Crystal-Field Engineering of Solid-State Laser Materials

by Brian Henderson , Ralph H. Bartram

• ISBN13: 9780521593496
• ISBN10: 0521593492
• Format: Hardcover
• Copyright: 2000-07-17
• Publisher: Cambridge University Press

Summary

This book examines the underlying science and design of laser materials. It emphasizes the principles of crystal-field engineering and discusses the basic physical concepts that determine laser gain and nonlinear frequency conversion in optical crystals. Henderson and Bartram develop the predictive capabilities of crystal-field engineering to show how modification of the symmetry and composition of optical centers can improve laser performance. They also discuss applications of the principles of crystal-field engineering to a variety of optical crystals in relation to the performances of laser devices. This book will be of considerable interest to physical, chemical and material scientists and to engineers involved in the science and technology of solid state lasers.

Table of Contents

Preface	xiii
An introduction to lasers	1	(29)
Historical notes	1	(3)
Principles of lasers	4	(5)
Stimulated and spontaneous radiative transitions	4	(4)
Light amplification by stimulated emission	8	(1)
Major loss mechanisms	9	(1)
Types of solid state laser	9	(10)
Three- and four-level lasers	9	(3)
Fixed wavelength lasers	12	(2)
Wavelength tunable solid state lasers	14	(4)
Laser ions in glasses and waveguides	18	(1)
Pumping solid state lasers	19	(1)
Gas lasers	19	(1)
Dye lasers	19	(1)
Semiconductor diode laser pumping	20	(1)
Laser output	20	(6)
Output coupling and tuning	20	(1)
Threshold and slope efficiency	21	(2)
Continuous wave (CW) and pulsed laser output	23	(2)
Nonlinear frequency conversion	25	(1)
Motivation, scope and organization of the book	26	(4)
Symmetry considerations	30	(31)
Introduction	30	(1)
Principles of group theory	31	(7)
Abstract groups	31	(1)
Symmetry groups	32	(1)
Matrix representations	33	(2)
Symmetry and quantum mechanics	35	(2)
Coupled systems	37	(1)
Crystal symmetry	38	(6)
Translation groups	38	(1)
Crystallographic point groups	39	(2)
Space groups	41	(3)
Lie groups	44	(7)
Lie algebras	44	(1)
The rotation group	45	(2)
SU(2)	47	(1)
Application to coupled systems	48	(1)
Wigner-Eckart theorem	49	(1)
Racah coefficients	50	(1)
Some additional applications of group theory	51	(10)
Evaluation of matrix elements	51	(1)
Projection operators	51	(1)
Subduced representations	52	(3)
Time-reversal invariance	55	(1)
Crystal-field levels	56	(2)
Pauli principle	58	(1)
Selected tables for symmetry groups	58	(3)
Optical crystals: their structures, colours and growth	61	(32)
Natural minerals and gemstones	61	(2)
Synthetic and imitation gemstones	63	(1)
Laser and other optical materials	64	(13)
Octahedral and distorted octahedral structures	66	(4)
Tetrahedral structures	70	(1)
The garnet structure	71	(2)
Apatites and related crystals	73	(1)
Nonlinear optical crystals	73	(1)
Laser glasses	74	(3)
Growth of optical crystals	77	(13)
Growth by directional solidification	79	(2)
Crystal pulling techniques	81	(5)
Other melt growth techniques	86	(1)
Hydrothermal growth	87	(2)
Growth from high temperature solutions (HTSG)	89	(1)
General materials considerations	90	(3)
Energy levels of ions in crystals	93	(41)
The Hamiltonian	93	(1)
Assumptions of crystal-field theory	93	(1)
Hierarchy of perturbations	94	(1)
Free-ion electronic structure	94	(8)
Central-field approximation	94	(2)
Electrostatic interaction	96	(5)
Spin-orbit interaction	101	(1)
Crystal potential	102	(5)
Point-ion crystal-potential expansion	102	(1)
Operator equivalents	103	(2)
Explicit formulas for crystal-potential matrix elements	105	(1)
Dominant symmetry	106	(1)
Transition metals	107	(16)
Free-ion energy levels	107	(2)
One-electron configuration	109	(4)
Intermediate-field approximation	113	(2)
Strong-field approximation	115	(2)
Tanabe-Sugano theory	117	(1)
Spin-orbit interaction	118	(4)
Lower symmetry fields	122	(1)
Empirical parameters	122	(1)
Rare earths	123	(3)
Free-ion energy levels	123	(1)
Crystal-field splitting of fine-structure levels	124	(2)
Colour centres	126	(8)
F centre	126	(3)
Laser-active colour centres	129	(1)
Perturbed F centres	129	(1)
F2+ centre	130	(1)
Tl0(1) centre	131	(3)
Spectra of ions in crystals	134	(43)
Theory of optical transitions	134	(12)
Free-ion transition probabilities	134	(2)
Free-ion selection rules	136	(3)
Crystal-field selection rules	139	(1)
Electric-dipole transitions	140	(2)
Spontaneous emission	142	(4)
Electron-lattice coupling	146	(10)
Born-Oppenheimer approximation	146	(1)
Harmonic approximation	146	(1)
Electric-dipole transitions between Born-Oppenheimer states	147	(1)
Configuration-coordinate diagram	148	(2)
Linear coupling to many modes	150	(1)
Static Jahn-Teller effect	151	(3)
Dynamic Jahn-Teller effect	154	(2)
Spectral intensities	156	(3)
