Problems in Laser Physics

By: Giulio Cerullo, Mauro Nisoli, Stefano Longhi

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Paperback | 31 October 2001

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This book presents the first comprehensive collection of solved problems in laser physics covering both fundamental and applied aspects of laser science and technology. The framework of the book, including structuring of topics and notations, closely follows that adopted in the Principles of Laser book by Professor O. Svelto. The collection of problems presented in this book appears therefore a natural complement to Svelto's textbook for testing and developing the skills acquired in the reading of the theory; however, it may also be a useful support to any general textbook on laser physics, wherein problems are usually not solved in detail. We remark that this is, to our knowledge, the first book to provide a complete and satisfactory set of solved problems in such a highly developing field of science and technology. The problems fall mainly into three distinct categories: (i) numerical/applied problems, which help the reader to become confident and familiar with the basic concepts and methods of laser physics, and to acquire a feeling for numerical parameters entering in real-world laser systems; (ii) complementary problems, that present in detail demonstrations of some analytical parts not given in the textbook; and (iii) advanced problems, aimed either to provide a deeper understanding of the subject or to cover more recent developments in the field.
Audience: This book is primarily intended for undergraduate and graduate students in physics, engineering, and chemistry. However, it may also be a useful tool for industrial professionals working in the field of laser technologies and laser applications, as well as for researchers interested in basic aspects of real-world lasers and related fields.

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Non-Fiction Engineering & Technology Other Technologies & Applied Sciences Applied Optics Laser Technology & Holography Science Physics Optical Physics Science in General Scientific Equipment Microscopy Materials & States of Matter

