Contents


Part 4 Solid-state lasers
4.1 Solid-state laser systems
R. Iffl3
ander ..........................................................

4.1.1 Solid-state laser systems.................................................. 3


4.1.1.1 Introduction............................................................ 3


4.1.1.2 Energy-level diagram and rate equations ................................... 3


4.1.1.2.1 Rate equations for a 4-level system ........................................ 4


4.1.1.3 Amplifiers.............................................................. 5


4.1.1.3.1 Stationary case for low intensities (J . Js)................................. 6


4.1.1.3.2 Stationary case (orT . t) and J = Js ..................................... 6


4.1.1.3.3 Pulse operation for short pulses (T . t) ................................... 7


4.1.1.4 Oscillator .............................................................. 8


4.1.1.4.1 Oscillator condition...................................................... 10


4.1.1.4.2 Output power........................................................... 10


4.1.1.4.3 Optimal reflection coefficient.............................................. 11


4.1.1.5 Influence of the temperature.............................................. 12


4.1.1.6 Oscillator in pulsed operation............................................. 14


4.1.1.6.1 Threshold .............................................................. 14


4.1.1.6.2 High pump power Pp . Pth .............................................. 14


4.1.1.6.3 Relaxation oscillation .................................................... 15


4.1.1.6.4 Spiking ................................................................ 16


4.1.1.6.5 Long-pulse regime ....................................................... 16


4.1.1.7 Q-switch operation ...................................................... 16


4.1.1.7.1 Single Q-switch pulse .................................................... 17


4.1.1.7.2 Periodical Q-switch for high pulse repetition rate (rt . 1) ................... 19


4.1.1.8 The 3-level system....................................................... 21


4.1.1.8.1 Stationary case with dN/dt=0 and dJ/dt=0.............................. 22


4.1.1.9 Efficiency and optimization............................................... 24


4.1.1.10 Stable resonators........................................................ 26


4.1.1.10.1 Eigenvalues for TEM-00 mode ............................................ 26


4.1.1.10.2 Introducing a virtual reference plane....................................... 28


4.1.1.10.3 Beam parameter product................................................. 29


4.1.1.11 Thermal effects ......................................................... 29


4.1.1.11.1 Steady-state temperature profile........................................... 30


4.1.1.11.2 Thermal load ........................................................... 31


4.1.1.11.3 Thermal lensing......................................................... 33


4.1.1.11.4 Experimental determination of the refracting power.......................... 34


4.1.1.12 Solid-state laser concepts................................................. 35


4.1.1.12.1 Multicavity resonators ................................................... 35


4.1.1.12.2 Two external mirrors and two rods ........................................ 35


4.1.1.12.3 Multiple cavities with flat mirrors ......................................... 36


4.1.1.12.4 Thermally invariant resonators............................................ 37


4.1.1.13 Excitation by diodes..................................................... 38


4.1.1.13.1 Rod ................................................................... 38


4.1.1.13.1.1 Longitudinally pumped rod............................................... 38


4.1.1.13.1.2 Transversally pumped rod ................................................ 39


4.1.1.13.2 Disk ................................................................... 40


4.1.1.13.2.1 Longitudinal disk........................................................ 40


4.1.1.13.2.2 Transversally pumped disk ............................................... 40


4.1.1.13.3 Fiber .................................................................. 40


4.1.1.13.3.1 Longitudinally pumped fiber.............................................. 40


4.1.1.13.3.2 Transversally pumped fiber ............................................... 41


4.1.1.13.4 Slab ................................................................... 41


4.1.1.13.4.1 Transversally pumped slab ............................................... 42


4.1.1.13.4.2 Longitudinal slab........................................................ 42


4.1.1.13.5 Diode-pumped solid-state lasers in research and development ................. 42


4.1.1.14 Solid-state laser products................................................. 43


4.1.2 Laser material parameter................................................. 45


4.1.2.1 Parameter specification .................................................. 45


4.1.2.1.1 Laser data.............................................................. 45


4.1.2.1.2 Optical properties ....................................................... 46


