國立交通大學開放式課程(OpenCourseWare, OCW). -...

OPTOELECTRONICS Prof. Wei-I Lee 1

Lasers


Light Amplification by Stimulated Emission or Radiation, Laser 3 features of stimulated emission :(1) 1 photon in, 2 photons out light amplification(2) emitted photon in the same direction as the incoming photon(3) emitted photon in phase ( coherent ) with the incoming photonbesides stimulated emission, need two more conditions to make lasers :(1) population inversion (2) metastable state ( long-lived state ) – a higher energy state in which e-

can stay for a much longer time than in an ordinary excited state (10-3

sec vs. 10-8 sec )a two-level system can not sustain laser

Stimulated Emission and Photon Amplification



E1, E2, and E3 : energy levels of Cr+3 ion in Al2O3 crystal

Principle of Ruby Laser



characteristics of a laser : (1) unidirectional (2) high intensity

( Ex : He-Ne laser : ~ 100 W/m2

which is ~ 4000 x sunlight )(3) nearly monochromatic(4) coherent

Characteristics of Laser


T.H. Maiman holding the first laser ( 1960 )


at thermal equilibrium :

ratio of stimulated emission to spontaneous emission :

ratio of stimulated emission to absorption :

Einstein Coefficients


B12, A21, and B21 : Einstein coefficients

(ρ

: photon energy density per unit freq.)


ratio of stimulated emission to spontaneous emission :

need large ρ(hυ) need optical cavity to contain photons

ratio of stimulated emission to absorption :

need to achieve N2 > N1 population inversion

from Boltzmann statistics (@T.E.) :

N2 > N1 negative T (K) laser based on non-T.E.

Lasing Requirements



Er3+ ions doped into the core region of an optical fiber to achieve light amplification need (stimulated emission > absorption)

population inversion required ( N2 > N1 ) optical gain, Gop = K ( N2 – N1 )K : a constant depends on pumping intensity Er-doped fiber is usually inserted into the fiber communication line by splicing

Erbium Doped Fiber Amplifier ( EDFA )

Optical Fiber Amplifiers

ebt


Er-doped fiber usually inserted into fiber communication line by splicing gain efficiency : 8-10 dB/mW

Erbium Doped Fiber Amplifier ( EDFA )

Optical Fiber Amplifiers


a gaseous mixture of He and Ne atoms ( 5:1 ) in a gas discharge tube stimulated emission from Ne atoms ( ground state : 1s22s22p6 )He atoms ( ground state : 1s2 ) excite Ne atoms by atomic collisionsHe + e- He* + e-

He* : 1s12s1 w. parallel spinselection rule : Δl = ±1 for photon emission/absorption

He* a metastable stateHe* build up

He* + Ne He + Ne*

Ne* : 1s22s22p55s1

population inversion

1s22s22p55s1 ~ 2p53p1

: laser emission @ 632.8 nm

He-Ne Laser

Gas Lasers : He-Ne Laser


~2p55s1 : 4 closely spaced levels, ~2p53p1 : ten closely spaced levelslasing emissions contain a variety of λ

there are also other levels which can generate lasing emissions ( e.g. in the infrared range )reflecting mirrors can be made λ

selective to suppress unwanted λ

1s22s22p53s1 1s22s22p6 requires change in e- spin, which can not be achieved by photon radiation 1s22s22p53s1 : a metastable level

needs collision w. the tube wall to return to the ground state thin tube required

tube length ↑ emission intensity ( optical gain ) ↑typical characteristics :

Gaussian beam 0.5-1 mm beam diameter 1 milliradians divergencea few mW power

More About He-Ne Laser

Gas Lasers : He-Ne Laser


gas atoms are in random motion with an average K.E. = 3/2 kBTassume these gas atoms emit radiation of freq. υo , due to Dopper effect :

atom moving away from observer observer detects

atom moving towards observer observer detects ( vx : relative v of atom along the laser tube w.r.t. the observer )

gas laser has an approximate “linewidth” Δυ = υ2 – υ1Doppler broadened linewidth of a laser radiation

gas atom velocity obeys Maxwell distributionstimulated emission λ exhibit distribution about a central λo= c/υooptical gain ( or photon gain ) shows similar distribution ( optical gain lineshape )

Doppler Broadening

Output Spectrum of Gas Laser


from Doppler broadening : optical gain lineshape ~ Gaussian function with typical spread in frequency of 2-5 GHz FWHM of the optical gain vs. freq. spectrum (assuming Maxwell velocity distribution) :

applied nearly to all gas lasers ( solid state lasers have different broadening mechanisms )

for Fabry-Perot optical resonator or etalon : only certain cavity modes with specified λ

can be

maintained as standing waves in the cavity

m : mode number ( longitudinal axial modes )