Mechanical Engineering & Materials Materials Science

Introductory Concepts	p. 1
Spectrum of laser emission	p. 1
Spectrum of visible light	p. 1
Energy of a photon	p. 1
Thermal energy	p. 1
Population under thermal equilibrium of two levels	p. 2
Small-signal gain of a ruby laser amplifier	p. 2
Threshold inversion of a laser cavity	p. 2
Temporal evolution of the population densities in a three-level system	p. 2
Brightness of a diffraction limited beam	p. 3
Comparison between the brightness of a lamp and that of an argon laser	p. 3
Intensity on the retina of the sun light and of a He-Ne laser beam	p. 3
Power spectrum of a wave-train of finite duration	p. 4
Coherence time and coherence length of filtered light	p. 4
Radiation pressure of a laser beam	p. 4
Radiation pressure	p. 4
Interaction of Radiation with Atoms and Ions	p. 17
Intensity and energy density of a plane em wave	p. 17
Photon flux of a plane monochromatic wave	p. 17
Number of modes of a blackbody cavity	p. 17
Wien's law	p. 17
Blackbody cavity filled with a dispersive medium	p. 18
Power irradiated by a blackbody emitter	p. 18
Average mode energy	p. 18
Spontaneous and stimulated emission rates	p. 18
Natural broadening	p. 18
Doppler broadening	p. 19
Temperature of a blackbody with the same energy density of a He-Ne laser	p. 19
Spontaneous lifetime and cross section	p. 19
Radiative lifetime and quantum yield of the ruby laser transition	p. 19
Radiative lifetime of the strongest transition of the Nd: YAG laser	p. 20
Transient response of a two-level system to an applied signal	p. 20
Gain saturation intensity	p. 20
Population inversion of a homogeneously broadened laser transition	p. 21
Strongly coupled levels	p. 21
Amplification of a monochromatic em wave	p. 21
Amplified Spontaneous Emission in a Nd: YAG rod	p. 22
Saturated absorption coefficient	p. 22
Peak absorption coefficient and linewidth	p. 22
Energy Levels, Radiative, and Nonradiative Transitions in Molecules and Semiconductors	p. 47
Vibrational frequency of a diatomic molecule	p. 47
Calculation of the elastic constant of a molecule	p. 47
From the potential energy to the vibrational frequency	p. 47
The Morse potential energy	p. 47
Calculation of the Franck-Condon factor	p. 48
Rotational constant of a diatomic molecule	p. 48
Far-infrared absorption spectrum of an HCl molecule	p. 49
The most heavily populated rotational level	p. 49
The emission lines of a CO[subscript 2] molecule	p. 49
The law of mass action	p. 49
Energies of the quasi-Fermi levels	p. 50
The quasi-Fermi levels in GaAs	p. 50
Derivation of the Bernard-Duraffourg condition	p. 50
Laser levels in a semiconductor	p. 50
Frequency dependence of the gain of an inverted semiconductor	p. 50
Gain calculation in a GaAs amplifier	p. 51
Differential gain of a GaAs amplifier	p. 51
Thickness of a quantum well: an order of magnitude estimate	p. 51
An ideal quantum well	p. 51
Energies of the quasi-Fermi levels in a semiconductor quantum well	p. 52
Calculation of the gain bandwidth in a GaAs quantum well	p. 52
Ray and Wave Propagation through Optical Media	p. 75
ABCD matrix of a spherical dielectric interface	p. 75
ABCD matrix of a thin lens	p. 75
ABCD matrix of a piece of glass	p. 75
Reflection at a plane interface	p. 75
An high reflectivity dielectric mirror	p. 76
A Fabry-Perot interferometer	p. 76
A scanning Fabry-Perot interferometer	p. 76
An imaging optical system	p. 76
The ABCD law for gaussian beams	p. 77
A collimating lens	p. 77
A simple optical processing system	p. 77
A laser driller	p. 78
An earth to moon laser rangefinder	p. 78
An He-Ne laser	p. 78
An Argon laser	p. 78
Gaussian beam propagation through an optical system	p. 79
Power conservation for a gaussian beam	p. 79
A "soft" or gaussian aperture	p. 79
A waist imaging system	p. 79
Gaussian beam transformation by a lens	p. 79
Focusing a gaussian beam inside a piece of glass	p. 80
Passive Optical Resonators	p. 105
Stability of a resonator with concave mirrors	p. 105
A concave-convex resonator	p. 105
A simple two-mirror resonator	p. 105
Number of longitudinal modes in a resonator	p. 105
Resonators for an Argon laser	p. 106
A resonator for a CO[subscript 2] laser	p. 106
A near-planar resonator	p. 106
Single-mode selection in a He-Ne laser	p. 106
Spot sizes on the mirrors of a stable resonator	p. 107
A plano-concave resonator	p. 107
A near-concentric resonator	p. 107
The unlucky graduate student	p. 107
