Principles of Laser Materials Processing E-Book

Elijah Kannatey-Asibu

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 1061

Veröffentlichungsjahr: 2023

Beschreibung

Principles of Laser Materials Processing Authoritative resource providing state-of-the-art coverage in the field of laser materials processing, supported with supplementary learning materials Principles of Laser Materials Processing goes over the most recent advancements and applications in laser materials processing, with the second edition providing a welcome update to the successful first edition through updated content on the important fields within laser materials processing. The text includes solved example problems and problem sets suitable for the readers' further understanding of the technology explained. Split into three parts, the text first introduces basic concepts of lasers, including the characteristics of lasers and the design of their components, to aid readers in their initial understanding of the technology. The text then reviews the engineering concepts that are needed to analyze the different processes. Finally, it delves into the background of laser materials and provides a state-of-the-art compilation of material in the major application areas, such as laser cutting and drilling, welding, surface modification, and forming, among many others. It also presents information on laser safety to prepare the reader for working in the industry sector and provide practicing engineers the updates needed to work safely and effectively. In Principles of Laser Materials Processing, readers can expect to find specific information on: * Laser generation principles, including basic atomic structure, atomic transitions, population distribution, absorption, and spontaneous emission * Optical resonators, including standing waves in a rectangular cavity, planar resonators, beam modes, line selection, confocal resonators, and concentric resonators * Laser pumping, including optical pumping, arc/flash lamp pumping, energy distribution in the active medium, and electrical pumping * Broadening mechanisms, including line-shape functions, homogeneous broadening such as natural and collision, and inhomogeneous broadening Principles of Laser Materials Processing is highly suitable for senior undergraduate and graduate students studying laser processing, and non-traditional manufacturing processes; it is also aimed at researchers to provide additional information to be used in research projects that are to be undertaken within the technology field.

Leseprobe

Table of Contents

Cover

Title Page

Copyright

Dedication

Preface to the Second Edition

Preface to the First Edition

About the Companion Website

PART I: Principles of Industrial Lasers

1 Laser Background

1.1 LASER GENERATION

1.2 OPTICAL RESONATORS

1.3 LASER PUMPING

1.4 SYSTEM LEVELS

1.5 BROADENING MECHANISMS

1.6 BEAM MODIFICATION

1.7 BEAM CHARACTERISTICS

1.8 SUMMARY

APPENDIX 1.A

PROBLEMS

BIBLIOGRAPHY

2 Types of Lasers

2.1 SOLID‐STATE LASERS

2.2 GAS LASERS

2.3 SEMICONDUCTOR (DIODE) LASERS

2.4 NEW DEVELOPMENTS IN INDUSTRIAL LASER TECHNOLOGY

2.5 SUMMARY

APPENDIX 2.A

APPENDIX 2.B

APPENDIX 2.C

PROBLEMS

BIBLIOGRAPHY

3 Beam Delivery

3.1 THE ELECTROMAGNETIC SPECTRUM

3.2 BIREFRINGENCE

3.3 BREWSTER ANGLE

3.4 POLARIZATION

3.5 BEAM EXPANDERS

3.6 BEAM SPLITTERS

3.7 BEAM DELIVERY SYSTEMS

3.8 BEAM SHAPING

3.9 SUMMARY

APPENDIX 3.A

PROBLEMS

BIBLIOGRAPHY

PART II: Engineering Background

4 Heat and Fluid Flow

4.1 ENERGY BALANCE DURING PROCESSING

4.2 HEAT FLOW IN THE WORKPIECE

4.3 FLUID FLOW IN MOLTEN POOL

4.4 SUMMARY

APPENDIX 4.A

APPENDIX 4.B DERIVATION OF EQUATION (4.2a)

