##### Document Text Contents

Page 1

Light Scattering in

Solids

Page 2

Proceedings of the Second Joint USA-USSR Symposium

Light Scattering in

Solids

Edited by

Joseph L. Birman and Herman Z. Cummins

Department of Physics

The City College of the City·University of New York

New York, New York

and

Karl K. Rebane

Institute of Physics

Academy of Sciences of the Estonian SSR

Tartu, Estonian SSR

PLENUM PRESS • NEW YORK AND LONDON

Page 262

K.K.REBANE

The conclusions of the theory are in reasonable agreement with

experiments (see an earlier review (19). HL of crystals was first

observed on a sample of KCl-N02 in (20). Afterwards, in the

laser-excited RSE of molecular anions all three components - OL,

HL and RRS are clearly demonstrated: on KI-Se2 by L. Rebane and

T. Haldre (21), on KCl-N02 by P. Saari (23,24). Recently full

RSE spectra were obtained and investigated in the case of mixed

(24) and pure molecular crystals (25); particularly, a rich RSE

spectrum in the strong exciton absorption region of anthracene

shows pecularities caused by polariton effects (26).

The HL studies have provided information on different energy

relaxation pathways and the corresponding characteristic times of

picosecond duration (see review papers (19,25». HL data combined

with the studies of homogeneous linewidths enable to get estimates

for the transverse relaxation times to be obtained as well (27).

3. TIME-DEPENDENT (TRANSIENT) SPECTRA OF RSE

There is quite a number of general problems about

time-dependent spectra such as mathematical definitions of what is

a time-dependent spectrum, and how to take into account the role

of the spectral apparatus when real physical spectra are concerned

(28-31». Recent success in pico- and subpicosecond pulse

experiments requires a corresponding development of theory, and

recently a number of papers on time-dependent RSE spectra of

luminescence centers in crystals has been published (30-33).

Naturally, time-dependent spectra display very clearly how all

three RSE components - scattered light, HL and OL - come into

being after a short-pulse excitation, how the intensities and

shapes of the lines of luminescence develop with the time of

collecting photons and how they depend on the choice of the

collection time interval. The models used in (30,32,34) and

especially in (35-37) by V. Hizhnyakov and I. Rebane are quite

complete for a proper discussion of the problem (see also (38,39».

I shall review some recent results of the theory mentioned

above. The details of the models under study and the

corresponding formulae may be found in (32,34,35,37). Let us give

here the list of the notations and the main features of the models.

The emission center is characterized by a usual potential

energy diagram with two parabolic curves of different curvatures

representing the local vibration in ground and excited electronic

states (Fig. 1). As we know, it is most important to take into

account the vibrational relaxation, without which we cannot get

the correct picture of RSE. Here it is supposed that the n-th

level of the oscillator decays exponentially with the

characteristic time Til ,n = Til ,lin = (Zr11n)-1 (model 1)

Page 263

RESONANT SECONDARY EMISSION BY IMPURITIES IN CRYSTALS 261

Q w"

Fig. 1. The diagram of the potential energy curves and the scheme

of the vibronic resonant secondary emissions lines of an emission

center in a crystal. The transitions and lines of ordinary

luminescence (broad lines), hot luminescence (narrow lines), and

scattered light (dashed lines) are shown. Because of the

different frequencies of vibration in the ground and excited

electronic states the luminescence lines corresponding to

different transitions are separated; owing to the excess of the

excitation energy x over the vibronic level the lines of

scattering are shifted from the luminescence ones (35,37).

