Comsol assignment

OMSOL Assignment (Advanced Optoelectronic Devices):
• Task 1 (40%): Basic simulation setup
Set up the waveguide simulation to determine the modes (both TE / TM) of a silicon on insulator
strip waveguide. The silicon layer thickness is 220 nm and the oxide (BOX) thickness is 2 µm. For task
1, assume silicon’s refractive index is constant 3.47, oxide is 1.5 and wavelength 1550 nm.
1. Vary the waveguide width between 200 nm and 1 um and plot the mode index (for
both TE and TM).
2. How do you tell the difference between TE and TM modes?
3. At what width does the waveguide become multi-moded? Note: here the second
mode we are interested in is the higher order TE mode.
4. Change the top cladding to oxide, how does this change the width at which the
waveguide becomes multi-moded?
• Task 2 (60%): Dispersion calculation and four wave mixing (FWM)
For task 2, we will keep the silicon waveguide’s width fixed at 500 nm and plot the mode index for
the fundamental TE mode as a function of wavelength (1.2-1.8 µm).
1. Assume silicon’s refractive index varies according to the Sellmeier equation for the
mode index calculation:
???
2
(?) = 1 +
10.6684293?
2
?
2 − 0.301516852 +
0.0030434748?
2
?
2 − 1.134751152 +
1.54133408?
2
?
2 − 11042
2. Calculate ??/?? and ?
2?/??
2
for the material index? Hint: numerical derivates are
fine, no need to do this analytically
3. Repeat the same calculation for the mode index. Hint: to calculate the mode index
as a function of wavelength, make sure you run the simulation with varying silicon
refractive index. This problem is asking, given the material dispersion of silicon
(changing refractive index as a function of wavelength), how does the mode index
for the fundamental TE mode change?
4. Calculate the effective mode area by:
???? =
(∫ |?|
2
)
2
∫ |?|
4
What is the ratio between the effective mode area and the geometrical area (cross-section
of the waveguide)? The nonlinear coefficient scales as ? =
?2?
?????
⁄ which is why
nonlinear processes become significantly enhanced in nanoscale waveguides. Comment on
the final result
Suppose we want to study the degenerate four wave mixing process in this silicon waveguide with
the pump wavelength fixed at 1550 nm. What are the wavelength(s) of the signal and idler photons
produces in this process