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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Stability of polarized modes in gas lasers

Guy Michel Stéphan, A. D. May

Published Feb 1, 1998• 10 citations
Publisher

Abstract

This tutorial paper is based on lectures delivered by G M Stéphan at PELS'97. The idea was to tell the students about the methodology used by the authors to understand and to quantitatively compute the flips observed between two polarization states in a single-frequency He-Ne laser. The study is limited to this phenomenon. Contents are: introduction, quasi-isotropic lasers and polarization flips; the passive Fabry-Perot interferometer, an illustrative example; a vectorial description of a two energy-level system with magnetic degeneracy; two useful tools: adiabatic elimination of fast variables and use of Lyapunov exponents to study the stability of a solution; medium polarization in the adiabatic approximation; the laser equations for the field. These contents are organized for people coming into the field: rather than being too general, we have preferred to focus on limited and well defined examples from which other cases can be studied.

DOI
10.1088/1355-5111/10/1/008

Related papers

On the theory of polarization effects in gas lasers

Daan Lenstra

Abstract Starting from a theory in which laser operation is described as the excitation of the natural modes of an open-resonator system, the case of a Fabry-Perot resonator with plane-parallel mirrors is treated. It is shown that, in the case of weakly anisotropic mirrors, the natural modes can be grouped in pairs, such that each pair corresponds to one scalar longitudinal mode. In that case, laser operation can and will be described in terms of these longitudinal modes, which then possess a vectorial field amplitude, in agreement with the usual formalism. The polarization preference in a single-mode gas laser operating on a transition between a singlet and a triplet state is investigated, taking into account differences in the relaxation constants for the various expectation values of atomic variables. A calculation of the effect on the relaxation constants due to interatomic collisions leads to the conclusion that theory and experiment are in good agreement with each other. Equations describing the time evolution of the polarization parameters of both modes in a two-mode operating gas laser are derived. It is found as a general rule that mode-mode interaction results in modes whose polarizations are mutually orthogonal. An exception to this rule is found in the case in which the single-mode preference is for circular polarization. The influence of two specific mirror anisotropies is discussed. The polarization behaviour of a single-mode gas laser in the presence of (partly) applied, transverse magnetic fields is extensively dealt with. It appears to be essential to distinguish between the case in which the magnetic field is applied only to a fraction of the active medium and the case in which the magnetic field is uniform in the entire medium. This distinction is shown to lead to a satisfactory theoretical description of a certain class of experiments. In the case of two other experiments, good agreement with the theory is obtained, by assuming the presence of mirror anisotropies of acceptable kind and size. Finally, the influence of small anisotropies on the degree of polarization of a single-mode gas laser is theoretically investigated, when the latter is polarized by means of a strong transverse magnetic field.

•Feb 1, 1979•0 citations

Polarization control mechanisms in vectorial bistable lasers for one-frequency systems

Guy Ropars, A. Le Floch, Roger Le Naour

The basic mechanisms of the polarization switching in vectorial bistable lasers are studied both theoretically and experimentally versus internal parameters. In particular, by scanning the frequency of a gas laser with two linearly polarized eigenstates, two quite different flipping processes with hysteresis occur according to the linear-phase-anisotropy value of the cavity. Indeed, when the anisotropy increases, rotation and inhibition mechanisms appear successively. The variations of the hysteresis loop for different anisotropy and excitation values are theoretically found to be opposed in the two processes. Additional evolutions of the polarization, such as multiple switchings in the inhibition mechanism and ``hybrid'' hysteresis loops, are predicted. The experiments, essentially performed on a monomode 3.39-\ensuremath{\mu}m $^{3}\mathrm{\ensuremath{-}}^{20}$Ne laser containing an adjustable linear phase anisotropy, confirm the existence of the two processes and their corresponding properties. These processes may also occur in other quasi-isotropic lasers versus other internal parameters, such as, for instance, the injection current in semiconductor lasers. In this case the TE and TM modes flip only in the inhibition mechanism when the bistability conditions are satisfied. The knowledge of the basic flipping mechanisms in the laser itself enables us to understand and realize the external optical-polarization control by an anisotropic feedback (one-frequency systems). Induced-rotation and induced-inhibition mechanisms are then theoretically predicted and experimentally verified. Sensitive optical gates are realized by varying the feedback phase in both processes.

