Table of contents

Recently, Bishop and co-workers (1996 Phys. Rev. A 54 R4657) applied the coupled-cluster method to study the ground state of the Jaynes - Cummings model without the rotating-wave approximation and reported strong evidence for a second-order quantum phase transition which was believed to be caused by spontaneous breaking of the parity symmetry of the system. In the present work we have re-investigated this conjecture via examining the nature of the exact (numerical) ground state of the system. Our analysis has indicated that the ground state has definite positive parity and there is no spontaneous breaking of the parity symmetry of the system.

We discuss generation and measurement strategies for maximum-likelihood estimation of small phase shifts. We demonstrate that optimal encoding of small phase shifts and optimal measurements of small phase shifts require different states. We also show that states with identical phase resolution may have rather different Pegg-Barnett phase distributions. Hence, the connection between phase distribution and quantum phase resolution is rather weak.

The possibility of storing information in an amplifying optical fibre loop operating in a laser regime is discussed. Numerical simulations show that storage is possible and optimal when data are encoded in one of the polarization eigenstates of the fibre, provided the polarization direction of the light propagating inside the loop is switched between two orthogonal states every round trip.

We describe an ongoing experiment to measure parity violation in atomic caesium, based on detection by stimulated emission. Our goal is to measure to 1 a left-right asymmetry of to test electroweak theory and look for new physics beyond the Standard Model. The Cs highly forbidden transition, , is excited in a vapour (5-10 mtorr) by a pump laser pulse in a longitudinal electric field . The PV asymmetry resulting from the weak interaction during optical excitation is converted into an anisotropy in the gain of a probe laser pulse which stimulates the allowed transition , and manifests itself as a tiny -odd rotation of the probe's linear polarization. Differential polarimetry allows dark-field detection of the rotation angle with a baseline defined to better than and discrimination between true and pseudo-rotation. Lineshape-independent angle calibration is performed using a parity-conserving -even anisotropy. To isolate the parity-violating effect, we exploit the symmetry of revolution of the experiment by (i) rotating pump and probe linear polarizations around the beam axis and (ii) reversing in a cylindrically symmetric cell. After describing the apparatus and data acquisition procedure, we summarize the current experimental status and short-term prospects.

If an atom interacts with a classical field and quantized mode simultaneously, exchange by photons between the different components of the field is possible. Such systems can be exploited in order to generate radiation in the quantized mode and can be considered as a micromaser with optical pumping. The process of generation of the quantized field and the quantum-statistical characteristics of this radiation are under investigation.

We study the coupled system of the dressed atom and the quantized mode of the electromagnetic field (an open modification of the Jaynes-Cummings model). The mode is initially excited to the coherent quantum state and exhibits Poissonian photon statistics. When the quasienergy levels of the dressed atom cross, the mean number of photons in the mode oscillates at high amplitude. Numerical results show that the photon statistics in the mode regularizes, correlating as the value of falls. Near the local minima of , the statistics can become sub-Poissonian with Fano factor many times smaller than unity.

Optical Nonlinear Dynamics (OND) is an effervescent field that has been continuously evolving during the last two decades. This assessment is arguably true beyond any rhetoric and the papers contained in this special issue show some of the most recent developments in the field.

It is customary to divide OND into two subfields, namely the study of the temporal dynamics of nonlinear optical systems - assuming that the spatial structure of the light field is kept fixed and thus in principle unimportant - (temporal OND) and the study of pattern formation in those systems (spatial OND). Although somewhat arbitrary, this division reflects the main lines of the historical development of the field. During the sixties emphasis was placed on the spontaneous emission of trains of pulses (mainly by lasers). Certainly the study of these pulsations did not constitute a front-line topic until the eighties, but it has maintained continuity over the three decades since the laser was invented and nowadays it is a mature discipline. A crucial date is 1975, when the famous work by Haken [1] on the equivalence between single longitudinal mode lasers and the Lorenz model gave solid roots to temporal OND in nonlinear science. Problems involving several longitudinal modes were, however, also studied over the same period, establishing a not fully appreciated link between temporal and spatial OND. The results of the investigations on temporal OND have been reviewed several times and have been the subject of several special issues of international journals [2,3], monographs [4] - [8], and compilations [9,10].

