代写Fundamentals of Photonics Fall 2024 Project description代做留学生Matlab程序

Fundamentals of Photonics Fall 2024 Project description

Due: December 04^th 4pm

Design a fiber-waveguides-fiber transmission system based on Silicon (n=3.5) and SiO2 (n=1.5). with ultra large bandwidth , compact and  robust to +5nm variations with a total area of less than 1mm². The system is composed of :

· fiber-waveguide coupler

· 1x2 splitters

· 1mm long waveguides

your goal is to ensure that A. the time delay for all channels is uniform. for all wavelength. This is determined by the dispersion of the 1mm waveguide. B. the transmission for all channels is uniform. and maximum. This is determined mainly by the splitting ratio and by the fiber-waveguide coupling, respectively.

Your input laser emits 10mW light from 1300nm to 1700nm. At the output of each channel there should be at least 1mW (due to the responsivity of the fiber coupled detectors). Assume that the output waveguides and the input laser is coupled to a fiber. with a mode profile that extends in one dimension (x) as where xo=5 microns . In other direction the mode extends infinitely (ie it is a slab-like waveguide). For all waveguides the bottom cladding is 3 micron thick.

Instructions:

· When using bends, the minimum bending radius is 5 microns for the maximum confined single mode waveguide  and 20 microns for a 10 times thinner waveguide. To find the radius for waveguides with in-between widths, linearly interpolate between these two extremes.

· Start by designing each of the components for 1500nm and then optimize them for wide bandwidth. Finally check (and optimize further if needed ) robustness to variations.

· When considering variations of +5nm, assume that All dimensions in all waveguides vary by 5nm.

· Use normalized parameters for all your calculations. For the fiber-waveguide coupler

· neglect reflections when calculating the transmission (ie include only overlap). Also assume that both waveguide and fiber are slab waveguide, ie infinite in one dimension.

· For the 1x2 splitter show (using plots) what is the most sensitive dimensions to variations and the just vary that dimensions. Calculate the change in amplitude at a given propagation length and then integrate the function numerically.

· For the 1mm waveguide with minimal dispersion, in order to find the optimal change of width as a function of propagation length:

o I. Choose a profile of the waveguide, discretize the waveguide along the propagation length every wavelength (this ensures that the discretization is fine enough while not requiring you to check the optimal discretization steps) and average the waveguide width over each discretized section.

o II. Calculate the amplitude in a higher order mode B exiting the discretized section considering that the input into the section is a fundamental mode A. Note that when calculating the amplitude in a higher order consider that the propagation length of discretized section is much smaller than the coupling rate. therefore the amplitude in a higher order should be independent of the discretization.

o III. If B/A is higher than 1% , change the profile to decrease the probability and repeat the process from II.

· Decide what is the wavelength range that your laser will operate (within the larger range of 1300-1700nm). Then decide how many channels your system will have. Build an 1xn (n>2) splitter by cascading 1x2 splitters)

· State what is the total bandwidth supported by your system (in THz). Note 1nm bandwidth is equal to 133GHz bandwidth.

· Plot a schematic of whole system (include all relevant dimensions in the schematics) and estimate the total area of the system.

· Plot the transmission out of each channel as a function of wavelength for both optimized and non-optimized geometry

· Plot the time delay of each channel (assume that the delay is only induced by the 1mm long waveguide) as a function of wavelength for both optimized and non-optimized geometry. The time delay is given by:

The project should be done either individually or in teams(preferred) by groups of up to 3 members. Please have a section that explains clearly what was the role of each group member. The project should be done using your favorite code writing software (matlab, mathematica, etc)  for your calculations and plotting your data. All assumptions and choices you made (dimensions, number of waveguides, etc) should be discussed. Neglect reflections.