11. reflection/transmission spectra contents 1.normal incidence on a simple dielectric slab 2....
TRANSCRIPT
11. Reflection/Transmission spectra
Contents
1.Normal incidence on a simple dielectric slab
2. Normal incidence on a photonic crystal slab 3. Normal incidence on a Distributed Bragg mirror
4. Normal incidence on a 1-D photonic crystal cavity
0 2000 4000 6000 8000 10000
-8
-6
-4
-2
0
2
4
6
8
Hx
fiel
dFDTD time step
0 2000 4000 6000 8000 10000-6
-4
-2
0
2
4
6
FDTD time step
Hx
fiel
d
Without slab
With slab
Planewave source
Detect
Slab (T=1a)
1. Simple dielectric slab
DD shouldn’t be this much long because the simple Fabry-Perot slab does not have a high-Q resonance. As we can see from the field data,
DD may be set 4000.
We will not use DS in this example
(1,1) may be set (0.1, 0.1).
Gamma point periodic boundary condition. The use of the planewave source ensures that the result will be only
for the exact kx=ky=0 point.
Two point detectors were set, one after the slab and the other between the planewave source and the slab
1) We now have modeR.dat and modeT.dat
2) We must run another simulation in the absence of the dielectric slab. Then, we get modeR0.dat and modeT0.dat, which will be used as reference data.
3) Let’s denote modeR.dat = R(t) modeT.dat = T(t) modeR0.dat = R0(t) modeT0.dat = T0(t)
Now let’s perform the following calculations.
FT[ R(t)-R0(t) ] / FT[ R0(t) ] = Refelctance spectrum in FT[ T(t) ] / FT[ T0(t) ] = Transmission spectrum in
,where FT denotes Fourier Transformation.
** How to obtain R & T spectra
(Important Node ) One must remember that the resolution of discrete FT will depend on the length of input data. We must add null values at the end of all ***.dat file before performing FT. I typically make the entire length of the input data file to be about 1 million (should be 2n format for accurate result)
0.1 0.2 0.3 0.4 0.5 0.60.0
0.2
0.4
0.6
0.8
1.0
Tra
nsm
itta
nce
Normalized Frequency0.1 0.2 0.3 0.4 0.5 0.6
0.0
0.2
0.4
0.6
0.8
1.0
Ref
lect
ance
Normalized Frequency
Result
In this example, DD should be carefully chosen. The 2-D photonic-crystal slab may contain very high-Q resonances
(See the Fan’s paper)
We will not use DS in this example
You cannot change this (1,1)
Two point detectors were set, one after the slab and the other between the planewave source and the slab
0.2 0.3 0.4 0.50.0
0.2
0.4
0.6
0.8
1.0
Ref
lect
ance
Normalized Frequency0.2 0.3 0.4 0.5
0.0
0.2
0.4
0.6
0.8
1.0
Tra
nsm
itta
nce
Normalized Frequency
Result
3. Distributed Bragg Reflector
20 pairs of AlAs/GaAs
Target wavelength = 950 nm
GaAs AlAs
Grid resolution ∆z = 2.5 nm
Periodic boundary condition for x-y directions
z
Planewave source
PML PML
In this example, DD should be carefully chosen. The time required to reach the steady-state could be
longer than you initially thought.
We will not use DS in this example
You can change this as 0.1
750 800 850 900 950 1000 1050 1100 11500.0
0.2
0.4
0.6
0.8
1.0R
efle
ctan
ce
Wavelength (nm)
- 10 pairs- 14 pairs- 20 pairs
Result
900 920 940 960 980 1000
0.85
0.9
0.95
1
Ref
lect
ance
(L
og
)
Wavelength (nm)
- 10 pairs- 14 pairs- 20 pairs 2
1 2tanh ln( / )R m n n
Accuracy
Analytic expression
(at the Bragg condition)
Exact FDTD
0.832424 0.83231
0.947996 0.94795
0.991636 0.99162
10
14
20
m
Errors less than 1 part per 10,000 !