Physical Review A•Jul 1, 1992•36 citations

Self-pulsing in Fabry-Perot lasers: An analytic scenario

Luigi A. Lugiato, Franco Prati

In this paper the authors demonstrate that in a Fabry-Perot laser under the condition of adiabatic elimination of the atomic polarization the multimode instability can arise very close to threshold, and the instability condition is given by a simple formula.

Physical Review Research•Dec 2, 2019•9 citations

Polarization effects in lasers and spectroscopy

This special issue includes a wide range of papers contributed by the participants in the International Workshop on Polarization Effects in Lasers and Spectroscopy, held at the University of Toronto in June 1997. Participants were not restricted to manuscripts reporting the work they presented, rather they were invited to present new and current research activities they might wish to report that fell within the topics of the meeting. In addition, some manuscripts in this special issue are more tutorial or review in nature at our request; these are for the most part from the invited speakers at the conference or from the lecturers at the graduate-level two-day school held prior to the Workshop. The effects of polarization of the electromagnetic field and its interaction with magnetic sublevels of material systems are, of course, fundamental to a practical understanding of almost all field - matter interactions. However, what has now become conventional training in laser physics, and in quantum mechanics more generally, has often restricted the theoretical analyses to `two-level' systems and scalar fields for simplicity, to such an extent that the intuition of many working in both laser dynamics and spectroscopy is often less sensitive to subtleties of polarization of either the material or the fields. This workshop was organized to re-emphasize the importance of the states of polarization of both the material and the field, to illustrate the current activities which take advantage of these phenomena and to bring together several otherwise disconnected topics. The history of polarization effects in lasers and spectroscopy is a venerable one. Well developed schools of thought are embodied in the work of van Haeringen and de Lang [ 1 ] and Sargent and coworkers [ 2 ] in the 1960s and texts and review articles of Professor Voitovich and his colleagues in Minsk, Belarus [ 3 ]. Much of the early work showed the importance of polarization-sensitive spectroscopy in atomic gases as laser media. As applications of lasers required more intense sources, laser science turned to dyes and solid state lasers, in which many polarization phenomena observed in atomic gas lasers seemed absent. However, polarization phenomena are important today in the dynamics of nonplanar ring lasers, fibre lasers, microchip lasers and vertical cavity surface-emitting, semiconductor lasers, as emphasized by various manuscripts in this special issue. It is also worth noting that when interest in nonlinear dyanamics (optical bistability and optical instabilities) in field-atom interactions was revived in the 1980s, polarization-selective optical pumping techniques were required to create the experimental analogue of the two-level atom so popular for theoretical analyses. Furthermore the principles of laser-based trapping and cooling of atoms which merited the recent award of the Nobel Prize in physics would not be realizable experimentally without the subtleties of the interaction of polarized light and transitions among magnetic sublevels, which find their roots in Kastler's work on optical pumping [ 4 ]. Polarization degrees of freedom in the electromagnetic field also bring new `channels' for noise to enter dynamical systems and new opportunities for studying coupled modes or the effects of classical and quantum noise including correlations at various orders. The range of spectroscopic interests is illustrated by the early work of Hänsch and coworkers [ 5 ] and is standard fare in textbooks of chemistry and physics on spectroscopic methods. The importance of considering polarization continues through modern studies of such phenomena as dark resonances and coherent population trapping [ 6 ], lasing without inversion [ 7 ] and electromagnetically induced transparency [ 8 ]. Polarization is also of importance in the consideration of fast processes in solids, which can be resolved by ultrashort optical pulses [ 9 ]. The range of interest in polarization-sensitive dynamics spans the parity nonconserving decays in nucleii and atoms and the advantages of polarized electromagnetic waves for subtle probings of materials [ 10 ]. We are grateful for the response of participants in the conference and school, and are appreciative of the support of