The formation of transverse patterns as a concern of researchers is as old as temporal dynamics, and goes back to the studies in the early sixties on the transverse modal structure of different laser resonators. Nevertheless the explosive growth of pattern formation studies occurred around the end of the eighties and it is worth mentioning that it was initiated in part by the same community involved in temporal OND.

Something that has characterized the development of theoretical studies on pattern formation in NDOS is a double (and parallel) approach to the problem. On the one hand there is the modal approach which is based in the derivation of ordinary differential equations for the amplitudes of a finite number of cavity modes. On the other hand there is the continuous approach that neglects the existence of transverse boundary conditions and treats the problem without reference to any set of transverse modes. Of course both ways are useful for approaching different experimental situations (roughly small or large Fresnel numbers, respectively) but perhaps the connection between both approaches has not been studied enough.

Probably the continuous approach is the one that has taught researchers how pattern formation in OND is connected with pattern formation in other fields of nonlinear science. In a sense the derivation of amplitude and order parameter equations for different optical systems has played the same role that the isomorphism discovered by Haken played for temporal OND, and now pattern formation in OND is a field with well established roots. Nevertheless the modal approach still plays a very important role especially for describing patterns in lasers and quantum features of patterns which is a topic of increasing activity.

Something that is perhaps new in OND is the increasing emphasis put on applications, both in temporal OND - for instance, cryptography - and especially in spatial OND, involving localized structures, control of patterns and information processing. Maybe this can be traced back in part to the increasingly stronger pressure that the science administrations exert on basic science researchers through the criteria used for project funding, which give priority to projects with an immediate technological application.

Perhaps this emphasis on applications may explain a difference between temporal and spatial OND studies: while lasers occupied a privileged position in temporal OND, in spatial OND lasers are just one among other nonlinear optical systems (liquid crystal light valves, parametric and photorefractive oscillators, semiconductor cavities, etc). The field of pattern formation has been the subject of several special issues and reviews, among which are [11] - [19].

The excellent health of the field of pattern formation in OND has shown up in the recent Euroconference `Patterns in Nonlinear Optical Systems' (PINOS), held in Pueblo Acantilado (Alicante, Spain) on 21 - 23 May, 1998. This Euroconference was funded by the European Union through its TMR Programme and was co-sponsored by the Spanish Education and Culture Ministry, Universitat Politècnica de València, Universitat Politècnica de Catalunya, Universitat de València, Universitat Autònoma de Barcelona, Universidad de Cantabria, and Bancaixa. The interest and variety of papers presented at that meeting has motivated Quantum and Semiclassical Optics (Journal of the European Optical Society Part B) and us to launch this Special Issue. Only authors attending the Euroconference could contribute to this issue, although the contents of the papers may not always be restricted to what was presented at the meeting (for a resumé of the conference contents see [20]).

The regular peer review procedure of Quantum and Semiclassical Optics has been followed, and given the large number of submitted contributions and accepted papers the special issue has been divided into two parts. The first part, published as part of the present issue, and the second to appear in February 1999, under the new title Journal of Optics B: Quantum and Semiclassical Optics, which from 1 January 1999 will replace Quantum and Semiclassical Optics.

We hope that this special issue (parts 1 and 2) will constitute a valuable and practical reference for people wishing to get a global view of the state of the art of the research in this field of optical nonlinear dynamics which is contributing significantly to the advancement of optics and physics in general.

Germán J de Valcárcel, Eugenio Roldán and RamonVilaseca

• [1] Haken H 1975 Phys. Lett. A 53 77

• [2]Abraham N B, Lugiato L A and Narducci L M (ed) 1985 J. Opt. Soc. Am. B 2 (issue 1) Special issue on instabilities in active optical media

• [3] Bandy D K, Oraevsky A N and Tredicce J R (ed) 1988 J. Opt. Soc. Am. B 5 (issue 5) Special issue on nonlinear dynamics of lasers

• [4] Abraham N B, Mandel P and Narducci L M 1988 Progress in Optics vol XXV, ed E Wolf (Amsterdam: North Holland)

• [5]Narducci L M and Abraham N B 1988 Laser Physics and Laser Instabilities (Singapore: World Scientific)

• [6] Weiss C O and Vilaseca R 1991 Dynamics of Lasers (Weinheim: VCH)

