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Dynamics of lasers
Book R e v i e w s of the radiation and the spectral sensitivity of the r e c e p t o r s involved in p h o t o g r a p h y rarely r e s e m b l e anything like the distributions implied in visual photometry. However, in spite of the small irritations caused b y the traditional p h o t o g r a p h e r s ' imprecision in physical terminology and the u n c o r r e c t e d e r r o r s (vital as they might p r o v e to be if e r r o n e o u s statements ar e taken as true) this is still a remarkable production, and v e r y valuable as a concise r e fe ren ce.
J. W. c. Gates
Electro-Optical Systems Performance Modeling G. Waldman and J. Wootton Artech House, 1993, ISBN 0890-065411, pp 241 + xiv, $85 In their own words, this book aims to take the authors' expertise in electro-optics systems design and pass this on to a new generation of designer. The book, as such, is full of useful tips, rules of thumb and practical guidance which can only come from years of hands-on e x p e r i e n c e . However, this in itself also p r o v i d e s the main source of weakness of the book. It concentrates primarily on the areas in which the authors have direct experience; it seems to home in on target acquisition systems b a s e d in the infra-red region of the spectrum. Although this emphasis obviously springs from the authors' largely military background, they have m a y b e missed an opportunity to widen the scope h e r e and make this book appeal to a m o r e general audience. In many ways, though, this is a useful, and novel, book. Systems design is an ar e a often n e g l e c t e d in textbooks on optics, optoelectronics or optical engineering. Messrs Waldmann and Wootton are to b e congratulated for trying to r e d r e s s the balance. However, I do not a g r e e with their claim that the b o o k could s e r v e as the basis of an u n d e r g r a d u a t e course. Certainly some aspects may be c o v e r e d in typical optics or optoelectronics courses, in particular some of the practical examples, but otherwise the material is too specialized and focused on one area. The main theme of the book is the design and p e r f o r m a n c e analysis of electro-optic systems. As indicated ab o v e this comes down heavily on infrar e d systems for image detection. Chapters are included on, for example, radiation sources and transfer, atmospheric behaviour, systems modOptics & Laser Technology Vol 25 No 4 1993
elling and case studies of complete systems. Within each of these chapters are sections on optics design, computational methods of p e r f o r m a n c e evaluation, displays and sensor performance. The sections on radiation transfer, optics and signal processing are particularly useful in the wider context. T here is a lot of valuable data contained in this book which is not easy to obtain e l s e w h e r e the systems modelling is to be com m ended. However, in some aspects the book is rather patchy. Some diagrams are good, clear and informative; others are a bit confusing. For example one figure which tries to illustrate p r o j e c t e d areas normal to the line of observation manages to confuse rather than help the appreciation of this simple concept. On another tack, how many diagrams of bl ackbody radiation curves does one book need? This one shows them twice, albeit with slightly different units. The blackb o d y equation itself is quoted several times in slightly different forms, giving an element of repetition to the text. Maybe this is what the authors intended. T h e r e are some strange quirks: why do they spend time talking about a sliding card infrar e d radiation 'calculator'? In these days of powerful pocket-size electronic calculators and laptop computers, surely n o b o d y still uses such a template? All in all, a qualified approval can be given to this text, mainly because the information is difficult to obtain in a single source. I think though, it is not for the u n d e r g r a d u a t e but for the practising systems designer.
