DBR and VCSEL
description
Transcript of DBR and VCSEL
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DBR and VCSEL
[Fumio Koyama, “Recent Advances of VCSEL Photonics,” JLT 24, 2006]
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DBR
Detuning
Bragg condition
operating (Bragg) wavelength
period
Assumptions: Bragg condition
Use CMT:
mirror length number of periods
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DBR (summary of CMT results)
CMT parameters:Bragg condition
i.e.
Amplitude reflection coefficient
Reflectivity
Reflectivity for
(coupling coefficient)
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DBR reflectivity at Bragg wavelength
Example:
Example:
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DBR: spectral characteristics
high reflectivity region -- photonic bandgap
Example (cont.):
Reflectivity
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DBR: spectral characteristics
Near Bragg wavelength:
Reflectivity
Phase of the reflection
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DBR: spectral characteristics
Penetration depth
Reflectivity
Group delay
Delay for homogenous medium
Near Bragg wavelength:
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VCSEL: oscillation condition
M quantum wells with thickness d and amplitude gain coefficient gm
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VCSEL: phase condition
(near Bragg wavelength)
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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)