Basic Concepts of Nonlinear and Photorefractive Optics

Windows or eyeglasses that darken in bright light are examples of nonlinear optical materials, in which the response of the medium, in this case the refractive index, changes dramatically with the light intensity. However, the response time, typically seconds, of these materials is too slow to be of practical use for electro-optic or all-optical switching processes. The combination of intense coherent radiation available from lasers together with newly developed photorefractive materials is providing nonlinear optical response times on ultrafast time scales. Such systems allow photons to be added, subtracted, mixed, and manipulated in ways impossible in our familiar low-light-intensity environment. The Reviews in this special issue of Science look at some of those developments in the field of nonlinear optics and the applications they are finding. To study the dynamics of an event too fast for our eyes to see, snapshots of the event are taken, pieced together, and then played back in slow motion. Cameras equipped with fast mechanical shutters allow us to view microsecond snippets of time. The detailed dynamics of chemical reactions or of electronic transitions in crystalline materials can be revealed in a similar manner by following processes with laser pulses on time scales of picoseconds (10−12 s) or femtoseconds (10−15 s). Steinmeyer et al. (p. [1507][1]) review the role of nonlinear optics in the generation of ultrafast laser pulses and focus on the role being played by direct laser oscillators. It is necessary in spectroscopy to tune in to the energy scale that is relevant to the particular system under study. However, lasers generally emit light at very precise and fixed wavelengths. Dunn and Ebrahimzadeh (p. [1513][2]) describe how high-quality monochromatic light can be generated with optical parametric oscillators in which the interaction between photons can be controlled. This approach achieves a flexibility in generating the output light that is not available to conventional lasers. The past decade has seen an explosion in communication technology. The continuing challenge is to transfer ever-larger amounts of information from one point to another at as high a rate as possible without losing any data in the process. One proposal to overcome the transfer rate limitation of semiconductors is to use all-optical networks. Today, thousands of kilometers of optical fibers encircle the globe. As more information is transferred down a fiber, however, nonlinearities become important and can actually limit the information capacity. As a light pulse propagates through a medium, it disperses or broadens, and repeater stations are needed periodically to prevent pulses from smearing into one another. However, with sufficiently high light intensity, the refractive index of the medium is locally increased and the light is confined to that region by total internal reflection. The light then traverses the medium without loss of intensity and is described as a spatial soliton. Stegeman and Segev (p. [1518][3]) review how such nonlinearities can be used to advantage in the generation and interaction of solitons in their role as information carriers, and Cotter et al. (p. [1523][4]) review the techniques required to implement processing of the optical signals at transfer rates in excess of 100 gigabits per second. A News story (p. [1502][5]) examines the promise of storing such torrents of data in holograms: durable optical inscriptions written in nonlinear optical materials. And two other News stories (pp. [1500][6] and [1504][7]) describe progress in other fields of optics: latticelike photonic crystals, which can trap or channel light; and adaptive optics technology, which helps telescopes undo the effects of atmospheric turbulence. [1]: /lookup/doi/10.1126/science.286.5444.1507 [2]: /lookup/doi/10.1126/science.286.5444.1513 [3]: /lookup/doi/10.1126/science.286.5444.1518 [4]: /lookup/doi/10.1126/science.286.5444.1523 [5]: /lookup/doi/10.1126/science.286.5444.1502 [6]: /lookup/doi/10.1126/science.286.5444.1500 [7]: /lookup/doi/10.1126/science.286.5444.1504

This joint issue of Optics Express and Optical Materials Express showcases 29 articles that report the latest advancements in nonlinear optics. These articles include contributions from authors who participated in the Optica Nonlinear Optics Topical Meeting, which took place in Honolulu, Hawaii, from July 10th to July 14th, 2023. The conference was organized by Optica (formerly known as OSA). As an introduction, the editors provide a summary of these articles, which cover a broad range of topics in nonlinear optics, spanning from fundamental nonlinear optical concepts to novel nonlinear effects, and from innovative nonlinear materials to topics such as ultrafast optics, machine learning empowered nonlinear optics, and unconventional applications. This diverse array of contributions reflects the dynamic and interdisciplinary nature of contemporary research in the field of nonlinear optics while showcasing some of the most recent developments.