APPENDIX 4.C MOVING HEAT SOURCE

APPENDIX 4.D

APPENDIX 4.E

APPENDIX 4.F

APPENDIX 4.G

PROBLEMS

BIBLIOGRAPHY

NOTE

5 The Microstructure

5.1 PROCESS MICROSTRUCTURE

5.2 DISCONTINUITIES

5.3 SUMMARY

APPENDIX 5.A

PROBLEMS

BIBLIOGRAPHY

6 Solidification

6.1 SOLIDIFICATION WITHOUT FLOW

6.2 SOLIDIFICATION WITH FLOW

6.3 RAPID SOLIDIFICATION

6.4 SUMMARY

APPENDIX 6.A

PROBLEMS

BIBLIOGRAPHY

7 Residual Stresses and Distortion

7.1 CAUSES OF RESIDUAL STRESSES

7.2 BASIC STRESS ANALYSIS

7.3 EFFECTS OF RESIDUAL STRESSES

7.4 MEASUREMENT OF RESIDUAL STRESSES

7.5 RELIEF OF RESIDUAL STRESSES AND DISTORTION

7.6 SUMMARY

APPENDIX 7.A

APPENDIX 7.B

PROBLEMS

BIBLIOGRAPHY

PART III: Laser Materials Processing

8 Background on Laser Processing

8.1 SYSTEM‐RELATED PARAMETERS

8.2 PROCESS EFFICIENCY

8.3 DISTURBANCES THAT AFFECT PROCESS QUALITY

8.4 GENERAL ADVANTAGES AND DISADVANTAGES OF LASER PROCESSING

8.5 SUMMARY

APPENDIX 8.A

PROBLEMS

BIBLIOGRAPHY

9 Laser Cutting and Drilling

9.1 LASER CUTTING

9.2 LASER DRILLING

9.3 NEW DEVELOPMENTS

9.4 SUMMARY

APPENDIX 9.A

PROBLEMS

BIBLIOGRAPHY

10 Laser Welding

10.1 LASER WELDING PARAMETERS

10.2 WELDING EFFICIENCY

10.3 MECHANISM OF LASER WELDING

10.4 MATERIAL CONSIDERATIONS

10.5 WELDMENT DISCONTINUITIES

10.6 ADVANTAGES AND DISADVANTAGES OF LASER WELDING

10.7 SPECIAL TECHNIQUES

10.8 SPECIFIC APPLICATIONS

10.9 SUMMARY

APPENDIX 10.A

PROBLEMS

BIBLIOGRAPHY

11 Laser Surface Modification

11.1 LASER SURFACE HEAT TREATMENT

11.2 LASER SURFACE MELTING

11.3 LASER DIRECT METAL DEPOSITION

11.4 LASER PHYSICAL VAPOR DEPOSITION (LPVD)

11.5 LASER SHOCK PEENING

11.6 LASER TEXTURING

11.7 SUMMARY

APPENDIX 11.A

APPENDIX 11.B

PROBLEMS

BIBLIOGRAPHY

12 Laser Forming

12.1 PRINCIPLE OF LASER FORMING

12.2 PROCESS PARAMETERS

12.3 LASER‐FORMING MECHANISMS

12.4 PROCESS ANALYSIS

12.5 ADVANTAGES AND DISADVANTAGES

12.6 APPLICATIONS

12.7 SUMMARY

APPENDIX 12.A

PROBLEMS

BIBLIOGRAPHY

13 Additive Manufacturing

13.1 COMPUTER‐AIDED DESIGN

13.2 PART BUILDING

13.3 POST‐PROCESSING

13.4 APPLICATIONS

13.5 ADVANTAGES AND DISADVANTAGES

13.6 SUMMARY

APPENDIX 13.A

PROBLEMS

BIBLIOGRAPHY

14 Medical and Nanotechnology Applications of Lasers

14.1 MEDICAL APPLICATIONS

14.2 NANOTECHNOLOGY APPLICATIONS

14.3 SUMMARY

BIBLIOGRAPHY

15 Sensors for Process Monitoring

15.1 LASER BEAM MONITORING

15.2 PROCESS MONITORING

15.3 SUMMARY

APPENDIX 15.A

PROBLEMS

BIBLIOGRAPHY

16 Processing of Sensor Outputs

16.1 SIGNAL TRANSFORMATION

16.2 DATA REDUCTION

16.3 PATTERN CLASSIFICATION

16.4 SUMMARY

APPENDIX 16.A

PROBLEMS

BIBLIOGRAPHY

17 Laser Safety

17.1 LASER HAZARDS

17.2 LASER CLASSIFICATION

17.3 PREVENTING LASER ACCIDENTS

17.4 SUMMARY

APPENDIX 17.A

PROBLEM

BIBLIOGRAPHY

Index

End User License Agreement

List of Tables

Chapter 1

Table 1.1 Wavelengths associated with the visible spectrum.

Chapter 2

Table 2.1 Output wavelengths for common fiber lasers.

Chapter 3

Table 3.1 Phase functions for Fresnel phase plate.

Chapter 4

Table 4.1 Measured values of the electron–phonon coupling factor, G, for so

...

Table 4.2 Thermalization τt and electron relaxation τFe times at 300 K for

...

Chapter 5

Table 5.1 Surface energies,

γ

nl

, of some common metals.

Chapter 8

Table 8.1 Comparison of power densities for various heat sources.

Chapter 9

Table 9.1 Sample cutting conditions for laser cutting of different material

...

Table 9.2 Surface tension values for some metals and oxides.

Table 9.3 Illustration of roughness variation of cut surface with workpiece

...

Chapter 10

Table 10.1 Sample conditions for deep penetration laser welding of differen

...

Table 10.2 Typical processing parameters for deep penetration laser welding

...

Table 10.3 Comparison of efficiency values for various welding processes.

...

Table 10.4 Suitability of materials for CO

2

laser welding.

Table 10.5 Comparison of two traditional methods of producing automotive bo

...

Chapter 11

Table 11.1 Typical laser heat treatment process parameters.

Table 11.2 Comparison of the three beam‐shaping devices.

Table 11.3 Typical process parameters used in laser cladding.

Table 11.4 Typical process parameters used in laser physical vapor depositi

...

Table 11.5 Typical process parameters used in laser shock peening.

Chapter 12

Table 12.1 Typical process parameters used in laser forming.

Table 12.2 Comparison of the three mechanisms for laser forming.

Chapter 13

Table 13.1 Bezier function values for different

t

values.

Table 13.2 Sample conditions for stereolithography by beam scanning.

Table 13.3 Sample conditions for selective laser sintering.

Table 13.4 Comparison of the powder bed fusion and direct energy deposition

...

Table 13.5 Sample conditions for laminated object manufacturing.

Table 13.6 Post‐processing operations.

Chapter 14

Table 14.1 Therapeutic applications of the laser.

Table 14.2 Diagnostic applications of the laser.

Chapter 15

Table 15.1 Rotating hollow needle analyzer parameters.

Table 15.2 Weld quality and its dependence on infrared/ultraviolet signals.

Chapter 16

Table 16.1 A general step of the contrastive divergence algorithm for RBMs

...

Table 16.2 Deep Belief Network Algorithm (Algorithm 2).

Chapter 17

Table 17.1 Maximum permissible exposure for the eye.

Table 17.2 Maximum permissible exposure for the skin.

Table 17.3 Relationship between the optical density, transmittance, and lev

...

Table 17.4 Optical densities for various laser outputs.

Table 17.5 Correction factors.

List of Illustrations

Chapter 1

Figure 1.1 The electromagnetic spectrum.

Figure 1.2 Schematic of Boltzmann's law. (a) Two‐level system. (b) More gene...

Figure 1.3 Schematic of (a) absorption, (b) spontaneous emission, and (c) st...

Figure 1.4 Illustration of the process of stimulated emission.

Figure 1.5 Propagation of a monochromatic beam in the

x

‐direction.

Figure 1.6 Population inversion.

Figure 1.7 Illustration of laser amplification.

Figure 1.8 The two‐photon absorption concept.

Figure 1.9 Electric and magnetic field vectors of an electromagnetic wave.

Figure 1.10 Rectangular cavity containing a dielectric medium.

Figure 1.11 Planar or Fabry–Perot resonator.

Figure 1.12 Longitudinal modes in a laser output. (a) Modes that can exist w...

Figure 1.13 Resonant frequencies of a Fabry–Perot resonator.

Figure 1.14 Mode shapes or schematic of TEM

mn

mode patterns.

Figure 1.15 Gaussian (TEM

00

) mode distribution.

Figure 1.16 Wavelength selection.

Figure 1.17 Confocal resonator.

Figure 1.18 Beam size and phase for a TEM

00

mode propagating in a confocal r...

Figure 1.19 Oscillating frequencies of a confocal resonator.

Figure 1.20 Concentric resonator.

Figure 1.21 Schematic of an optical pumping system using an elliptical cavit...

Figure 1.22 Schematic of an optical pumping system using a helical flashlamp...

Figure 1.23 Longitudinal pumping using a diode laser.

Figure 1.24 Transverse pumping using a diode laser.

Figure 1.25 Schematic of an electrical pumping system.

Figure 1.26 Schematic of a three‐level system. (a) No pumping. (b) Intense p...

Figure 1.27 Schematic of a four‐level system.

Figure 1.28 Lorentzian and Gaussian line shape functions.

Figure 1.29 Phase changes associated with radiation emission resulting from ...

Figure 1.30 Time evolution of the Q‐switching process: (a) single pulse and ...

Figure 1.31 Mirror rotation for mechanical shutter action.

Figure 1.32 Amplitude modulation of cavity losses.

Figure 1.33 (a) Divergent light from an ordinary light source. (b) Light fro...

Figure 1.34 Beam divergence.

Figure 1.35 Comparison of the spectral characteristics of a conventional lig...

Figure 1.36 Coherence: (a) perfect coherence. (b) Spatially coherent beam wi...

Figure 1.37 Young's experiment.

Figure 1.38 Michelson interferometer.

Figure 1.39 Variation of fringe visibility with optical path difference.

