(b) Spontaneous emission. Absorption, spontaneous (random photon) emission and stimulated emission.

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1 Lecture 10 Stimulated Emission Devices Lasers Stimulated emission and light amplification Einstein coefficients Optical fiber amplifiers Gas laser and He-Ne Laser The output spectrum of a gas laser Laser oscillation conditions Semiconductor lasers, (laser diodes) Rate equation Light emitters for optical fiber communications

2 E 2 E 2 E 2 hυ hυ hυ In hυ Out hυ E 1 E 1 E 1 (a) Absorption (b) Spontaneous emission (c) Stimulated emission Absorption, spontaneous (random photon) emission and stimulated emission.

3 hυ 32 E 3 E 3 E 3 E 3 hυ 13 E 2 Metastable state E 2 E 2 IN E 2 OUT hυ 21 hυ 2 E 1 E 1 E 1 E 1 Coherent photons (a) (b) (c) (d) The principle of the LASER. (a) Atoms in the ground state are pumped up to the energy level E 3 by incoming photons of energy hυ 13 = E 3 E 1. (b) Atoms at E 3 rapidly decay to the metastable state at energy level E 2 by emitting photons or emitting lattice vibrations; hυ 32 = E 3 E 2. (c) As the states at E 2 are long-lived, they quickly become populated and there is a population inversion between E 2 and E 1. (d) A random photon (from a spontaneous decay) of energy hυ 21 = E 2 E 1 can initiate stimulated emission. Photons from this stimulated emission can themselves further stimulate emissions leading to an avalanche of stimulated emissions and coherent photons being emitted.

4 Energy of the Er 3+ ion in the glass fiber EDFA 1.54 ev 1.27 ev E 3 E 3 Non-radiative decay 980 nm 0 Pump 0.80 ev E nm In E nm Out Energy diagram for the Er 3+ ion in the glass fiber medium and light amplification by stimulated emission from E 2 to E 1. Dashed arrows indicate radiationless transitions (energy emission by lattice vibrations)

5 Signal in Optical isolator Wavelength-selective coupler Splice Er 3+ -doped fiber (10-20 m) Splice Optical isolator Signal out λ = 1550 nm λ = 1550 nm Pump laser diode λ = 980 nm Termination A simplified schematic illustration of an EDFA (optical amplifier). The erbium-ion doped fiber is pumped by feeding the light from a laser pump diode, through a coupler, into the erbium ion doped fiber.

6 Flat mirror (Reflectivity = 0.999) Concave mirror (Reflectivity = 0.985) Very thin tube He-Ne gas mixture Laser beam Current regulated HV power supply A schematic illustration of the He-Ne laser

7 He Ne ev (1s 1 2s 1 ) Collisions (2p 5 5s 1 ) ev nm Lasing emission (2p 5 3p 1 ) Fast spontaneous decay ~600 nm Electron impact (2p 5 3s 1 ) Collisions with the walls 0 (1s 2 ) Ground states (2p 6 ) The principle of operation of the He-Ne laser. He-Ne laser energy levels (for nm emission).

8 Laser radiation θ r Laser tube L θ The output laser beam has a divergence characterized by the angle 2θ (highly exaggerated in the figure)

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11 Optical Gain Relative intensity (a) Doppler broadening (c) λ ο λ λ δλ m Allowed Oscillations (Cavity Modes) m(λ/2) = L L (b) δλ m λ Mirror Stationary EM oscillations Mirror (a) Optical gain vs. wavelength characteristics (called the optical gain curve) of the lasing medium. (b) Allowed modes and their wavelengths due to stationary EM waves within the optical cavity. (c) The output spectrum (relative intensity vs. wavelength) is determined by satisfying (a) and (b) simultaneously, assuming no cavity losses.

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16 Optical gain between FWHM points δλ m Cavity modes (a) (b) 5 modes 4 modes λ Number of laser modes depends on how the cavity modes intersect the optical gain curve. In this case we are looking at modes within the linewidth λ 1/2.

17 hυ E 2 Laser medium E 1 Optical Gain g(υ o ) P δx P+δP x υ υ ο g(υ) υ (a) (b) (a) A laser medium with an optical gain (b) The optical gain curve of the medium. The dashed line is the approximate derivation in the text.