The 3rd topical conference Nonlinear Optics at Interfaces (NOPTI 2001) was held from October 15 to 19, 2001 at the Faculty of Science at the University of Nijmegen, The Netherlands. NOPTI 2001 followed the very successful meetings at Kassel (1993) and Berlin (1998) in bringing together active researchers in this field to discuss recent developments and applications of nonlinear optical techniques for surface and interface studies. The conference programme consisted of 15 invited lectures, 25 oral contributions and 35 posters, covering recent advances in timeresolved studies of surface chemistry, electron and spin dynamics, higher-order mixing processes, nano-optics, magnetization-induced nonlinear optical effects and other areas. The field of nonlinear optics in general, and time-resolved nonlinear optical studies in particular, has greatly benefited from the strong development of solid-state pulsed laser sources. This is particularly clear in the strong development of magnetization-induced second harmonic generation and its application to the studies of ultrathin magnetic films. This new area would never have developed so strongly if we were still limited to Q-switched nanosecond laser sources. This is a nice example of the mutually beneficial interaction between science and engineering, a topic that was so beautifully addressed by Nicolas Bloembergen in his well attended evening lecture on the “Synergy of Science and Technology in Nonlinear Optics”. We were indeed very pleased to have both the founding father of the field of nonlinear optics, Nicolas Bloembergen, and the pioneer of the nonlinear optical probing of interfaces, Ron Shen, actively participate at NOPTI 2001, in addition to many other leading experts in the field. NOPTI 2001 was chaired by Th. Rasing, University of Nijmegen, and was organized by the local committee consisting further of A. Kirilyuk, J. Hohlfeld, A. Fasolino andM. van Breemen, all from Nijmegen. The programme committee were M. Aeschlimann, J. Hohlfeld, B. Jerome, B. Koopmans, Th. Rasing and H. Zacharias. NOPTI 2001 gratefully acknowledges financial support from the University of Nijmegen, the NSRIM Institute of the University of Nijmegen, Spectra Physics, Coherent and Springer-Verlag. Finally the editors would like to thank all the authors and reviewers for their contributions and cooperation.

The growth and overlap of research in the fields of photonic crystals (PhCs) and nonlinear optics should lead to new exciting, active functions and high-efficiency nonlinear optical applications because nonlinear optical effects in PhCs may allow for significant advances in various optical processes by using resonantly stored light and anomalous band dispersions, in combination with nonlinear optical host materials. To show the experimental and theoretical evidences of great potentials of the nonlinear PhCs for the realization of the high-efficient and very compact nonlinear optical devices and applications, we have examined the typical second- and third-order nonlinear optical responses and the photonic band structure of the nonlinear two-dimensional (2D) PhC waveguides. We have demonstrated for the first time the second harmonic generation (SHG), the sum-frequency mixing (SFM) in the ultraviolet (UV) region, and the strong enhancement of the SHG intensity originating from the photonic band resonance in this waveguide. Moreover, by probing the nonlinear optical changes of the band resonances in angle-resolved reflectivity,we have shown direct evidence that the nonlinear optical changes arising from modifications of the photonic bands by purely optical means are dominated by the dispersion nature and the group velocity of the photonic bands, which are essential for the realization of desirable nonlinear applications, such as practical all-optical switching devices with very low operational power and ultra-small dimensions. These results agree well with the bhavior predicted from band structures, indicating that the design of nonlinear optical properties of material systems is realistically possible by band dispersion and group velocity engineering.

