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25 August 1994 Comparison between different methods to calculate grating assisted asymmetrical couplers
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Proceedings Volume 2212, Linear and Nonlinear Integrated Optics; (1994)
Event: Integrated Optoelectronics '94, 1994, Lindau, Germany
Tunable filters are key components for future transparent WDM networks'. In a wavelength-routed network add and drop functions can be performed in a cross c.onnect module. Electrically tunable filters in combination with direct detection may be an alternative to coherent detection for high density wavelength division multiplexing (HDWDM) systems. Promising device structures for the implementation of filter functions in optoelectronic circuits are grating assisted (meander-type) couplers, both for passive waveguides and for tunable lasers. Such filters are traditionally analysed and designed by using coupled mode theory. The accuracy of this method, however, depends on the choice of basic eigenfunctions2 and is limited to weak guiding and weak coupling structures. Recently, to overcome these problems, a transfer matrix description has been proposed, which exists in a hierachy of different approximations. The method with the highest accuracy, called bidirectional eigenmode propagation method (BEP)3, solves the Helmholtz equation in forward and backward direction by propagation of eigenmodes of the waveguide structure and calculates the energy transfer at interfaces with abrupt changes of the refractive index by mode matching (overlap integrals). Radiation modes are included by using a finite window with metallic or magnetic walls. An unidirectional version which neglects either the forward or backward travelling waves is also possible. Very important for practical applications is a reduction of the eigenmode series expansion to only (guiding) waveguide modes (guided eigenmode matching and propagation method (GEMP)4). This allows an analysis of a grating assisted coupler to be carried out using only 2 eigenmodes (odd and even coupler modes) in the transfer matrix algorithm and calculating 4 overlap integrals and 4 propagation constants. This mode expansion approach leads to a deep understanding of the physical behaviour of the device. In this paper we present the basic formulation of the eigenmode expansion method (B), coupled mode theory (C) and show, in case of resonance, the equivalence of GEMP with simple coupled mode theory on the basis of coupler eigenmodes in the limit of weak coupling (D). It will be shown, that the key parameters arot of GEMP and the coupling coefficient 1 of CMT are correlated and that for practical applications a combination of both methods are advantageous (E). Some results on codirectional grating assisted couplers and the recently published sampled grating structure5, which is the basis of an electro-optically tunable filter, will be discussed in F. A short conclusion is given in G.
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Hans Peter Nolting and M. Grawert "Comparison between different methods to calculate grating assisted asymmetrical couplers", Proc. SPIE 2212, Linear and Nonlinear Integrated Optics, (25 August 1994);

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