1

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

2

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−⎛ ⎞= =⎜ ⎟+⎝ ⎠

3

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

QQ

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