Eigenvalue computation of open periodically composed waveguides by series expansion

Abstract

Eigenvalues of periodically constituted waveguides with complicated material distribution are efficiently determined, where eigensolvers in software packages show difficulties in finding the eigensolutions. Moreover, the treated waveguide structures are open, causing even more trouble with available numerical solvers or rather demanding procedures within analytical approaches. Since open configurations are essential for the evaluation of radiating structures, we suggest to convert the open problem setting into a closed equivalent configuration but without disturbing the actual field behaviour. Thus, the original continuous mode spectrum is turned into a discrete and proper set of eigenmodes. The field solution of the periodically modified waveguide is obtained by series expansion with the eigensolutions of the homogeneous background waveguide as basis functions. An eigenproblem is still to solve, but it is considerably reduced in size and easy to solve by the use of a-priori information.

Solving Periodic Eigenproblems by Solving Corresponding Excitation Problems in the Domain of the Eigenvalue

“…12, which is operated in TE mode and which has also been analyzed in [27] with an SMA and with the matrix pencil method based on the electric field distribution computed by CST MWS for a waveguide of finite length and with waveguide port excitation. The FEBI method from Section 4 was employed for the dispersion analysis of this configuration, where one Floquet mode has been chosen in x-and a series from −19 to +19 in y-direction.…”

“…The utilized tetrahedral FE-mesh comprised 37 360 unknowns and the computation time for one excitation was around Figure 12. 1D periodic unit cell of grounded corrugated dielectric waveguide (infinite in x) as also considered in [27]. 10 sec.…”

“…13, where the computed modal electric field is illustrated in a cut plane through the unit cell for a frequency of 16 GHz. The complex propagation constant k y0 = β − jα has been directly searched with the FEBI code for every considered frequency, where the sum of the and comparison with data computed by the SMA as discussed in [27]. electric field in several observation points within the dielectric was chosen as observable to monitor the resonance behavior.…”

“…15. They are compared with SMA results according to the approach discussed in [27], where 8 modes in the SMA have been used and where the absorber was placed 110.5 mm above the ground plane. The observed agreement is very good.…”

Driven eigenproblem computation in periodic structures accelerated with Brent's method

“…Fig. 6 indicates a comparison of the dispersion behaviours obtained with the driven method and the scattering matrix approach (SMA) with absorbing layers and eight modes considered in the port planes [13]. The light line separates the radiating waves from the purely guided waves.…”