Paper Review IEEE Journal of Quantum Electronics, Feb 1985
Contents Semiconductor laser review High speed semiconductor laser Parasitic elements limitations Intermodulation products Intensity noise Large signal effects Conclusion
Interaction between light and matters <Photon interacting with an hydrogen atom> + - hν Three interaction processes are possible Absorption Spontaneous Emission Stimulated Emission R 12 = B 12 N 1 ρ R sp = B sp N 2 R 21 = B 21 N 2 ρ ρ : photon density, N 1,2 : electron density at E 1,2 B 12,21,sp : constants
Interaction between light and matters R 12 = R sp + R 21 : Equilibrium condition N 2 = exp E 2 E 1 : Statistical mechanics N 1 kt ρ hν = 8πhν 3 c 3 {exp hν kt 1} : Black-body radiation B 21 = 1, B sp = 8πhν3 B 12 B 12 c 3 Absorption Spontaneous Emission Stimulated Emission R 12 = B 12 N 1 ρ R sp = B sp N 2 R 21 = B 21 N 2 ρ ρ : photon density, N 1,2 : electron density at E 1,2 B 12,21,sp : constants
Optical amplifier Amplifier Stimulated emission should be dominant P in P out = G P in Pumping N 2 > N 1 (Population Inversion)
LASER LASER : Light Amplification by Stimulated Emission of Radiation LASER = Optical amplifier + Mirrors Use initial photon produced by spontaneous emission Recycle photons produced by stimulated emission Use mirrors for recycling photons Condition for sustaining photons in laser ⑴e gl = 1 R (Gain > mirror loss) ⑵e j2nk 0L = 1 (No loss after one round trip)
Conditions for lasing Lasing conditions : ⑴e gl = 1 g R th = 1 ln 1 L R ⑵e j2nk0l = 1 λ = 2L (m = 1,2,3, ) n m
Semiconductor laser Absorption Spontaneous Emission Stimulated Emission R 12 hν = B 12 N 1 (E 1 ) P 2 (E 2 ) ρ(hν) R sp hν = B sp N 2 (E 2 ) P 1 (E 1 ) R 21 hν = B 21 N 2 (E 2 ) P 1 (E 1 ) ρ(hν) For population inversion, N 2 P 1 N 1 P 2 > 1 Electron & hole should be injected (Forward bias in PN junction)
Semiconductor laser structure
High speed semiconductor laser Rate equations ⑴ dn dt = J ed N τ s A N N om P ⑵ dp dt = A N N om P P τ p + β N τ s N: carrier density N om : carrier density for transparency P: photon density J: pump current density d: thickness of active layer τ s : spontaneous recombination lifetime of carriers τ p : photon lifetime A: optical gain coefficient β: fraction of spontaneous emission entering to lasing mode Small signal & linearization f T relaxation oscillation frequency = 1 2π Ap 0 τ p A, p 0, τ p high speed semiconductor laser
Parasitic elements limitation Semiconductor laser I Bonding wire I oxide insulator active layer p doped confining layer n doped confining layer Contact resistance Substrate Parasitic capacitance Intrinsic diode Circuit modeling current flowing into the intrinsic diode η = voltage of the signal source 1 = s 2 2 ω + s 0 ω 0 Q + 1 ω 0 = 50 + R LRC(50 + R), Q = LRC L + 50RC Second-order low pass filter type
Parasitic elements limitation
Parasitic elements limitation Circuit modeling 1+e Z = Z 2kW 0 1 e 2kW, W : width of top contact Z 0 = R dist jωc dist, k = jωr dist C dist Higher frequency higher propagation constant(k) electric field cannot penetrate far beyond laser junction
Intermodulation products Third order intermodulation Third order intermodulation can be a problem in multichannel frequency division transmission
Intensity noise Relative Intensity Noise RIN = P 0 : average light output power < ΔP > 2 : mean square intensity fluctuation spectral density of the light output < ΔP >2 < P 0 > 2 With rate equations, RIN ~ 1 p 0 ω 3 ω 2 ω R 2 1 2 + ω2 ω R 4 τr 2
Large signal effects Non-linearity problem for large signal Optical modulation depth for high speed below ~70 percent <Effects of increasing optical modulation depth>
Conclusion Rate equations ⑴ dn dt = J ed N τ s A N N om P ⑵ dp dt = A N N om P P τ p + β N τ s N: carrier density N om : carrier density for transparency P: photon density J: pump current density d: thickness of active layer τ s : spontaneous recombination lifetime of carriers τ p : photon lifetime A: optical gain coefficient β: fraction of spontaneous emission entering to lasing mode f T = 1 2π Ap 0 τ p A, p 0, τ p high speed semiconductor laser Parasitic elements limitations Intermodulation products Intensity noise Large signal effects