Analysis of spatial hole burning and temperature effects in vertical-cavity surface-emitting lasers with internal photonic crystal waveguide

Gholamhossein Haghighat

doi:10.1364/AO.51.007765

Applied Optics
Vol. 51,
Issue 32,
pp. 7765-7770
(2012)
•https://doi.org/10.1364/AO.51.007765

Analysis of spatial hole burning and temperature effects in vertical-cavity surface-emitting lasers with internal photonic crystal waveguide

Gholamhossein Haghighat

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Gholamhossein Haghighat, "Analysis of spatial hole burning and temperature effects in vertical-cavity surface-emitting lasers with internal photonic crystal waveguide," Appl. Opt. 51, 7765-7770 (2012)

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- Optoelectronics
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About this Article
History
- Original Manuscript: August 27, 2012
- Revised Manuscript: October 11, 2012
- Manuscript Accepted: October 12, 2012
- Published: November 6, 2012

Abstract

We investigate theoretically the effect of two-dimensional photonic crystal (PC) defect waveguide parameters embedded into vertical-cavity surface-emitting lasers (VCSELs) on static operation of PC-VCSEL, including spatial hole burning (SHB) and temperature in the active regions. In structures with larger pitch of PC holes, SHB occurs dramatically and temperature increases in the active region. In large-hole diameter to pitch ratio, SHB has little effect and temperature is decreased in the active regions. We also show that with higher input current, temperature rises and SHB occurs.

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Symbol	Parameter	Value
$s$	Radius of oxide aperture	2 μm
$r_{s}$	Radius of the VCSEL chip	8 μm
$d$	Active layer thickness	30 nm
$L_{eff}$	Effective cavity length	1.14 μm
$R_{t}$	Reflection coefficient of top DBR	0.9981
$R_{b}$	Reflection coefficient of bottom DBR	1

Symbol	Parameter	Value
$D_{n}$	Electron diffusion coefficient	$25 {cm}^{2} / s$
$τ_{n}$	Carrier lifetime	2 ns
$N_{tr}$	Carrier concentration for transparency	$1.5 \times 10^{18} {cm}^{- 3}$
$q$	Electron charge	$1.6 \times 10^{- 19}$
$ν$	Laser frequency	$3.529 \times 10^{14} s^{- 1}$
$h$	Planck’s constant	$6.63 \times 10^{- 34}$
$n_{r 0}$	GaAs refractive index @ 850 nm	3.53
$g_{0}$	Differential gain coefficient	$2.5 \times 10^{- 16} {cm}^{2}$
$β_{s}$	Spontaneous emission coefficient	$4 \times 10^{- 3}$
$B_{sp}$	Bimolecular carrier recombination coefficient	$1 \times 10^{- 10} {cm}^{3} s^{- 1}$
$Γ_{z}$	Longitudinal optical confinement factor	0.0548
$Δ n_{ox}$	Refractive index step provided by the oxide	$6.567 \times 10^{- 3}$
$T_{0}$	Ambient temperature	300 K
$η_{i}$	Quantum efficiency for stimulated emission	0.9
$η_{sp}$	Quantum efficiency for spontaneous emission	0.9
$f_{sp}$	Escape coefficient of spontaneous emission from active region	0.95
$ρ_{spc}$	Resistivity of spacer layer	$0.245 Ω cm$
$k_{T 0}$	GaAs thermal conductivity	$0.44 W {cm}^{- 1} K^{- 1}$
$j_{s}$	Reverse saturation current density	$6 \times 10^{- 9} A {cm}^{- 2}$

Symbol	Parameter	Value
$s$	Radius of oxide aperture	2 μm
$r_{s}$	Radius of the VCSEL chip	8 μm
$d$	Active layer thickness	30 nm
$L_{eff}$	Effective cavity length	1.14 μm
$R_{t}$	Reflection coefficient of top DBR	0.9981
$R_{b}$	Reflection coefficient of bottom DBR	1

Symbol	Parameter	Value
$D_{n}$	Electron diffusion coefficient	$25 {cm}^{2} / s$
$τ_{n}$	Carrier lifetime	2 ns
$N_{tr}$	Carrier concentration for transparency	$1.5 \times 10^{18} {cm}^{- 3}$
$q$	Electron charge	$1.6 \times 10^{- 19}$
$ν$	Laser frequency	$3.529 \times 10^{14} s^{- 1}$
$h$	Planck’s constant	$6.63 \times 10^{- 34}$
$n_{r 0}$	GaAs refractive index @ 850 nm	3.53
$g_{0}$	Differential gain coefficient	$2.5 \times 10^{- 16} {cm}^{2}$
$β_{s}$	Spontaneous emission coefficient	$4 \times 10^{- 3}$
$B_{sp}$	Bimolecular carrier recombination coefficient	$1 \times 10^{- 10} {cm}^{3} s^{- 1}$
$Γ_{z}$	Longitudinal optical confinement factor	0.0548
$Δ n_{ox}$	Refractive index step provided by the oxide	$6.567 \times 10^{- 3}$
$T_{0}$	Ambient temperature	300 K
$η_{i}$	Quantum efficiency for stimulated emission	0.9
$η_{sp}$	Quantum efficiency for spontaneous emission	0.9
$f_{sp}$	Escape coefficient of spontaneous emission from active region	0.95
$ρ_{spc}$	Resistivity of spacer layer	$0.245 Ω cm$
$k_{T 0}$	GaAs thermal conductivity	$0.44 W {cm}^{- 1} K^{- 1}$
$j_{s}$	Reverse saturation current density	$6 \times 10^{- 9} A {cm}^{- 2}$

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Equations (19)

Applied Optics