Stimulated Emission Devices: LASERS

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1. Stimulated Emission and Photon Amplification

E2 E2 E2 υ h hυ hυ hυ In Out hυ

E E E1 1 1 (a) Absorption (b) Spontaneous emission (c) Stimulated emission

The Principle of LASER

Example: Solid State Laser

Cr+3 Doped Ruby (Al2O3) Crystal

υ h 32 E E3 3 E3 E3 υ h 13 E E E 2 2 E2 2 Metastable IN OUT state υ h 21 υ h 21

Coherent photons E E1 E 1 1 E1 (a) (b) (c) (d)

The principle of the LASER. (a) Atoms in the ground state are pumped up to the energy level E3 by υ incoming photons of energy h 13 = E3–E1. (b) Atoms at E3 rapidly decay to the metastable state at υ energy level E2 by emitting photons or emitting lattice vibrations; h 32 = E3–E2. (c) As the states at E2 are long-lived, they quickly become populated and there is a population inversion between E2 and E1. υ (d) A random photon (from a spontaneous decay) of energy h 21 = E2–E1 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 Er3+ ion in the glass fiber

′ 1.54 eV E 3 1.27 eV E3 Non-radiative decay 980 nm Pump 0.80 eV E2 1550 nm 1550 nm Out In

0 E1

Energy diagram for the Er3+ ion in the glass fiber medium and light amplification by stimulated emission from E2 to E1. Dashed arrows indicate radiationless transitions (energy emission by lattice vibrations)

Er3+-doped fiber (10 - 20 m) Optical Wavelength-selective Optical isolator coupler isolator Signal in Splice Splice Signal out

λ = 1550 nm λ = 1550 nm

Pump laser diode Termination λ = 980 nm 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

Laser beam He-Ne gas mixture

Current regulated HV power supply

He Ne 5 1 (1s12s1) Collisions (2p 5s ) 20.61 eV 20.66 eV 632.8 nm Lasing emission

(2p53p1) Fast spontaneous decay ~600 nm (2p53s1) Electron impact

Collisions with the walls

2 6 0 (1s ) (2p ) Ground states 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

3. Spectral Purity

Optical Gain Relative intensity

(a) Doppler (c) broadening

λο λ λ δλ m

Allowed Oscillations (Cavity Modes) m(λ/2) = L L (b) λ Stationary EM oscillations δλ m Mirror 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 Cavity modes δλ m Number of laser modes (a) 5 modes depends on how the cavity modes intersect the optical gain curve. In this case we are looking at modes 4 modes within the linewidth (b) ∆λ1/2. λ

LASER OSCILLATION CONDITIONS

A. Optical Gain Coefficient

E2 hυ E 1 Optical Gain Laser medium υ g( o)

x g(υ) ∆υ P P+δP υ υ ο δx (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 gth

Reflecting Pf Pi Reflecting surface E surface f Ei

2 Steady state EM oscillations 1 Cavity axis x

R R 2 L 1

− (N2 N1) and Po − P = Lasing output power N2 N1 o − Threshold population (N2 N1)th inversion

Pump rate

Threshold pump rate

C. Phase Condition and Laser Modes

TEM 00 TEM10 TEM00 TEM10 Optical cavity

(a)

Spherical mirror

(b)

TEM TEM TEM TEM11 01 11 Wave fronts 01 (c) (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+

Ec + + E p n g eV E o c EFn Inversion E E region c v Holes in VB Eg E EFn eV Fp Electrons Electrons in CB Ec

EFp

Ev (a) (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

Optical gain E − E CB Fn Fp E Fn Electrons E c in CB

eV 0 hυ

Eg E Holes in VB v = Empty states At T > 0 EFp VB At T = 0 Optical absorption

Density of states (a) (b) (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 EFn − EFp > Eg. Holes in the VB are empty states. (b) Gain vs. photon energy.