Page 523

534

SiC:Ti

exciton bound to isoe1ectronic

trap in, 204

Six-photon process, 462

S~

order parameter, 369

Smectic A (S~) phase, 367

Smectic B (SmB) phase, 373

Smectic liquid crystals, 48

Soft mode, 334

Solvent electron, 417

Solvent induced shift and

broadening, 414

Spatial dispersion, 133

Specific heat ratio, 5

Spectral density of scattered

light, 333

Spectral width, 458

Spectrum

of x-magnons in COC03, 185

of y-magnons in COC03, 185

Spin cluster formation, 195

Spin diffusion, 190

no charge transport, 191

from transverse part of donor

spin exchange, 193

Spin flip cross sections

(2_g)2 rule, 201

Spin flip for free electron

and holes in SiC, 202

Spin flip Raman scattering, 189

Spin flip scattering, 199

with charge diffusion, 189

excitons in SiC, 199

Spin-orbit splitting in traps

in SiC, 205

Spin wave, 177

acoustic branch, 238

optic branch, 238

Spin-wave parameters

COC03, 180

FeB03, 180

Spin-wave relaxation, 181

Spin-wave therma1ization, 183

Spinodal line, 33

Stark shift of resonance

level, 460

Stimulated Raman scattering,

167

SUBJECT INDEX

Stokes/anti-Stokes asymmetry

in bulk spin wave

scattering, 210

Stokes/anti-Stokes correlation,

287

Structural phase transition

imperfect crystals, 331

pure crystals, 331

Structure disorder, 447

Structure factor, 52

Superconducting gap, 347

Super1attices, 308

Surface carrier

bulk phonon coupling, 301

Surface electromagnetic wave, 115

Surface enhanced Raman scattering

499, 504

wavelength dependence, 504

Surface fields

microscopic theory of, 513

Surface plasmon, 500, 504, 511

Surface plasmon damping, 507

Surface plasmon energy of Ag, 505

Surface polariton, 113, 120, 121,

490

scattering at phase-transitions,

126

wedge light diffraction, 124

Surface polariton dispersion, 113,

114

Surface Raman scattering, 483

matrix elements for, 507

Surface roughness, 126, 480

of metal, 483

and photon coupling, 505

Surface spin-wave

angular anisotropy, 209

dispersion of, 209

Surface waves, 119

Swelling of gels, 31

TI and T2 relaxation, 321

TaSe2 (2H)~ 34~

Tay10r-Couette flow, 24

Taylor vortex pattern, 16

Thermal conductivity above

A point, 8

Thermal diffusivity

E expansion, 9

Thermal radiation

odd moments, 290

Page 524

SUBJECT INDEX

Thermalized luminescence from

real states, 216

Thick films

critical behavior, 39

Three-photon scattering, 460

Three-wave Raman scattering

in diamond, 428

Tilted molecules, 53

Time resolved CARS

molecular crystals, 447

Time resolved Raman scattering,

403

Transient pulse propagation,

133

Transient reflection, 133

Transient reflectivity, 131

Transient in scattering and

luminescence, 321

Transient spectra, 260

oscillating structure, 264

Transverse collective resonance

of electrons, 491

Triangular lattice

melting, 49

Tunnel hot luminescence, 278

Turbulence, 15, 17, 20, 23

Two-magnon production by

photon, 183

Two-phonon processes, 363

Two-phonon resonant Brillouin

scattering, 148

A exciton in CdS, 154

Two-photon absorption in RbBr,

431

Two-photon Kirchoff law, 289

2,6-lutidine, 39

2 + 2' scattering, 150

Universality

turbulence, 25

Vapor deposition of molecules

on metals, 484

Velocity power spectrum, 18, 21

Vibrational relaxation, 260

Vibrational spectrum of

monolayer, 167

Vibrations

bending and stretching, 74

Vibrons, 448

Visual pigments, 391

S3S

Vortex pattern, 15

Vortices and disclination pairs,

51

Wurtzite, 150

X-ray scattering from SmA, 368

Zeeman splitting, 101

ZnTe:Na, 200

electron and hole spin

flip in, 200

Light Scattering in

Solids

Page 2

Proceedings of the Second Joint USA-USSR Symposium

Light Scattering in

Solids

Edited by

Joseph L. Birman and Herman Z. Cummins

Department of Physics

The City College of the City·University of New York

New York, New York

and

Karl K. Rebane

Institute of Physics

Academy of Sciences of the Estonian SSR

Tartu, Estonian SSR

PLENUM PRESS • NEW YORK AND LONDON

Page 262

K.K.REBANE

The conclusions of the theory are in reasonable agreement with

experiments (see an earlier review (19). HL of crystals was first

observed on a sample of KCl-N02 in (20). Afterwards, in the

laser-excited RSE of molecular anions all three components - OL,

HL and RRS are clearly demonstrated: on KI-Se2 by L. Rebane and

T. Haldre (21), on KCl-N02 by P. Saari (23,24). Recently full

RSE spectra were obtained and investigated in the case of mixed

(24) and pure molecular crystals (25); particularly, a rich RSE

spectrum in the strong exciton absorption region of anthracene

shows pecularities caused by polariton effects (26).

The HL studies have provided information on different energy

relaxation pathways and the corresponding characteristic times of

picosecond duration (see review papers (19,25». HL data combined

with the studies of homogeneous linewidths enable to get estimates

for the transverse relaxation times to be obtained as well (27).

3. TIME-DEPENDENT (TRANSIENT) SPECTRA OF RSE

There is quite a number of general problems about

time-dependent spectra such as mathematical definitions of what is

a time-dependent spectrum, and how to take into account the role

of the spectral apparatus when real physical spectra are concerned

(28-31». Recent success in pico- and subpicosecond pulse

experiments requires a corresponding development of theory, and

recently a number of papers on time-dependent RSE spectra of

luminescence centers in crystals has been published (30-33).

Naturally, time-dependent spectra display very clearly how all

three RSE components - scattered light, HL and OL - come into

being after a short-pulse excitation, how the intensities and

shapes of the lines of luminescence develop with the time of

collecting photons and how they depend on the choice of the

collection time interval. The models used in (30,32,34) and

especially in (35-37) by V. Hizhnyakov and I. Rebane are quite

complete for a proper discussion of the problem (see also (38,39».

I shall review some recent results of the theory mentioned

above. The details of the models under study and the

corresponding formulae may be found in (32,34,35,37). Let us give

here the list of the notations and the main features of the models.

