Lasers & Integrated Optics – ENG5298
ASSIGNMENT ON INTEGRATED PHOTONICS - 2023
Mach-Zehnder Interferometers and Microring Resonators

1) Consider a Mach-Zehnder Interferometer (MZI) fabricated on a silicon-on-insulator photonic
chip operating at a wavelength ?=1500 nm. The waveguides have an effective index neff=3,
and the two interferometer arms have equal length L1=L2=0.5 mm (a top-view schematic of
the MZI is shown below).

a) Calculate the optical length of the MZI arms (the optical length is defined as the product
between the geometrical length and the effective refractive index of the waveguide).
b) The effective index of arm 1 is linearly increased by 1% by locally heating the waveguide (i.e.
neff in arm 1 varies from 3.00 to 3.03). Plot the output intensities of output 1 and output 2 as
a function of the change in neff when a constant optical signal is injected from input 1.
c) To increase the sensitivity of the MZI, the arm lengths are increased by folding the waveguides
into a spiral geometry (see top-view below). If the effective index in arm 1 is changed by
0.01%, calculate the minimum arm length that gives a phase difference between the arms of
Δ = .

d) The MZI design is now changed into an asymmetric geometry, in which L1 is kept at 0.5 mm
and L2 is increased to 5mm. Plot the optical intensities of output 1 and output 2 when the
wavelength of the input 1 signal is swept from 1500 nm to 1501 nm. Briefly discuss a possible
application of this device.

2) The intensity transmission of a micro-ring resonator connected to a single bus waveguide is
given by the following equation:

Where k=neff2?/? is the wave vector, r is the self-coupling field coefficient, ? is the single-pass
field amplitude transmission given by 2 = ?, ? are the waveguide losses, Lr=2?*R is the
cavity round trip and R is the cavity radius.
a. Calculate the Free-Spectral Range (FSR) of a resonator operating at a wavelength
??=1550 nm with radius R=10 ?m, losses ?=3 cm-1, a self-coupling field coefficient
r=0.9, and effective index neff=3.5 (assume ng=neff).
b. Using the resonator parameters defined in section a) and a self-coupling field
coefficient r=0.9, plot the intensity transmission as a function of the wavelength over
a few spectral ranges. Consider a centre wavelength ??=1550 nm for your plot.
c. Using the resonator parameters defined in section a), plot the intensity transmission
at resonance over the range of self-coupling field coefficients r=0.98 - 0.995 with
increments ?r= 0.001.
d. Calculate the single-pass field amplitude transmission and discuss the results of
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