What happens when light (or photon) interact with a matter? Assume photon energy is compatible with energy transition levels. Electron energy levels in an hydrogen atom n=5 n=4 - + n=3 n=2 13.6 = [ev] n E = n 2 - n=1 Energy levels inside every matter are quantized; details depend on the matter
Consider for simplicity only two energy levels: ground and excited states Assume hν = E 2 E 1 E 2 Three interaction processes are possible E 1 Absorption Spontaneous Emission Stimulated Emission E 2 E 2 In E 2 Out E 1 E 1 E 1 out photons are out photons are identical random to in photons: amplification
Determine the rate for each process Absorption Spontaneous Emission Stimulated Emission E 2 E 2 E 2 R E E 1 1 E 1 12 = B 12 N 1 ρ R = A N R = B N sp 21 2 21 21 2 ρ ρ : photon density N : electron density at E 1,2 1,2 B, B, B : constants 12 sp 21 It can be shown B 21 1 B = 3 A21 8π hυ = 3 12 B12 c
Absorption Spontaneous Emission Stimulated Emission E 2 E E 2 2 R = B12 1 ρ 12 N E 1 E 1 R sp = A 21 N 2 R E 1 = B21 2 21 N ρ B 21 1 B = 12 3 A21 8π hυ = 3 B c 12 Interpretations: -Absorption and simulated emission have the same coefficeint The only difference is N 1 and N 2 -Spontaneous emission i and stimulated t emission i are intrinsically related Spontaneous emission is simulated emission due to vacuum fluctuation ti
Which process is dominant at equalibrium? Stimulated emission vs. absorption R B N ρ N E E R B N ρ N kt 21 21 2 2 2 1 = = = exp << 1 12 12 1 1 λ=1.55μm E 2 E 2 -E 1 =1.55μm E 1 R 21 N 2 0.8 ev = = exp ~ 2 10 R N 0.04eV 12 1 9 Virtually no possibility for stimulated emission at equalibrium
Which process is dominant at equalibrium? Stimulated emission vs. spontaneous emission 3 3 R 21 B 21N 2ρ B 21 c 8πhυ 1 3 R = sp A21N = ρ 2 A = 21 8πhυ 3 hυ = E2 E1 c exp 1 exp 1 kt kt E 2 E 1 λ=1.55μm R21 1 1 = = ~2 10 8 R sp 08 0.8eV 4.84 10 1 exp 1 0.04eV 9 Virtually all photon emission is due to spontaneous emission at equalibrium
How can we induce stimulated emission? Absorption Spontaneous Emission Stimulated Emission E 2 E 2 E 2 R E E 1 1 E 1 12 = B 12 N 1 ρ R = A N R = B N sp 21 2 21 21 2 ρ Make N 2 larger than N 1 : Break equalibrium and pump carriers into E 2 N 2 = N 1 : transparent N 2 > N 1 : population inversion
Optical Amplifier P in E 2 P out = G P in E 1 Which process is useful for optical amplifier? How can we make stimulated emission dominant over absorption? Pump carriers into N 2 so that N 2 > N 1 Optical Pumping and Electrical Pumping
Optical Pumping: Consider Er Energy levels in Er -Pump light is absorbed at E 3 generating g carriers 1.27 ev E 3 980 nm 0 Pump Non-radiative decay 0.80 ev E 2 1550 nm In E 1 1550 nm Out - Carriers at E 3 rapidly transfer to E 2 N 2 builds up -When N 2 >N 1 (population inversion), stimulated t emission i > absorption for 1550nm light Er can be easily added to core of Silica fiber EDF (Er-Doped Fiber)
Lect. 18: Laser Optical Basics Amplifiers Optoelectronics Special Topics and in Optical Photonics Comm.: Si Photonics High-Speed (11/1) Circuits and Systems W.-Y. Laboratory Choi
Si lattice structure Electron energy levels in semiconductors Covalent bond Si ion core (+4e ) Electrons in each Si atom have discrete energy levels. But in Si crystal, energy bands are formed. + +
Band diagram Conduction Band E Band Gap (=E c -E v ) Ec E v k Valence Band
Direct semiconductor E Indirect Semiconductor E k k Momentum conservation not possible by photon emission => No emission (Examaple: Si)
Absorption Spontaneous Emission Stimulated Emission k k R ( hν ) = B N ( E ) P( E ) ρ( hν) R ( sp hν ) = A ( ) ( ) 21 N2 E2 P1 E1 R21( hν ) = B21 N2( E2) P1 ( E1 ) ρ( hν) 12 12 1 1 2 2 For population inversion, N N P P 2 1 1 2 > 1 Electron and hole injection needed.