4.1.2.1.3 Thermal parameters ..................................................... 48


4.1.2.1.4 Mechanical properties.................................................... 49


4.1.2.1.5 Crystal properties ....................................................... 49


4.1.2.1.6 Derived data............................................................ 52


4.1.2.1.7 Supplier data ........................................................... 53


4.1.2.1.8 Measured values......................................................... 53


4.1.2.2 Active ions ............................................................. 54


4.1.2.2.1 Overview............................................................... 54


4.1.2.2.2 Most important ions..................................................... 55


4.1.2.2.2.1 Chromium.............................................................. 55


4.1.2.2.2.2 Erbium Er3+ ........................................................... 57


4.1.2.2.2.3 Holmium Ho3+ .......................................................... 59


4.1.2.2.2.4 Neodymium Nd3+ ....................................................... 60


4.1.2.2.2.5 Praseodymium Pr3+ ..................................................... 63


4.1.2.2.2.6 Titanium............................................................... 65


4.1.2.2.2.7 Thulium ............................................................... 65


4.1.2.2.2.8 Ytterbium.............................................................. 67


4.1.3 Laser crystals........................................................... 69


4.1.3.1 Alexandrite............................................................. 69


4.1.3.2 BEL(lanthanum beryllate) ............................................... 70


4.1.3.3 Emerald................................................................ 70


4.1.3.4 GGG (gallium gadolinium garnet) ......................................... 71


4.1.3.5 GSAG (gadolinium scandium aluminum garnet)............................. 72


4.1.3.6 GSGG (gadolinium scandium gallium garnet)............................... 73


4.1.3.7 GVO(4) (gadolinium (ortho)vanadate) ..................................... 74


4.1.3.8 	KGW (potassium gadolinium tungstate) ................................... 75


4.1.3.9 	LICAF (lithium calcium aluminum fluoride) ................................ 75


4.1.3.10 	LNA (lanthanum neodymium hexa-aluminate), LMA (lanthanum magnesium hexa-aluminate) .............................. 76


4.1.3.11 	LSB (lanthanum scandium borate) ........................................ 77


4.1.3.12 NYAB (neodymium yttrium aluminum borate).............................. 77


4.1.3.13 	Quartz................................................................. 78


4.1.3.14 	Sapphire ............................................................... 79


4.1.3.15 	YAG (yttrium aluminum garnet) .......................................... 80


4.1.3.16 	YAP (yttrium aluminum perovskite), YALO (yttrium aluminum oxide).......................................... 82


4.1.3.17 	YLF (yttrium lithium fluoride)............................................ 83


4.1.3.18 	YOS (yttrium ortho-silicate).............................................. 84


4.1.3.19 	YSAG (yttrium scandium aluminum garnet)................................ 84


4.1.3.20 	YSGG (yttrium scandium gallium garnet) .................................. 85


4.1.3.21 YVO(4) (yttrium (ortho)vanadate) ........................................ 86

References for 4.1 ....................................................... 87



4.2 	Glasses
H.-J. Hoffmann ....................................................... 97


4.2.1 	General properties of laser glasses ......................................... 97


4.2.1.1 	Basic considerations ..................................................... 97


4.2.1.2 	Lanthanides as active ions................................................ 98


4.2.1.3 	Glasses doped with Nd3+ .................................................100


4.2.1.4 	Radiative lifetime and concentration quenching..............................102


4.2.1.5 	Glasses doped with other active ions, codoping..............................103


4.2.2 	Temperature effects......................................................103


4.2.2.1 	Thermal load of cylindrical rods...........................................103


4.2.2.2 	Thermal lensing.........................................................104


4.2.2.3 	Increasing the maximum laser power.......................................105


4.2.3 	Quantities to characterize properties of laser glasses
.........................107


4.2.3.1 	Density of ions..........................................................107


4.2.3.2 	Refractive index.........................................................107


4.2.3.3 	The refractive index as a function of the temperature........................108


4.2.3.4 	Photoelastic coefficients..................................................110


4.2.3.5 	Nonlinear effects
........................................................110


4.2.4 	Properties of commercial laser glasses doped with Nd3+ (Er3+) ions from different
manufacturers...................................................113