John Watson University of A b e r d e e n
Dynamics of Lasers C. O. Weiss and R. Vilaseca VCH Publishers, 1991, ISBN 3-527-26586-4 (VCH, Weinheim), pp 432, £66 (Hardback) The authors are to b e c o m m e n d e d for producing a m o n o g r a p h which clarifies many aspects of laser behaviour (excluding m o d e locking) and enables p h e n o m e n a such as unstable emission, p o o r r e p r o ducibility of laser pulses, limitations of attainable widths and the like which have hitherto b e e n diagnosed by frustrated experimentalists as 'noise nuisance' to be understood, classified in terms of chaos, and dealt with accordingly. While the title Dynamics of Lasers will obviously attract laser engi neers and physicists, the book is such a g o o d introduction to research-level non-linear dynamics in general, that 'non-linear' should a p p e a r in the title for a second edition to reach this particular
273
Book Reviews readership; however, the fact that the book is Volume 1 of a p r o j e c t e d series on Nonlinear Systems may help in this regard. The laser systems c o n s i d e r e d are of 2, 3 and 4 levels, respectively. Mathematical treatments to d e s c r i b e the nonlinear dynamics are through either differential equations (time-continuous dynamics) or logistic maps (time-discontinuous or discrete dynamics) e v e n though the latter, in principle, do not correspond to any kind of laser. Throughout the book, the pattern of presentation is to give background, lay foundations, d e v e l o p the topic, and illustrate with practical examples; the result is a book (suitable as a textbook) which establishes technical terms and teaches with clarity in subject areas which are often opaque. The basic assumptions underlying all the calculations and interpretations of experimental results mad e throughout the book up to Chapter 10 are that the laser field is confined b e t w e e n plane infinitely e x t e n d e d mirrors and that the medium extends to infinity and is h o m o g e n e o u s throughout. To d e s c r i b e the book, note that binding, paper, and print are of the highest quality. There are about 500 words p e r p a g e and a total of 276 pages. Displayed and n u m b e r e d equations a p p e a r on about 70 p ag es only. This is a relatively small n u m b e r for a r e s e a r c h level book in an area which is quantitative in character. The mathematical treatments are illustrated c o m p r e h e n s i v e l y with 234 figures (mostly line diagrams and oscilloscope traces), about 33% of which are original; only 86 pages are without diagrams. The 8-page index is thorough. The c o m p r e h e n s i v e bibliography up to and including 1989 is a r r a n g e d alphabetically by chapter o v er 12 pages. Of the 307 r e f e r e n c e s quoted, 175 are m o r e r e c e nt than 1984. The two earliest r e f e r e n c e s are to Shannon and W e a v e r (1949) and Statz and de Mars (1960). In relation to the stage of d e v e l o p m e n t of understanding of nonlinear dynamics and laser dynamics, as shown by the literature, the timing of publication of this monog ra p h is 'spot on'. The substance of the book begins in Chapter 2 with the Lorenz-Haken laser model. Haken (1975) r e c o g n i z e d that certain coupled first-order differential equations for the simplest laser ar e isomorphic with the three equations us ed by Lorenz (1963) to study Rayleigh-B6nard convection flow. These equations relate time derivatives of field amplitude, i n d u ced polarization and population inversion, respectively, to functions of these same variables and relaxation rate constants ~, y~ and ~p, which are for the field amplitude, polarizatibn (dipole moment), and population inversion, respectively. Lasers are classified as A, B or C according to the relative sizes of the par a m et er s ~, y± and yp. In class C lasers, the three p a r a m e t e r s are about" equal to one another (same magnitude). For class A lasers we have ~_ ~ 7p_~ ~ (polarization and population
274