the members of the organizing committee (N B Abraham, USA (co-chair); M A Gubin, Russia ; S Haroche, France ; A Klehr, Germany ; L A Lugiato, Italy ; A D May, Canada (local co-ordinator); R A Morgan, USA ; K Otsuka, Japan ; W J Sandle, New Zealand ; G M Stephan, France (co-chair); L Svirina, Belarus ; C Tang, USA ; R Vilaseca, Spain ; J P Woerdman, The Netherlands ; N I Zheludev, UK ). We are also grateful for the support and encouragement of the honorary editor of Quantum Semiclass. Opt. , Professor P Mandel, the editorial staff of the Journals of the European Optical Society and of the publisher, IOP Publishing, for their patience and persistence in bringing this larger-than-usual special issue to fruition. We look forward to a continued expansion of work in this field which will be illustrated in the next conference on Polarization Effects in Lasers and Spectroscopy to be held at the University of Southhampton, UK just before the IQEC/Euro-CLEO in September 2000. The local organizer will be Dr N I Zheludev (E-mail: n.i.zheludev@soton.ac.uk; websites: http://www.nonlinear-optics.phys.soton.ac.uk/ and PELS conference website: http://www.phys.soton.ac.uk/PELS/INDEX.HTM ). We would like to particularly acknowledge the scientific inspiration that we have drawn personally from our colleague A D May and to express our gratitude for his boundless energy and tireless organizational skills that brought the meeting at the University of Toronto to such a successful conclusion. The help of our sponsors is also gratefully acknowledged, particularly the Embassade de France au Canada, the University of Toronto, and the French organizations region de Bretagne and departement des Cotes d'Armor. Other sponsors included JDS Fitel Inc (Canada), John Wiley and Sons, the Universitat Politecnica de Catalunya, Bryn Mawr College, and the Université de Rennes (Lannion). We are also grateful for the co-sponsorship of the following cooperating societies: European Optical Society, Quantum Electronics Divsion of the European Physical Society, American Physical Society and Optical Society of America. As a final note, we call to the attention of the readers of this special issue that three other manuscripts accepted too late for inclusion in this issue will appear in later issues of Quantum and Semiclassical Optics : Polarization of radiation amplified by dye solutions A Chernayavsky, L G Pikulik, K I Rudik and A F Grib Competition of active medium and empty cavity anisotropies in a single-mode gas class-A laser L Svirina Intensity and intermode beat frequency fluctuations in a two-mode He - Ne laser with synchronized modes N V Naumov, V N Petrovskiy, E D Protsenko and V M Yermachenko . References [1] de Lang H 1964 Philips Res. Rep. 19 429 de Lang H, Polder D and van Haeringen W 1971 Philips Tech. Rev. 32 190 Lenstra D 1980 Phys. Rep. 59 299 [2] Fork R L and Sargent III M 1965 Phys. Rev. A 139 617 Sargent III M, Lamb Jr W E and Fork R L 1967 Phys. Rev. 164 436 Sargent III M, Lamb Jr W E and Fork R L 1967 Phys. Rev. 164 450 Tomlinson W J and Fork R L 1967 Phys. Rev. 164 466 Wang C H, Tomlinson W J and George R T 1969 Phys. Rev. 181 125 Culshaw W and Kannelaud J 1967 Phys. Rev. A 156 308 [3] Voitovich A P 1987 J. Sov. Laser Res. 8 555 Voitovich A P and Severikov V N 1988 Lasers with Anisotropic Resonators (Minsk: Nauka and Technika) in Russian [4] Kastler A 1950 J. Phys. Rad. 11 255 [5] Wieman C and Hänsch T W 1976 Doppler Free laser polarization spectroscopy Phys. Rev. Lett. 36 1170 Teets R E, Kowalski F V, Hill W T, Carlson N and Hänsch T W 1977 Laser polarization spectroscopy Advances in Laser Spectroscopy SPIE Proc. 113 80 Teets R, Feinberg R, Hänsch T W and Schawlow A L 1976 Simplification of spectra by polarization labeling Phys. Rev. Lett. 37 683 See also: Sargent III M 1974 Polarized field saturation spectroscopy Phys. Rev. A 14 524 Raab M, Höning G, Castell R and Demtröder W 1979 Chem. Phys. Lett. 66 307 D'Yakonov M I and Perel V I 1964 Zh. Eksp. Teor. Fiz. 47 1483 Happer W and Saloman E B 1965 Phys. Rev. Lett. 15 441 [6] Arimondo E 1996 Progress in Optics vol XXXV ed E Wolf (Amsterdam: Elsevier) pp 257 - 354 [7] 1994 Special Issue on Atomic Coherence and Interference Quantum Opt. 6 no 4 [8] See for example: Kasapi A, Jain M, Yin G Y and Harris S E 1995 Phys. Rev. Lett. 74 2447 Harris S E 1988 Phys. Rev. Lett. 2 1033 [9] Citrin D S and Kuhl J (eds) 1996 Special Issue on Radiative Processes and Dephasing in Semiconductors J. Opt. Soc. Am. B 13 no 6 [10] Schutz G and Fischer P 1996 X-ray circular magnetic dichroism Europhys. News 27 101 Guest Editors N B Abraham Department of Physics, Bryn Mawr College, 101 N Merion Ave, Bryn Mawr, PA, 19010-2899, USA G M Stephan ENSSAT, 6 Rue de Kérampont, Lannion, France