4.2.4.1 	Meaning of the symbols..................................................113


4.2.4.2 	Manufacturer: Schott Glass Technologies...................................114


4.2.4.3 	Manufacturer: Hoya Optics...............................................116


4.2.4.4 Manufacturer: Kigre.....................................................118

References for 4.2
.......................................................120



4.3 	Diode-pumped fiber lasers
A. T
unnermann, J. Limpert, A. Bruns .................................125


4.3.1 	Introduction............................................................125


4.3.2 	Historical background of fiber lasers
.......................................125


4.3.3 	Basic principles of a fiber laser............................................126


4.3.4 	Fundamentals of fiber optics..............................................127


4.3.5 	Double-clad fiber lasers
..................................................128


4.3.6 	Ytterbium-doped fiber lasers..............................................130


4.3.7 	Fiber lasers versus bulk lasers.............................................131

4.3.8 Nonlinearity  the main performance limitation of a fiber laser ................132


4.3.9 Photonic crystal structures in a fiber laser..................................134

4.3.10 Power scaling consideration for cw fiber lasers...............................137

References for 4.3
.......................................................138



4.4 Color-center lasers
R. Beigang ............................................................141


4.4.1 Introduction............................................................141


4.4.2 Physics of color centers..................................................141


4.4.2.1 Classification of color centers.............................................141


4.4.2.2 Preparation of laser-active color centers....................................142


4.4.2.3 Excitation and emission processes.........................................143


4.4.3 Laser systems...........................................................143

4.4.3.1 Continuous-wave laser systems............................................144


4.4.3.2 Pulsed laser systems.....................................................145

References for 4.4
.......................................................146


Part 5 Diode lasers
5.1 Fundamentals of diode lasers
E. Gornik .............................................................151


5.1.1 Introduction............................................................151


5.1.2 Basic diode laser operational principles.....................................151


5.1.2.1 Gain in semiconductors
..................................................152


5.1.2.2 Round-trip condition
....................................................153


5.1.2.3 Rate equations..........................................................154


5.1.2.4 Threshold behavior and optical output.....................................155


5.1.2.5 Thermal aspects
........................................................156


5.1.3 Lateral light/current confinement..........................................156


5.1.3.1 Longitudinal mode controlsingle-mode lasers..............................157


5.1.4 Laser modulation........................................................158


5.1.4.1 Large-signal amplitude modulation........................................159


5.1.4.2 Small-signal amplitude modulation........................................159


5.1.5 Linewidth.............................................................160

References for 5.1.......................................................161



5.2 Diode lasers in the visible spectral region
H. Wenzel ............................................................163


5.2.1 Introduction............................................................163


5.2.2 Diode lasers based on III-nitrides..........................................164


5.2.2.1 Material properties......................................................164


5.2.2.2 Substrate...............................................................165


5.2.2.3 Doping.................................................................165


5.2.2.4 Active region
...........................................................166


5.2.2.5 Waveguide and cladding layers............................................166


5.2.2.6 Contact layer...........................................................167


5.2.2.7 Distributed Bragg reflectors in VCSELs....................................167


5.2.2.8 Epitaxial structure ......................................................167


5.2.2.9 Results.................................................................167


5.2.3 Diode lasers based on II-VI sulfo-selenides..................................168


5.2.3.1 Material properties......................................................168


5.2.3.2 Substrate...............................................................169


5.2.3.3 Doping.................................................................169


5.2.3.4 Active region...........................................................169


5.2.3.5 Waveguide and cladding layers............................................169


5.2.3.6 Contact layer...........................................................170


5.2.3.7 Distributed Bragg reflectors in VCSELs....................................171


5.2.3.8 Epitaxial structure......................................................171


5.2.3.9 Results.................................................................171


5.2.4 Diode lasers based on I-III-IV2 compounds.................................172


5.2.5 Diode lasers based on phospho-arsenides...................................173


5.2.5.1 Material properties......................................................173


5.2.5.2 Substrate...............................................................173


5.2.5.3 Doping.................................................................174


5.2.5.4 Active region...........................................................174


5.2.5.5 Waveguide and cladding layers............................................175


5.2.5.6 Contact layer...........................................................176


5.2.5.7 Distributed Bragg reflectors in VCSELs....................................176


5.2.5.8 Epitaxial structure......................................................176


5.2.5.9 Results.................................................................176

References for 5.2
.......................................................179


Part 6 Free-electron lasers
6.1 Free-electron lasers
M.J. Kelley, G.R. Neil ...............................................187