Figure 1.40 Beam focusing.

Chapter 2

Figure 2.1 Energy levels of neodymium lasers.

Figure 2.2 Energy levels of the He‐Ne system.

Figure 2.3 Schematic of a He‐Ne laser (external mirrors).

Figure 2.4 Energy levels of the Ar

+

system.

Figure 2.5 Schematic of an Ar

+

laser.

Figure 2.6 Energy levels of a molecule. (a) Electronic. (b) Vibrational. (c)...

Figure 2.7 Vibrational modes of the CO

2

molecule.

Figure 2.8 Energy level scheme of the CO

2

laser.

Figure 2.9 Schematic of the axial flow CO

2

laser.

Figure 2.10 One possible resonator configuration.

Figure 2.11 Simplified two‐dimensional sectional view of a transverse flow C...

Figure 2.12 (a) Potential energy well of a diatomic molecule. (b) Potential ...

Figure 2.13 Energy bands of: (a) insulators, (b) metals and (c) semiconducto...

Figure 2.14 Creation of holes in a valence band. (a) Filled valence band. (b...

Figure 2.15 Covalent bonding in an intrinsic semiconductor.

Figure 2.16 (a) n‐Type semiconductor. (b) p‐Type semiconductor.

Figure 2.17 Basic concepts in semiconductor laser operation. (a) A completel...

Figure 2.18 p–n junction diode (Forward bias)

Figure 2.19 Energy levels of a heavily doped p–n junction diode. (a) Zero bi...

Figure 2.20 Schematic of a semiconductor laser.

Figure 2.21 Schematic of a double heterojunction laser.

Figure 2.22 High‐power diode laser construction. (a) Diode laser bar. (b) St...

Figure 2.23 Setup of a stacked diode laser with beam transformation optics....

Figure 2.24 General schematic of a slab laser.

Figure 2.25 Schematic of a CO

2

slab laser.

Figure 2.26 Schematic of a disk laser.

Figure 2.27 Principle of chirped‐pulse amplification for ultrashort pulse ge...

Figure 2.28 Chirped‐pulse amplification. (a) Pulse stretching using an antip...

Figure 2.29 Basic structure of a fiber laser. (a) Overall setup. (b) Section...

Figure 2.30 Pumping a fiber laser.

Figure 2.31 Illustration of end and side pumping techniques.

Figure 2.32 Schematic of a three‐stage amplifier MOPA.

Figure 2.33 Relative operating costs for industrial lasers.

Chapter 3

Figure 3.1 Electric vector of (a) a plane‐polarized light and (b) an unpolar...

Figure 3.2 Reflection coefficients: (a) reflection coefficients for an air–g...

Figure 3.3 One‐dimensional electromagnetic wave propagation: (a) a single wa...

Figure 3.4 Plane‐polarized electromagnetic waves in two orthogonal planes.

Figure 3.5 (a) Instantaneous configuration of the resultant electric vector ...

Figure 3.6 Examples of beam expanders: (a) mirrors and (b) lenses.

Figure 3.7 Wedge‐shaped beam splitter.

Figure 3.8 Partially reflective, partially transmissive beam splitter.

Figure 3.9 (a) Simplified laser beam delivery system and (b) beam delivery s...

Figure 3.10 Schematic of a fiber optic system.

Figure 3.11 Basic structure of a fiber optic cable.

Figure 3.12 Propagation of a light ray in an optical fiber.

Figure 3.13 Cross section of a single‐mode fiber.

Figure 3.14 (a) Cross section of a multimode graded‐index fiber and (b) peri...

Figure 3.15 Dispersion coefficient as a function of wavelength.

Figure 3.16 Sources of beam loss within a glass fiber.

Figure 3.17 Illustration of how a diffractive optical element (to the right)...

Figure 3.18 Fresnel zones.

Figure 3.19 Fresnel phase plate.

Figure 3.20 Multilevel Fresnel phase plate. (a) Two‐level Fresnel phase plat...

Figure 3.21 Basic beam shapes: Gaussian and Flat top.

Figure 3.22 Generating a flat‐top beam from a Gaussian beam by geometric map...

Figure 3.23 Variation of beam profile with propagation distance.

Figure 3.24 Propagation distance from aperture plane to the plane of interes...

Figure 3.25 Production of a diffractive optical element profile: (a) binary ...

Figure 3.26 Principle of CBC technique.

Figure P3.14

Chapter 4

Figure 4.1 Schematic of moving coordinate system associated with laser proce...

Figure 4.2 Three‐dimensional configuration.

Figure 4.3 Two‐dimensional configuration.

Figure 4.4 Plot of the modified Bessel function of the second kind of order ...

Figure 4.5 Temperature distribution in a plate for (a) low thermal conductiv...

Figure 4.6 Temperature distribution as a function of processing speed, other...

Figure 4.7 Temperature distribution as a function of plate thickness, other ...

Figure 4.8 Representative regions for the cooling rate equations.

Figure 4.9 (a) Electron and lattice temperature variations with time on the ...

Figure 4.10 Configuration of the molten pool.

Figure 4.11 (a) Flow pattern for a negative gradient. (b) Flow pattern for a...

Figure 4B.1 Heat flux in a control volume.

Figure P4.6 Schematic of the multiple‐beam laser welding concept.

Chapter 5

Figure 5.1 Major microstructural zones associated with laser processing.

Figure 5.2 Free energy change associated with the formation of a spherical n...

Figure 5.3 Heterogeneous nucleation at the base metal–molten pool interface....

Figure 5.4 Epitaxial solidification from the base metal grains at the fusion...

Figure 5.5 (a) Planar, (b) cellular, (c) columnar dendritic, and (d) equiaxe...

Figure 5.6 Pictorial illustrations of (a) planar, (b) cellular, (c) columnar...

Figure 5.7 Dependence of solidification structure on liquid temperature grad...

Figure 5.8 Schematic of dendrite formation.

Figure 5.9 Variation of solidification rate along the molten pool edge.

Figure 5.10 (a) Grain structure at high traverse velocities. (b) Grain struc...

Figure 5.11 Pictorial illustration of a banded grain structure.

Figure 5.12 Preferential growth of crystals which have the two preferred dir...

Figure 5.13 HAZ microstructure for (a) previously annealed pure metal and (b...

Figure 5.14 Stress variation with grain size for copper.

Figure 5.15 HAZ microstructure for a previously work‐hardened precipitation‐...

Figure 5.16 Schematic of HAZ microstructure for a previously work‐hardened s...

Figure 5.17 Corrosion in an austenitic stainless steel after welding, as a r...

Figure 5.18 Classification of common discontinuity types.

Figure 5.19 Porosity in the fusion zone.

Figure 5.20 Schematic illustration of weld cracks.

Figure 5.21 Pictorial illustration of weld cracks. (a) Hot crack in a fillet...

Figure 5.22 Lack of fusion.

