Coupled Waves

1
Coupled Waves
Unperturbed wave equation
Solutions
2
Coupled Equations
nn?n/k0 k0?/c
-matrix of coupling coefficients
Effective mode index
??r(x,y,z) is eitehr a periodic function of z or
does not depend on z
3
Coupled Equations
Diagonal coupling coefficients
Only zero-order term is important
Introduce
Drop prime
4
Two wave interactions
resonance
Normalization
Coupling coefficient
5
Directional coupler
6
Directional coupler
7
Mach Zehnder Interferometer
A1,inA0 and A2,in0.
8
MZI modulator
Pockels Effect
9
Electro-Optic Modulator
10
Mismatched coupler
??gt0
11
Mismatched coupler
Beat length
12
Electro-optic modulator based on directional
coupler
13
Grating-assisted coupler
Mismatch
Grating
At f0 perfect match
14
Filtering properties of long period grating
15
Distributed Bragg reflector
Mismatch
Coupling
Bragg frequency
16
Distributed Bragg reflector
Near Bragg resonance
At Bragg frequency
17
Reflectivity
18
Reflectivity Spectrum
19
Phase delay
20
Effective length of DBR
21
DBR Laser
Single mode lasing
22
DBR with gain-DFB
23
DFB Oscillation
Amplitude condition
Phase condition
Mode spacing same as in FP laser
24
Single mode DFB laser
25
VCSEL
?W 3?10-3