Investigation of Guided Power Expressions in TE and TM Modes for Symmetric Dielectric Slab Waveguides

This paper precisely evaluates the existing theoretical expressions for calculating guided power in symmetric dielectric slab waveguides for both transverse-electric (TE) and transverse-magnetic (TM) modes. In this work, we derive the relationships between electric and magnetic fields in both TE and TM modes by assessing potential values for propagation phase constant and subsequently assess the corresponding power expressions for determining total guided power flowing through the cross-section of symmetric dielectric slab waveguide. As a numerical example, we examine a typical dielectric slab waveguide consisting of a silicon core with a refractive index n = 3.5, surrounded by silicon dioxide cladding with refractive index n = 1.5, operating in optical frequency of 194 THz (i.e., λ ≈ 1.55 µm). Finally, we compare the calculated TE and TM mode field components and guided powers presented in figures and tables, respectively, validated by simulation results.