanism of rect- B.Power Transfer Between Two Waveguides Coupled angular dielectric waveguides which lay in the different, to Each Other with Varying Coupling Coefficient parallel,layers.One waveguide crosses over the other. To analyze the power transfer phenomena between This crossed waveguide will conduct us to the new design crossed-over guides,we consider first that the coupling concept of"'multilayered integrated circuit.'' coefficient C varies with axial distance z.In the coupled An electromagnetic field expression for the guided dielectric waveguide system,let us assume that the trans- mode along the rectangular dielectric waveguide is intro- mitted mode in each guide have the same propagation duced [10]and used to analyze the coupling mechanism. constant.This is true if the guides are separated enough Experimental studies are carried out on the 50 GHz band. With the mode A launched on the dielectric wave- Measurements of coupled powers between two guides are guide-1(DWG-1)at z=zo,it is required to find the power also shown and described. coupled to the mode 42 in the DWG-2 as a function of z. Coupling phenomenon between the two forward mode II.COUPLING CHARACTERISTICS OF CROSSED OVER A1(z)and A2(z)is,as well known,described approxi- DIELECTRIC WAVEGUIDES mately by the coupled wave equations [11]. A.Structure of the Coupling Dielectric Waveguides Fig.I shows the crossed over rectangular dielectric waveguide (RDWG)structure and their coordinate sys- dA =-jBA()+C(A() d Manuscript received September 24.1985;revised January 28.1986. dA②=C)A(a-jBA2 (1) The authors are with the Faculty of Engineering,Utsunomiya Univer- dz sity.Utunomiya 321.Japan. IEEE Log Number 8608179. where A(z)and A2(z)are the amplitudes of the guided 0018-9197/86/0600-0959Ss01.00©1986IEEEIEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. QE-22, NO. 6, JUNE 1986 959 Coupling Characteristics of Two Rectangular Dielectric Waveguides Laid in Different Layers Abstract-The coupling characteristic of rectangular dielectric waveguides which lay in different, parallel layers and one waveguide crossed over the other one are studied. Step-like approximation and the variational method are used for calculating the coupling coefficient which varies with axial distance z. Electromagnetic field expression for the dielectric waveguide mode of rectangular cross section is newly in￾troduced and used. Calculated coupling characteristics are compared with experimental, results carried on 50 GHz band. The principle of crossed waveguides leads us to the new design concept of “multilay￾ered integrated circuit.” I I. INTRODUCTION N recent years much research has been directed towards the use of dielectric waveguide (DWG) for the milli￾meter, submillimeter and optical wave transmission. To realize millimeter through optical wavelength integrated circuits, several ideas for the waveguiding mechanism and circuit component have been proposed [ 11-[4]. The coupling mechanism of dielectric waveguides has been analyzed [5] and the results applied to the design of directional couplers [6], [7]. Relating to these applica￾tions, couplings of nonparallel dielectric waveguide have also discussed [8], [9]. In most of the previous work, the axes of the coupled dielectric waveguides are coplanar. In this paper, we treat the coupling mechanism of rect￾angular dielectric waveguides which lay in the different, parallel, layers. One waveguide crosses over the other. This crossed waveguide will conduct us to the new design concept of “multilayered integrated circuit. ” An electromagnetic field expression for the guided mode along the rectangular dielectric waveguide is intro￾duced [lo] and used to analyze the coupling mechanism. Experimental studies are carried out on the 50 GHz band. Measurements of coupled powers between two guides are also shown and described. 11. COUPLING CHARACTERISTICS OFROSSED OVER DIELECTRIC WAVEGUIDES A. Structure of the Coupling Dielectric Waveguides Fig. 1 shows the crossed over rectangular dielectric waveguide (RDWG) structure and their coordinate sys￾Manuscript received September 24, 1985; revised January 28, 1986. The authors are with the Faculty of Engineering, Utsunomiya Univer￾IEEE Log Number 8608 179. sity, Utunomiya 32 1, Japan. Fig. 1. Coupled rectangular dielectric waveguide and their coordinate sys￾tems. tems. Each guide lays in different layers (parallel to x-z plane) and are separated by a distance d in the y-direction. The projection of the guides axes in the x-z plane makes small angle 6. This dielectric waveguide structure is a typ￾ical model of circuit elements or waveguide components in the multilayered integrated circuit. In this paper, we assume that the each dielectric waveguide supports only one fundamental mode. B. Power Transfer Between Two Waveguides Coupled to Each Other with Varying Coupling Coeficient To analyze the power transfer phenomena between crossed-over guides, we consider first that the coupling coefficient C varies with axial distance z. In the coupled dielectric waveguide system, let us assume that the trans￾mitted mode in each guide have the same propagation constant. This is true if the guides are separated enough. With the mode AI launched on the dielectric wave￾guide-1 (DWG-1) at z = zo, it is required to find the power coupled to the mode A, in the DWG-2 as a function of z. Coupling phenomenon between the two forward mode A,(z) and A2(z) is, as well known, described approxi￾mately by the coupled wave equations [ 111. where A ,(z) and A2(z) are the amplitudes of the guided 0018-919718610600-0959$01 .OO O 1986 IEEE