ee 232 lightwave devices lecture 2: basic concepts of lasersee232/sp15/lectures...ee232 lecture 2-9...
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EE232 Lecture 2-1 Prof. Ming Wu
EE 232 Lightwave Devices Lecture 2: Basic Concepts of Lasers
Instructor: Ming C. Wu
University of California, Berkeley Electrical Engineering and Computer Sciences Dept.
EE232 Lecture 2-2 Prof. Ming Wu
Basic Concept of Lasers
• Laser: – Light Amplification by
Stimulated Emission of Radiation
• Basic elements: – Gain media – Optical cavity
• Threshold condition: – Bias point where laser
starts to “lase” – Gain (nearly) equals
loss
Gain Mirror
Semiconductor Laser Cleaved Facet
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EE232 Lecture 2-3 Prof. Ming Wu
L-I Curve of Semiconductor Lasers • Distinctive threshold (at least in
classical lasers)
• Semiconductor laser is a forward-biased p-n junction, so mainly a current-biased device
• Threshold current : – Minimum current at which the
laser starts to “lase”
• Quantum efficiency – “Differential” electrical-to
-optical conversion efficiency, i.e., how many photons generated by injected electrons beyond threshold
• Wall-plug efficiency – Total electrical-to-optical
conversion efficiency
Ligh
t (O
ptic
al P
ower
, mW
)
Current (mA)
Threshold Current
Spontaneous Emission
Dominates
Stimulated Emission
Dominates
Slope = Quantum Efficiency
Slope = Wall-plug Efficiency
EE232 Lecture 2-4 Prof. Ming Wu
“Edge-Emitting” Semiconductor Lasers
Semiconductor Laser Cleaved
Facet
1
0
1 2
: gain coefficient [cm ]Light ampflication: ( ) : confinement factor (fraction of energy in gain media)Threshold condition: Round-trip gain = 1
1i i
gz
gL L gL L
th
gI z I
R
g
e
e
Re
g
α α
α
Γ −
−
Γ
− Γ
=
Γ
=
= =1 2
1 2
: intrinsic loss mirror loss
= : (i.e.,
1 1ln2
output light1 l
)1n
2
i
i i m
m
L R R
L R R
α
α
α α⎛ ⎞ ++ =⎜ ⎟Γ Γ Γ⎝ ⎠
⎛ ⎞
⎧
⎜ ⎟⎝ ⎠
⎪⎨⎪⎩
( )I z
zL
21 , ~ 30% for 3.51
nR R nn−⎛ ⎞= =⎜ ⎟+⎝ ⎠
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EE232 Lecture 2-5 Prof. Ming Wu
Modern Lasers
• Optical cavity does not necessarily consist of mirrors
EE232 Lecture 2-6 Prof. Ming Wu
Generic Description of Optical Cavity
Gain
Cavity
Quality Factor:Energy Stored
Energy Dissipated per Cycle
1
: photon lifetime [sec]
: loss rate per cm1 1/ : loss rate per sec
p
p
pp
p
Q
Q
cn
Q
ωω
ωτ
τ
αα
ττ
ωτ
=
=Δ
Δ =
⎛ ⎞= ⎜ ⎟
⎝ ⎠
=
Ener
gy
ω
1
p
ωτ
Δ =
4
EE232 Lecture 2-7 Prof. Ming Wu
Photon Lifetime and Spectral Width
0
/0
/20
Decay of optical energy when input is turned off(ring-down measurement):
( ) for 0Electrical (optical) field:
( ) for 0Frequency domain response (Fourier trans
p
p
t
tj t
I t I e t
E t E e e t
τ
τω
−
−
= ≥
= ≥
0 /2
00
20
form):
1( )( ) 1/ 2
1FWHM of ( ) : 2
1
ptj t j t
p
p
p
H e e e dtj
H
τω ωωω ω τ
ω ω ωτ
ωτ
∞− −= =
− +
− = ±
Δ =
∫
Ener
gy
ω
1
p
ωτ
Δ =
Ener
gy
Time
Frequency
/0( ) ptI t I e τ−=
( )H ω
EE232 Lecture 2-8 Prof. Ming Wu
Threshold Condition of Generic Lasers
Gain
Cavity
1 1
1 1 1
Gain = Loss(rate of gain = rate of loss)
1
Quantum efficiency:
=
=
thp
th
m rad rad
m i rad loss
rad
cgn Q
ngQ c
Q QQ Q Q
ωτ
ω
αη
α α
η
− −
− − −
Γ = =
=Γ
= =+ +
Ener
gy
ω
1
p
ωτ
Δ =
5
EE232 Lecture 2-9 Prof. Ming Wu
Typical Q of Semiconductor Laser
Edge-emitting laser:L =100µm, R = 30%, ω ~ 100THz , τ p ~ 1ps, Q ~ 600
Vertical Cavity Surface-Emitting Laser (VCSEL)L =1µm,R = 99%, Q ~ 700
Microdisk (Whispering Gallery Mode or WGM) Laser
Q ~ 1000 (up to 1011 possible in low loss materials)
Photonic crystal laser: Q ~ 1000 (up to 106 possible)
Metal cavity laser (plasmonic laser): Q ~ 10 to 100
EE232 Lecture 2-10 Prof. Ming Wu
Gain Cross-Section
2
Gain cross-section (instead of gain coefficient) is often used to measure the gain in gas or solid-state lasers:
: [cm ]Gain cross-section is related to gain by:
where is concentration of active g N
N
σ
σ=
1
18 3
16 2 2
molecules
For comparison, in semiconductor lasers:~ 100 cm~ 10 cm (typical electron concentration at threshold)
~10 cm (= (0.1nm) )
gNσ
−
−
−
Note: more precise relation between gain and carrier concentration will be discussed in future lectures