18 Reflecting surface P f E f E i P i Reflecting surface 2 Steady state EM oscillations 1 Cavity axis x R 2 L R 1 Optical cavity resonator

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20 (N 2 N 1 ) and P o P o = Lasing output power (N 2 N 1 ) th N 2 N 1 Threshold population inversion Threshold pump rate Pump rate Simplified description of a laser oscillator. (N 2 N 1 ) and coherent output power (P o ) vs. pump rate under continuous wave steady state operation.

21 Optical cavity TEM 00 TEM 10 TEM 00 TEM 10 (a) Spherical mirror (b) Wave fronts TEM 01 TEM 11 (c) TEM 01 TEM 11 (d) Laser Modes (a) An off-axis transverse mode is able to self-replicate after one round trip. (b) Wavefronts in a self-replicating wave (c) Four low order transverse cavity modes and their fields. (d) Intensity patterns in the modes of (c).

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23 p + Junction n + E c E v E F p E g Holes in V B Electro ns ev o Electro ns in C B E F n E c E c E g p + Inversion regio n n + E c ev E F n E F p (a) E v (b) The energy band diagram of a degenerately doped p-n with no bias. (b) Band diagram with a sufficiently large forward bias to cause population inversion and hence stimulated emission. V

24 Energy CB Optical gain E F n E F p E F n E c Electrons in CB ev 0 hυ E v E F p VB Holes in VB = Empty states E g Optical absorption At T > 0 At T = 0 Density of states (a) (a) The density of states and energy distribution of electrons and holes in the conduction and valence bands respectively at T 0 in the SCL under forward bias such that E Fn E Fp > E g. Holes in the VB are empty states. (b) Gain vs. photon energy. (b)

25 Current Cleaved surface mirror p + L L GaAs Electrode n + GaAs Electrode Active region (stimulated emission region) A schematic illustration of a GaAs homojunction laser diode. The cleaved surfaces act as reflecting mirrors.

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27 Optical Power Optical P ower Laser Optical P ower LED Stimulated emission λ λ Spontaneous emission Optical P ower Laser 0 I th I λ Typical output optical power vs. diode current (I) characteristics and the corresponding output spectrum of a laser diode.

28 (a) (b) Electrons in CB E c E v 2 ev n AlGaAs p GaAs (~0.1 µm) 1.4 ev AlGaAs E c Holes in VB p 2 ev E c E v (a) A double heterostructure diode has two junctions which are between two different bandgap semiconductors (GaAs and AlGaAs). (b) Simplified energy band diagram under a large forward bias. Lasing recombination takes place in the p- GaAs layer, the active layer Refractive index Photon density (c) (d) Active region n ~ 5% (c) Higher bandgap materials have a lower refractive index (d) AlGaAs layers provide lateral optical confinement.

29 Cleaved reflecting surface W Stripe electrode L Oxide insulator p-gaas (Contacting layer) p-al x Ga 1-x As (Confining layer) p-gaas (Active layer) n-al x Ga 1-x As (Confining layer) n-gaas (Substrate) Current paths Substrate Electrode Substrate Elliptical laser beam Cleaved reflecting surface Active region where J > J th. (Emission region) Schematic illustration of the the structure of a double heterojunction stripe contact laser diode

30 Oxide insulation p + -AlGaAs (Contacting layer) p-algaas (Confining layer) n-algaas p-gaas (Active layer) n-algaas (Confining layer) Electrode n-gaas (Substrate) Schematic illustration of the cross sectional structure of a buried heterostructure laser diode.

31 Dielectric mirror Fabry-Perot cavity Length, L Height, H Width W Diffraction limited laser beam The laser cavity definitions and the output laser beam characteristics.

32 Relative optical power P o = 5 mw P o = 3 mw P o = 1 mw λ (nm) Output spectra of lasing emission from an index guided LD. At sufficiently high diode currents corresponding to high optical power, the operation becomes single mode. (Note: Relative power scale applies to each spectrum individually and not between spectra)

33 P o (mw) C 25 C 50 C I (ma) Output optical power vs. diode current as three different temperatures. The threshold current shifts to higher temperatures.

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35 λ o (nm) Single mode Mode hopping Case temperature ( C) Single mode (a) (b) (c) Case temperature ( C) Multimode Case temperature ( C) Peak wavelength vs. case temperature characteristics. (a) Mode hops in the output spectrum of a single mode LD. (b) Restricted mode hops and none over the temperature range of interest (20-40 C). (c) Output spectrum from a multimode LD.