Optical Gain and Cavity Modes



laser output : (optical gain curve) x (allowed cavity modes) peaks at certain λ corresponding to various cavity modes with the envelop of optical gain curve due to Doppler broadening ( which is a Gaussian distribution )

the intensity spikes have finite width ( ~ 1kHz – 1 MHz ) due to nonidealities of the optical cavity ( e.g. thermal fluctuation of cavity length, nonideal mirrors etc. )

Laser Output Spectrum



if light intensity decreases along x due to absorption light intensity ∝ exp(-αx) , α : absorption coef.

if light intensity increases along x: light intensity ∝ exp(g x) g : optical gain coefficient ( optical gain per unit length )

, ( )

Optical Gain Coefficient

Laser Oscillation Conditions

( ρ

: photon energy density per unit freq. )


assuming reached a steady state lasing emission in an optical cavity net round-trip optical gain, Gop = Pf / Pi = 1

exp( gx ) includes : stimulated emission and counter absorptionsexp(- γx) includes : losses in cavity/wall acting against stimulated emission gain, e.g. light scattering at defects, absorption by impurities/free carriers etc. ( γ

: attenuation or loss coefficient of the medium )

( R1, R2 : reflectance at reflecting surface )

Pf = Pithreshold gain gth :

threshold population inversion :

Threshold Gain



round-trip optical gain = 1 threshold gain gth :

threshold population inversion :

simplified description of (N2 – N1) and Po vs. pump rate under steady state continuous waver operation

Pump Rate and Output Power



round trip phase change :

assume constant n and neglect phase changes at the mirrorsonly k values that satisfy the following phase condition can exist

( longitudinal axial modes )

Phase Condition



simplified ideal analysis : plane wave & perfectly parallel mirrors assumedall practical laser cavities have finite transverse size and not all cavities have flat reflectors at the ends off-axis self-replicating rays can exist non-axial modes greater transverse size more off-axis modes a mode : a particular spatial electric field pattern at one reflector that can replicate itself after one round trip through the cavity

Laser Modes



All modes can be represented by fields ( E & B ) that are nearly normal to the cavity axis transverse electric and magnetic (TEMpqm) modesp , q # of nodes in the field distribution along y and z ( transverse to the cavity axis x ) m ( longitudinal mode number ) # of nodes along the x-axis, usually

very large ( ~ 106 in gas laser )and not written TEM00 :

• lowest order mode• radially symmetric • lowest divergence • requires restric-

tions in transverse size of the cavity

Laser Modes - TEMpqm



degenerately doped direct bandgapp-n junction diode

EFn > Ec , EFp < Evforward bias with eV > Eg

population inversion at the junction incoming phonon hυ

= Eg in active region

more likely to cause stimulated emission than being absorbed optical gain

Population Inversion in Homojunction Laser Diode

Principle of Laser Diode


reflectors formed by cleaved surfaces ( ~ 30% reflecting )

mode of the cavity : , ( n : refractive index )

Formation of Cavity in Laser Diode



pumping mechanism : forward diode current at I = Itrans ( transparency current )

stimulated emission balances counter absorption at I > Ith ( threshold current ) optical gain g reached gth

optical gain overcome photon losses from the cavity optical gain reached gth lasing emission

Jth in homojunction laser diode is too high for practical uses ( can operate only at very low temp. )

Threshold Current



Heterostructure Laser Diodes


to reduce Ith need better (1) carrier confinement (2) photon confinementimproved carrier confinement in DH structure

easier to achieve population inversion in narrow Eg active layer Ith ↓

narrow Eg semiconductor usually has higher refractive index

better photon confinement in narrow Eg active region photon conc. ↑stimulated emission rate ↑Ith ↓

advantage of the AlGaAs DH laser lattice matched to substrate


Gain Guided Laser Diode


Ex. stripe geometrical AlGaAs/GaAs/AlGaAs DH laser diode current flow confined to between path 2 & 3 J at path 1 > path 2 & 3 , region where J > Jth defines active regionwidth of the active region decided by J and hence the optical gain

gain guided laser advantages of stripe geometry :

1. reduced contact area Ith ↓

2. reduced emission areaeasier coupling to optical fibers

typical W ~ a few μmIth ~ tens of mA

poor lateral optical confinement of photons


Index Guided Laser Diode


Ex. buried double heterostructure laser diode good lateral optical confinement by lower refractive index material

stimulated emission rate ↑active region confined to the waveguide defined by the refractive index variation index guided laser diode buried DH with right dimensions compared with the λ

of radiation

only fundamental mode can existsingle mode laser diode

DH AlGaAs/GaAs LD ~ 900 nm LD

DH InGaAsP/InP LD 1.3/1.55 μm LD


Output Modes of LD

Elementary Laser Diode Characteristics

output spectrum depends on 1. optical gain curve of the active medium 2. nature of the optical resonator

L decides longitudinal mode separation W & H decides lateral mode separation

with sufficiently small W & Honly TEM00 lateral mode will exist

( longitudinal modes depends on L )

diffraction at the cavity ends laser beam divergence

( aperture ↓ diffraction ↑)