Resonator with an intracavity lens	p. 108
Resonator for a cw-pumped Nd:YAG laser	p. 108
Resonator for a Ti:sapphire laser	p. 108
Location of the beam waist in a stable resonator	p. 109
Properties of a symmetric confocal resonator	p. 109
Asymmetric confocal resonators	p. 109
A confocal unstable resonator	p. 110
Unstable resonator with gaussian mirrors: properties of the output beam	p. 110
Designing a gaussian mirror for an unstable resonator	p. 110
Unstable resonator with a supergaussian mirror	p. 110
Pumping Processes	p. 135
Critical pump rate in a lamp-pumped Nd:YLF laser	p. 135
Pump rate expression for longitudinal pumping	p. 135
Laser spot size in a longitudinally pumped Ti:Al[subscript 2]O[subscript 3] laser under optimum pumping conditions	p. 135
Optical pumping of a Ti:Al[subscript 2]O[subscript 3] laser: a design problem	p. 136
Doping in a solid-state laser medium	p. 136
A transversely pumped high-power Nd:YAG laser	p. 136
Longitudinal vs. transverse pumping in Nd:YAG laser	p. 136
Threshold power in a double-end pumped Nd:YVO[subscript 4] laser	p. 137
Threshold power in a quasi-three level laser: the Yb:YAG case	p. 137
Threshold pump power of a Nd:glass fiber laser	p. 137
Pump absorption in a Nd:glass fiber laser	p. 138
Maximum output intensity in a Nd:glass amplifier	p. 138
Electron temperature in a Boltzmann distribution	p. 138
How to reduce the size of a He-Ne laser tube?	p. 138
Thermal and drift velocities of electrons in a He-Ne laser	p. 139
A He-Ne laser: pump rate vs. pump current	p. 139
Scaling laws and performances in longitudinally pumped gas lasers	p. 139
Pump rate vs. pumping current in Ar[superscript +] lasers	p. 139
Ar[superscript +] lasers: pump efficiency vs. pump power	p. 140
Continuous Wave Laser Behavior	p. 155
Calculation of logarithmic loss	p. 155
Calculation of cavity photon lifetime	p. 155
Four-level laser with finite lifetime of the lower laser level	p. 155
Rate equations analysis of a three-level laser	p. 156
Threshold condition in a ruby laser	p. 156
Thermal lensing in a microchip Nd:YAG laser	p. 156
Transverse efficiency in an end-pumped four-level laser	p. 157
Threshold and slope-efficiency calculations in a longitudinally-pumped Nd:YAG laser	p. 157
Estimate of internal laser losses	p. 157
Calculation of optimum output coupling	p. 158
Longitudinal efficiency in a standing-wave laser	p. 158
Dispersion relation for a Lorentzian line	p. 158
Frequency pulling in a homogeneously-broadened laser	p. 159
Calculation of frequency pulling in a He-Xe laser	p. 159
Quantum limit to the laser linewidth	p. 159
Tuning of a Ti:sapphire laser by a birefringent filter	p. 159
Transverse mode selection	p. 160
Single longitudinal mode oscillation in an inhomogeneously broadened laser	p. 160
Suppression of spatial hole burning by the twisted-mode technique	p. 160
Single-longitudinal mode selection by an intracavity etalon	p. 161
Transient Laser Behavior	p. 187
Relaxation oscillations in a Nd:YAG laser	p. 187
Noise spectrum of the output power for a four-level laser	p. 187
Fast Q-switching in a Nd:YLF laser	p. 187
Calculation of the pulse energy and pulse duration in a repetitively Q-switched Nd:YAG laser	p. 188
Quarter-wave voltage in a Q-switch Pockels cell	p. 188
Active Q-switching in a three-level laser	p. 188
Calculation of the beam deflection angle by an acoustooptic modulator	p. 189
Mode-locking of sidebands modes with random amplitudes	p. 189
Chirped Gaussian pulses with quadratic phase locking relations	p. 189
On the periodicity of mode-locked signals	p. 189
Phase locking condition for second-harmonic mode-locking	p. 190
Pulsewidth calculation in an actively mode-locked Nd:YAG laser	p. 190
Gaussian pulse analysis of frequency mode locking	p. 190
Mode-locking in a He-Ne laser	p. 190
Harmonic mode-locking of a laser in a linear cavity	p. 191
Calculation of pulse energy and peak power in a passively mode-locked Nd:YAG laser	p. 191
Pulse duration in an idealized Kerr lens mode-locked Ti:Sapphire laser	p. 191
Pulse duration in a soliton-type Ti:sapphire mode-locked laser	p. 192
Pulse broadening in a quartz plate	p. 192
Self-imaging of a mode-locked pulse train	p. 192
Solid-State, Dye, and Semiconductor Lasers	p. 215
Slope efficiency in a Ti:Al[subscript 2]O[subscript 3] laser	p. 215
Output power from a Nd:YAG laser	p. 215
A Nd:YVO[subscript 4] laser in the fog	p. 215
A green solid-state laser	p. 216