Intensity-dependent properties of semiconductors (SCs) are of great significance since they reveal a lot of information about materials’ nonlinear behavior. Field of nonlinear optics (NLO) has been revolutionized due to the invention of lasers. Lasers have made possible to discuss nonlinear effects in detail with great precision. Nonlinear optical properties, their basic theory and formulism, and nonlinear effects are explored in the chapter with concise details and attention. NLO is utilized to understand the nonlinear susceptibility and its dependence on field and frequency and its symmetry properties and effects. Maxwell equations are at the heart of NLO. The higher terms in the nonlinear susceptibility give rise to harmonics of higher order that are discussed in detail. Here, second harmonic generation (SHG) is discussed for biological visualization, and another nonlinear multiphoton imaging method that is called third harmonic generation (THG) is deliberated briefly. In non-centrosymmetric framework, the second-order nonlinearity is the most reduced order of nonlinear interaction. Third-order nonlinearities in SCs provide absorption coefficient and refractive index (RI) that depend upon intensity. On the basis of photon energies close or below to absorption edge, there are two types of nonlinearities called resonant and nonresonant optical nonlinearities. Some optical nonlinearities in SCs are also explained, such as optical nonlinearities due to photothermal effects. The electro-optic effect and intensity-dependent RI are elaborated in detail. Application of nonlinear effects and nonlinear optical SCs such as composites and polymers are studied. Application of nonlinear effects in photonic materials is reviewed. Nonlinear effects in bulk SCs such as aromatic derivatives benzil (Bz) and like meta-dinitrobenzene (m-DNB) have been briefly investigated.

Quantum chemical study on the high nonlinear optical effect of MMONS

Progress in the development of new tools for modem apphed mathematics resulted in a better scientific under­ standing of nonlinear waves in various fields of nonlinear optics, hydrodynamics, and plasmas. The universahty of the equations describing wave processes is one of the most important components of this success. Nonlinear Schrodinger equation (NLS) and Korteweg de Vries equation are among best illustrations of successful application of apphed mathematics as a tool to analyze various nonlinear phenomena ranging from optical communications and Bose con­ densation to ocean waves. Solutions of nonlinear equations usually result in the formation of singularities , coherent structures or solitary waves. Examples of the corresponding phenomena can be observed in filamentation of laser beams in nonlinear media, wave breaking in hydrodynamics, collapse, and Langmuir waves in plasmas. NLS in dimension one (ID) is a basis for the description of modem optical fiber communication systems. A key technological tool for development of ultrafast high-bitrate optical communication lines is a dispersion management. A dispersion-managed optical fiber is described by NLS with periodic variation of dispersion along an optical line which dramatically reduces pulse broadening. Solitary wave solutions in such systems are important information carriers in optical lines. NLS in 2D describes a stationary self-focusing of light in optical media with Kerr nonlinearity, Bose-Einstein condensate in plane geometry as well as a self-focusing in plasma. Due to self-focusing the amplitude of an NLS solution tends to infinity after finite distance of propagation, representing a blow up phenomenon. The blow up is accompanied by a dramatic contraction of the spatial size of solution, which is called collapse. Near the collapse point NLS loses its applicability and there is usually a quahtative change in the underlying nonlinear phenomena, the new mechanisms become important such as dissipation, inelastic two- and three-body collisions, which can cause a loss of atoms from the Bose-Einstein condensate, breakdown of slow envelope approximation in nonlinear optical media and plasma density depletion. If optical power is very large in optics or if a number of particles in the BoseEinstein condensate significantly exceeds the critical number, then collapse turbulence occurs with random positions of collapses in space and time. A study of collapse regularization is important in describing collapse turbulence and to be able to go beyond an individual collapse event. 3D NLS is a model for non-stationary self-focusing of hght in optical media with Kerr nonlinearity, Bose-Einstein condensate in 3D geometry and laser-plasma interactions. Self-focusing results in collapse, which is of a different type as compare with 2D, and it is called weak collapse. NLS in 3D is a model for ultrashort pulse (optical bullet) that is a key for current developments in microfabrication of photonics devices by means of intense femtosecond laser pulses. Regularization of collapse for such pulses requires an extension of the model beyond NLS and a study of the full set of MaxwellSs equations. Maxwell's equations are also necessary to study ultrashort hght propagation through thin films and guided-wave metamaterials. New challenges for nonlinear optics and apphed mathematics include description of nonlinear optical phenomena in negative-refractive-index metamaterials, which are artificial nano-composites materials that show great promise for opening the new avenues in manipulating light. Light propagating through them could exhibit extraordinary properties and brings a wealth of novel phenomena to nonlinear optics. Electrodynamical properties of metamaterials result from many factors: plasmonic oscillations in metallic nanostructures, multi-scale interaction of near field electromagnetic resonances with optical far field dynamics, surface roughness of nanostructures, high values of local fields that cause nonlinear response and etc. It has recently been shown that mathematical modeling of hght interaction with thin film metamaterials requires the use of classical hydrodynamics models. Therefore, metamaterials represent a new research