Quantum and Semiclassical Optics Journal of the European Optical Society Part B•Feb 1, 1998•2 citations

Polarization stability and dynamics in a model for a polarization-isotropic laser that goes beyond third-order Lamb theory

N. B. Abraham, Mark D. Matlin, R. S. Gioggia

Instabilities and dynamical pulsations are common features of solutions of a model that includes the material variable dynamics for a laser with a polarization isotropic resonator and with a homogeneously broadened j=1\ensuremath{\rightarrow}j=0 transition. These resemble in some respects features found in third-order Lamb theories under anisotropic conditions, such as splitting of the optical field into two relatively independent orthogonally polarized modes with different optical frequencies. At higher intensities the amplitudes and frequencies of these modes exhibit such strong coupling that a ``two-mode'' description loses its usefulness or effectiveness. Various periodic attractors with strong intensity and polarization pulsations are found for moderate excitation levels. Some of these attractors preserve the breaking of the polarization isotropy on average just as does any linearly polarized solution. But in some cases the dynamics restore the polarization isotropy on average. We also find other dynamical phenomena, including periodic and apparently chaotic states, often involving rapid switching between long interludes of nearly constant polarization, and homoclinic behavior. \textcopyright{} 1996 The American Physical Society.

Physical Review A•May 1, 1996•44 citations

Lectures on laser physics and laser instabilities

L.N. Narducci, N. B. Abraham

This book is an edited version of lectures given by the authors at the 1985 Summer School on Lase Physics. The School was held in Jilin University in Changchun, Peoples' Republic of China. Contents: The book is divided into 2 parts, the first is ''An Outline of Laser Physics and Laser Instabilities'': An Introduction to the Theory of the Laser: The Rate Equations; The Interaction of Light and Matter: The Classical Picture; The Basic Laser Equations: Homogeneously Broadened Systems; Steady State Behavior of a Homogeneously Broadened Ring Laser; Linear Stability Analysis: The Resonant Case; The Adiabatic Elimination of the Fast Variables; Linear Stability Analysis: The General Case; The Single Mode Laser: Deterministic Chaos; Dynamical Behavior of the Maxwell-Bloch Equations; The Spectral Analysis of the Output Field; Theory of a Laser with Inhomogeneous Broadening. The second part is on the ''principles of Laser Physics and Laser Instabilities'': Background Notes for the Discussion of Experimental Laser Systems; Amplified Spontaneous Emission; The Two-Level Atom; Laser Cavities and Modes; Types of Laser Systems and Classification of Lasers; the Xe 3.51 ..mu..m Laser; Chaos in Single Mode Lasers; Forced Laser Systems, Modulated Lasers and Lasers with an Injected Signal; Dynamical Phenomena in Multimode Laser Systems.