Figure 5.23 Incomplete penetration.

Figure 5.24 Undercut.

Figure P5.1 Aging curve and strength variation in a processed zone.

Figure P5.3 Typical time temperature transformation curve.

Figure P5.4 Variation of strength with time during aging.

Figure P5.6 Stress variation with grain size for different alloys.

Chapter 6

Figure 6.1 Temperature field for one‐dimensional solidification of a pure ma...

Figure 6.2 Schematic temperature field for one‐dimensional solidification of...

Figure 6.3 Relationship between morphological and constitutional supercoolin...

Figure 6.4 Schematic temperature field for one‐dimensional solidification of...

Figure 6.5 Mushy zone with solid particles dispersed within the liquid mediu...

Figure 6.6 Columnar dendritic mushy zone at the solidifying interface.

Figure 6.7 Enthalpy‐temperature diagram.

Chapter 7

Figure 7.1 Three‐rod frame with rods of equal length which are rigidly conne...

Figure 7.2 Stress–temperature curve for the middle rod of a three‐rod frame....

Figure 7.3 Stress and temperature changes during welding.

Figure 7.4 Longitudinal residual stress distribution in a weld. (a) Weld con...

Figure 7.5 Stress–strain curve with elastic recovery and permanent set.

Figure 7.6 Beam bending and resulting stress distribution. (a) The beam. (b)...

Figure 7.7 Stress distribution in a bent beam after unloading. (a) Ideal str...

Figure 7.8 Indentation in a body.

Figure 7.9 Plane stress state in a body.

Figure 7.10 Plane strain state in a body.

Figure 7.11 Residual stresses developed in a steel rod after quenching. (a) ...

Figure 7.12 Redistribution of residual stresses in a weldment after loading ...

Figure 7.13 Residual stresses developed in a glass plate after uniform heati...

Figure 7.14 Various modes of distortion in weldments. (a) Transverse shrinka...

Figure 7.15 The sectioning method of residual stress measurement. (a) Thick ...

Figure 7.16 The drilling method of residual stress measurement.

Figure 7.17 A general arrangement of strain gages.

Figure 7.18 Principle of X‐ray diffraction.

Figure 7.19 Schematic of the X‐ray film technique.

Figure 7.20 Schematic of the diffractometer technique.

Figure 7.21 Principle of the neutron diffraction measurement technique.

Figure 7.22 Schematic of a neutron diffractometer.

Figure P7.4

Figure P7.5

Figure P7.6

Figure P7.7

Figure P7.10

Figure P7.12

Figure P7.13

Chapter 8

Figure 8.1 Power densities and interaction times for various laser processes...

Figure 8.2 Lens focal length and corresponding depth of focus.

Figure 8.3 Beam distributions. (a) Low‐order (Gaussian) mode. (b) High‐order...

Figure 8.4 Schematic of pulsed outputs. (a) Gated pulsing. (b) Superpulsing....

Figure 8.5 (a) Wavelength dependence of absorption for different materials (...

Figure 8.6 Temperature dependence of absorption for Nd:YAG and CO

2

laser bea...

Figure 8.7 Set‐up for measuring absorptivity calorimetrically. Source: From

Figure 8.8 Beam alignment using a cross‐hair. (a) Misaligned beam. (b) Align...

Chapter 9

Figure 9.1 Schematic of the laser cutting process.

Figure 9.2 Components of a laser cutting system.

Figure 9.3 Effect of plane‐polarized laser orientation on cut quality.

Figure 9.4 Variation of cutting speed (maximum cutting rates) with workpiece...

Figure 9.5 Limiting curves for cutting speed with workpiece thickness variat...

Figure 9.6 Cutting speed as a function of oxygen gas purity. Mild steel of t...

Figure 9.7 Comparison of maximum cutting speed with O

2

and Ar assist gases f...

Figure 9.8 Nozzle designs for laser cutting.

Figure 9.9 Effect of Focal position on kerf width for a 7075‐T6 aluminum all...

Figure 9.10 Schematic variation of melt thickness with cutting speed.

Figure 9.11 Angle of incidence of laser beam on cut surface, and inclination...

Figure 9.12 Variation of absorption efficiency of a p‐polarised beam with be...

Figure 9.13 Variation of reflectivity of mild steel with beam incidence angl...

Figure 9.14 A two‐dimensional view of the cutting process.

Figure 9.15 Schematic of pressure distribution along the cutting front.

P

0

i...

Figure 9.16 Schematic of shear stress distribution along the cutting front.

Figure 9.17 Illustration of striations formed on a surface after laser cutti...

Figure 9.18 Dross formed on the lower edge of the workpiece after laser cutt...

Figure 9.19 Illustration of oxygen content variation with distance from the ...

Figure 9.20 Comparison of thermal cutting processes.

Figure 9.21 Comparison of electrical discharge machining (EDM), laser cuttin...

Figure 9.22 Schematic of the laser‐assisted oxygen cutting process.

Figure 9.23 Different ways in which a hole may be produced by laser drilling...

Figure 9.24 Schematic of material removal by a pulsed beam.

Figure 9.25 Setting the breakdown threshold to a specific level of beam mode...

Figure 9.26 SEM photographs of holes drilled through a 100 μm steel foil usi...

Figure 9.27 Schematic of the laser‐assisted machining process. (a) Two‐dimen...

Chapter 10

Figure 10.1 Effect of welding speed and laser power on weld penetration.

Figure 10.2 Effect of welding speed on depth‐to‐width ratio.

Figure 10.3 Influence of beam polarization on penetration. (a) Variation of ...

Figure 10.4 Plasma formation in keyhole welding.

Figure 10.5 Effect of shielding gas, laser power, intensity, and welding spe...

Figure 10.6 Schematic of a plasma suppression setup.

Figure 10.7 Effect of plasma suppression helium gas flow rate on depth of pe...

Figure 10.8 Effect of focal point positioning on penetration and bead width....

Figure 10.9 Some common joint designs. (a) Butt joint. (b) Lap joint. (c) T‐...

Figure 10.10 (a) Butt joint and (b) lap joint specifications in laser weldin...

Figure 10.11 Schematic of conduction mode welding.

Figure 10.12 Schematic of the keyhole mode laser welding process. (a) Simpli...

Figure 10.13 Schematic of the keyhole cavity shape.

Figure 10.14 Typical top view of the weld pool during keyhole welding.

Figure 10.15 Absorption mechanisms inside the keyhole. (a) Inverse bresmsstr...

Figure 10.16 A fiber laser beam distribution with an outer ring surrounding ...

Figure 10.17 Variation of crack sensitivity with composition for various alu...

Figure 10.18 Micrograph of a Cu–Al joint cross section produced by laser lap...

Figure 10.19 Variation of porosity formation with welding speed for a 20 mm‐...

Figure 10.20 Schematic of the multiple‐beam laser welding concept.

Figure 10.21 Effect of preheating with a dual beam on cooling rates.