Photonic platforms with excellent nonlinear optical characteristics are very important to improve the devices' performance parameters such as integration, modulation speeds and working bandwidths for all-optical signal processing. The traditional processing technology of photonic platforms based on silicon, silicon nitride and silicon oxide is mature, but the nonlinear function of these optical platforms is limited due to the characteristics of materials; Although two-dimensional (2D) materials possess excellent nonlinear optical properties, their nonlinear potentials cannot be fully utilized because of their atomic layer thickness. Integrating 2D materials with mature photonic platforms can significantly improve the interaction between light and matter, give full play to the potentials of 2D materials in the field of nonlinear optics, and improve the nonlinear optical performances of the integrated platforms on the basis of fully utilizing the mature processing technology of the photonic platforms. Based on the above ideas, starting from the basic principle of nonlinear optics (Section 2), this review combs the research progress of various nonlinear photonic platforms (resonators, metasurfaces, optical fibers, on-chip waveguides, etc.) heterogeneously integrated with 2D materials, realized by traditional transfer methods (Section 3) and emerging direct-growth methods (Section 4) in recent years, and the introduction is divided into second-order and third-order nonlinearity. Comparing with the transfer methods, the advantages of using direct-growth methods to realize the heterogeneous integration of 2D materials and photonic platforms for the study of nonlinear optics are expounded, and the technical difficulties to be overcome in preparing the actual devices are also pointed. In the future, we can try to grow 2D materials directly onto the surfaces of various cavities to study the enhancement of second-order nonlinearity; we can also try to grow 2D materials directly onto the on-chip waveguides or microrings to study the enhancement of third-order nonlinearity. Generally speaking, the research on integrated nonlinearity by directly growing 2D materials onto various photonic structures has aroused great interest of researchers in this field. As time goes on, breakthrough progress will be made in this field, and technical problems such as continuous growth of high-quality 2D materials onto photonic structures and wafer-level large-scale preparation will be broken through, further improving the performance parameters of chips and laying a good foundation for optical communication, signal processing, optical sensing, all-optical computing, quantum technology and so on.

In its 60 years of existence, the field of nonlinear optics has gained momentum especially over the past two decades thanks to major breakthroughs in material science and technology. In this article, we present a new set of data tables listing nonlinear-optical properties for different material categories as reported in the literature since 2000. The papers included in the data tables are representative experimental works on bulk materials, solvents, 0D–1D–2D materials, metamaterials, fiber waveguiding materials, on-chip waveguiding materials, hybrid waveguiding systems, and materials suitable for nonlinear optics at THz frequencies. In addition to the data tables, we also provide best practices for performing and reporting nonlinear-optical experiments. These best practices underpin the selection process that was used for including papers in the tables. While the tables indeed show strong advancements in the field over the past two decades, we encourage the nonlinear-optics community to implement the identified best practices in future works. This will allow a more adequate comparison, interpretation and use of the published parameters, and as such further stimulate the overall progress in nonlinear-optical science and applications.

The field of nonlinear optics has grown significantly within the last two decades. Photorefractive materials in particular have been utilized in a wide variety of applications. Recently, the photorefractive inorganic crystals used to demonstrate nonlinear optical phenomena and applications have begun to decrease significantly in cost, bringing them within the budgetary limits of smaller physics departments. In addition, within the last five years photorefractive organic polymers have been developed which could serve as the focus of interesting interdisciplinary activities between undergraduate physics and chemistry programs. This article provides a starting point for educators in such programs who have an interest in developing undergraduate laboratory projects based on photorefractive materials. We present some background on the physics of photorefractive phenomena and materials, brief descriptions of some of the demonstrations and applications that employ these materials, and original references on these applications.

