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The Asymmetric Planar Waveguide. Examine the TE field in an asymmetric planar wave- guide consisting of a dielectric slab of width d and refractive index ni placed on a substrate of lower refractive index n2 and covered with a medium of refractive index n3 < n2 < n1, as illustrated in Fig. 9.2-10. (a) Determine an expression for the maximum inclination angle 0 of plane waves undergoing total internal reflection, and the corresponding numerical aperture NA of the waveguide. (b) Write an expression for the self-consistency condition, similar to (9.2-4). (c) Determine an approximate expression for the number of modes M (valid when M is very large). Figure 9.2-10 Asymmetric planar waveguide. n3 d n1

The Asymmetric Planar Waveguide. Examine the TE field in an asymmetric planar wave- guide consisting of a dielectric slab of width d and refractive index ni placed on a substrate of lower refractive index n2 and covered with a medium of refractive index n3 < n2 < n1, as illustrated in Fig. 9.2-10. (a) Determine an expression for the maximum inclination angle 0 of plane waves undergoing total internal reflection, and the corresponding numerical aperture NA of the waveguide. (b) Write an expression for the self-consistency condition, similar to (9.2-4). (c) Determine an approximate expression for the number of modes M (valid when M is very large). Figure 9.2-10 Asymmetric planar waveguide. n3 d n1

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The Asymmetric Planar Waveguide. Examine the TE field in an asymmetric planar wave- guide consisting of a dielectric slab of width d and refractive index n1 placed on a substrate of lower refractive index n2 and covered with a medium of refractive index ng < n2 < n1, as illustrated in Fig. 9.2-10. (a) Determine an expression for the maximum inclination angle 0 of plane waves undergoing total internal reflection, and the corresponding numerical aperture NA of the waveguide. (b) Write an expression for the self-consistency condition, similar to (9.2-4). (c) Determine an approximate expression for the number of modes M (valid when M is very large). Figure 9.2-10 Asymmetric planar waveguide. n3 d n1
Transcribed Image Text:The Asymmetric Planar Waveguide. Examine the TE field in an asymmetric planar wave- guide consisting of a dielectric slab of width d and refractive index n1 placed on a substrate of lower refractive index n2 and covered with a medium of refractive index ng < n2 < n1, as illustrated in Fig. 9.2-10. (a) Determine an expression for the maximum inclination angle 0 of plane waves undergoing total internal reflection, and the corresponding numerical aperture NA of the waveguide. (b) Write an expression for the self-consistency condition, similar to (9.2-4). (c) Determine an approximate expression for the number of modes M (valid when M is very large). Figure 9.2-10 Asymmetric planar waveguide. n3 d n1
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