Stimulated Emission Devices: LASERS

Stimulated Emission Devices: LASERS 1. Stimulated Emission and Photon Amplification 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

The Principle of LASER Example: Solid State Laser Cr+3 Doped Ruby (Al2O3) Crystal 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 21 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.

The Principle of OPTICAL FIBER AMPLIFIERS Er+3 Doped Glass Fiber Energy of the Er 3+ ion in the glass fiber 1.54 ev 1.27 ev E 3 E 3 Non-radiative decay 980 nm 0 Pump 0.80 ev E 2 1550 nm In E 1 1550 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) Signal in Optical isolator Er 3+ -doped fiber (10-20 m) Wavelength-selective coupler Splice 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.

The Principle of GAS LASERS: The He-NE LASER Flat mirror (Reflectivity = 0.999) Concave mirror (Reflectivity = 0.985) Very thin tube He-Ne gas mixture Laser beam Current regulated HV power supply He Ne 20.61 ev (1s 1 2s 1 ) Collisions (2p 5 5s 1 ) 20.66 ev 632.8 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 632.8 nm emission).

STIMULATED EMISSION RATE and EINSTEIN COEFFICIENTS

PROPERTIES OF LASER LIGHT 1. Coherence 2. Beam Divergence (Collimation) Laser radiation θ r Laser tube L θ

3. Spectral Purity 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.

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.

LASER OSCILLATION CONDITIONS A. Optical Gain Coefficient 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.

B. Threshold Gain g th 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 (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

C. Phase Condition and Laser Modes 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).

The Principle of THE LASER DIODE Population Inversion via Carrier Injection and Recombination p + Junction n + E c E v E Fp E g Holes in VB Electrons ev o Electrons in CB E Fn E c E c E g p + Inversion region n + E c ev E Fn E Fp (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. Energy V CB Optical gain E Fn E Fp E Fn E c Electrons in CB ev 0 hυ E v E Fp 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)

GaAs Homojunction Laser Diode Current Cleaved surface mirror p + L L GaAs Electrode n + GaAs Electrode Active region (stimulated emission region) Optical Power Optical Power Laser Optical Power LED Stimulated emission λ λ Spontaneous emission Optical Power Laser 0 I th I λ Typical output optical power vs. diode current (I) characteristics and the corresponding output spectrum of a laser diode.

HETEROSTRUCTURE LASER DIODES Double Heterostructure Laser Diode: 1. Carrier Recombination Confinement, 2. Photon Confinement (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 (c) Photon density (d) Active region n ~ 5% (c) Higher bandgap materials have a lower refractive index (d) AlGaAs layers provide lateral optical confinement.

Double Heterostructure Laser Diode with Stripe Contact: 1. Carrier Recombination Confinement, 2. Photon Confinement 3. Carrier Injection Current Confinement 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) 2 1 3 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

Buried Double Heterostructure Laser Diode 1. Carrier Recombination Confinement (full cross section control) 2. Photon Confinement (full cross section control) ( index guided ) 3. Carrier Injection Current Confinement (full cross section control) Oxide insulation p + -AlGaAs (Contacting layer) p-algaas (Confining layer) n-algaas p-gaas (Active layer) n-algaas (Confining layer) Electrode n-gaas (Substrate) These laser diodes can operate in single mode because of full photon confinement and small lateral dimensions of the optical fiber-like cavity formed for the photons propagating inside.

PROPERTIES OF LASER DIODE OUTPUT Dielectric mirror Fabry-Perot cavity Length, L Height, H Width W Diffraction limited laser beam 1. Coherence 2. Modes (lateral and longitudinal) 3. Beam Divergence (Collimation)

4. Electrical Chs. And Optical Output Power and Spectrum P o (mw) 10 8 6 4 2 0 C 25 C 50 C 0 0 20 40 60 80 I (ma) Relative optical power P o = 5 mw P o = 3 mw P o = 1 mw λ (nm) 778 780 782 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)

3. Mode Hopping λ o (nm) 788 786 784 782 780 778 Single mode Mode hopping 776 20 30 40 50 Case temperature ( C) Single mode (a) (b) (c) 20 30 40 50 Case temperature ( C) Multimode 20 30 40 50 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.

STEADY STATE SEMICONDUCTOR RATE EQUATIONS

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.

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. 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Figure 4.1

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. 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Figure 4.2

Corrugated grating Λ Ideal lasing emission Optical power Guiding layer Active layer (a) (b) λ B λ (c) 0.1 nm λ (nm) (a) Distributed feedback (DFB) laser structure. (b) Ideal lasing emission output. (c) Typical output spectrum from a DFB laser. 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Figure 4.3

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 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Figure 4.4

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 E g1 QW Bulk ² E v Density of states (a) (b) (c) 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. 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Figure 4.5

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. 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Figure 4.6

E E c Active layer Barrier layer E v A multiple quantum well (MQW) structure. Electrons are injected by the forward current into active layers which are quantum wells. 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Figure 4.7

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). 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Figure 4.8

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 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Figure 4.9

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 image 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. 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Figure 4.10

He Ne (1s 1 2s 1 Lasing emissions ) (2p 5 5s 1 ) 20.6 ev 3.39 µm Collisions (1s 1 2s 1 ) (2p 5 4s 1 (2p 5 4p 1 ) ) 632.8 nm 19.8 ev 543.5 nm 1523 nm 1152 nm 1118 nm (2p 5 3p 1 ) Electron impact Fast spontaneous decay (2p 5 3s 1 ~600 nm ) 0 (1s 2 ) Ground states Collisions with the walls (2p 6 ) Various lasing transitions in the He-Ne laser 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Figure 4.11

Energy 4p levels 4s 488 nm 514.5 nm 15.75 ev Pumping 72 nm Ar + ion ground state 0 Ar atom ground state The Ar-ion laser energy diagram 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Figure 4.12

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. 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Figure 4.13