• [7] Khanin Ya 1995 Principles of Laser Dynamics (Amsterdam: North Holland)

• [8]Mandel P 1997 Theoretical Problems in Cavity Nonlinear Optics (Cambridge: Cambridge University Press)

• [9] Arecchi F T and Harrison R G (ed) 1987 Instabilities and Chaos in Quantum Optics (Berlin: Springer)

• [10] Arecchi F T and Harrison R G (ed) 1993 Selected Papers on Optical Chaos ( SPIE Milestones Series, vol MS75)

• [11] Abraham N B and Firth W J (ed) 1990 J. Opt. Soc. Am. B 7 (issues 6 and 7) Special issues on transverse effects in nonlinear optical systems

• [12] Lugiato L A and El Naschie M S (ed) 1994 Chaos, Solitons and Fractals 4 Special issue on Nonlinear Optical Structures, Patterns and Chaos

• [13] Harrison R G and Uppal J S (ed) 1993 Nonlinear Dynamics and Spatial Complexity in Optical Systems (Bristol: IOP Publishing)

• [14] Arecchi F T 1991 Physica D 51450

• [15] Lugiato L A 1992 Phys. Rep. 210 293

• [16]Weiss C O 1992 Phys. Rep. 210 311

• [17]Firth W J 1995 Self-Organization in Optical Systems and Application to Information Technology ed M Vorontsov and W B Miller (Berlin: Springer)

• [18]Newell A C and Moloney J V 1992 Nonlinear Optics (Reading, MA: Addison-Wesley)

• [19] Lugiato L A, Brambilla M and Gatti A 1999 Optical Pattern Formation Adv. At. Mol. Opt. at press

• [20] de Valcàrcel G J 1998 European Optical Society Newsletter 2/98 Opt. Commun. 154 (issue 4)

Structure formation in a fibre resonator synchronously driven by short light pulses is considered. Light pulses develop a rich substructure which, for the case of anomalous fibre dispersion, can take the form of an ensemble of bright solitons which may exist in an irregular state (soliton gas) or as a regular array. If the fibre dispersion is normal, an ensemble of dark solitons in an irregular state can exist, but it cannot take the form of an ordered array. Cavity-dressed modulational instability at normal fibre dispersion is observed.

We perform a study of the quantum image phenomenon appearing below threshold in the optical parametric oscillator for the near and far field, for the case of a cavity with spherical mirrors and Gaussian pump profile. Because of the finite size of the pump, the whole set of Gauss-Laguerre cavity modes are coupled and therefore an analytical solution cannot be found. We propose a numerical treatment taking into account the mode couplings up to a finite order, and using an input-output formalism we evaluate the correlation functions for an arbitrary quadrature component of the signal field in the frequency domain. Major quantum spatial features of the plane-wave pump case are shown to persist when the pump waist is progressively decreased to realistic experimental values.

Starting from a simple hexagonal pattern stabilized and selected with the spatial perturbation method in a wide-aperture laser, we observed the transition to a dodecagonal pattern via the doubling of the azimuthal spatial frequency by changing the cavity detuning. Further increasing the detuning induces more complicated patterns, such as double hexagons. The symmetry-breaking effect on the stabilized and selected patterns, introduced by a slight misalignment of a laser mirror, is observed. We also find that the complicated temporal instabilities of the unperturbed patterns are eliminated by the spatial perturbations. Numerical simulations, based on the Fox and Li theory for the field propagation inside the cavity, are able to reproduce the patterns with the simplest symmetry.

We analyse the spatiotemporal dynamics of a broad-area two-level laser in the presence of a dressing field which is coupled to an adjacent transition. The dressing field induces Rabi splitting on one of the energy levels of the laser transition, which modifies the traditional scenario of pattern formation in two-level lasers. In particular, it is observed that phase rolls appear for any sign of the cavity detuning, and that two travelling-wave patterns with different wavenumbers can coexist near the threshold for a certain range of detuning values. Reciprocally, it can be seen that the spatial dynamics alters the standard framework of electromagnetically induced gain splitting.