Figure 10.22 Schematic of humping during single‐beam welding. (a) Sound bead...

Figure 10.23 (a) Mechanism of humping during single‐beam welding. (b) Preven...

Figure 10.24 (a) Effect of welding current on laser‐augmented arc welding....

Figure 10.25 Illustration of wobble welding. (a) Common wobble patterns. (b)...

Figure 10.26 Comparison of welds produced by: (a) wobble welding and (b) tra...

Figure 10.27 (a) Beam delivery system for remote laser welding. (b) Work env...

Figure 10.28 Cadillac center pillar inner.

Figure 10.29 Illustration of the separation (divided) and integration (one‐s...

Figure 10.30 (a) Automotive body‐in‐white showing typical laser‐welded tailo...

Figure 10.31 Illustration of (a) joint gap and (b) beam misalignment.

Figure 10.32 Tensile specimens of tailor welded blanks. (a) Longitudinal spe...

Figure 10.33 Cracking during forming of tailor welded blanks. (a) Crack runn...

Figure 10.34 Force equilibrium in the transverse direction of a tailored wel...

Figure 10.35 Schematic of the laser transmission welding process.

Chapter 11

Figure 11.1 Laser surface heat treatment. (a) Set‐up.(b) Cross‐section o...

Figure 11.2 Hardness variation for different scanning velocities for AISI 43...

Figure 11.3 Optical integration.

Figure 11.4 Schematic of the resonator geometry and diffraction of the outpu...

Figure 11.5 Beam rastering.

Figure 11.6 Common beam shapes used in laser surface treatment and their cor...

Figure 11.7 Grain boundary impregnation by coatings. Source: Gnanamuthu and ...

Figure 11.8 Variation of depth of hardening with angle of incidence of a p‐p...

Figure 11.9 Effect of initial microstructure on laser surface treatment.

Figure 11.10 Transformation of pearlite to austenite.

Figure 11.11 Homogenization of austenite. (a) Diffusion of carbon from pearl...

Figure 11.12 Solution treatment.

Figure 11.13 Illustration of the aging process. (a) Variation of hardness wi...

Figure 11.14 Hardness and ductility variation on a surface‐hardened workpiec...

Figure 11.15 Transverse residual stress variation on a surface‐hardened work...

Figure 11.16 Schematic of the cladding process – The powder feed method.

Figure 11.17 Effect of traverse speed on clad configuration. (a) Cross‐secti...

Figure 11.18 Preplaced powder method of laser cladding.

Figure 11.19 Dilution during the cladding process.

Figure 11.20 Schematic of the laser physical vapor deposition process.

Figure 11.21 Effect of target–substrate distance on film thickness and hardn...

Figure 11.22 Schematic of the laser shock peening process.

Figure 11.23 Schematic of the confined ablation process.

Figure 11.24 (a) SEM micrograph and (b) 2D profile illustrating the geometry...

Figure 11.25 SEM micrograph of grooves generated on a multi‐crystalline sili...

Figure B11.1 The iron–carbon diagram.

Chapter 12

Figure 12.1 (a) Schematic of the laser beam bending process.(b) Photos o...

Figure 12.2 Influence of sheet thickness on bend angle for a plain carbon st...

Figure 12.3 Temperature gradient mechanism. (a) Temperature variation in the...

Figure 12.4 An illustration of a shape produced by the temperature gradient ...

Figure 12.5 Buckling mechanism – sequence of steps leading to bending of a p...

Figure 12.6 Upsetting mechanism. (a) Isotherms in the workpiece. (b) Tempera...

Figure 12.7 Sample product resulting from the upsetting mechanism.

Figure 12.8 Two‐layer model of laser beam bending.

Chapter 13

Figure 13.1 General overview of additive manufacturing systems.

Figure 13.2 A spline function.

Figure 13.3 A Bezier curve.

Figure 13.4 (a) A surface constructed from patches: (b) a ruled surface and ...

Figure E13.1

Figure 13.5 Boolean operations on simple geometric figures.

Figure 13.6 Tree structure with Boolean operations for a simple object.

Figure 13.7 Accuracy specification for a CAD system. (a) Absolute deviation....

Figure 13.8 Sample support structure.

Figure 13.9 Slicing of a CAD model. (a) Original object. (b) Sliced object....

Figure 13.10 Variation of build time with slice thickness for liquid‐based s...

Figure 13.11 Basic principle of stereolithography.

Figure 13.12 Hatch types. (a) Triangular hatch. (b) Rectangular hatch. (c) O...

Figure 13.13 Depth profile of a laser scan.

Figure 13.14 Parallel exposure of the resin to the laser beam.

Figure 13.15 3D object produced by two‐photon polymerization. (a) Original C...

Figure 13.16 Setup for the two‐photon polymerization process.

Figure 13.17 Schematic of the selective laser sintering process.

Figure 13.18 Principle of the binder jetting process.

Figure 13.19 Principle of the fused deposition modeling process.

Figure 13.20 Principle of the laminated object manufacturing process.

Figure 13.21 Qualitative comparison of laser‐based additive manufacturing sy...

Figure 13.22 The investment casting process. (a) Making basic unit of patter...

Figure P13.11

Chapter 14

Figure 14.1 Coronary stent. (a) Multi‐link stent on a balloon. (b) Uniform s...

Figure 14.2 (a) A matrix of nanoholes generated using four femtosecond laser...

Figure 14.3 Nano‐features on a gold film irradiated with four interfering fe...

Figure 14.4 Ellipsoidal bumps formed from three beams. (a) Top view. (b) Ato...

Figure 14.5 Linear bumps formed from two beams. (a) Pictorial view. (b) Atom...

Chapter 15

Figure 15.1 Schematic of a cone calorimeter beam dump.

Figure 15.2 Principle of the rotating rod laser beam analyzer.

Figure 15.3 Schematic of the rotating hollow needle‐based laser beam analyze...

Figure 15.4 Section view of the rotating hollow needle‐based laser beam anal...

Figure 15.5 Schematic of knife‐edge scanning slit laser beam profiler.

Figure 15.6 Beam attenuation by diversion and/or neutral density filters.

Figure 15.7 Schematic of simple damped spring‐mass system.

Figure 15.8 Schematic of a piezoelectric transducer.

Figure 15.9 Traditional acoustic emission signal processing terminology.

Figure 15.10 An acoustic mirror detector.

Figure 15.11 An acoustic mirror output signal.

Figure 15.12 Acoustic emission nozzle setup.

Figure 15.13 Acoustic emission nozzle response during laser cutting.

Figure 15.14 Noncontact detection system for audible sound, infrared, and ul...

Figure 15.15 Energy distribution for (a) blackbody on a log scale and (b) bl...

Figure 15.16 Energy distribution for a graybody and a non‐graybody.

Figure 15.17 Basic schematic of a thermocouple junction.

Figure 15.18 (a) Thermal image of a stationary weld pool with heat source di...