•Jan 1, 1987•1 citation
This tutorial paper is based on lectures delivered by G M Stéphan at PELS'97. The idea was to tell the students about the methodology used by the authors to understand and to quantitatively compute the flips observed between two polarization states in a single-frequency He-Ne laser. The study is limited to this phenomenon. Contents are: introduction, quasi-isotropic lasers and polarization flips; the passive Fabry-Perot interferometer, an illustrative example; a vectorial description of a two energy-level system with magnetic degeneracy; two useful tools: adiabatic elimination of fast variables and use of Lyapunov exponents to study the stability of a solution; medium polarization in the adiabatic approximation; the laser equations for the field. These contents are organized for people coming into the field: rather than being too general, we have preferred to focus on limited and well defined examples from which other cases can be studied.
Abstract Starting from a theory in which laser operation is described as the excitation of the natural modes of an open-resonator system, the case of a Fabry-Perot resonator with plane-parallel mirrors is treated. It is shown that, in the case of weakly anisotropic mirrors, the natural modes can be grouped in pairs, such that each pair corresponds to one scalar longitudinal mode. In that case, laser operation can and will be described in terms of these longitudinal modes, which then possess a vectorial field amplitude, in agreement with the usual formalism. The polarization preference in a single-mode gas laser operating on a transition between a singlet and a triplet state is investigated, taking into account differences in the relaxation constants for the various expectation values of atomic variables. A calculation of the effect on the relaxation constants due to interatomic collisions leads to the conclusion that theory and experiment are in good agreement with each other. Equations describing the time evolution of the polarization parameters of both modes in a two-mode operating gas laser are derived. It is found as a general rule that mode-mode interaction results in modes whose polarizations are mutually orthogonal. An exception to this rule is found in the case in which the single-mode preference is for circular polarization. The influence of two specific mirror anisotropies is discussed. The polarization behaviour of a single-mode gas laser in the presence of (partly) applied, transverse magnetic fields is extensively dealt with. It appears to be essential to distinguish between the case in which the magnetic field is applied only to a fraction of the active medium and the case in which the magnetic field is uniform in the entire medium. This distinction is shown to lead to a satisfactory theoretical description of a certain class of experiments. In the case of two other experiments, good agreement with the theory is obtained, by assuming the presence of mirror anisotropies of acceptable kind and size. Finally, the influence of small anisotropies on the degree of polarization of a single-mode gas laser is theoretically investigated, when the latter is polarized by means of a strong transverse magnetic field.
The basic mechanisms of the polarization switching in vectorial bistable lasers are studied both theoretically and experimentally versus internal parameters. In particular, by scanning the frequency of a gas laser with two linearly polarized eigenstates, two quite different flipping processes with hysteresis occur according to the linear-phase-anisotropy value of the cavity. Indeed, when the anisotropy increases, rotation and inhibition mechanisms appear successively. The variations of the hysteresis loop for different anisotropy and excitation values are theoretically found to be opposed in the two processes. Additional evolutions of the polarization, such as multiple switchings in the inhibition mechanism and ``hybrid'' hysteresis loops, are predicted. The experiments, essentially performed on a monomode 3.39-\ensuremath{\mu}m $^{3}\mathrm{\ensuremath{-}}^{20}$Ne laser containing an adjustable