6.1.1 Overview...............................................................187


6.1.2 Components of a FEL
...................................................188


6.1.2.1 Injector
................................................................188


6.1.2.2 Accelerator.............................................................189


6.1.2.3 Wiggler
................................................................190


6.1.2.3.1 Processes in the wiggler..................................................191


6.1.3 Output
................................................................193


6.1.4 Summary and outlook
...................................................195

References for 6.1
.......................................................198


Part 7 X-ray lasers
7.1 X-ray lasers
P.V. Nickles, K.A. Janulewicz, W. Sandner ..........................203


7.1.1 Introduction............................................................203


7.1.2 Principles of X-ray lasers.................................................205


7.1.2.1 Active medium..........................................................205


7.1.2.1.1 Pump energy absorption.................................................205


7.1.2.1.2 Population inversion and gain.............................................206


7.1.2.1.3 Pump power requirements for soft X-ray lasers in plasmas
....................207


7.1.2.1.4 Kinetics of the active mediumworking regimes............................208


7.1.2.1.4.1 Steady-state approximation...............................................209


7.1.2.1.4.2 Quasi-steady-state approximation
.........................................209


7.1.2.1.4.3 Non-stationary or transient approximation..................................210


7.1.2.1.5 Medium size and output geometryrefraction..............................210


7.1.2.1.5.1 Refraction..............................................................211


7.1.2.2 Excitation mechanisms...................................................213


7.1.2.2.1 Electron collisional excitation.............................................213


7.1.2.2.1.1 Ne-like scheme..........................................................213


7.1.2.2.1.2 Ni-like schemes..........................................................214


7.1.2.2.2 Recombination X-ray lasers...............................................216


7.1.2.2.3 Inner-shell photoionization(ISPI)
.........................................217


7.1.2.2.4 Photoresonant pumping..................................................218


7.1.2.2.5 Other excitation schemes.................................................219


7.1.2.2.5.1 Charge-transfer schemes..................................................219


7.1.3 Output characteristics
...................................................220


7.1.3.1 Output intensity
........................................................220


7.1.3.2 Output energy and conversion efficiency....................................221


7.1.3.3 Saturation..............................................................221


7.1.3.4 Wavelength.............................................................222


7.1.3.5 Spectral linewidth.......................................................223


7.1.3.6 Pulse duration..........................................................223


7.1.3.7 Coherence..............................................................223


7.1.3.7.1 Transverse (spatial) coherence
............................................224


7.1.3.7.2 Longitudinal (temporal) coherence.........................................224


7.1.4 Practical X-ray laser schemes.............................................225


7.1.4.1 Collisionally pumped X-ray lasers
.........................................225


7.1.4.1.1 Quasi-steady state (QSS) scheme..........................................225


7.1.4.1.2 Low-energy prepulse pumping.............................................225


7.1.4.1.3 Multi-pulse pumping.....................................................226


7.1.4.1.4 Transient excitation scheme...............................................226


7.1.4.1.4.1 Traveling-wave pumping..................................................228


7.1.4.1.4.2 Grazing incidence pumping (GRIP)........................................228


7.1.4.1.4.3 XUV master oscillatorpower amplifier(XMOPA)...........................229


7.1.4.1.5 Fast capillary discharge..................................................230


7.1.4.1.6 Hybrid X-ray lasers......................................................231


7.1.4.1.7 Dense gases.............................................................232


7.1.4.1.8 Review of realized collisional X-ray lasers...................................233


7.1.4.2 Recombination-pumped X-ray lasers.......................................233


7.1.4.3 Optical-field ionization (OFI) X-ray lasers..................................242


7.1.4.3.1 Optical-field ionization as a plasma source..................................242


7.1.4.3.2 Propagation issues of OFI................................................242


7.1.4.3.3 OFI with linearly polarized pumping pulse..................................245


7.1.4.3.4 OFI with circularly polarized pumping pulse................................246


7.1.4.4 Inner-shell photoionization X-ray lasers
....................................247


7.1.5 Applications............................................................250


7.1.5.1 Diagnostics with X-ray lasers
.............................................250


7.1.5.2 Interferometry
..........................................................253


7.1.5.3 Reflectometry...........................................................254


7.1.5.4 Excitation of nonlinear processes..........................................254


7.1.6 Conclusion
.............................................................255

References for 7.1
.......................................................256


Index ............................................................................265