Figure 15.19 (a) Thermal image for a nonsymmetrically located heat source. (...

Figure 15.20 (a) Illustration of a structured light set‐up. (b) Illustration...

Figure 15.21 (a) Vision monitoring system. (b) Typical weld pool image befor...

Figure 15.22 (a) Three‐dimensional view of the weld pool image in Figure 15....

Figure 15.23 (a) Results of application of nondirectional edge detector. (b)...

Chapter 16

Figure 16.1 Basic classification scheme.

Figure 16.2 (a) A real signal. (b) Its complex discrete Fourier transform....

Figure 16.3 The Fourier transform of a finite length continuous cosine wavef...

Figure 16.4 Illustration of aliasing on a frequency scale.

Figure 16.5 An example of low‐frequency “impersonating” a high frequency....

Figure 16.6 A two‐dimensional, three‐class feature space with linear decisio...

Figure 16.7 Class‐conditional probability density functions for two hypothet...

Figure 16.8

A posteriori

probabilities for two hypothetical classes.

Figure 16.9 An

n

‐dimensional

s

‐class pattern classifier.

Figure 16.10 Schematic of a standard neural network.

Figure 16.11 Schematic of a restricted Boltzmann machine.

Figure 16.12 Schematic of a deep belief network.

Figure 16.13 Windowed function to be used for the short‐time Fourier transfo...

Figure 16.14 The Mexican hat wavelet.

Chapter 17

Figure 17.1 Schematic of the basic components of the human eye.

Figure 17.2 Focusing of (a) an object and (b) a collimated beam.

Figure 17.3 Absorption characteristics of the different components of the ey...

Figure 17.4 Extent to which different wavelengths of radiation penetrate the...

Figure 17.5 Illustration of interlocked access to a laser hazard area.

Figure 17.6 ANSI warning signs for lasers. (a) Class 2 and 2M lasers. (b) Cl...

Figure 17.7 International warning signs for lasers.

Guide

Cover

Table of Contents

Title Page

Copyright

Dedication

Preface to the Second Edition

Preface to the First Edition

About the Companion Website

Begin Reading

Index

End User License Agreement

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PRINCIPLES OF LASER MATERIALS PROCESSING: DEVELOPMENTS AND APPLICATIONS

Second Edition

Elijah Kannatey‐Asibu, Jr.University of MichiganAnn ArborMI, USA

This second edition first published 2023© 2023 John Wiley & Sons, Inc.

Edition HistoryJohn Wiley & Sons, Inc. (1e, 2009)

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

The right of Elijah Kannatey‐Asibu, Jr., to be identified as the author of this work has been asserted in accordance with law.

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Limit of Liability/Disclaimer of WarrantyIn view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of experimental reagents, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each chemical, piece of equipment, reagent, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

Library of Congress Cataloging-in-Publication Data

Names: Kannatey‐Asibu, E., author.Title: Principles of laser materials processing : developments and applications / Elijah Kannatey‐Asibu, Jr.Description: Second edition. | Hoboken, NJ : Wiley, 2023. | Includes bibliographical references and index.Identifiers: LCCN 2022035658 (print) | LCCN 2022035659 (ebook) | ISBN 9781119881605 (cloth) | ISBN 9781119881612 (adobe pdf) | ISBN 9781119881629 (epub)Subjects: LCSH: Lasers–Industrial applications. | Materials science.Classification: LCC TA1675 .K36 2023 (print) | LCC TA1675 (ebook) | DDC 621.36/6--dc23/eng/20221006LC record available at https://lccn.loc.gov/2022035658LC ebook record available at https://lccn.loc.gov/2022035659

Cover Design: WileyCover Image: © Aumm graphixphoto/Shutterstock

To the memory of my parentsKofi Kannatey and Efuwa EdziibaAnd my childrenBianca, Araba, and Kwame

PREFACE TO THE SECOND EDITION

The second edition emphasizes new developments since the first edition was published. Major additions include a more detailed treatment of fiber lasers, diffractive optics, beam shaping, additive manufacturing, and deep learning networks. More specifically, the following additions or changes have been made:

Chapters 1

to

7

have been condensed into

Chapter 1

since the material is extensively covered in current books on laser physics.

Discussion on Applications of High‐Power Diode Lasers in Section 8.4.5 (now 2.4.6) is expanded to include blue lasers.

Fiber Lasers are given a more detailed treatment in Section 2.5.4.

New material on Beam Shaping Using Diffractive Optics as well as the Coherent Beam Combining with Optical Phase Array technique is introduced in

Section 3.8

.

Subsection 7.5.1.3 has been added on Limitations of Thermal Stress Relief.

A paragraph on

carbon fiber‐reinforced plastic

(

CFRP

) composites has been added to

Section 9.1.6.2

on Nonmetals.

Micro‐Explosions are extensively discussed in

Section 9.3.1.3

.

A brief paragraph on Micromachining Applications is added to

Section 9.3.1.4

.

Additional material on laser welding of galvanized steel is added to

Section 10.4.1

on Steels, where a new method for eliminating porosity in lap welding of galvanized steel is discussed.

In

Section 10.4.2

on Non‐Ferrous Alloys, a paragraph is added on laser welding of aluminum for the casing of lithium ion cells used in electric vehicles.

Section 10.4.4

on Dissimilar Metals is expanded to include a more detailed discussion on the effect of composition differences between the welded materials, using copper and aluminum as an example.

In

Section 10.7

on Special Techniques, two major subsections are introduced: 10.7.3 on Wobble Welding and 10.7.4 on Remote Laser Welding.

Two new sections, 10.8.3 on Laser Transmission Welding of Plastics and 10.8.4 on Laser Brazing, are added, with laser brazing covering both autogenous and non‐autogenous processes.

In

Section 11.1

on Laser Surface Heat Treatment, two major subsections, 11.1.8 on Semiconductors and 11.1.9 on Polymers, are added.

Additional material on the use of femtosecond pulse lasers for laser shock peening is added to

Section 11.5

.

Section 11.5.1

on Background Analysis of laser shock peening is expanded.

A new section (11.5.2) on Thermal Relaxation at High Temperatures is added.

A brief section (11.5.4) on Applications of Laser Shock Peening is added.

A major section (11.6) on Laser Surface Texturing is added.

Chapter 13

, originally titled “Rapid Prototyping,” has been retitled “Additive Manufacturing” with new material. These include

Section 13.2.2.2

on

Direct Metal Deposition

(

DMD

),

Section 13.2.3.3

on Wire Deposition,

Section 13.4.4

on Personalized Production, and

Section 13.5

on Advantages and Disadvantages. Manufacturers of equipment for the different processes have also been updated. Two‐photon polymerization, which was originally in Chapter 20 (now 14), has been moved to this chapter, since it involves building components on a micro‐scale.

Measurement of beam mode,

Section 15.1.2

, has been organized into three categories that include new subsections on camera‐based and knife‐edge methods.