36 n P o n th n Threshold population inversion P o = Lasing output power N ph I I th Simplified and idealized description of a semiconductor laser diode based on rate equations. Injected electron concentration n and coherent radiation output power P o vs. diode current I.

37 Rate Equations g g mir g p N g c p sp n c v v N N G g v G GP N q I t N P R GP t P = + = = = Γ = + = ) ( 1 ) ( d d d d int 0 α α τ τ τ

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39 Light power Laser diode 10 mw LED 5 mw 0 50 ma 100 ma Current Typical optical power output vs. forward current for a LED and a laser diode.

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41 Distributed Bragg reflector A B Λ q(λ B /2n) = Λ (a) Active layer Corrugated dielectric structure (b) (a) Distributed Bragg reflection (DBR) laser principle. (b) Partially reflected waves at the corrugations can only constitute a reflected wave when the wavelength satisfies the Bragg condition. Reflected waves A and B interfere constructive when q(λ B /2n) = Λ.

42 Corrugated grating Λ Ideal lasing emission Optical power Guiding layer Active layer 0.1 nm (a) (b) λ B λ (c) λ (nm) (a) Distributed feedback (DFB) laser structure. (b) Ideal lasing emission output. (c) Typical output spectrum from a DFB laser.

43 L (a) D Active layer In L In D In both L and D Cavity Modes (b) λ λ λ Cleaved-coupled-cavity (C 3 ) laser

44 E D y d E c E ² E c n = 2 n = 1 d E 3 E 2 E 1 QW Bulk D z AlGaAs AlGaAs z y x GaAs E g2 E v ² E v (a) (b) (c) E g1 QW Bulk Density of states g(e) A quantum well (QW) device. (a) Schematic illustration of a quantum well (QW) structure in which a thin layer of GaAs is sandwiched between two wider bandgap semiconductors (AlGaAs). (b) The conduction electrons in the GaAs layer are confined (by ² E c ) in the x-direction to a small length d so that their energy is quantized. (c) The density of states of a two-dimensional QW. The density of states is constant at each quantized energy level.

45 E E c E 1 hυ = E 1 E 1 E 1 E v In single quantum well (SQW) lasers electrons are injected by the forward current into the thin GaAs layer which serves as the active layer. Population inversion between E 1 and E 1 is reached even with a small forward current which results in stimulated emissions.

46 Active layer Barrier layer E E c E v A multiple quantum well (MQW) structure. Electrons are injected by the forward current into active layers which are quantum wells.

47 Contact λ/4n 2 λ/4n 1 Dielectric mirror Active layer Dielectric mirror Substrate Contact Surface emission A simplified schematic illustration of a vertical cavity surface emitting laser (VCSEL).

48 Pump current Signal in Active region Signal out AR = Antireflection coating AR (a) Traveling wave amplifier Partial mirror Partial mirror (a) Fabry-Perot amplifier Simplified schematic illustrations of two types of laser amplifiers

49 Mirror Observer Laser beam Laser beam E ref (x,y) E cat (x,y) Through beam E ref (x,y) E cat (x,y) Cat Hologram Photographic plate (a) Virtual cat image (b) Real cat imag A highly simplified illustration of holography. (a) A laser beam is made to interfere with the diffracted beam from the subject to produce a hologram. (b) Shining the laser beam through the hologram generates a real and a virtual image.

50 He (1s 1 2s 1 ) 20.6 ev Collisions (1s 1 2s 1 ) (2p 5 4s 1 ) 19.8 ev (2p 5 5s 1 ) nm (2p 5 3p 1 ) Ne 3.39 µm nm 1523 nm 1152 nm 1118 nm Lasing emissions (2p 5 4p 1 ) Electron impact (2p 5 3s 1 ) Fast spontaneous decay ~600 nm 0 (1s 2 ) Ground states Collisions with the walls (2p 6 ) Various lasing transitions in the He-Ne laser

51 Energy 4p levels 4s 488 nm nm Pumping 72 nm ev Ar + ion ground state 0 Ar atom ground state The Ar-ion laser energy diagram

52 E c p + A e n + E c E Fn E g E Fp E v h + B E v V The energy band diagram of a degenerately doped p-n with with a sufficiently large forward bias to just cause population inversion where A and B overlap.

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