d e c a y much faster than the field amplitude) and for class B, 7~ ~ ~ ~ Y~ (only the polarization dec a y s fast). Class C lasers are the only ones with the three d e g r e e s of f r e e d o m (under resonance conditions) n e c e s s a r y for chaotic dynamics. Lasers of classes A and B n e e d additional d e g r e e s of f r e e d o m to b e h a v e chaotically. Methods for introducing these include periodic modulation of one laser p a r a m e t e r such as resonator loss, resonator frequency, or pum p rate. Other methods are b y addition of feedback, or by injection of an external optical field. After a short introduction (two pages) which gives an overvi ew of the book, there follows a brief history of the study of laser dynamics and a rev ie w of laser propert i es (13 pages) in the b r o a d terms n e c e s s a r y for classification and subsequent application in the dynamical equations to be d e v e l o p e d and studied. Chapter 2 (18 pages) discusses the Lorenz-Haken laser model and the logistic map to illustrate two of the a p p r o a c h e s in studying dynamical problems. In the next two chapters (46 pages), mathematical concepts g o v e r n i n g the general features of non-linear dynamical behaviour to b e c o n s i d e r e d in later chapters are described, along with characterization and quantification of chaos with emphasis on asymptotic dynamic behaviour. The laser and non-linear dynamic theories d e v e l o p e d are adapted in the remaining chapters to descri be examples of the three laser classes (A, B, C) in p r o g r e s s i v e l y m o r e complicated conditions which finally include transverse variations of laser param et ers and variables in Chapter 10. The simplest case of a two-level, h o m o g e n e o u s l y b r o a d e n e d , travelling wave, single-mode laser is introduced in Chapter 5 (38 pages). Equations of the semi-classical Maxwell-Bloch type are d e r i v e d in the plane-wave uniform-field approximation and e x t e n d e d to include inhomogeneous broadening. These equations, or similar ones d e v e l o p e d for different kinds of lasers are used in subsequent chapters. Also used are the laser equations of Sargent, Scully and Lamb in which the atomic medium is d e s c r i b e d by the e n s e m b l e - a v e r a g e d density matrix, the elements of which descri be the level populations and induced polarization cre a te d at time t and point z b y the atoms close to this point. The t heory d e v e l o p e d is first applied to class C lasers with h o m o g e n e o u s b r o a d e n i n g and is then e x t e n d e d to include inhomogeneous broadening. Experimental results obtained with HeXe and HeNe lasers operating on infra-red transitions are discussed and c o m p a r e d with theory. It is noted that the dynamical behaviour of the HeXe laser is most completely understood. Chapter 6 (18 pages) considers mid-infrared gas lasers and semiconductor lasers containing intracavity saturable a b s o r b e r s (for example, COz laser, CH3I absorber; semiconductor laser with a gain section and an a b s o r b e r section in series). A Optics & Laser Technology vol 25 No 4 1993
Book R e v i e w s number of models of a gas laser with gas absorber are described and discussed. The range in sophistication is from a simple two-level model to a so-called 'three-level-two-level' model which gives agreement with experimental results. A set of rate equations for semiconductor lasers is given and experimental results including period doubling and chaotic dynamics for semiconductor diode lasers are described. Chapter 7 (44 pages) considers the dynamical behaviour of class B lasers (described by two-level rate equation models) with a d d e d d e g r e e s of freedom using carbon dioxide, semiconductor and solid-state lasers as examples. Unusually, the radio frequency NMR ruby 'laser' is also included. The theory given covers C Q lasers with modulation of resonator loss, resonator frequency, and pumping. Equations are also discussed for lasers with feedback (electrical, optical) and injected optical field. Experimental results receive careful attention. Chapter 8 (28 p a g e s ) i s devoted to three-level optically (laser) p u m p e d single-mode gas lasers with an emphasis on experimental results and scant theory b e y o n d a discussion of the greater complexity introduced by the coherence of the pump radiation and the necessity for a three-level model which leads to many more coupled equations than those necessary to describe two-level systems. Dynamics of lasers operating with multiple longitudinal modes are described in Chapter 9 (32 pages). Some theory and experimental results for
Optics & Laser Technology Vol 25 No 4 1993
