volume | PIER Journals

Abstract

The results of the development of an approximate approach for describing structured waveguides, which can be considered as an analogue of the WKB method, are presented. This approach gives possibility to divide the electromagnetic field in structured waveguides with slow varying geometry into forward and backward components and simplify the analysis of the field characteristics, especially the phase distribution. The accuracy of this method was estimated by comparing the solution of the approximate system of equations with the solution of the general system of equations. For this, a special code was written that combines the proposed approach with the more accurate one developed earlier. For the case of fast damping of evanescent waves, a simple solution of the matrix equations is obtained. Based on this approach, the possibility of correcting the phase distribution in a chain of coupled resonators has been studied.

1. Schnitzer, O., "Waves in slowly varying band-gap media," SIAM Journal on Applied Mathematics, Vol. 77, No. 4, 1516-1535, 2017.
doi:10.1137/16M110784X

2. Pereyaslavets, M., M. Sorella Ayza, B. Z. Katsenelenbaum, and L. Mercader Del Rio, Theory of Nonuniform Waveguides, IEE, 1998.
doi:10.1049/PBEW044E

3. Rulf, B., "An asymptotic theory of guided waves," Journal of Engineering Mathematics, Vol. 4, No. 3, 261-271, 1970.
doi:10.1007/BF01534885

4. Hashimoto, M., "Asymptotic vector modes of inhomogeneous circular waveguides," Radio Science, Vol. 17, No. 1, 3-9, 1982.
doi:10.1029/RS017i001p00003

5. Marcuse, D., Theory of Dielectric Optical Waveguides, 2nd Ed., Academic Press, 1991.

6. Skorobogatiy, M. A., M. Ibanescu, E. Lidorikis, J. D. Joannopoulos, S. G. Johnson, and P. Bienstman, "Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals," Physical Review E, Vol. 66, 066608, 2002.

7. Noda, S., J. D. Joannopoulos, S. P. Boyd, S. G. Johnson, A. Oskooi, and A. Mutapcic, "Robust optimization of adiabatic tapers for coupling to slow-light photonic-crystal waveguides," Optics Express, Vol. 20, No. 19, 21558, 2012.
doi:10.1364/OE.20.021558

8. Ayzatsky, M. I., "Model of finite inhomogeneous cavity chain and approximate methods of its analysis," Problems of Atomic Science and Technology, No. 3, 28-37, 2021.
doi:10.46813/2021-133-028

9. Amari, S., R. Vahldieck, J. Bornemann, and P. Leuchtmann, "Spectrum of corrugated and periodically loaded waveguides from classical matrix eigenvalues," IEEE Trans. Microw. Theory and Tech., Vol. 48, No. 3, 453-459, 2000.
doi:10.1109/22.826846

10. Ayzatsky, M. I., "Inhomogeneous travelling-wave accelerating sections and WKB approach," Problems of Atomic Science and Technology, No. 4, 43-48, 2021.
doi:10.46813/2021-134-043

11. Ayzatsky, M. I., "Modification of coupled integral equations method for calculation the accelerating structure characteristics," Problems of Atomic Science and Technology, No. 3, 56-61, 2022.
doi:10.46813/2022-139-056

12. Ayzatsky, M. I., "Fast code CASCIE (Code for Accelerating Structures --- Coupled Integral Equations). Test results,", https://doi.org/10.48550/arXiv.2209.11291, 2022.

13. Ayzatsky, M. I., "Transformation of the linear difference equation into a system of the first order difference equations," Problems of Atomic Science and Technology, No. 4, 76-80, 2019.
doi:10.46813/2019-122-076

14. Neal, R. B., The Stanford Two-mile Accelerator, W. A. Benjamin, 1968.

15. Khabiboulline, T., V. Puntus, M. Dohlus, N. Holtkamp, G. Kreps, S. Ivanov, and K. Jin, "A new tuning method for traveling wave structures," Proceedings of PAC 95, 1666-1668, 1995.

16. Ayzatsky, M. I. and E. Z. Biller, "Development of inhomogeneous disk-loaded accelerating waveguides and RF-coupling," Proceedings of LINAC 96, 119-121, 1996.

Dr. Mykola I. Ayzatsky