Index

A

ABCD matrices

applications, 375–376

astronomical refractive telescope, 370, 372

description, 369

imaging systems, 369

multiple-prism beam expanders, 373–374

optical element/system, 370, 371–372

propagation, 367, 368

properties, 369–370

ray transfer matrix, 368, 371–372

telescopes in series, 374–375

thin convex lens, 368

transformation, 367

Angular dispersion, 79

B

BBA, see Bennett and Brassard approach (BBA)

Beam divergence

and astronomy, 31–32

control, 30

diffraction limit, 31

Bell’s inequalities

correlation, observables, 328

detectors, 330

probability alternatives, 329

PWS probability amplitude, 328

two-photon entanglement experimental configuration, 329

Bennett and Brassard approach (BBA)

canonical bases, 295

Mach–Zehnder interferometer configuration, 298

quantum key distribution protocol, 296

raw quantum transmission, 296

signal interception, 297

transmission methodology, 296, 297

Birefringent polarization rotators, 245–246

Bohm polarization projection, 327

Brewster’s angle, 83, 85, 92

Broadband prismatic polarization rotators

collinear polarization rotation, 246, 248

π/2 prismatic polarization rotator, 246, 249

prism operator, 246, 247

transmission fidelity, 246, 248

Broadband resonators, 358–359

C

Calculus basics

chain rule, 386

integration by parts, 386

power rule, 385–386

product rule, 385

quotient rule, 385

Cascade interferometric technique, 54, 55

Cavity linewidth equation, 32–33

Circular polarization, 256–258, 262

Classical logic gates

CNOT gate, 286

AND gate, 285

NAND gate, 284, 285

NOR gate, 285, 286

NOT gate, 284, 285

OR gate, 286

primitive elements, 284

reversible primitives, 284

Classical polarization

Brewster angle, 233, 234

degree of polarization, 233

Fresnel formulae, 232

incident electric vector, 232

Jones calculus, 235–237

Maxwell equations, 229–231

orthogonal/normal incidence, 233

plane of incidence, 234

prisms, 238–244

reflection boundary, 231, 232

rotators, 244–249

Coherent and semicoherent interferograms

broadband emission, 56

double-slit, 56–58

interferometric equation, 56

photons/narrow-linewidth emission, 56

single-photon propagation, 56

single-wavelength, 56

Colliding-pulse-mode locking (CPM), 365

Commutation rule, 207, 217, 218

Complex numbers, 379–381

Continuous-wave (CW)

cooled-stabilized, 104

dye lasers

femtosecond pulse dye lasers, 344, 345

high-power, 344, 345

gas lasers

ionized, 341, 342

visible transitions, He-Ne lasers, 341

liquid organic dye lasers, 108

metal ion lasers, 105

tunable cavities

femtosecond laser cavities, 365

generic linear, 364, 365

unidirectional, 364

Conversion quantities, 397, 398

CPM, see Colliding-pulse-mode locking (CPM)

Cryptography

description, 293

public key cryptography, 293, 294

quantum cryptography, see Quantum cryptography

quantum teleportation, 301–305

symmetric key algorithm, 293

CW, see Continuous-wave (CW)

