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Unformatted text preview: Slab Waveguide - Phase Velocity, Group Velocity A slab waveguide consists of a glass ﬁlm of 5 ,um thickness with a refractive index
of 1.515. This ﬁlm is surrounded by a substrate and cover both with a refractive index
of 1.500. Light of freespace wavelength 1.00 pm is launched into the waveguide. The po— larization of the light is such that it excites TE modes in the waveguide. For the lowest-order TE mode, calculate, showing all work, the phase velocity and
the group velocity. Give the velocity both as a fraction of the freespace speed of light
and in m/ sec. You may use the slab waveguide program, SLWG, provided. You may
determine the group velocity using numerical methods. Express all your answers accu- rately to Within ﬁve signiﬁcant ﬁgures. Put your ﬁnal answers in the spaces provided below.
Phase velocity = c
Phase velocity = m/sec Group velocity ||
0 Group velocity m/ sec Slab Waveguide - Phase Velocity, Group Velocity h = 511m n f = 1.515 715 = no = 1.500 /\ = 1.00 pm The lowest-order TE mode is TE; and from SLWG it is characterized by 0 = 87.103493°, N = 1.513064, 6 = 9.506864pm“1.
vph 2 NC = 0.6609100 'uph = 1.981359 X 108 m/sec The group velocity
dw d 27rc 27rc d)‘ 27m AA _ ~ EB=EE(T)“ AzdﬁN AzAﬁ Select wavelengths above and below A = 1.00 pm vgr /\ = 1.005pm, ,8 = 9.459475pm‘1. A = 0.995pm, ,8 = 9.554729um‘1.
and so vgr = 0.6596243c 1.977527 m/ sec. C
., H ...
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- Spring '08