Section 16.3.2

on Neural Network Analysis has been expanded to include a new subsection (16.3.2.2) on Deep Learning Networks.

Section 16.3.2.1

on Standard Neural Networks has also been expanded.

Several new references and problems have been added to a number of chapters.

ELIJAH KANNATEY-ASIBU, JR.

Professor Emeritus of Mechanical EngineeringUniversity of MichiganAnn Arbor

PREFACE TO THE FIRST EDITION

Application of lasers in materials processing has been evolving since the development (first demonstration) of the laser in 1960. The early applications focused on processes such as welding, machining, and heat treatment. Newer processes that have evolved over the years include laser forming, shock peening, micromachining, rapid prototyping, and nano processing. The book provides a state‐of‐the‐art compilation of material in the major application areas and is designed to provide the background needed by graduate students to prepare them for industry; researchers to initiate a research program in any of these areas; and practicing engineers to update themselves and gain additional insight into the latest developments in this rapidly evolving field.

The book is partitioned into three parts. The first part, Principles of Industrial Lasers (Chapters 1 to 9), introduces the reader to basic concepts on the characteristics of lasers, design of their components, and beam delivery. It is presented in a simple enough format that an engineering student without any prior knowledge of lasers can fully comprehend. It helps the reader acquire a basic understanding of how a laser beam is generated, its basic properties, propagation of the beam, and the various types of lasers available and their specific characteristics. Such knowledge is useful to all engineering students, irrespective of their specific interests or area of application. It will enable them to select an appropriate laser for a given application and help them to determine how best to utilize the laser. The coverage starts with a discussion on laser generation – basic atomic structure and how it leads to atomic transitions (absorption, spontaneous emission, and stimulated emission). The concepts of population inversion and gain criterion for laser action are introduced. Optical resonators (planar and spherical) are discussed in relation to beam modes (longitudinal and transverse) and stability of optical resonators. Techniques for line and mode selection are outlined. Various pumping techniques that can be used to achieve inversion are then presented, including more recent developments such as diode pumping. The rate equations are then introduced to provide some insight into the conditions necessary for achieving population inversion for both 3‐ and 4‐level systems. This is followed by a discussion on broadening mechanisms that are responsible for the spread of a laser frequency over a finite range. These include both homogeneous (natural and collision broadening) and inhomogeneous (Doppler) broadening. Beam modification mechanisms such as Q‐switching and mode‐locking are presented. Having obtained a fundamental background on laser generation, the characteristics of beams that have a more direct impact on their application are then discussed. These include beam characteristics such as divergence, monochromaticity (with reference to broadening), coherence, polarization, intensity and brightness, frequency stabilization, and focusing. Different types of lasers are then discussed with specific emphasis on high‐power lasers used in industrial manufacturing. These include solid‐state lasers (Nd:YAG and Nd:Glass); gas lasers (neutral atom, ion, metal vapor (copper‐vapor) and molecular lasers (CO2 and excimer); dye lasers; and semiconductor (diode) lasers. Finally, beam delivery systems are introduced, discussing concepts such as the Brewster angle, polarization, beam expanders, beam splitters, and transmissive, reflective, and fiber optics.

The second part, Engineering Background (Chapters 10 to 13), reviews the engineering concepts that are needed to analyze the different processes. Topics that are discussed include thermal analysis and fluid flow, the microstructure that results from the heat effect, solidification of the molten metal for processes that involve melting, and residual stresses that evolve during the process.

The third part, Laser Materials Processing (Chapters 14 to 23), provides a more rigorous and detailed coverage on the subject of laser materials processing and discusses the principal application areas such as laser cutting and drilling, welding, surface modification, laser forming, rapid prototyping, sensor systems, process monitoring, and medical and nanoapplications. Sensors that are normally used for monitoring process quality are also discussed, along with methods for analyzing the sensor outputs. Finally, basic concepts on laser safety are presented. The range of processing parameters associated with each process are outlined. The impact of the basic laser characteristics such as wavelength, divergence, monochromaticity, coherence, polarization, intensity, stability, focusing, and depth of focus, as discussed in Part I, on each process, is emphasized.

The material in this book is suitable for a two‐course sequence on laser processing. The material in Part I is adequate for an upper division/first‐year graduate course in engineering. Parts II and III can then be used for a follow‐up course, or the material in Part I can be skipped if only one course needs to be offered. In either case, Part II can be quickly reviewed and more time spent on Part III.

Two sets of nomenclature are used in this text. There is an overall nomenclature that is reserved for variables that are used throughout the text. In addition, each chapter has its own nomenclature that is used for variables that are used primarily in that chapter.

The author wishes to express his gratitude to all his colleagues and friends who have provided feedback on the manuscript. Special gratitude goes to all the graduate students who critiqued the course pack on which the book is based and to Mr. Rodney Hill (rodhillgraphics.com) for the skillful illustrations.

ELIJAH KANNATEY-ASIBU, JR.

University of MichiganAnn Arbor

ABOUT THE COMPANION WEBSITE

This book is accompanied by a companion website.

www.wiley.com/go/Kannatey-Asibu/PrinicplesLaserMaterialsProcessing

This website includes Solutions Manual

PART IPrinciples of Industrial Lasers

1Laser Background

1.1 LASER GENERATION

The term laser is an acronym for light amplification by stimulated emission of radiation, and thus a laser beam is a form of electromagnetic radiation. Light may be simply defined as electromagnetic radiation that is visible to the human eye. It has a wavelength range of about 0.37–0.75 μm, between ultraviolet and infrared radiation. Lasers, on the other hand, may have wavelengths ranging from 0.2 to 500 μm, that is, from X‐ray to infrared radiation. In its simplest form, laser generation is the result of energy emission associated with the transition of an electron from a higher to a lower energy level or orbit within an atom.

Figure 1.1 illustrates the electromagnetic spectrum. The colors associated with the various wavelengths in the visible range are shown in Table 1.1.

1.1.1 Atomic Transitions

Under the right conditions, electrons within an atom can change their orbits. Light or energy (photon) is emitted as an electron moves from a higher level or outer orbit to a lower level or inner orbit and is absorbed when the reverse transition takes place. There is a specific quantum of energy (photon), ΔE, of specific wavelength or frequency associated with each transition from one energy level to another and is given by:

(1.1)

where c is the velocity of light = 3 × 108 (exactly 299,792,458) m/s, hp is Planck's constant = 6.625 × 10−34 J s, λ is the wavelength (m), ν is the frequency of transition between the energy levels (Hz), and ΔE is the energy difference between the levels of interest.

1.1.1.1 Population Distribution

For simplicity, let us focus our initial discussion on a single frequency, which corresponds to two specific energy levels, E1 and E2, where E1 is the lower energy level and E2 is a higher energy level, that is, E2 > E1. Furthermore, we let the population or number of atoms (or molecules or ions) per unit volume at level 1 be N1, and that at level 2 be N2. We also assume conditions of non‐degeneracy. Degeneracy exists when there is more than one level with the same energy.