D

Density matrix

characteristics, 223

circularly polarized light, 224

circular polarization, 262

definition, 223

differentiation, time yields, 223

Jones vector, 258

linearly polarized light, 224

Pauli matrices, 260–261

right-handed polarized light, 262

Schrödinger equation, 222–223

Stokes parameters, 259–261

transitions, 225–226

Diagonal polarization, 255–256

Diffraction

generalized, see Generalized diffraction

grating equation, 48–49

orders, 63, 64

positive, 72

Dirac notation

application, 127

complex conjugate, 97

description, 39, 143

Heisenberg uncertainty principle, 143

ket vectors, 39

laser oscillators, see Laser oscillators

lasers emitting, 144

linear operations, 100–101

Mach–Zehnder interferometer, 99, 143

macroscopic phenomena, 42

monochromatic, 143

multiple-beam interferometer, 101

N-slit interference, 144

photon propagation, 39, 40

probability amplitude, 39–42, 97–98

Pryce–Ward probability amplitude, 101

quantum mechanics principles, 39

Sagnac interferometer, 101

Schrödinger’s equation, 184–185

subcomponents, 144

visibility, 144

Dirac quantum optics

base states, 43

bra–ket vectors, 43

coherent and semicoherent interferograms, 56–58

Dirac notation, 39–42

Hilbert space, 43

interference equation, see Interference

interferometric equation, see Interferometric equation

polarization, interference and diffraction, 59–60

Dispersive laser oscillators, 79

Double-longitudinal mode (DLM) emission

definition, 135–136

mode beating, 133

and SLM, 133

Double-pass generalized multiple-prism dispersion

angle prism, 85

Brewster angle, 85

grating dispersion, 85

mirror system, 85

narrow-linewidth tunable lasers, 86

prismatic contribution, 85

return pass, 84–85

three-prism beam expander design, 84

tunable laser oscillators, 84

zero-dispersion, 86–88

Double-prism pulse compressor, 93–94

Dye lasers

continuous wave, 344–345

divisions, 342

pulsed, 343–344

E

Einstein, Podolsky and Rosen (EPR) paradox

Bohm polarization projection, 327

eigenfunction, 326

Eisenberg’s uncertainty principle, 332–333

relative probability, 326

WS experiment, 275

Ekert approach, 300

Electrically excited gas lasers

chemical recombination, 106, 107

CW metal ion lasers, 105

Duffendack reactions, 105

electrons ionize helium atoms, 106

He–CdI₂, 106

He–Zn laser, 105

He–ZnX₂ systems, 106

hollow-cathode rare-gas metal-vapor lasers, 107

Penning ionization, 106

rare-gas metal-vapor laser discharge, 105, 106

transition cross sections, 108

transmission line excitation circuit, 105, 106

Electrically excited semiconductor lasers

conduction and valence bands, 112, 113

description, 112

electrons, 112–113

quantum cascade laser (QCL), 112, 113

simple excitation circuit, 112

Entangled polarizations

Hamiltonian approach, 265–269

interferometric approach, 269–270

Pryce–Ward experimental arrangement, 274

PWS probability, see Pryce–Ward–Snyder (PWS) probability

Wu–Shaknov experiment, 274–275

EPR paradox, see Einstein, Podolsky and Rosen (EPR) paradox

F

FELs, see Free electron laser (FELs)

Feynman approximation

He–Ne laser illumination, 20, 21

two-slit experiment, 19–20

The Feynman Lectures on Physics, 4–5

Feynman path integrals

description, 197

historical perspective, 197

Lagrangian, 197–198

in optics, 203–205

principle, 197

quantum link, 199–200

S₁ and S₂ paths, 198

slit and uncertainty principle, 200–203

two-photon absorption process, 205

Four-prism pulse compressor, 94

Free electron laser (FELs)