co-propagating and counter-propagating modes in two-level lasers are discussed. Special cases considered include dye lasers, lasers with intracavity frequency doubling, transverse modes and diode lasers with external reflectors. Transverse effects and spatial instabilities are the subject of Chapter 10 (15 pages) but, here, modelling and theory become quite involved so the approach is more of a review, albeit a good one. The laser (whether homogeneously or inhomogeneously broadened) e m e r g e s as an archetypical system suitable for the experimental studies of nonlinear dynamics applicable to other technically important dynamic, chaotic and turbulent processes. In the simplest case, laser behaviour may be described by the Lorenz model which is discussed in some detail. Among the many advantages of lasers over fluids for experimental investigations of non-linear dynamics may be placed the greater d e g r e e of control of boundary conditions for laser systems, than is possible for fluid systems. Also, the number of d e g r e e s of freedom (for example, modes) are easier to control. In summary, the book contains a wealth of information and good teaching in both non-linear dynamics and laser physics which should make its way into many lecture courses; it has been a pleasure to review. Arthur Maitland University of St A n d r e w s
275
J. W. c. Gates
Electro-Optical Systems Performance Modeling G. Waldman and J. Wootton Artech House, 1993, ISBN 0890-065411, pp 241 + xiv, $85 In their own words, this book aims to take the authors' expertise in electro-optics systems design and pass this on to a new generation of designer. The book, as such, is full of useful tips, rules of thumb and practical guidance which can only come from years of hands-on e x p e r i e n c e . However, this in itself also p r o v i d e s the main source of weakness of the book. It concentrates primarily on the areas in which the authors have direct experience; it seems to home in on target acquisition systems b a s e d in the infra-red region of the spectrum. Although this emphasis obviously springs from the authors' largely military background, they have m a y b e missed an opportunity to widen the scope h e r e and make this book appeal to a m o r e general audience. In many ways, though, this is a useful, and novel, book. Systems design is an ar e a often n e g l e c t e d in textbooks on optics, optoelectronics or optical engineering. Messrs Waldmann and Wootton are to b e congratulated for trying to r e d r e s s the balance. However, I do not a g r e e with their claim that the b o o k could s e r v e as the basis of an u n d e r g r a d u a t e course. Certainly some aspects may be c o v e r e d in typical optics or optoelectronics courses, in particular some of the practical examples, but otherwise the material is too specialized and focused on one area. The main theme of the book is the design and p e r f o r m a n c e analysis of electro-optic systems. As indicated ab o v e this comes down heavily on infrar e d systems for image detection. Chapters are included on, for example, radiation sources and transfer, atmospheric behaviour, systems modOptics & Laser Technology Vol 25 No 4 1993
elling and case studies of complete systems. Within each of these chapters are sections on optics design, computational methods of p e r f o r m a n c e evaluation, displays and sensor performance. The sections on radiation transfer, optics and signal processing are particularly useful in the wider context. T here is a lot of valuable data contained in this book which is not easy to obtain e l s e w h e r e the systems modelling is to be com m ended. However, in some aspects the book is rather patchy. Some diagrams are good, clear and informative; others are a bit confusing. For example one figure which tries to illustrate p r o j e c t e d areas normal to the line of observation manages to confuse rather than help the appreciation of this simple concept. On another tack, how many diagrams of bl ackbody radiation curves does one book need? This one shows them twice, albeit with slightly different units. The blackb o d y equation itself is quoted several times in slightly different forms, giving an element of repetition to the text. Maybe this is what the authors intended. T h e r e are some strange quirks: why do they spend time talking about a sliding card infrar e d radiation 'calculator'? In these days of powerful pocket-size electronic calculators and laptop computers, surely n o b o d y still uses such a template? All in all, a qualified approval can be given to this text, mainly because the information is difficult to obtain in a single source. I think though, it is not for the u n d e r g r a d u a t e but for the practising systems designer.