How to pump electrons and holes into a semiconductor? Forward-bias PN junction Electron in CB Hole in VB Light emitting diode (LED) Light output E g p Insulator (oxide) n + hυ - E g n + Substrate V Metal electrode Light emission by spontaneous emission Does any semiconductor emit light? What determines the color of LED?
Bandgap energies for major LED materials: III-V compound semiconductor Indirect bandgap InGaN GaAs 1-y P y x = 0.43 In 1-x Ga x As 1-y P y Al x Ga 1 x As x 1-x In 0.49 Al x Ga 0.51-x P 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 Infrared 1.7 λ Free space wavelength coverage by different LED materials from the visible spectrum to the infrared including wavelengths used in optical communications. Hatched region and dashed lines are indirect E g materials.?1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Current injection into PN Junction can be used for SOA (Semiconductor Optical Amplifier) Current Injection P in P out =GP in
Gain spectrum for SOA Energy ev E Fn E c CB Electrons in CB Optical gain 0 E Fn E Fp hυ E Holes in VB v = Empty states At T > 0 E Fp VB E g At T = 0 Optical absorption
Optical Amplifier P in E 2 P out = G P in E 1 Light source based on stimulated emission? - Use photons produced by spontaneous emission as initial seeds - Recycle output photons as seeds for further stimulated emission - Use mirror for recycling output t photons LASER: Light Amplification by Stimulated Emission Radiation
LASER: Optical Amplifier + Mirror Pump Gain Medium R L R Optical property of gain medium: n, g g k = nk0 + j g depends on λ and the amount of pumping 2
Pump Gain Medium R Z=L R k = nk + j Assume there is an initial photon moving in z-direction inside gain medium. What is the condition that this photon is sustained? No loss after one round trip. E e r e r = E jkl jkl 0 0 2 2 r e j kl e = 1 j2nk L gl 1 0 e R e j2kl 1 1 = = 2 r R 1 and j nk L e = e = 1 R gl 2 0 = 0 g 2
gl e 1 and j2nk0l e 1 = = R Pump 1 1 1 gl From e =, gth = ln R L R ==> Sufficient gain to compensate mirror loss R Gain Medium L R e = 2nk0L = 2mπ j2nk0l From 1, λ 2L = or n m L = λ m 2 n cavity length should be multiples of half wavelength Identical photons are continuously produced d at two outputs t
1 1 λ 2L Two conditions for lasing: (1) gth = ln and (2) = L R n m g th <= (1) λ λ <= (2) Lasing spectrum λ Lasing peaks (modes) has non-zero linewidth
Various LASERs Any optical gain material with mirrors can form a laser First Laser: Ruby doped with Cr (Al 2 O 3 :Cr 3+ ) Maiman with first laser in 1960. Optical Gain: Cr in Al 2 O 3 Pump: Flash Lamp
Gas Laser (HeNe) Flat mirror (Reflectivity = 0.999) Concave mirror (Reflectivity=098 0.98 (1s 1 2s 1 ) Very thin tube 20.61 ev He Collisions (2p 5 5s 1 ) (2p 5 3p 1 ) 20.66 ev Ne 632.8 nm Lasing emission Fast spontaneous decay He-Ne gas mixture Laser beam Electron impact (2p 5 3s 1 ) ~600 nm Collisions with the walls Current regulated HV power supply A schematic illustration of the He-Ne laser 0 (1s 2 ) (2p 6 ) Ground states