description, 348–349

emission, 349

Frequency-selective resonators, 359

G

Gas lasers

continuous wave, 341–342

pulsed atomic metal vapor lasers, 341

pulsed molecular, 339–340

Generalized diffraction

far field, 72

geometrical expressions, 70, 71

grating equation, 71–72

N-slit plane, 67

phase differences, 70

Generalized multiple-prism dispersion

angular dispersion, 79

Brewster’s angle, 83

Dirac quantum principles, 79

dispersive laser oscillators, 79

double-pass, 84–88

identical apex angle, 83

and laser pulse compression, see Laser pulse compression

multiple-return-pass, 88–90

optics and quantum optics applications, 79–80

orthogonal beam, 82, 83

positive/negative refraction, 80, 82

sequences, 80, 81

single-pass dispersion equation, 80, 82

spectrophotometers and wavelength meters, 79

Generalized uncertainty principle, 25–27

Grazing-incidence grating (GIG), 360, 362

H

Hamiltonian approach, entangled polarizations

photons, different polarizations, 267–268

probability amplitude, 266–268

two-state system, 265, 266

Hanbury Brown–Twiss interferometer

conventional Fourier techniques, 146

Feynman Lectures in Physics, 145

“intensity interferometer”, 144–145

N-slit interferometric equation, 145–146

Heisenberg equation of motion, 218

Heisenberg uncertainty principle

coherence time, 28

description, 17

interferometric identity, 27

optimized multiple-prism grating solid-state organic dye laser, 28–29

Heuristic explicit approach

advantages, 182

classical kinetic energy, 182–183

classical wave equation, 184

de Broglie’s expresssion, 183

Planck’s quantum energy, 183

time and displacement derivatives, 183

Hybrid multiple-prism preexpanded near-grazing-incidence (HMPGI), 360, 362

I

Interference

diffraction orders, 63, 64

double-slit, 46

Feynman approach, 43

interferogram, 64–66

intra-interferometric distance, 63

near field diffraction distribution, 67

optics, 64

quadruple-slit, 46

quintuple-slit, 47

triple-slit, 46

Interferograms

coherent and semicoherent, see Coherent and semicoherent interferograms

intra-interferometric path, 50

measurement, 51–53

Interferometric approach

double-slit experiment, 269

probability amplitudes, 270

two-photon polarization entanglement geometry, 269, 270

Interferometric approximation, 21–23

Interferometric characters

beam splitter (BS), 168, 170–171

catastrophic collapse, 167, 169

description, 163

entanglement, 168, 169

homogeneous laboratory air, 172, 173–174

interferograms calculation, 166, 167–168

probability amplitude, 169

secure free-space optical communications, 166

Interferometric computer

Boolean algebra program, 282

computational time, mainframe universal computer, 282, 283

description, 283

input information, universal computer program, 282

interferograms, 280

NSLI, 280

Interferometric equation

architecture, 43–44

2D depiction, 58–59

1D generalized, 45–46

3D transmission grating, 59

laser cavity equation, 138–140

N-slit laser, see N-slit laser interferometer (NSLI)

probability amplitudes, 44–45

propagation probability amplitude, 45

Interferometric irreversible measurements

1D N-slit interferometric distribution, 308

irreversible, 309, 310

macroscopic, 309

probability amplitudes, 309

quantum probability, 309

single-photon propagation, 308

Interpretational issues, quantum mechanics

Bell’s inequalities, 327–330

Copenhagen interpretation, 336

and EPR paradox, see Einstein, Podolsky and Rosen (EPR) paradox

pragmatic perspective, 330–332

probabilities and probability amplitudes, 334–336

van Kampen’s quantum theorems, 333–334

Intuitive approach

beam divergence, 137

description, 136

gain medium, 137

multiple-prism grating configuration, 136–137

narrow-linewidth emission, 137

resonant emission, 138

unfolded optical path, 136

J

Jones calculus

circular polarization, 235

definition, 235

generalized rotation matrix, birefringent rotators, 237

linearly polarized light, 236–237

linear polarization, 235

polarization alternatives, 235, 236

polarized laser beam, 237

quarter-wave plate, 237

L

Laser emission

description, 113

dye lasers, see Dye

lasers and FELs, see Free electron laser (FELs)

gain media, 113

gas lasers, 339–342

long-pulse approximation laser pump intensity, 120

time derivatives vanish, 118

triplet-level quenchers, 119

multiple-level system, 115–118

semiconductor lasers, 348

solid-state lasers, 345–348

two-level molecular system, 113–115

Laser excitation

application, 105

chemical recombination, 106, 107

coherent radiation, 103

CW metal ion lasers, 105

Duffendack reactions, 105

electrically excited semiconductor lasers, see Electrically excited semiconductor lasers

electrons ionize helium atoms, 106

emission, see Laser emission

forced oscillator (FO), 104

He–CdI₂, 106

Heisenberg uncertainty principle, 103

He–Zn laser, 105

He–ZnX₂ systems, 106

high-power broadband tunable lasers, 104

hollow-cathode rare-gas metal-vapor lasers, 107

laser optics, 105

light amplification, 103

MOFO system, 104

MOPA chains, 104

optically pumped gas and liquid lasers, see Optically pumped gas and liquid lasers

optically pumped solid-state lasers, see Optically pumped solid-state lasers

optical resonator, 104

Penning ionization, 106

radio oscillator, 104

rare-gas metal-vapor laser discharge, 105, 106

spatial and spectral coherence, 103

transition cross sections, 108

transition probabilities and cross sections, see Quantum transition probabilities and cross sections