( from Kasap Ex. 4.5.1 : Number of laser modes depends on how the cavity modes intersect the optical gain curve. )


Current Dependence of Power Spectrum


output spectrum depends on (1) optical gain curve of the active medium, and (2) nature of the optical resonatoroutput spectrum depends on pumping current level Ex. output spectrum from an index guided LDlow current multimodehigh current single mode spectrum of most gain guided LD remain multimode even at high diode current


Temperature Dependence of Ith and λ


Tj ↑ Ith ↑

Tj ↑ Eg ↓ , n ↑ , cavity length ↑ λ0 ↑

in single mode LD :when shift of peak gain causes mode change to an adjacent longer λ

mode

mode hoppingto restrict mode hopping design the device structure to keep modes sufficiently separated

Tj depends on (1) ambient

temperature (2) operation

current


Slope Efficiency


slope efficiency ηslope :

typical ηslope < 1 W/A

Po = ηslope ( I – Ith )


Rate Equations and Laser Diode Equation I

Steady State Semiconductor Rate Equations

Po = ? x ( J – Jth )

( Δt = nL/c )

Nph = ? x ( J – Jth )

at steady state :

( neglecting nonradiative recombinations )

at I = Ith , n = nth, Nph ≈

0

nth = Ithτsp / edLW


Rate Equations and Laser Diode Equation II

Steady State Semiconductor Rate Equations

at steady state :

( τph : average time for a photon to be lost due to transmission through the end-faces, scattering and absorption )

nth = 1 / C τph

( laser diode equation )


Light Emitters for Optical Fiber Communications

Light Emitters For Optical Fiber Communications

LED adv. : simpler to drive, more economic, longer lifetime

disadv. : wider output spectrum, less power

usually used with multimode graded index fibers for short haul appl. LD adv. : narrow linewidth, high output power

wide bandwidth long haul appl.rise time : the time for light output to rise from 10% to 90% of the final value ( with a step input )


Distributed Bragg Reflector Laser Diode

Single Frequency Solid State Lasers

typical Δλ

of single frequency ( single mode ) lasers < 0.1 nm

one way to achieve single mode operation freq. selective mirrors

, λB : Bragg wavelength , q : diffraction order

in-phase interferenceonly particular Fabry-Perot cavity mode within the optical gain curve that is close to λB can lase and exist in the output


Distributed Feedback Laser Diode I.


radiation fed from active layer into guiding layer in the whole cavity lengthcorrugated grating periodic refractive index change partially reflected wavesoppositely traveling waves can only coherently coupled to set up a standing wave, a mode, if their frequency is related to the corrugation periodictiy Λ


Distributed Feedback Laser Diode II.


allowed DFB modes with λm :

, m = 0, 1, 2 …, L : effective length of diffraction grating

relative threshold gain for higher mode is high only m = 0 mode can effectively lase

asymmetry introduced by fabrication process or on purpose only one mode appear

L >> Λ ( λm λB )


Cleaved-Coupled-Cavity Laser


couple two different laser optical cavities

only waves that can exist as modes in both cavities are allowedrestriction in modes and increase separation between modessingle mode operation more easily


Single Quantum Well Structure

Quantum Well Devices

very thin ( < 50 nm ) narrow Eg active region sandwiched between wider Egsemiconductors ( Ex. GaAs/AlGaAs SQW : ΔEc > ΔEv )

two-dimensional electron gas confined in the x-direction

, d << Dy , Dz

density of electronic states changes in a steplike fashion


SQW and MQW Lasers

Quantum Well Devices

advantages of QW lasers to DH lasers : 1. lower threshold current 2. narrower linewidth in λ

advantages of SQW can be extended by using MQW

MQW design can be combined with a distributed feedback structure to obtain a single mode operation


Vertical Cavity Surface Emitting Laser

Vertical Cavity Surface Emitting Lasers (VCSELs)

optical cavity along current flow direction distributed Bragg reflectors as mirrors with high reflectance at λ

:

λ

chosen to coincide with the optical gain of the active layer

very short cavity length ( a few μm ) : 1. need high reflectance end mirrors (~99%)2. large separation between longitudinal

modes single mode more probable unwanted voltage drop thru DBR mirrors usually circular cross section matrix emitters possible applications in optical interconnect, optical computing , and higher optical power


Optical Laser Amplifiers

Optical Laser Amplifiers

traveling wave semiconductor laser amplifier : 1. incoming light with λ

within optical gain bandwidth of the laser structure

stimulated emission and light amplification 2. AR coating at ends to suppress cavity oscillation 3. noise induced by spontaneous emission can be overcome by optical

filter at the output Fabry-Perot laser amplifier : 1. operated below threshold current to suppress optical gain 2. presence of optical resonator λ around cavity resonant wavelength

experience higher gain higher gain,

but less stable

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