1

DBR and VCSEL

[Fumio Koyama, “Recent Advances of VCSEL Photonics,” JLT 24, 2006]

2

DBR

Detuning

Bragg condition

operating (Bragg) wavelength

period

Assumptions: Bragg condition

Use CMT:

mirror length number of periods

3

DBR (summary of CMT results)

CMT parameters:Bragg condition

i.e.

Amplitude reflection coefficient

Reflectivity

Reflectivity for

(coupling coefficient)

4

DBR reflectivity at Bragg wavelength

Example:

Example:

5

DBR: spectral characteristics

high reflectivity region -- photonic bandgap

Example (cont.):

Reflectivity

6

DBR: spectral characteristics

Near Bragg wavelength:

Reflectivity

Phase of the reflection

7

DBR: spectral characteristics

Penetration depth

Reflectivity

Group delay

Delay for homogenous medium

Near Bragg wavelength:

8

VCSEL: oscillation condition

M quantum wells with thickness d and amplitude gain coefficient gm

9

VCSEL: phase condition

(near Bragg wavelength)

10

VCSEL: phase condition

Example (cont.):

penetration depth

assume

effective length of the Bragg mirror resonator

intermode frequency spacing

photonic bandgap (high reflectivity region of the Bragg mirror)