Electrodynamics Time remaining: 00:09:00 1. Consider the three layer planar dielectric waveguide m. Ixkd/2 n2. else...

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Electrodynamics Time remaining: 00:09:00 1. Consider the three layer planar dielectric waveguide m. Ixkd/2 n2. else with refractive profile n(x) =- where n >n2 For the TE case, with Ey component the only non-zero element, the general solution can be written as: Acos AY+B sin Ax |xkd/2 E, (x) = { Ce x<-d/2 De ax x>d/2 Write down the boundary conditions that the TE general solution must satisfy at x=+d. a. b. Derive the transcendental equations that relate u and v for the TE symmetric and anti-symmetric modes. Where d d x² = kồn - B; a² = B² - kin ; u = xv = a c. In Ray optics, the mode in a symmetric slab waveguide can be thought of as a plane wave that is either traveling upwards or downwards with the general solution for the E field as E(x,z) = E,e kon,(±cos@ x+sin ở =) State the condition the x-component of the propagation vector of the waveguide mode must satisfy for it to be a guided mode? 3 d. Derive the set of transcendental equations that relates the components k, and k. (ork and B) of the propagation vector. Describe how one should solve these types of equations. Electrodynamics Time remaining: 00:09:00 1. Consider the three layer planar dielectric waveguide m. Ixkd/2 n2. else with refractive profile n(x) =- where n >n2 For the TE case, with Ey component the only non-zero element, the general solution can be written as: Acos AY+B sin Ax |xkd/2 E, (x) = { Ce x<-d/2 De ax x>d/2 Write down the boundary conditions that the TE general solution must satisfy at x=+d. a. b. Derive the transcendental equations that relate u and v for the TE symmetric and anti-symmetric modes. Where d d x² = kồn - B; a² = B² - kin ; u = xv = a c. In Ray optics, the mode in a symmetric slab waveguide can be thought of as a plane wave that is either traveling upwards or downwards with the general solution for the E field as E(x,z) = E,e kon,(±cos@ x+sin ở =) State the condition the x-component of the propagation vector of the waveguide mode must satisfy for it to be a guided mode? 3 d. Derive the set of transcendental equations that relates the components k, and k. (ork and B) of the propagation vector. Describe how one should solve these types of equations.