Numerical computation of optical loss presentation in semiconductor

1. DEPARTMENT OF PHYSICS AND NANOTECHNOLOGY
SRM INSTITUTE OF SCIENCE AND TECHNOLOGY
1
21PYB102J –Semiconductor Physics
Unit-III : Session- S8 : SLO-1
Numerical computation of
optical loss
21PYB102J Module-I Lecture-31

2. Optical loss
Definition:
Optical loss is the ‘reduction in intensity of light’ or reduction of optical
power as light propagates through a material or device.
It is usually expressed in units of decibels per unit length (dB/cm) or
decibels per unit distance (dB/m)
To numerically calculate optical loss, We can use the following formula:
Optical Loss (in dB) = -10log (Pout/Pin)
where Pout is the output optical power and Pin is the input optical power.
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21PYB102J Module-I Lecture-31

3. Computation of optical loss
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21PYB102J Module-I Lecture-31
Input power
(0.1mW)
Power
meter
(0.05mW)
Light Source Optical Fiber facility
Light Loss = -10* log (Poutput power/Pinput power)
= -10* log (0.05mW/0.1mW)
= 3dB
The light power loss of this
optical fiber is 3 dB

4. Two numerical techniques
Finite difference method & Finite element method
1. Restricted to handle rectangular shapes
2. High error may possible than the actual
result
1. Has ability to solve complex
geometries
2. Less error is expected

5. Finite difference method
http://www.multiphysics.us/FDM.html
We can also approximate the derivative
using the function values at points
I. Finite difference methods are
numerical techniques used to
approximate the solutions of
differential equations.
II. These methods work by replacing the
derivatives in a differential equation
with finite difference approximations.

6. Numerical computation of optical loss
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21PYB102J Module-I Lecture-31
Finite Difference Time Domain
(FDTD) method
1. A numerical technique that discretizes
the electromagnetic field equations into
finite-difference equations that can be
solved iteratively.
2. The computational domain will be
discretized into a mesh or a grid which
consists of multiple subdomains called
cells or elements.
3. The FDTD method solves Maxwell’s
equations on a mesh and computes E
and H at grid points spaced Δx, Δy, and
Δz apart, with E and H interlaced in all
three spatial dimensions.
Applications for this method include:
• LEDs, solar cells, filters, optical switches,
• semiconductor-based photonic devices,
• Sensors,
• Nano- and micro-lithography, nonlinear
devices
mesh

7. Numerical computation of optical loss
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21PYB102J Module-I Lecture-31
Transfer Matrix Method (TMM)
I. The transfer
matrix is a
matrix that
describes the
transformation
of a wave as it
passes
through a layer
or region
within the
system.
I. It is a matrix that
relates the
amplitudes and
phases of waves
on one side of the
structure to those
on the other side.
I. The transfer
matrix relates the
incoming wave to
the outgoing
wave, taking into
account the
reflection and
transmission
coefficients at the
boundary
between the two
regions.
I. Once we have the
transfer matrix of
each individual
layer, we can
calculate the
overall transfer
matrix of the
entire structure
by multiplying the
transfer matrices
of all the layers
together in the
order they appear
in the structure.

8. Numerical computation of optical loss
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21PYB102J Module-I Lecture-31
Beam Propagation Method (BPM):
1. The Beam Propagation Method (BPM) is a popular simulation technique for
evaluating the evolution of optical fields in waveguides and photonic devices, and
Optoelectronic Integrated Circuits .
1. In this method, numerical solution of the Helmholtz equation, and Schroedinger
equation have been performed.
1. The BPM includes Fast Fourier Transform (FFT) algorithm, finite-difference based
BPM schemes (FD-BPM), and finite-element BPM (FE-BPM) and many others.
1. The Beam Propagation Method relies on the slowly varying envelope
approximation, and is inaccurate for the modeling of discretely or fastly varying
structures.

9. DEPARTMENT OF PHYSICS AND NANOTECHNOLOGY
SRM INSTITUTE OF SCIENCE AND TECHNOLOGY
9
21PYB102J –Semiconductor Physics
Unit-III : Session- S8 : SLO-2
Finite element method to calculate
Photon density of states
21PYB102J Module-I Lecture-31

10. Finite element method and Photon
density of states
Finite element method(FEM) is sometimes referred to as finite element analysis, is a computational
technique used to obtain approximate solutions of boundary value problems in engineering.
1. The discretization
involves finite number
of points and
subdomains in the
problem’s domain.
2. The values of the given
function are held at the
points, so-called nodes.
I. The non-overlapping subdomains, so-called finite elements, are connected together at nodes on their
boundaries
https://doi.org/10.1007/978-3-642-20617-7_16699
21PYB102J Module-I Lecture-31

11. Finite element method (FEM) and
Photon density of states (PDOS)
I. Define the geometry of the system: The first step is to define the geometry of the system, which
may involve specifying the shape and dimensions of the system.
I. Discretize the system: Model body is divided into an equivalent system of many smaller bodies or
units are called finite elements.
I. Solve for the eigenmodes: Use a finite element solver, such as COMSOL Multiphysics or Ansys. The
polarization characteristics including both the transverse electric (TE) and transverse magnetic
(TM) modes are considered in simulation model.
I. The solver will typically output the eigenmode spectrum, which includes the eigenvalues and
eigenfunctions with proper periodic boundary conditions following the Bloch theorem.
I. Calculate the PDOS: As per definition dN(ω) ≡ D(ω)dω.
Where S is surface
ω is an arbitrary value of the frequency
For light propagating in the xy-plane only
21PYB102J Module-I Lecture-31