transmission line excitation circuit, 105, 106

Laser oscillators

broadband emission, 129

Dirac notation approach, 127

HMPGI, 128

interferometric equation, 138–140

intuitive approach, see Intuitive approach

longitudinal-mode emission, see Longitudinal-mode emission

longitudinal modes, 129

multiple-return-pass beam divergence, 127

optimized multiple-prism grating solid-state, 127, 128, 140

single transverse electromagnetic mode, 129

spatial emission, 129

transverse-mode structure, see Transverse-mode structure

Laser pulse compression

Brewster angle, 92

cavity linewidth equation, 91

double-prism pulse compressor, 93–94

four-prism pulse compressor, 94

intracavity dispersion, 91–92

single-prism pulse compressor, 93

Laser-pumped dye lasers

flashlamp-pumped, 343, 344

high-power, 343

narrow-linewidth liquid dye lasers, 343

narrow-linewidth solid-state organic dye-laser oscillators, 344

Linear polarization

generalized rotation matrix, 252

Jones calculus, 251

polarization configuration, 254

probability amplitude, 253, 254

rotation relations, 251

transformation identities, 253

transmission probability, 254

Longitudinal-mode emission

approximation and non-Gaussian temporal representation, 134

complex and chaotic, 133

and DLM, see Double-longitudinal mode (DLM) emission

Fabry–Perot interferogram, 135

longitudinal-mode spacing (δn), 132

mode beating, 133

nanosecond regime, 134

narrower cavity linewidth, 133

near-Gaussian temporal pulse, 135

and SLM, see Single-longitudinal mode (SLM) emission

square-law temporal detector, 134

temporal pulse, interference, 134

M

Mach–Zehnder interferometer, 99, 148–150, 298

Macroscopic interferometric experiment, 7

“Master equations”, 226

Master oscillator (MO), 104

Matrix algebra

determinants, 213, 214

inverse matrix, 213

multiplication, 211–212

unitary matrices, 212

2 × 2 matrix, 211, 213

3 × 3 matrix, 213

Matrix mechanics

commutation rule, 207

density matrix, 222–226

matrix algebra, 211–214

operators, see Quantum operators

Pauli matrices, see Pauli matrices

vector algebra, 207–211

Maxwell equations

coexistence, electric and magnetic field, 230

expression, velocity of propagation, 231

Gaussian systems of units, 230, 231, 249

rationalized metric system, 229, 231

Michelson interferometer, 150–151

Microelectromechanical system (MEMS)-driven miniature laser cavities, 33

MO, see Master oscillator (MO)

Multiple-beam interferometers Airy formula and function, 155

effective finesse, 155

Fabry–Perot etalons, 152, 153, 155

internal reflection geometry, 153

intracavity etalon, 152

N-slits interferometer, 151–152

probability amplitudes, 154

reflective finesse, 156

single-longitudinal-mode oscillation, 155, 156

Multiple-prism beam expander (MPBE), 50

Multiple-prism dispersion series, 377–378

Multiple-prism grating/mirror assembly

beam compression, 90

beam divergence, 89

diffracted back/reflected back, 88

dispersive laser oscillator, 88–89

narrow-linewidth high-power dispersive dye-laser oscillators, 90

unfolded depiction, 88

N

Narrow-linewidth oscillators, 360–363

Near-field diffraction distribution, 54, 55

Nondemolition measurements, 310–311

Normalized density matrix, 224

NSLI, see N-slit laser interferometer (NSLI)

N-slit interferometric calculations, 389–392, 393–395

N-slit laser interferometer (NSLI)

beam profile, 50

cascade interferometric technique, 54, 55

characterization, 54

cryptographic diagram, 163, 164

description, 50

Gaussian beam, 51

interferogram measurement, 48, 51–53

interferometric computer, 280–283

intra-interferometric optical path, 164

MPBE, 50

near-field diffraction distribution, 54, 55

optical communications, 163, 165–166

phase difference, 47–48

probability amplitudes, 172

single-longitudinalmode laser, 50

symmetry deterioration, 54

transmission grating, 47, 48

wavelength meter, see Wavelength meter, NSLI

Young’s interference experiment, 51

O

OPO, see Optical parametric oscillator (OPO)