John Watson University of A b e r d e e n
Dynamics of Lasers C. O. Weiss and R. Vilaseca VCH Publishers, 1991, ISBN 3-527-26586-4 (VCH, Weinheim), pp 432, £66 (Hardback) The authors are to b e c o m m e n d e d for producing a m o n o g r a p h which clarifies many aspects of laser behaviour (excluding m o d e locking) and enables p h e n o m e n a such as unstable emission, p o o r r e p r o ducibility of laser pulses, limitations of attainable widths and the like which have hitherto b e e n diagnosed by frustrated experimentalists as 'noise nuisance' to be understood, classified in terms of chaos, and dealt with accordingly. While the title Dynamics of Lasers will obviously attract laser engi neers and physicists, the book is such a g o o d introduction to research-level non-linear dynamics in general, that 'non-linear' should a p p e a r in the title for a second edition to reach this particular
273
Book Reviews readership; however, the fact that the book is Volume 1 of a p r o j e c t e d series on Nonlinear Systems may help in this regard. The laser systems c o n s i d e r e d are of 2, 3 and 4 levels, respectively. Mathematical treatments to d e s c r i b e the nonlinear dynamics are through either differential equations (time-continuous dynamics) or logistic maps (time-discontinuous or discrete dynamics) e v e n though the latter, in principle, do not correspond to any kind of laser. Throughout the book, the pattern of presentation is to give background, lay foundations, d e v e l o p the topic, and illustrate with practical examples; the result is a book (suitable as a textbook) which establishes technical terms and teaches with clarity in subject areas which are often opaque. The basic assumptions underlying all the calculations and interpretations of experimental results mad e throughout the book up to Chapter 10 are that the laser field is confined b e t w e e n plane infinitely e x t e n d e d mirrors and that the medium extends to infinity and is h o m o g e n e o u s throughout. To d e s c r i b e the book, note that binding, paper, and print are of the highest quality. There are about 500 words p e r p a g e and a total of 276 pages. Displayed and n u m b e r e d equations a p p e a r on about 70 p ag es only. This is a relatively small n u m b e r for a r e s e a r c h level book in an area which is quantitative in character. The mathematical treatments are illustrated c o m p r e h e n s i v e l y with 234 figures (mostly line diagrams and oscilloscope traces), about 33% of which are original; only 86 pages are without diagrams. The 8-page index is thorough. The c o m p r e h e n s i v e bibliography up to and including 1989 is a r r a n g e d alphabetically by chapter o v er 12 pages. Of the 307 r e f e r e n c e s quoted, 175 are m o r e r e c e nt than 1984. The two earliest r e f e r e n c e s are to Shannon and W e a v e r (1949) and Statz and de Mars (1960). In relation to the stage of d e v e l o p m e n t of understanding of nonlinear dynamics and laser dynamics, as shown by the literature, the timing of publication of this monog ra p h is 'spot on'. The substance of the book begins in Chapter 2 with the Lorenz-Haken laser model. Haken (1975) r e c o g n i z e d that certain coupled first-order differential equations for the simplest laser ar e isomorphic with the three equations us ed by Lorenz (1963) to study Rayleigh-B6nard convection flow. These equations relate time derivatives of field amplitude, i n d u ced polarization and population inversion, respectively, to functions of these same variables and relaxation rate constants ~, y~ and ~p, which are for the field amplitude, polarizatibn (dipole moment), and population inversion, respectively. Lasers are classified as A, B or C according to the relative sizes of the par a m et er s ~, y± and yp. In class C lasers, the three p a r a m e t e r s are about" equal to one another (same magnitude). For class A lasers we have ~_ ~ 7p_~ ~ (polarization and population
274
d e c a y much faster than the field amplitude) and for class B, 7~ ~ ~ ~ Y~ (only the polarization dec a y s fast). Class C lasers are the only ones with the three d e g r e e s of f r e e d o m (under resonance conditions) n e c e s s a r y for chaotic dynamics. Lasers of classes A and B n e e d additional d e g r e e s of f r e e d o m to b e h a v e chaotically. Methods for introducing these include periodic modulation of one laser p a r a m e t e r such as resonator loss, resonator frequency, or pum p rate. Other methods are b y addition of feedback, or by injection of an external optical field. After a short introduction (two pages) which gives an overvi ew of the book, there follows a brief history of the study of laser dynamics and a rev ie w of laser propert i es (13 pages) in the b r o a d terms n e c e s s a r y for classification and subsequent application in the dynamical equations to be d e v e l o p e d and studied. Chapter 2 (18 pages) discusses the Lorenz-Haken laser model and the logistic map to illustrate