The emission center is characterized by a usual potential

energy diagram with two parabolic curves of different curvatures

representing the local vibration in ground and excited electronic

states (Fig. 1). As we know, it is most important to take into

account the vibrational relaxation, without which we cannot get

the correct picture of RSE. Here it is supposed that the n-th

level of the oscillator decays exponentially with the

characteristic time Til ,n = Til ,lin = (Zr11n)-1 (model 1)

Page 263

RESONANT SECONDARY EMISSION BY IMPURITIES IN CRYSTALS 261

Q w"

Fig. 1. The diagram of the potential energy curves and the scheme

of the vibronic resonant secondary emissions lines of an emission

center in a crystal. The transitions and lines of ordinary

luminescence (broad lines), hot luminescence (narrow lines), and

scattered light (dashed lines) are shown. Because of the

different frequencies of vibration in the ground and excited

electronic states the luminescence lines corresponding to

different transitions are separated; owing to the excess of the

excitation energy x over the vibronic level the lines of

scattering are shifted from the luminescence ones (35,37).

Page 523

534

SiC:Ti

exciton bound to isoe1ectronic

trap in, 204

Six-photon process, 462

S~

order parameter, 369

Smectic A (S~) phase, 367

Smectic B (SmB) phase, 373

Smectic liquid crystals, 48

Soft mode, 334

Solvent electron, 417

Solvent induced shift and

broadening, 414

Spatial dispersion, 133

Specific heat ratio, 5

Spectral density of scattered

light, 333

Spectral width, 458

Spectrum

of x-magnons in COC03, 185

of y-magnons in COC03, 185

Spin cluster formation, 195

Spin diffusion, 190

no charge transport, 191

from transverse part of donor

spin exchange, 193

Spin flip cross sections

(2_g)2 rule, 201

Spin flip for free electron

and holes in SiC, 202

Spin flip Raman scattering, 189

Spin flip scattering, 199

with charge diffusion, 189

excitons in SiC, 199

Spin-orbit splitting in traps

in SiC, 205

Spin wave, 177

acoustic branch, 238

optic branch, 238

Spin-wave parameters

COC03, 180

FeB03, 180

Spin-wave relaxation, 181

Spin-wave therma1ization, 183

Spinodal line, 33

Stark shift of resonance

level, 460

Stimulated Raman scattering,

167

SUBJECT INDEX

Stokes/anti-Stokes asymmetry

in bulk spin wave

scattering, 210

Stokes/anti-Stokes correlation,

287

Structural phase transition

imperfect crystals, 331

pure crystals, 331

Structure disorder, 447

Structure factor, 52

Superconducting gap, 347

Super1attices, 308

Surface carrier

bulk phonon coupling, 301

Surface electromagnetic wave, 115

Surface enhanced Raman scattering

499, 504

wavelength dependence, 504

Surface fields

microscopic theory of, 513

Surface plasmon, 500, 504, 511

Surface plasmon damping, 507

Surface plasmon energy of Ag, 505

Surface polariton, 113, 120, 121,

490

scattering at phase-transitions,

126

wedge light diffraction, 124

Surface polariton dispersion, 113,

114

Surface Raman scattering, 483

matrix elements for, 507

Surface roughness, 126, 480

of metal, 483

and photon coupling, 505

Surface spin-wave

angular anisotropy, 209

dispersion of, 209

Surface waves, 119

Swelling of gels, 31

TI and T2 relaxation, 321

TaSe2 (2H)~ 34~

Tay10r-Couette flow, 24

Taylor vortex pattern, 16

Thermal conductivity above

A point, 8

Thermal diffusivity

E expansion, 9

Thermal radiation

odd moments, 290

Page 524

SUBJECT INDEX

Thermalized luminescence from

real states, 216

Thick films

critical behavior, 39

Three-photon scattering, 460

Three-wave Raman scattering

in diamond, 428

Tilted molecules, 53

Time resolved CARS

molecular crystals, 447

Time resolved Raman scattering,

403

Transient pulse propagation,

133

Transient reflection, 133

Transient reflectivity, 131

Transient in scattering and

luminescence, 321

Transient spectra, 260

oscillating structure, 264

Transverse collective resonance

of electrons, 491

Triangular lattice

melting, 49

Tunnel hot luminescence, 278

Turbulence, 15, 17, 20, 23

Two-magnon production by

photon, 183

Two-phonon processes, 363

Two-phonon resonant Brillouin

scattering, 148

A exciton in CdS, 154

Two-photon absorption in RbBr,

431

Two-photon Kirchoff law, 289

2,6-lutidine, 39

2 + 2' scattering, 150

Universality

turbulence, 25

Vapor deposition of molecules

on metals, 484

Velocity power spectrum, 18, 21

Vibrational relaxation, 260

Vibrational spectrum of

monolayer, 167

Vibrations

bending and stretching, 74

Vibrons, 448

Visual pigments, 391

S3S

Vortex pattern, 15

Vortices and disclination pairs,

51

Wurtzite, 150

X-ray scattering from SmA, 368

Zeeman splitting, 101

ZnTe:Na, 200

electron and hole spin

flip in, 200