linear phase anisotropy, confirm the existence of the two processes and their corresponding properties. These processes may also occur in other quasi-isotropic lasers versus other internal parameters, such as, for instance, the injection current in semiconductor lasers. In this case the TE and TM modes flip only in the inhibition mechanism when the bistability conditions are satisfied. The knowledge of the basic flipping mechanisms in the laser itself enables us to understand and realize the external optical-polarization control by an anisotropic feedback (one-frequency systems). Induced-rotation and induced-inhibition mechanisms are then theoretically predicted and experimentally verified. Sensitive optical gates are realized by varying the feedback phase in both processes.
This special issue includes a wide range of papers contributed by the participants in the International Workshop on Polarization Effects in Lasers and Spectroscopy, held at the University of Toronto in June 1997. Participants were not restricted to manuscripts reporting the work they presented, rather they were invited to present new and current research activities they might wish to report that fell within the topics of the meeting. In addition, some manuscripts in this special issue are more tutorial or review in nature at our request; these are for the most part from the invited speakers at the conference or from the lecturers at the graduate-level two-day school held prior to the Workshop. The effects of polarization of the electromagnetic field and its interaction with magnetic sublevels of material systems are, of course, fundamental to a practical understanding of almost all field - matter interactions. However, what has now become conventional training in laser physics, and in quantum mechanics more generally, has often restricted the theoretical analyses to `two-level' systems and scalar fields for simplicity, to such an extent that the intuition of many working in both laser dynamics and spectroscopy is often less sensitive to subtleties of polarization of either the material or the fields. This workshop was organized to re-emphasize the importance of the states of polarization of both the material and the field, to illustrate the current activities which take advantage of these phenomena and to bring together several otherwise disconnected topics. The history of polarization effects in lasers and spectroscopy is a venerable one. Well developed schools of thought are embodied in the work of van Haeringen and de Lang [ 1 ] and Sargent and coworkers [ 2 ] in the 1960s and texts and review articles of Professor Voitovich and his colleagues in Minsk, Belarus [ 3 ]. Much of the early work showed the importance of polarization-sensitive spectroscopy in atomic gases as laser media. As applications of lasers required more intense sources, laser science turned to dyes and solid state lasers, in which many polarization phenomena observed in atomic gas lasers seemed absent. However, polarization phenomena are important today in the dynamics of nonplanar ring lasers, fibre lasers, microchip lasers and vertical cavity surface-emitting, semiconductor lasers, as emphasized by various manuscripts in this special issue. It is also worth noting that when interest in nonlinear dyanamics (optical bistability and optical instabilities) in field-atom interactions was revived in the 1980s, polarization-selective optical pumping techniques were required to create the experimental analogue of the two-level atom so popular for theoretical analyses. Furthermore the principles of laser-based trapping and cooling of atoms which merited the recent award of the Nobel Prize in physics would not be realizable experimentally without the subtleties of the interaction of polarized light and transitions among magnetic sublevels, which find their roots in Kastler's work on optical pumping [ 4 ]. Polarization degrees of freedom in the electromagnetic field also bring new `channels' for noise to enter dynamical systems and new opportunities for studying coupled modes or the effects of classical and quantum noise including