We present a review of our recent theoretical and experimental results on the interaction of two-dimensional solitary beams in photorefractive SBN crystals. We show that the collision of coherent solitons may result in energy exchange, fusion of the interacting solitons, the birth of a new solitary beam or the complete annihilation of some of them, depending on the relative phase of the interacting beams. In the case of mutually incoherent solitons, we show that the photorefractive nonlinearity leads to an anomalous interaction between solitons. Theoretical and experimental results reveal that a soliton pair may experience both attractive and repulsive forces, depending on their mutual separation. We also show that strong attraction leads to periodic collision or helical motion of solitons depending on initial conditions.

Amplitude instabilities near the threshold of phase locking are investigated in a system of two coupled microchip lasers. The compact semimonolithic resonator set-up allows a systematic study of the relevant parameter regime, including the observation of synchronous amplitude oscillations and, for the first time in coupled solid-state lasers, localized synchronization. The measurements are compared with numerical simulations.

A description of multimode lasers is presented in the frequency domain where the laser Airy function plays a central role. The laser linewidths are calculated in the case of relaxed modes.

The peak power emitted from a photorefractive oscillator over one free spectral range of the cavity decreases monotonically with the rate of cavity detuning, offering a dynamical measure of the characteristic grating formation/dissipation rate.

Using a weakly nonlinear theory, we analyse the stability and the relative stability of the three-dimensional patterns that spontaneously appear in a coherently driven passive optical ring cavity filled with a dispersive dielectric medium with instantaneous Kerr nonlinearity. We show that in the anomalous dispersion regime, the body-centred cubic lattice structure is stable over patterns of lower symmetry in the vicinity of the bifurcation point.

Institute of Physics Publishing is pleased to announce the merger of two current optics titles, Journal of Optics (formerly Nouvelle Revue d'Optique) and Pure and Applied Optics. The new journal, to be titled Journal of Optics A: Pure and Applied Optics, will cover all aspects, both theoretical and experimental, of modern and classical optics. It is intended that this merger will unite the editorial strengths of each journal, eradicate overlap, and create a strong platform for the development of a world-class optics journal.

In conjunction with this merger, Quantum and Semiclassical Optics is to be relaunched under the new title Journal of Optics B: Quantum and Semiclassical Optics. Journal of Optics, comprising parts A and B, will be an integral part of Institute of Physics Publishing's dedicated optics programme.

A feature of these journals has always been strong European support, and we are delighted to confirm that Journal of Optics will be the official journal of the European Optical Society (EOS). Each title will consist of six bi-monthly issues, published in A4 format, beginning with the first issue of Journal of Optics A in January 1999, and Journal of Optics B in the following month. Subscribers to these journals will receive all the benefits that Institute of Physics Publishing journals offer; full text electronic access including six-year archives, a thirty-year abstract archive and new Hypercite^TM citation linking.

Both titles will begin under new Editorship, and we would like to take this opportunity to thank Professor Boccara, Professor Bertolotti and Professor Mandel for their achievements during their respective terms of office. We hope that both journals will continue in the tradition of excellence that has been established through their efforts.

In association with the changes outlined above, all editorial processing will be transferred to the main Institute of Physics Publishing offices. Our special thanks go to Françoise Chavel and Michèle Bouchareine at the EOS offices in Paris for their hard work and important contribution over recent years.

All new submissions should therefore be sent directly to:

Publishing Editor Journal of Optics Institute of Physics Publishing Dirac House Temple Back Bristol, BS1 6BE United Kingdom

We are also pleased to introduce electronic submission for both titles. Please refer to Notes for Authors for full details.

This is the last issue of the journal to be published under my editorship. It offers a good example of what the journal has become: a balanced mix of quantum optics and semiclassical optics. On the eve of my retirement, it is a pleasure to look back and consider the evolution of the journal. The recent publication of the 1997 impact factors by ISI has confirmed our position as the premier European journal devoted exclusively to optics research. Such a result could only have been achieved through teamwork, and I wish to express my gratitude to all those who contributed to this result: Michèle Bouchareine and Françoise Chavel from the EOS secretariat in Paris, John Haynes, Liz Martin and Tom Spicer from Institute of Physics Publishing in Bristol, and all the members of the Board. But I cannot conclude without a special expression of gratitude to Neal B Abraham whose experience in journal management is probably unsurpassed by anyone in our field, and who always found time to advise me when necessary.

Paul Mandel