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Opto-Electronics and

Photonics

Woo-Young Choi

Dept. of Electrical and Electronic EngineeringYonsei University

Lecture 21 : Optical Gain

Opto-Electronics and Photonics (2020/2) W.-Y. Choi

Lecture 21: Optical Gain

2

Simulated emission for optical gain

è Population inversion: ‘Pump’ carriers into N2 so that N2 > N1

Optical pumping and electrical pumping possible

(Optical amplifier)



3

Optical pumping

Consider 3-level systems

2-level system not practical

Pump signal has the same wavelength as input/output signal

In Out

Pump

E

E1

E2

3

(1) carriers at E3 quickly come down to E2

Requirements:

(2) Carriers at E2 radiativelycome down to E1



4

Optical gain materials for 3-level systems

Erbium

One of rare earth metals



5

Erbium

E10

1.27 eV

0.80 eV E2

E3

1550 nm 1550 nm

InOut

980 nm

Non-radiative decay

Pump

-Pump light (l=980nm) absorbedgenerating carriers at E3

- When N2>N1 (population inversion),stimulated emission > absorption

for 1550nm light

- Carriers at E3 rapidly transfer to E2

building up N2

- Er can be easily added to core of Silica fiber

- High-power semiconductor lasers easily available for 980nm pumping source

- Very useful for optical communication applications

è EDF (Er-Doped Fiber)



6

EDFA: Er-Doped Fiber Amplifier

A key component for long-distance optical communication systems

Roughly, one EDFA for every ~100km fiber



7

Other optical gain materials

- Crystals doped with impurities: Ruby doped with Cr (Al2O3:Cr3+)

Used for first laser demonstration



8

- Gases:

(1s2)

(1s12s1)

0

20.61 eV

He

(2p6)Ground states

(2p55s1)Ne

(2p53p1)

(2p53s1)

Collisions

Lasing emission632.8 nm

~600 nm

Collisions with the walls

Fast spontaneous decay

20.66 eV

Electron impact

The principle of operation of the He-Ne laser. He-Ne laser energy levels(for 632.8 nm emission).

?1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Other optical gain materials

Mixture of He and Ne gases (9:1)

è Used for HeNe lasers

High voltage applied

è He plasma (He ion + electrons)

èEnergetic electrons collide with ground-state He electronics

è Collision between He and Ne

Electrical pumping



9

Semiconductors with direct bandgap

- Continuous energy levels across the band gap

Conduction band: more holes than electrons

Valence band: more electrons than holes

(E-k diagrams: Dispersion diagram for electron waves)



10

Interaction with photons if hv > Eg

Unlike 2-level, 3-level systems, continuous spectrum for absorption and emission

Absorption SpectrumFor GaAs12 2 1 12 1 1 2 2( ) ( ) ( ) ( )R h E E B N E P E hn r n= - = × × ×

èMore absorption for larger photon energies

More electrons as E1 becomes smaller

More holes as E2 becomes larger



11

12 12 1 1 2 2( ) ( ) ( ) ( )R h B N E P E hn r n= × × ×

Absorption

21 21 2 2 1 1( ) ( ) ( ) ( )R h B N E P E hn r n= × × ×

Stimulated Emission

( )1 1 2 2 2 2 1 1( ) or ( ) ( )?N E P E N E P E× ×Which is larger?

Depends how much pumping and photon energy (E2-E1)

Spontaneous emission not considered

è Noise



12

How to electrically pump electrons and holes?

hu Eg

Eg

V

p n+

Electron in CBHole in VB

Forward-biased PN junction



13

Optical Amplifier

Pout = G Pin

Pin Pout

E1

E2

pumpOptical Gain Material withlength z = exp(gz) Pin

Eout = exp(-jkz)Ein

k = ,β jα-

outE = exp( )exp( ) inj z z Eb a- -

outP = exp( 2 ) inz Pa-

2g a= -



14

Homework ( Due on 12/4)

(a) Determine the expression for N2 – N1 at the steady-state in which dN2/dt = - dN1/dt = 0.

(b) Determine R required for transparency (N2 =N1)

Assume t32 is very small so that N3 = 0, t21 = t,

2 22 1

dN NR WN WNdt t

= - - +

1 22 1

dN NR WN WNdt t

= - + + -

N1 + N2 = N

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