GaAs Homojunction Laser Diode

Current

Cleaved surface mirror

L Electrode p + GaAs L

+ n GaAs Electrode

Active region (stimulated emission region)

Optical Power Laser Optical Power

Optical Power LED Stimulated emission λ

Optical Power Laser Spontaneous λ emission I 0 I th 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) A double n p p heterostructure diode has two junctions which are (a) AlGaAs GaAs AlGaAs between two different bandgap semiconductors (~0.1 µm) (GaAs and AlGaAs). Electrons in CB E ∆ c Ec (b) Simplified energy Ec 2 eV band diagram under a 1.4 eV 2 eV large forward bias. Lasing recombination (b) Ev takes place in the p- Ev GaAs layer, the active layer Holes in VB

Refractive (c) Higher bandgap index materials have a ∆n ~ 5% (c) Active lower refractive region index Photon density (d) AlGaAs layers provide lateral optical (d) confinement.

Double Heterostructure Laser Diode with Stripe Contact:

1. Carrier Recombination Confinement, 2. Photon Confinement 3. Carrier Injection Current Confinement

Cleaved reflecting surface W

L Stripe electrode

Oxide insulator p-GaAs (Contacting layer) p-Al Ga As (Confining layer) x 1-x p-GaAs (Active layer) n-Al Ga As (Confining layer) 2 x 1-x 1 3 Substrate n-GaAs (Substrate) Current pathsSubstrate Electrode

Elliptical Cleaved reflecting surface laser Active region where J > J . beam 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)

Electrode Oxide insulation p+-AlGaAs (Contacting layer) p-AlGaAs (Confining layer) n-AlGaAs p-GaAs (Active layer) n-AlGaAs (Confining layer) 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

Po (mW) 10 0 °C 50 °C 8 25 °C

0 I (mA) 0 20 40 60 80

Relative optical power

Po = 5 mW

Po = 3 mW

Po = 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

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

Threshold population nth n inversion

∝ Po = Lasing output power Nph I

Ith

Simplified and idealized description of a semiconductor laser diode based on rate equations. Injected electron concentration n and coherent radiation output power P vs. diode current I. o

Light power Laser diode

10 mW LED

5 mW

Current 0 50 mA 100 mA

Distributed Bragg Λ reflector λ Λ A q( B/2n) = B

Active layer Corrugated (a) 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 λ Λ q( B/2n) = . © 1999 S.O. Kasap, Optoelectronics (Prentice Hall)

Figure 4.2

Ideal lasing emission Optical power Λ Corrugated grating Guiding layer Active layer 0.1 nm λ λ (nm) λ (a) (b) B (c)

(a) Distributed feedback (DFB) laser structure. (b) Ideal lasing emission output. (c) Typical output spectrum from a DFB laser.

Cavity Modes In L λ Active layer In D λ L D In both λ L and D (a) (b) Cleaved-coupled-cavity (C3) laser

E QW Bulk Dy d Ec E3 E ² E c n = 2 E2 d n = 1 E1

Eg2 Dz AlGaAs AlGaAs z Eg1 y QW Bulk ² E v x Ev g(E) GaAs Density of states (a) (b) (c) 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 Ec) 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.

Ec E

E1 υ ′ h = E1 – E 1

′ E 1 Ev

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 E1 and E 1 is reached even with a small forward current which results in stimulated emissions.

Active layer Barrier layer E E c

A multiple quantum well (MQW) structure. Electrons are injected by the forward current into active layers which are quantum wells.

Contact

λ /4n2 Dielectric mirror λ/4n1

Active layer

Dielectric mirror

Substrate

Contact

Pump current

Signal in Signal out Active region

AR = Antireflection AR Partial mirror Partial mirror coating (a) Traveling wave amplifier (a) Fabry-Perot amplifier

Mirror Observer

Ecat(x,y) Eref(x,y) Laser beam Laser beam Through beam

Cat Eref(x,y) Hologram

Ecat(x,y)

Photographic plate Virtual cat image Real cat image (a) (b)

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.

He Ne Lasing emissions (1s12s1) (2p55s1) 20.6 eV 3.39 µm Collisions 5 1 5 1 (2p 4p ) (1s12s1) (2p 4s )632.8 nm 19.8 eV 543.5 nm 1523 nm 1152 nm 1118 nm (2p53p1)

Electron impact Fast spontaneous decay ~600 nm (2p53s1)

Collisions with the walls

6 2 (2p ) 0 (1s ) Ground states

Energy

4p levels 488 nm 514.5 nm 4s

72 nm Pumping 15.75 eV Ar+ ion ground state

Ar atom 0 ground state

p+ n+ − E e c A EFn Ec Eg

Ev B EFp E h+ 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.