Optically pumped gas and liquid lasers B³Π⁺_ou–X¹Σ⁺_g electronic system, 108

continuous tunability, 108

coumarin 545 T laser dye, 108, 109

dye lasers, 108

laser-pumped molecular iodine dimer laser, 108

narrow-linewidth tunable dye-laser oscillator, 109, 110

optical excitation, 108

Optically pumped solid-state lasers diode-pumped Nd:YAG laser, 110, 111

fiber lasers, 110

ruby laser, 110, 111

transition cross sections, 112

tunable Ti-sapphire laser, 110

Optical parametric oscillator (OPO), 347–348

Optical quantities, 398

Optics, uncertainty principle

beam divergence, 29–32

cavity linewidth equation, 32–33

sub-microcavities, 35

tuning laser microcavities, 33–35

P

Pair theory, 270–271, 275

Pauli matrices

conjugate transpose, 220

and density matrix, 260–261

Hermitian property, 221

properties, 220

and quantum logic, 288–289

spin one-half particle, 219, 221–222

time-dependent equation, two-state system, 219

PBS, see Polarizer beam splitter (PBS)

Physical constants, 397

Planck’s quantum energy equation energy distribution, light emission, 13

and wave optics, 14–15

Poincaré’s space, 387–388

Polarization rotators

birefringent, 245–246

broadband prismatic, 246–249

double Fresnel rhomb, 244, 245

Polarizer beam splitter (PBS), 301

Polarizing prisms

attenuation, laser beam intensity, 243–244

double-refraction polarizers, 240–243

induced polarization, double-prism beam expander, 238–240

transmission efficiency, multiple-prism arrays, 238

The Principles of Quantum Mechanics, 3–4

Pryce–Ward–Snyder (PWS) probability

amplitude, 273–274

entanglement amplitude, 270–273

horizontal and vertical polarization, 299

Public key cryptography, 293, 294

Pulsed atomic metal vapor lasers, 341

Pulsed molecular gas lasers

narrow-linewidth tunable CO₂ lasers, 340

tunable narrow-linewidth excimer lasers, 340

ultraviolet and visible, 339, 340

Q

Quantum cascade laser (QCL), 112, 113

Quantum computing

classical logic gates, 283–286

description, 279

interferometric computer, 280–283

quantum computer, 279–280

quantum logic, 287–290

qubits, 280, 286–287

transistor-based computers, 279

Quantum cryptography

BBA, 295–298

polarization entanglement approach, 298–301

Quantum gates, 289–290

Quantum logic

2 × 2 matrix, 287

and Pauli matrices, 288–289

quantum gates, 289–290

Quantum measurements

Dirac and von Neumann approaches, 307

error, 307

interferometric irreversible, 308–310

nondemolition, 310–311

soft intersection, see Soft intersection, interferometric characters

soft polarization, 311–312

Stern–Gerlach measurements, 307

Quantum Mechanical Computers, 279

Quantum mechanics

bra–ket notation, 2

developments, quantum era, 3

energy distribution, light sources, 1

interpretational issues, see Interpretational issues, quantum mechanics

lightquanta, 2

photoelectric effect, 2

photon, 5–7

quantum optics, 7–8

Quantum Mechanics and Path Integrals, 19

Quantum operators

commutation rule, 217

energy operator, 218

Heisenberg equation of motion, 218

momentum operator, 215–217

position operator, 214–215

Quantum optics, 7–8

Quantum physics, see Quantum mechanics

Quantum polarization

density matrix notation, 258–262

linear, see Linear polarization

as two-state system, 255–258

Quantum teleportation, see Teleportation

Quantum transition probabilities and cross sections

complex conjugate, 122

description, 119

Dirac notation, 119–120

electric field, 121

Feynman notation, 120

Franck–Condon factor, 123

Hamiltonian matrix elements, 121

intensity, 123–124

long-pulse approximation, 124

perturbation term, 121

stimulated emission probability, 122–123

vibrational-rotational, 123

Qubits, 280, 286–287

R

Ramsey interferometer, 158–159

Raw quantum transmission, 296

Ray transfer matrices

ABCD matrices, see ABCD matrices

description, 367

spatially coherent beams, 367

Reflection

domain, 75

infinitesimal distance, N-slit array, 74–75

interferometer, 74

law, 75

Refraction

focusing, 74

positive and negative, 72–73

S

Sagnac interferometer

beam splitter, 146–147

Dirac notation, probability amplitude, 147