Yb:YAG laser vs. Nd:YAG laser	p. 216
Anisotropy in a Cr:LiSAF laser rod	p. 217
Threshold pump power in longitudinal pumping: ground and excited states contribution	p. 217
Threshold pump power in a dye laser: triplet-triplet contribution	p. 218
Slope efficiency in a dye laser	p. 218
A laser cascade	p. 218
Longitudinal modes in a semiconductor laser	p. 218
Beam astigmatism in a semiconductor laser	p. 219
Current threshold in a GaAs/AlGaAs laser	p. 219
Slope efficiency in a GaAs/AlGaAs laser	p. 219
Distributed feedback in a semiconductor laser	p. 220
Current threshold in a quantum-well laser	p. 220
Carrier density in a VCSEL at threshold	p. 220
Gas, Chemical, Free-Electron, and X-Ray Lasers	p. 239
Low-density laser emitting in the infrared	p. 239
Low-density laser emitting in the UV - soft X region	p. 239
High-power lasers for material processing	p. 239
Internal structure of He-Ne lasers	p. 239
Maximum output power in He-Ne lasers	p. 240
Internal structure of high-power Ar[superscript +] lasers	p. 240
Output vs. pump power in Ar[superscript +] lasers	p. 240
Current density in a low power CO[subscript 2] laser	p. 240
Voltage drop in a low power CO[subscript 2] laser tube	p. 240
Rotational transitions in a CO[subscript 2] laser	p. 241
Mode locking of a CO[subscript 2] laser	p. 241
ASE threshold for a N[subscript 2] laser	p. 241
Pump power in a KrF excimer laser at threshold	p. 242
Cold reaction in a HF chemical laser	p. 242
Transition linewidths in the soft-X-ray spectral region	p. 242
A free-electron laser operating in the soft-X-ray region	p. 242
Properties of Laser Beams	p. 255
Complex degree of coherence for a quasi monochromatic wave	p. 255
Measurement of the spatial coherence by a Young interferometer	p. 255
Destroy of spatial coherence by rotation of a ground glass	p. 255
Comparison of temporal coherence between a thermal source and a laser	p. 256
Temporal coherence of white light	p. 256
Relation between first-order degree of temporal coherence and fringe visibility in a Michelson interferometer	p. 256
Degree of temporal coherence for a low-pressure discharge lamp	p. 256
Temporal coherence of a gas laser oscillating on N axial modes	p. 257
An interference experiment with partially coherent light	p. 257
Spatial coherence of the light from the sun	p. 257
An astronomic calculation based on spatial coherence of stellar radiation	p. 258
Beam divergence of a partially-coherent laser beam	p. 258
Focusing of a perfectly-coherent spatial beam	p. 258
M[superscript 2] factor of a Nd:YAG laser	p. 258
Brightness of a high-power CO[subscript 2] laser	p. 259
Grain size of the speckle pattern as observed on a screen	p. 259
Grain size of the speckle pattern as seen by a human observer	p. 259
Correlation function and power spectrum of a single-longitudinal mode laser	p. 259
Laser Beam Transformation: Propagation, Amplification, Frequency Conversion, Pulse Compression, and Pulse Expansion	p. 277
Propagation of a multimode beam	p. 277
Amplification of long pulses by a Nd:YAG amplifier	p. 277
Amplification of short pulses by a Nd:YAG amplifier	p. 277
Extraction efficiency of a two-pass amplifier	p. 278
Saturation fluence in a quasi-three-level amplifier	p. 278
Maximum output fluence from an amplifier with losses	p. 278
Theoretical limit to the maximum intensity of an amplifier	p. 279
Index of refraction of an extraordinary wave in a uniaxial crystal	p. 279
Double refraction in a uniaxial crystal	p. 279
Second harmonic conversion of a Ti:sapphire laser in a BBO crystal	p. 279
Second harmonic conversion efficiency in a KDP crystal	p. 280
Second harmonic generation with a Gaussian beam	p. 280
Frequency doubling of a Gaussian beam in a KDP crystal	p. 281
Effective nonlinear coefficient of a KDP crystal	p. 281
Threshold pump intensity of an optical parametric oscillator	p. 282
Collinear parametric generation in a BBO crystal	p. 282
Noncollinear parametric generation in a BBO crystal	p. 282
Nonlinear index n[subscript 2] of sapphire	p. 283
Pulse spectral broadening due to self-phase modulation in a Kerr medium	p. 283
Spectral broadening of a 20-fs pulse in a hollow fiber filled with argon	p. 283
Group delay dispersion of a medium	p. 284
Dispersion-induced broadening of a 10-fs pulse in a fused silica plate	p. 284
Table of Contents provided by Syndetics. All Rights Reserved.

Problems in Laser Physics

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