Electric-dipole-allowed transitions	156	(1)
Crystal-field spectra	156	(1)
Odd modes of vibration	157	(1)
Judd-Ofelt theory	158	(1)
Examples of crystal-field spectra	159	(9)
Octahedrally-coordinated Cr3+	159	(5)
Tetrahedrally-coordinated Cr4+	164	(2)
Octahedrally-coordinated Ti3+	166	(2)
Approximate line-shape functions	168	(7)
Alternative energy units	168	(1)
Typical Huang-Rhys factors	169	(1)
Strong-coupling limit	170	(1)
Approximations for linear coupling to many modes	171	(1)
Lattice Green's function method for linear coupling to many modes	172	(2)
Approximations for quadratic and anharmonic coupling	174	(1)
Zero-phonon line	174	(1)
Nonlinear susceptibilities	175	(2)
Radiationless transitions	177	(17)
Physical principles	177	(2)
Prepared state	177	(1)
Radiationless transition rate	178	(1)
Static processes	179	(4)
Mott theory	179	(1)
Adiabatic-coupling scheme	180	(1)
Static-coupling scheme	181	(1)
Linear coupling	182	(1)
Quadratic and anharmonic coupling	183	(1)
Dynamic processes	183	(5)
Landau-Zener theory	183	(1)
Seitz criterion	184	(1)
Dexter-Klick-Russell criterion	185	(2)
Extended crossing	187	(1)
Coherent state	187	(1)
Manifestations of radiationless transitions	188	(6)
Thermal activation	188	(2)
Transition-metal and rare-earth impurities	190	(2)
Colour centres	192	(1)
Recombination-enhanced defect reactions	193	(1)
Energy transfer and excited state absorption	194	(28)
Microscopic theory of donor-acceptor energy transfer	195	(4)
Macroscopic theory of donor-acceptor energy transfer	199	(5)
No donor-donor transfer	199	(1)
Influence of donor-donor energy transfer	200	(4)
Excited state absorption	204	(4)
Experimental studies of excited state processes	208	(14)
Quenching of luminescence and laser efficiency	209	(2)
High dopant concentrations	211	(2)
Energy transfer and sensitization	213	(4)
Upconversion processes	217	(5)
Covalency	222	(31)
Ligand-field theory	222	(5)
Limitations of crystal-field theory	222	(1)
Molecular orbitals	222	(2)
Variational principle	224	(2)
Valence bonds	226	(1)
Charge transfer model	227	(1)
Hartree-Fock method	227	(5)
Hamiltonian	227	(2)
Hartree-Fock approximation	229	(2)
Basis functions	231	(1)
Open shells	231	(1)
Correlation	232	(5)
Correlation energy	232	(1)
Configuration interaction	233	(1)
Perturbation theory	234	(1)
Excited states	235	(2)
Additional approximations	237	(5)
Effective core potentials	237	(2)
Local exchange approximation	239	(1)
Approximate SCF semi-empirical methods	240	(1)
Extreme semi-empirical methods	241	(1)
Embedded clusters	242	(3)
Embedding potentials	242	(1)
Lattice relaxation	243	(2)
Applications	245	(8)
Cr3+ in halide elpasolites	245	(2)
The Tl0(1) centre and its analogues	247	(1)
Ti3+ in distorted octahedral coordination	248	(3)
Odd-parity distortions of (CrF6)3-	251	(2)
Engineering the crystal field	253	(48)
Principles and objectives	253	(2)
Manipulating the unit cell	253	(1)
Composition of the unit cell	254	(1)
The positions and shapes of optical transitions	255	(15)
F-type centres in the alkali halides	257	(4)
Tl0(1)- centre in the alkali halides	261	(1)
Transition-metal ions	261	(4)
Rare-earth ions	265	(1)
Optical line shape and laser tuning	266	(4)
Other aspects of transition-metal ion spectroscopy	270	(9)
Mixed vibronic states and avoided level crossings	270	(5)
Dominant symmetry and low symmetry distortions	275	(4)
Laser efficiency and threshold	279	(5)
Strength of optical transitions	279	(2)
Quenching of luminescence and laser efficiency	281	(1)
Excited state absorption	282	(2)
Energy transfer processes	284	(3)
Empirical rules for transition-metal and rare-earth ions	287	(7)
Unit cell dimensions	287	(1)
Spectrochemical series	288	(1)
Nephelauxetic effect	289	(1)
Crystal-field stabilization energies	289	(4)
The σe&tao;R product rule	293	(1)
All-solid-state lasers	294	(2)
Optical nonlinearities	296	(2)
Other considerations	298	(3)
The crystal field engineered	301	(71)
Tunable and solid state lasers	302	(1)
Colour centre lasers	303	(3)
Transition-metal ion lasers	306	(30)
Alexandrite laser	307	(4)
Cr3+ : colquiriite lasers	311	(7)
Other Cr3+ -activated lasers	318	(8)
Ti3+-activated lasers	326	(2)
Lasers based on Co2+ ions	328	(2)
Lasers based on (3d)2 and (3d)8 configuration ions	330	(6)
Mid-infrared laser transitions of Cr2+-doped chalcogenides	336	(1)
Tunable rare-earth ion lasers	336	(6)
Fixed-wavelength rare-earth ion lasers	342	(9)
Spectroscopy and laser transitions of Pr3+ and Tm3+	343	(3)
Nd3+ and Er3+ -activated lasers	346	(5)
Other rare-earth ions	351	(1)
Energy transfer and upconversion lasers	351	(6)
Glass fibre lasers	357	(6)
All-solid-state lasers (ASSLs)	363	(7)
Fixed wavelength LD-pumped solid state lasers	363	(2)
Tunable solid state lasers pumped by laser diodes	365	(1)
Opical nonlinearities and diode-pumped lasers	366	(3)
Microchip lasers	369	(1)
Concluding remarks	370	(2)
References	372	(21)
Index	393