Consider a symmetric slab waveguide, of core index = 3.6, and cladding/substrate index = 3.55. Theheight of the waveguide is 7 microns. Assume a wavelength of 1 μm for parts a-f.a) What is the critical angle for this structure?b) What is the range of the effective refractive index for the structure?c) What is the V-parameter for this waveguide? (normalized frequency).d) Without any plotting, find the number of allowed modes for the waveguide. Careful: the value ofm in lecture notes denotes the highest allowed mode, but the mode counting starts from m=0!Now, we want to use the graphical method to find the modes.e)Using the graphical method, find the transverse and longitudinal wavevector for the allowedmodes. Make sure to label them as symmetric or anti-symmetric.f)For the first mode (TEo) plot the mode structure, i.e. E(x) in all three regions (core, cladding, andsubstrate). You can normalize the electric field to | Emax| =1.The dispersion relation is easiest to plot in normalized parameters. Plot the normalized guide index b asa function of the normalized frequency V for the first 4 modes (TE, to TE3). Make sure to identify the cut-off frequencies for each mode.g) At what wavelength/frequency (real, not normalized) does this waveguide become single mode?

When a question with multiple subparts is given then, according to the guidelines, only the first…

Consider a symmetric slab waveguide, of core index = 3.6, and cladding/substrate index = 3.55. The height of the waveguide is 7 microns. Assume a wavelength of 1 μm for parts a-f. a) What is the critical angle for this structure? b) What is the range of the effective refractive index for the structure? c) What is the V-parameter for this waveguide? (normalized frequency).

Consider a symmetric slab waveguide, of core index = 3.6, and cladding/substrate index = 3.55. The height of the waveguide is 7 microns. Assume a wavelength of 1 μm for parts a-f. a) What is the critical angle for this structure? b) What is the range of the effective refractive index for the structure? c) What is the V-parameter for this waveguide? (normalized frequency).

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Chapter1: Units, Trigonometry. And Vectors

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Question

Consider a symmetric slab waveguide, of core index = 3.6, and cladding/substrate index = 3.55. The
height of the waveguide is 7 microns. Assume a wavelength of 1 μm for parts a-f.
a) What is the critical angle for this structure?
b) What is the range of the effective refractive index for the structure?
c) What is the V-parameter for this waveguide? (normalized frequency).
d) Without any plotting, find the number of allowed modes for the waveguide. Careful: the value of
m in lecture notes denotes the highest allowed mode, but the mode counting starts from m=0!
Now, we want to use the graphical method to find the modes.
e)
Using the graphical method, find the transverse and longitudinal wavevector for the allowed
modes. Make sure to label them as symmetric or anti-symmetric.
f)
For the first mode (TEo) plot the mode structure, i.e. E(x) in all three regions (core, cladding, and
substrate). You can normalize the electric field to | Emax| =1.
The dispersion relation is easiest to plot in normalized parameters. Plot the normalized guide index b as
a function of the normalized frequency V for the first 4 modes (TE, to TE3). Make sure to identify the cut-
off frequencies for each mode.
g) At what wavelength/frequency (real, not normalized) does this waveguide become single mode?

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