Project 4: Beam propagation analysis (20 points)

12141418 Numerical Method in Electromagnetics

From the previous lecture, finite difference beam propagation method (FD-BPM) was introduced to study the propagation of light from a known source in a defined refractive index structure.

Various defined refractive index structures composed are shown below. The FD-BPM can be used to model the light propagating through the below structures in which the input field is Gaussian beam located at 𝑧 = 0.

(a) (b) (c)

𝑦

𝑧

𝑛1 𝑛1 𝑛1

𝑛1

𝑛2 𝑛2

22141418 Numerical Method in Electromagnetics

Determine the propagation of the Gaussian beam in different mediums along z-axis Provide the FD-BPM equations for both fast and slow varying amplitudes Specify the dimensions of the refractive index structures (Assume finite boundary)

and their refractive index values Specify operating wavelength Plot 2D-refractive index structures (All 3 structures) Plot 2D- and 3D-field propagating along the refractive index structures (All 3

structures) Compare the fields between each structure

Write the report explaining your results. Please follow the template. Do not forget to Include the Matlab code in the appendix.

Oral presentation (10 mins: 7 mins presentation and 3 mins Q&A)

Project 4: Beam propagation analysis (20 points)

32141418 Numerical Method in Electromagnetics

Tips:

• To plot the contour image:

The function ‘imagesc’ is used to display image with scaled colors.

• To plot the 3D structure: The function ‘waterfall’ is used to view vectors of data over time.

Project 4: Beam propagation analysis (20 points)

42141418 Numerical Method in Electromagnetics

Example: Fast varying amplitude (E) in structure a

Project 4: Beam propagation analysis (20 points)

52141418 Numerical Method in Electromagnetics

Example: Slow varying amplitude (A) in structure a

Project 4: Beam propagation analysis (20 points)