Photonics and Optical Communication, Spring 2007, Dr. D. Knipp
Homework 2
Optical fibers and waveguides (4 credit points)
Modes in planar waveguides (1.0 credit point)
The mode chart of a symmetric waveguide (slab) is shown in figure 1. The slab is part of a
GaAs laser diode. The emitted wavelength of the GaAs laser diode is 860nm.
Parameters: Refractive index of the core: n1=3.6,
Refractive index of the cladding: n2=3.55.
Fig. 1: Mode chart of a symmetric slab (AlGaAs structure).
Ref.: J.C. Palais, Fiber Optic Communication
(a) Determine the propagation angles, the effective refractive indices and the number of
TE and TM modes, which can propagate in the AlGaAs waveguide. The thickness of the
core is assumed to be d=1.64µm and the wavelength is 0.82µm.
(b) Reduce the thickness of the core until only a single TE-mode can propagate at a
wavelength of 0.82µm in the AlGaAs slab waveguide. Calculate the maximum possible
thickness of the core.
(c) Schematically sketch the propagation of higher and lower modes in a slab waveguide.
Describe the influence on the effective refractive index and the propagation angle?
Homework 2
Photonics and Optical Communication, Spring 2007, Dr. D. Knipp
Modes in optical fibers (0.5 credit points)
Determine the TE, TM modes and the polarized modes for the following electric field
pattern:
Fig. 2: Electric field pattern of optical fibers.
Attenuation in optical fibers (1 credit point)
An optical power of 150µW is launched in an optical fiber. The optical fiber has an
attenuation of 0.52dB/km. Determine the maximum possible length of the optical link
without having the signal amplified. The minimum optical power which can be detected by
an optical detector on the receiver side is 2µW. Every 10km an optical fiber joint (optical
fibers interconnect) with an attenuation of 1.5dB is required.
Modal dispersion in optical fibers (0.5 credit point)
Compare a step-index and a graded-index fiber in terms of modal dispersion (pulse
broadening). Assume that the fiber is 100km long and the refractive index difference
between the cladding and the core is 0.01.
Parameters: c=2.99 x 108 m/s
Material dispersion in optical fibers (1 credit point)
The material dispersion of a 10 km long optical fiber should be calculated. The dispersion
coefficient is given by
Homework 2
Photonics and Optical Communication, Spring 2007, Dr. D. Knipp
Dλ =
λ
c
⋅
d 2n
dλ 2
where
n (λ ) = 2 ⋅ 10 −3 µm −2 ⋅ λ 2
(a) Calculate the pulse spreading if the light of a GaAs LED with a spectral width of 30 nm
is coupled in the fiber. The emitted wavelength is 860 nm.
(b) The GaAs LED is replaced by a GaAS laser diode. The emitted wavelength is again
860nm. Make an estimate by how much the pulse spreading can be reduced.
Deadline for Submission: 19.03.2007 at 11:15 in class!
Homework 2