correlations at various orders. The range of spectroscopic interests is illustrated by the early work of Hänsch and coworkers [ 5 ] and is standard fare in textbooks of chemistry and physics on spectroscopic methods. The importance of considering polarization continues through modern studies of such phenomena as dark resonances and coherent population trapping [ 6 ], lasing without inversion [ 7 ] and electromagnetically induced transparency [ 8 ]. Polarization is also of importance in the consideration of fast processes in solids, which can be resolved by ultrashort optical pulses [ 9 ]. The range of interest in polarization-sensitive dynamics spans the parity nonconserving decays in nucleii and atoms and the advantages of polarized electromagnetic waves for subtle probings of materials [ 10 ]. We are grateful for the response of participants in the conference and school, and are appreciative of the support of the members of the organizing committee (N B Abraham, USA (co-chair); M A Gubin, Russia ; S Haroche, France ; A Klehr, Germany ; L A Lugiato, Italy ; A D May, Canada (local co-ordinator); R A Morgan, USA ; K Otsuka, Japan ; W J Sandle, New Zealand ; G M Stephan, France (co-chair); L Svirina, Belarus ; C Tang, USA ; R Vilaseca, Spain ; J P Woerdman, The Netherlands ; N I Zheludev, UK ). We are also grateful for the support and encouragement of the honorary editor of Quantum Semiclass. Opt. , Professor P Mandel, the editorial staff of the Journals of the European Optical Society and of the publisher, IOP Publishing, for their patience and persistence in bringing this larger-than-usual special issue to fruition. We look forward to a continued expansion of work in this field which will be illustrated in the next conference on Polarization Effects in Lasers and Spectroscopy to be held at the University of Southhampton, UK just before the IQEC/Euro-CLEO in September 2000. The local organizer will be Dr N I Zheludev (E-mail: n.i.zheludev@soton.ac.uk; websites: http://www.nonlinear-optics.phys.soton.ac.uk/ and PELS conference website: http://www.phys.soton.ac.uk/PELS/INDEX.HTM ). We would like to particularly acknowledge the scientific inspiration that we have drawn personally from our colleague A D May and to express our gratitude for his boundless energy and tireless organizational skills that brought the meeting at the University of Toronto to such a successful conclusion. The help of our sponsors is also gratefully acknowledged, particularly the Embassade de France au Canada, the University of Toronto, and the French organizations region de Bretagne and departement des Cotes d'Armor. Other sponsors included JDS Fitel Inc (Canada), John Wiley and Sons, the Universitat Politecnica de Catalunya, Bryn Mawr College, and the Université de Rennes (Lannion). We are also grateful for the co-sponsorship of the following cooperating societies: European Optical Society, Quantum Electronics Divsion of the European Physical Society, American Physical Society and Optical Society of America. As a final note, we call to the attention of the readers of this special issue that three other manuscripts accepted too late for inclusion in this issue will appear in later issues of Quantum and Semiclassical Optics : Polarization of radiation amplified by dye solutions A Chernayavsky, L G Pikulik, K I Rudik and A F Grib Competition of active medium and empty cavity anisotropies in a single-mode gas class-A laser L Svirina Intensity and intermode beat frequency fluctuations in a two-mode He - Ne laser with synchronized modes N V Naumov, V N Petrovskiy, E D Protsenko and V M Yermachenko . References [1] de Lang H 1964 Philips Res. Rep. 19 429 de Lang H, Polder D and van Haeringen W 1971 Philips Tech. Rev. 32 190 Lenstra D 1980 Phys. Rep. 59 299 [2] Fork R L and Sargent III M 1965 Phys. Rev. A 139 617 Sargent III M, Lamb Jr W E and Fork R L 1967 Phys. Rev. 164 436 Sargent III M, Lamb Jr W E and Fork R L 1967 Phys. Rev. 164 450 Tomlinson W J and Fork R L 1967 Phys. Rev. 164 466 Wang C H, Tomlinson W J and George R T 1969 Phys. Rev. 181 125 Culshaw W and Kannelaud J 1967 Phys. Rev. A 156 308 [3] Voitovich A P 1987 J. Sov. Laser Res. 8 555 Voitovich A P and Severikov V N 1988 Lasers with Anisotropic Resonators (Minsk: Nauka and Technika) in Russian [4] Kastler A 1950 J. Phys. Rad. 11 255 [5] Wieman C and Hänsch T W 1976 Doppler Free laser polarization spectroscopy Phys. Rev. Lett. 36 1170 Teets R E, Kowalski F V, Hill W T, Carlson N and Hänsch T W 1977 Laser polarization spectroscopy Advances in Laser Spectroscopy SPIE Proc. 113 80 Teets R, Feinberg R, Hänsch T W and Schawlow A L 1976 Simplification of spectra by polarization labeling Phys. Rev. Lett. 37 683 See also: Sargent III M 1974 Polarized field saturation spectroscopy Phys. Rev. A 14 524 Raab M, Höning G, Castell R and Demtröder W 1979 Chem. Phys. Lett. 66 307 D'Yakonov M I and Perel V I 1964 Zh. Eksp. Teor. Fiz. 47 1483 Happer W and Saloman E B 1965 Phys. Rev. Lett. 15 441 [6] Arimondo E 1996 Progress in Optics vol XXXV ed E Wolf (Amsterdam: Elsevier) pp 257 - 354 [7] 1994 Special Issue on Atomic Coherence and Interference Quantum Opt. 6 no 4 [8] See for example: Kasapi A, Jain M, Yin G Y and Harris S E 1995 Phys. Rev. Lett. 74 2447 Harris S E 1988 Phys. Rev. Lett. 2 1033 [9] Citrin D S and Kuhl J (eds) 1996 Special Issue on Radiative Processes and Dephasing in Semiconductors J. Opt. Soc. Am. B 13 no 6 [10] Schutz G and Fischer P 1996 X-ray circular magnetic dichroism Europhys. News 27 101 Guest Editors N B Abraham Department of Physics, Bryn Mawr College, 101 N Merion Ave, Bryn Mawr, PA, 19010-2899, USA G M Stephan ENSSAT, 6 Rue de Kérampont, Lannion, France
Instabilities and dynamical pulsations are common features of solutions of a model that includes the material variable dynamics for a laser with a polarization isotropic resonator and with a homogeneously broadened j=1\ensuremath{\rightarrow}j=0 transition. These resemble in some respects features found in third-order Lamb theories under anisotropic conditions, such as splitting of the optical field into two relatively independent orthogonally polarized modes with different optical frequencies. At higher intensities the amplitudes and frequencies of these modes exhibit such strong coupling that a ``two-mode'' description loses its usefulness or effectiveness. Various periodic attractors with strong intensity and polarization pulsations are found for moderate excitation levels. Some of these attractors preserve the breaking of the polarization isotropy on average just as does any linearly polarized solution. But in some cases the dynamics restore the polarization isotropy on average. We also find other dynamical phenomena, including periodic and apparently chaotic states, often involving rapid switching between long interludes of nearly constant polarization, and homoclinic behavior. \textcopyright{} 1996 The American Physical Society.
This book is an edited version of lectures given by the authors at the 1985 Summer School on Lase Physics. The School was held in Jilin University in Changchun, Peoples' Republic of China. Contents: The book is divided into 2 parts, the first is ''An Outline of Laser Physics and Laser Instabilities'': An Introduction to the Theory of the Laser: The Rate Equations; The Interaction of Light and Matter: The Classical Picture; The Basic Laser Equations: Homogeneously Broadened Systems; Steady State Behavior of a Homogeneously Broadened Ring Laser; Linear Stability Analysis: The Resonant Case; The Adiabatic Elimination of the Fast Variables; Linear Stability Analysis: The General Case; The Single Mode Laser: Deterministic Chaos; Dynamical Behavior of the Maxwell-Bloch Equations; The Spectral Analysis of the Output Field; Theory of a Laser with Inhomogeneous Broadening. The second part is on the ''principles of Laser Physics and Laser Instabilities'': Background Notes for the Discussion of Experimental Laser Systems; Amplified Spontaneous Emission; The Two-Level Atom; Laser Cavities and Modes; Types of Laser Systems and Classification of Lasers; the Xe 3.51 ..mu..m Laser; Chaos in Single Mode Lasers; Forced Laser Systems, Modulated Lasers and Lasers with an Injected Signal; Dynamical Phenomena in Multimode Laser Systems.