Figure 1.1 The electromagnetic spectrum.

Table 1.1 Wavelengths associated with the visible spectrum.

Wavelength range (nm)

Color

400–450

Violet

450–480

Blue

480–510

Blue‐Green

510–550

Green

550–570

Yellow‐Green

570–590

Yellow

590–630

Orange

630–700

Red

Under conditions of thermal equilibrium, the lower energy levels are more highly populated than the higher levels, and the distribution is given by Boltzmann's law that relates N1 and N2 as:

(1.2)

where kB is Boltzmann's constant = 1.38 × 10−23 J/K and T is the absolute temperature (K).

This is illustrated in Figure 1.2a. Figure 1.2b illustrates the equilibrium distribution for the more general case. Boltzmann's law holds for thermal equilibrium conditions.

Figure 1.2 Schematic of Boltzmann's law. (a) Two‐level system. (b) More general case for a multilevel system.

1.1.1.2 Absorption

When atoms in a ground state, E1, are excited or stimulated, that is, subjected to some external radiation or photon whose energy is the same as the energy difference between E1 and a higher state, E2, the atoms will change their energy level, as shown in Figure 1.3a. This process is called stimulated absorption. The rate at which energy is absorbed by the atoms is given by:

(1.3)

where B12 is a proportionality constant referred to as the Einstein coefficient for stimulated absorption, or stimulated absorption probability per unit time per unit spectral energy density (m3 Hz/J s), N1 is the population of level 1 (per m3), e(ν) is the energy density (energy per unit volume) at the frequency ν(J/m3 Hz), and nabs is the absorption rate (number of absorptions per unit volume per unit time).

Figure 1.3 Schematic of (a) absorption, (b) spontaneous emission, and (c) stimulated emission.

Once the atom has been excited to a higher energy level, it can make a subsequent transition to a lower energy level, accompanied by the emission of electromagnetic radiation. The emission process can occur by spontaneous emission or stimulated emission. Each absorption removes a photon, and each emission creates a photon.

1.1.1.3 Spontaneous Emission

Spontaneous emission occurs when transition from the excited to the lower energy level is not stimulated by any incident radiation (Figure 1.3b). The transition results in the emission of a photon of energy:

(1.4)

where ν is the frequency of the emitted photon. In spontaneous emission, the rate of emission per unit volume, nsp, to the lower energy level is only proportional to the population, N2, at the higher energy level, and is independent of radiation energy density:

(1.5)

where Ae is the Einstein coefficient for spontaneous emission, or spontaneous emission probability per unit time.

1.1.1.4 Stimulated Emission

If the atom in energy level 2 is subjected to electromagnetic radiation or photon of frequency ν corresponding to the energy difference ΔE = E2 − E1 between levels 1 and 2, the photon will stimulate the atom to undergo a transition to the lower energy level. The energy emitted is the same as the stimulating photon and is superimposed on the incident photon, thereby reinforcing the emitted light (Figure 1.3c). This results in stimulated emission, where the incident and emitted photons have the same characteristics and are in phase, resulting in a high degree of coherence, and the direction, frequency, and state of polarization of the emitted photon are essentially the same as those of the incident photon. The two photons can generate yet another set, with a resulting avalanche of photons. This is illustrated schematically in Figure 1.4. The rate of emission per unit volume, nst, in the case of stimulated emission is given by:

(1.6)

where B21 is the Einstein coefficient for stimulated emission, or stimulated emission probability per unit time per unit energy density (m3 Hz/J s).

Figure 1.4 Illustration of the process of stimulated emission.

Source: From Chryssolouris (1991)/Springer Nature.

1.1.1.5 Einstein Coefficients: , ,

Under conditions of thermal equilibrium, the rates of upward (E1 → E2) and downward (E2 → E1) transitions must be the same. Thus, we have

(1.7)

or from Eqs. (1.3), (1.5), and (1.6),

(1.8)

This gives the energy density as:

(1.9)

This can be compared with the energy density from Planck's law on blackbody radiation:

(1.10)

Equations (1.9) and (1.10) are equivalent only if

(1.11a)

and

(1.11b)

Example 1.1

(a) Compare the rates of spontaneous and stimulated emission at room temperature (T = 300 K) for an atomic transition where the frequency associated with the transition is 3 × 1010 Hz, in the microwave region.

Solution:

From Eqs. (1.10) and (1.11),

Thus,

This indicates that the stimulated emission rate is much greater than the spontaneous emission rate, and thus amplification is feasible in the microwave range at room temperature.

(b) Repeat Example 1.1a for a transition frequency in the optical region of

ν

 = 10

15

.

Solution:

indicating that spontaneous emission is then predominant, resulting in incoherent emission from normal light sources. In other words, under conditions of thermal equilibrium, stimulated emission in the optical range is very unlikely.

(c) What will be the wavelength of the line spectrum resulting from the transition of an electron from an energy level of 40 × 10

−20

 J to a level of 15 × 10

−20

 J?

Solution:

From Eq. (1.1), we have

Therefore,

1.1.2 Lifetime

The lifetime, τsp, of atoms in an excited state is a measure of the time period over which spontaneous transition occurs. Strictly speaking, this is how long it takes for the number of atoms in the excited state to reduce to 1/e of the initial value. It can be shown that τsp is related to the Einstein coefficient for spontaneous emission by:

(1.12)

1.1.3 Optical Absorption

The intensity, I, of a laser beam diminishes as it propagates through an absorbing medium. The variation of the beam intensity with distance (Figure 1.5) can be expressed as:

(1.13)

Figure 1.5 Propagation of a monochromatic beam in the x‐direction.

Integration of Eq. (1.13) results in the following expression for the beam variation in the material:

(1.14)

where I0 is the intensity of the incident beam (W/m2) and α is the absorption coefficient (m−1). This is known as the Beer–Lambert law and indicates that the beam intensity varies exponentially as it propagates into the medium.

Example 1.2

A medium absorbs 1% of the light incident on it over a distance of 1.5 mm into the medium. Determine

(i) The medium's absorption coefficient.

(ii) The length of the medium if it transmits 75% of the light.

Solution:

(i) From

Eq. (1.14)

, we have

If 1% of the incident light is absorbed over a distance of 1.5 mm, then

Therefore,

(ii) If 75% of the incident light is transmitted, then

Therefore,

1.1.4 Population Inversion

The absorption coefficient, α, is positive if N1 > N2. The beam intensity then decreases exponentially with distance into the material. Since N1 > N2 under normal thermal equilibrium conditions, the beam will be attenuated as it propagates through the medium.

However, if conditions are such that the number of atoms at the higher energy level is greater than those at the lower energy level, that is, N2 > N1, then α will be negative, in which case the beam intensity will increase exponentially as it propagates through the medium. Equation (1.14) can then be written as:

(1.15)