Semiconductor Laser Structure: PN Junction + Mirror (Cleaved Facets) Cleaved reflecting surface W Stripe electrode L Oxide insulator p-al x Ga 1-x As (Confining layer) GaAs (Active layer) n-al x Ga 1-x As (Confining layer) n-gaas (Substrate) 2 1 3 Current paths Substrate Electrode Substrate Elliptical laser beam Cleaved reflecting surface Active region where J > J th. (Emission region)
Efficient carrier confinement: PIN structure with large E g for P, N regions P N P I N Injected carriers are spread-out => smaller density For population inversion, N N P P 2 1 1 2 > 1 Double heterojunction: Confinement of Injected carriers => larger density
Efficient photon confinement: PIN structure with smaller n for P, N regions Smaller E g material has larger n (n 1 >n 2 ) cladding (n 2 ) Active (n 1 ) Dielectric waveguide! cladding (n 2 ) => More photons interacting with injected electrons and holes in the active region larger Γ With Γ<1, 1 1 1 1 = = => Γ g th = ln = α m L R λ 2L λ 2 L β = ==> = ; neff = n m neff m k0 g th ln α m (mirror loss) L R
Optical lp Power (mw) Optical Power Laser Optical Power LED λ Spontaneous emission λ Slope Efficiency:dP/dI 0 I th I (ma) Threshold current: I th
λ Two conditions for lasing: (1) Γ gth = αm + αint and (2) = n eff 2L m There can be several lasing modes: several λ s satisfying above conditions. -Multiple values for n eff if there are multiple waveguide modes Different modes have different n eff cladding Active cladding (n (n 1 ) 2 ) (n 2 ) Design for single guided mode. TE, TM modes?
- Multiple cavity modes Mode separation j2nk0l From e = 1 2neff k0l= 2mπ π Δ ( neff k0) L= π => Δ ( k0) = n L g th λ 2L = for g( λ) > g n m eff th eff 2 2 2 2 λ 0 2 0 2 0 λ = π k k k k Δ λ = δλ π π λ δ k Δ = k Δ = 2π Δ = 0 0 0 2n eff L λ With typical semiconductor lasers with cleaved facets, Δλ is less than gain bandwidth => multi lasing modes λ Fabry-Perot laser Optical Power Laser λ
Problems with multi-mode laser? Modal dispersion even with single-mode fiber How to make single-mode laser? Use another type of mirror: Grating Remember θ i θ d ( sin ) θ sinθ i = m λ Incident o o light wave For mirror, θ = 90 and θ = 90, i d = m λ 2
How to implement diffraction grating within semiconductor laser? Distributed Feedback (DFB) Laser grating d Optical power Guiding layer Active layer λ (nm) d = m λ 2 n eff (typically m=1)
Another approach: Make L very small so that Δλ larger than gain bandwidth g th gain bandwidth: in the order of 10nm λ: 1.5μm λ n eff : 3.5 L ~30μm; Not easy to fabricate by cleaving λ 1 1 2 From α m = ln, too much mirror loss λ Δ λ = L R n L 2 eff
Solution: Very short cavity vertical lasers with very high reflectivity mirrors (VCSEL: Vertical Cavity Surface Emitting Laser) λ/4n2 λ/4n1 P N Contact Dielectric mirror Active layer In semiconductor fabrication, vertical thickness can be very precisely controlled. Dielectric mirror can have high h reflectivity approaching R=1. Dielectric mirror Substrate Contact 1 1 From α m = ln, L R α can be made small m if R approaches 1. Surface emission VCSELs are cheaper because it is more mass-producible.