triangular configuration, 148

Schrödinger’s equation

atomic and molecular physics, 179

description, 179

Dirac notation, 184–185

Hamiltonian principle, 180, 181

heuristic explicit approach, see Heuristic explicit approach

hydrogen equation, 192–193

kinetic energy, 179

Laplacian operator, 181

ordinary wave equation, 180

“phase” velocity, 180

physics perspective, 182

Planck’s quantum energy equation, 180

stationary solutions, 194–195

time-independent, see Time-independent Schrödinger’s equation

wave function, 181

Secure interferometric communications advantages, 177

clear-air turbulence, 175–176

cryptographic diagram, 163, 164

homogeneous laboratory air, 172

interception, 176–177

interferometric character, see Interferometric characters

macroscopic optical interception, 177

and NSLI, see N-slit laser interferometer (NSLI)

optical communications, 163

practical perspective, 177

theory, 164–165

Semiconductor lasers

external cavity tunable, 349

MEMS^a tunable, 350

power performance, 349

tunable external cavity quantum cascade lasers, 350

ultrashort-pulse external cavity, 350

wavelength coverage, 348

Single-longitudinal mode (SLM) emission and DLM, 133

Fabry–Perot interferometric rings, 135

narrower cavity linewidth, 132–133

near-Gaussian temporal pulse, 135

single-transverse-mode beam, 132

Single-prism pulse compressor, 93

Snell’s law, 73, 74

Soft intersection, interferometric characters

calculated control interferogram, 316, 318

cascade approach, 316

intensity profile, 315–317

interferometric distribution, 312–314

intra-interferometric distances, silk fiber insertion, 315

N-slit interferometer, 312, 313, 323

probing, 320–322

spider silk web fiber, optical path, 314

superposition, diffraction signal, 318, 319

Soft polarization measurements

Gaussian beams, 311

two-beam interference pattern, 312

Solid-state lasers

diode-laser-pumped fiber lasers, 347

ionic, 345–346

and OPO, 347–348

transition metal, 346–347

Stokes parameters, 259–261

Symmetric key algorithm, 293

T

Teleportation

entanglement, two linearly polarized photons, 301–302

methodology, 304

recovery transformation, 304

three-particle state, 303

Time-independent Schrödinger’s equation

Feynman approach, 186

quantized energy levels, 186–187

quantum cascade lasers, 190–191

quantum dots, 191

quantum wells, 188–190

semiconductor emission, 187–188

semiconductor physics and lasers, 186

Transverse-mode structure

cross section, diffraction distribution, 130, 131

Fresnel number, 130, 131

interferometric equation, 129–130

intracavity, 129

laser cavity, 129

mirror-mirror laser cavity, 129, 130

narrow-linewidth tunable solid-state dye laser, 131, 132

single-pass transverse-mode structure, 129

TEM₀₀ emission, 131, 132

Trigonometric identities, 383–384

Tuning laser microcavities, 33–35

Two-beam interferometers

Mach–Zehnder interferometer, 148–150

Michelson interferometer, 150–151

Sagnac interferometer, 146–148

Two-state system polarization

circular polarization, 256–258

diagonal polarization, 255–256

U

Uncertainty principle

Feynman approximation, 19–21

generalized, 25–27

Heisenberg uncertainty principle, 17–18, 27–29

interferometric approximation, 21–23

minimum, 23–24

optics, see Optics, uncertainty principle

wave-particle duality, 18–19

Universal computer, 279, 280, 282, 283

Unstable resonators, 359–360

V

van Kampen’s quantum theorems, 333–334

Vector algebra

cross product, 210

derivative operators, 210

dot product, 209

length, 209

multiplication, 208

subtraction, 208, 209

sum, 207, 208

three dimensions, 207, 208

W

Wavelength meter, NSLI

interferograms calculation, 157–158

phase difference, 156–157

signals and profiles, 156

Wave optics, 14–15

Wave–particle duality, 18–19

Wollaston prism (WP), 297, 300

Wu–Shaknov experiment

description, 274–275

relevance, 275

Y

Young’s interference experiment, 51

Z

Zero-dispersion multiple-prism beam expander designs

advantages, 86

description, 87

double-prism expander, 87–88

intracavity beam expansion, 88

laser tuning characteristics, 86

quasi achromatic, 87