1. 1 L8 Lasers UConn ECE 4211 03/10/2015 F. Jain Operating parameters: Operating wavelength: green, red, blue, fiber optic wavelength 1.55 microns Optical power output, expected external and wall conversion efficiency, Operating structure Cavity or Distributed Feedback type Edge emitting or surface emitting. Conditions of Lasing Threshold Current Density J th Reduction of J th : Heterostructure Lasers Optical Power-Current Behavior Carrier confinement in a double Heterostructure (DH) laser Laser Design Exercise Quantum Well/Wire/dot Lasers Distributed Feedback Lasers

2. General Conditions of Lasing: 2 Rate of emission = Rate of absorption Rate of spontaneous emission + rate of stimulated emission =Rate of absorption A 21 N 2 +B 21 r(h 12 ) N 2 = B 12  (h 12 ) N 1 (1) Rate of stimulated emission >> rate of absorption gives B 21  (h 12 ) N 2 >>B 12  (h 12 ) N 1 Or, ( N 2 /N 1 ) >> 1 ………Condition known as population inversion. (Using Planck’s distribution law, we can show that B 12 =B 21 ). (2) Rate of stimulated emission >> rate of spontaneous emission gives B 21  (h 12 ) N 2 >> A 21 N 2 Or,  (h 12 ) >> A 21 /B 21 Photon density higher than a value.

3. Conditions of Lasing: 3

4. General Conditions of Lasing: 4

5. 5 (a)Representing the amplitude/magnitude (b) Phase condition

6. Resonant Cavity: Condition I for Lasing 6 Figure2. Cavity with parallel end faces

7. The emission spectrum high lighting cavity modes 7 Figure3 shows the emission spectrum highlighting cavity modes (also known as the longitudinal or axial modes) for the GaAs laser diode. Conditions and Calculations: GaAs λ = 0.85μm n r = 3.59 L = 1000μm Δλ=2.01 Å

8. Equivalent of population inversion in semiconductor lasers: Condition II for Lasing 8 This condition is based on the fact that the rate of stimulated emission has to be greater than the rate of absorption. (23) Strictly speaking, the rate of stimulated emission is proportional to: (i)the probability per unit time that a stimulated transition takes place (B 21 ) (ii)probability that the upper level E 2 or E c in the conduction band is occupied (iii)joint density of states N j (E=hv 12 ) (iv)density of photons with energy hv 12, ρ(hv 12 ) (v)probability that a level E 1 or E v in the valence band is empty (i.e. a hole is there), E fn = quasi-fermi level for electrons.(24) (25) The rate of stimulated emission: (26) Similarly, the rate of absorption: (27)

9. 9 Using the condition that the rate of stimulated emission > rate of absorption; (assuming B 21 =B 12 ), simplifying Equation (26) and Equation (27) (28) Further mathematical simplification yields if we use (29) (30) Bernard - Douraffourg Condition [1] [1] [1] M.G.A. Bernard and G.Duraffourg, Physica Status Solidi, vol. 1, pp.699-703, July 1961 (31) Equation (31) is the equivalent of population inversion in a semiconductor laser. For band to band transitions (32)

10. Definition of quasi Fermi-levels 10 Gain coefficient g and Threshold Current Density J th The gain coefficient g is a function of operating current density and the operating wavelength λ. It can be expressed in terms of absorption coefficient α(hv 12 ) involving, for example, band-to-band transition.

11. Derivation of J TH 11 Rate of stimulated emission = B 21 f e N j (E=h )  (h 12 ) f h (Where  (h 12 ) = P v h  s ) = B 21 f e f h (  v g) n N  s Rate of absorption = (1-f h )(1-f e )  v g n N  s B 12 Net rate = Stimulated – absorption = [f e f h – (1-f e )(1-f h )]  v g n N  s B 21 = -[1-f e -f h ]  v g n N  s B 21 and also note that B12 = B 21 ) The gain coefficient is (34) Rate of spontaneous emission

12. 12 where: α o v g = probability of absorbing a photon N v = number of modes for photon per unit frequency interval Δv s = width of the spontaneous emission line Equation (34) gives (35) The total rate of spontaneous emission where: R c = Rate per unit volume η = quantum efficiency of photon (spontaneous) emission d = active layer width A = junction cross-section Equations (33), (35), (36) and (37) give (36) (37) (38)

13. 13 (39) (40) Substituting for N v and, we get (41) The condition of oscillation, Equation (15), gives (15)

14. Threshold current density 14 Using Equation (15) and Equation (42) (43) (44) When the emitted stimulated emission is not confined in the active layer thickness d, Equation (44) gets modified by Γ, the confinement factor (which goes in the denominator).