two of the a p p r o a c h e s in studying dynamical problems. In the next two chapters (46 pages), mathematical concepts g o v e r n i n g the general features of non-linear dynamical behaviour to b e c o n s i d e r e d in later chapters are described, along with characterization and quantification of chaos with emphasis on asymptotic dynamic behaviour. The laser and non-linear dynamic theories d e v e l o p e d are adapted in the remaining chapters to descri be examples of the three laser classes (A, B, C) in p r o g r e s s i v e l y m o r e complicated conditions which finally include transverse variations of laser param et ers and variables in Chapter 10. The simplest case of a two-level, h o m o g e n e o u s l y b r o a d e n e d , travelling wave, single-mode laser is introduced in Chapter 5 (38 pages). Equations of the semi-classical Maxwell-Bloch type are d e r i v e d in the plane-wave uniform-field approximation and e x t e n d e d to include inhomogeneous broadening. These equations, or similar ones d e v e l o p e d for different kinds of lasers are used in subsequent chapters. Also used are the laser equations of Sargent, Scully and Lamb in which the atomic medium is d e s c r i b e d by the e n s e m b l e - a v e r a g e d density matrix, the elements of which descri be the level populations and induced polarization cre a te d at time t and point z b y the atoms close to this point. The t heory d e v e l o p e d is first applied to class C lasers with h o m o g e n e o u s b r o a d e n i n g and is then e x t e n d e d to include inhomogeneous broadening. Experimental results obtained with HeXe and HeNe lasers operating on infra-red transitions are discussed and c o m p a r e d with theory. It is noted that the dynamical behaviour of the HeXe laser is most completely understood. Chapter 6 (18 pages) considers mid-infrared gas lasers and semiconductor lasers containing intracavity saturable a b s o r b e r s (for example, COz laser, CH3I absorber; semiconductor laser with a gain section and an a b s o r b e r section in series). A Optics & Laser Technology vol 25 No 4 1993
Book R e v i e w s number of models of a gas laser with gas absorber are described and discussed. The range in sophistication is from a simple two-level model to a so-called 'three-level-two-level' model which gives agreement with experimental results. A set of rate equations for semiconductor lasers is given and experimental results including period doubling and chaotic dynamics for semiconductor diode lasers are described. Chapter 7 (44 pages) considers the dynamical behaviour of class B lasers (described by two-level rate equation models) with a d d e d d e g r e e s of freedom using carbon dioxide, semiconductor and solid-state lasers as examples. Unusually, the radio frequency NMR ruby 'laser' is also included. The theory given covers C Q lasers with modulation of resonator loss, resonator frequency, and pumping. Equations are also discussed for lasers with feedback (electrical, optical) and injected optical field. Experimental results receive careful attention. Chapter 8 (28 p a g e s ) i s devoted to three-level optically (laser) p u m p e d single-mode gas lasers with an emphasis on experimental results and scant theory b e y o n d a discussion of the greater complexity introduced by the coherence of the pump radiation and the necessity for a three-level model which leads to many more coupled equations than those necessary to describe two-level systems. Dynamics of lasers operating with multiple longitudinal modes are described in Chapter 9 (32 pages). Some theory and experimental results for
Optics & Laser Technology Vol 25 No 4 1993
co-propagating and counter-propagating modes in two-level lasers are discussed. Special cases considered include dye lasers, lasers with intracavity frequency doubling, transverse modes and diode lasers with external reflectors. Transverse effects and spatial instabilities are the subject of Chapter 10 (15 pages) but, here, modelling and theory become quite involved so the approach is more of a review, albeit a good one. The laser (whether homogeneously or inhomogeneously broadened) e m e r g e s as an archetypical system suitable for the experimental studies of nonlinear dynamics applicable to other technically important dynamic, chaotic and turbulent processes. In the simplest case, laser behaviour may be described by the Lorenz model which is discussed in some detail. Among the many advantages of lasers over fluids for experimental investigations of non-linear dynamics may be placed the greater d e g r e e of control of boundary conditions for laser systems, than is possible for fluid systems. Also, the number of d e g r e e s of freedom (for example, modes) are easier to control. In summary, the book contains a wealth of information and good teaching in both non-linear dynamics and laser physics which should make its way into many lecture courses; it has been a pleasure to review. Arthur Maitland University of St A n d r e w s
275