TM Mode Analysis in Optical Waveguide Study Anup Kumar Thander and Sucharita Bhattacharyya Abstract An accurate and efficient polarized mode solver in the form of a higher (fourth) order compact finite difference method (FDM) along with the successive over-relaxation technique is presented here for transverse magnetic or TM mode analysis of propagating electromagnetic waves through rib-structured GaAs and GeSi waveguides. For analysis of performances of such waveguides, the effective index concept has been identified as a key parameter. Accordingly, modal/effective index, normalized index and modal birefringence parameters are introduced in the present study and their obtained values show close agreement with other published data. Most significantly, the scheme successfully identified the optimized values of used waveguide structure parameters and explained their importance in the efficient prop- agation of transverse electromagnetic waves which might play a crucial role in the fabrication of such waveguides. Keywords Polarized mode solver · Higher (fourth) order compact · Rib-structured waveguide · Finite difference method · Successive over-relaxation technique 1 Introduction In the case of communication and signals processing, the optical beam is chosen as a carrier for which waveguide is used as a basic guiding component. To realize the transmission properties of various waveguides appropriately, their geometric shapes and corresponding refractive index profiles are studied in detail [1–12]. Specially structured rib waveguides have drawn much attention in recent days, particularly, to mention, in the field of photonics and opto-electronics because of their functional variations at the output, though their fabrications are easier. It may be noted that even A. K. Thander · S. Bhattacharyya (B ) Department of Applied Science and Humanities, Guru Nanak Institute of Technology, Kolkata 700114, India e-mail: sucharita.bhattacharyya@gnit.ac.in A. K. Thander e-mail: anup.thander@gnit.ac.in © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022 S. Dhar et al. (eds.), Advances in Communication, Devices and Networking, Lecture Notes in Electrical Engineering 776, https://doi.org/10.1007/978-981-16-2911-2_23 213