Optical event horizons in fibers, driven by coherent pumps, have been a prominent subject of study within the field of nonlinear optics. Previously, optical event horizons involving a potent pump and a linear-wave were interpreted as phase-matching processes wherein new spectral components are derived from the linear-wave due to the influence of the strong pump. This nonlinear interaction, coupled with the wave mixing mechanism, has been elaborated upon in the spectral domain. It’s portrayed as a cascaded four-wave mixing process, achieving quasi-phase-matching through intermediate spectral components. Until now, research focused on event horizons or soliton linear-wave interactions has predominantly relied on coherent laser pump sources. However, there has been a recent resurgence in the exploration of incoherently pumped nonlinear optics. While the specific dynamics of incoherent light fields and their subsequent nonlinear processes might be elusive due to their inherent random field fluctuations, their incoherent nature unveils a multitude of statistical dynamics for nonlinear phenomena. In this work, we delve into optical event horizons encountered by linear-waves propelled by an incoherent light field within nonlinear optical fibers. Our numerical analysis scrutinizes the dynamics of linear-waves during optical event horizons under incoherent pumping. We further dissect the temporal statistics of the newly birthed idler-waves emerging from these event horizon processes.

Halide perovskites provide an ideal platform for engineering highly promising semiconductor materials for a wide range of applications in optoelectronic devices, such as photovoltaics, light-emitting diodes, photodetectors, and lasers. More recently, increasing research efforts have been directed toward the nonlinear optical properties of halide perovskites because of their unique chemical and electronic properties, which are of crucial importance for advancing their applications in next-generation photonic devices. Here, the current state of the art in the field of nonlinear optics (NLO) in halide perovskite materials is reviewed. Halide perovskites are categorized into hybrid organic/inorganic and pure inorganic ones, and their second-, third-, and higher-order NLO properties are summarized. The performance of halide perovskite materials in NLO devices such as upconversion lasers and ultrafast laser modulators is analyzed. Several potential perspectives and research directions of these promising materials for nonlinear optics are presented.

Extending covalent organic frameworks (COFs) into crystalline carbon‐free covalent backbones is an important strategy to endow these materials with more exotic functions. Integrating metal‐free inorganic and organic components into one covalent framework is an effective way to address the issue of poor thermal/solvent stability in the field of nonlinear optics (NLO). However, constructing such structures is very challenging. Here, we linked 3‐connected nods (BO3) and 2‐connected organic building blocks (Te(Ph)2) together to produce colorless single crystals (size up to 400 μm) of a three‐dimensional (3D) chiral covalent framework (CityU‐22). The single‐crystal X‐ray diffraction (SCXRD) analysis reveals that CityU‐22 has a non‐carbon Te−O−B−O bond‐based network with the srs topology. The chiral CityU‐22 displays good stability under the treatment of different common solvents or heat (the decomposition temperature above 300 °C). Due to its non‐π‐conjugated backbone (−Te−O−B−O−), CityU‐22 shows an ultraviolet NLO behavior with a second‐harmonic generation (SHG) response similar to KH2PO4 (KDP).

Graphene has become a promising nonlinear optical medium due to its ultra-high nonlinear coefficients and tight light mode confinement ability. By optimizing the geometry parameters, a 3.9-mm-long graphene-covered silicon ridge waveguide is demonstrated, resulting in a maximum bandwidth of 498 nm and a peak conversion efficiency of -15.2 dB in mid-infrared band, with the pump power of 1 W. The results in this article show that graphene has unparalleled potential in the field of nonlinear optics.

This article investigates the optical soliton solutions for the Kuralay-IIA equation using the analytical approach. This model has a wide scope in the fields of nonlinear optics, proving gauge equivalency among different models, the motion of integrating space curves, and ferromagnetic materials. To find the exact solutions, the kuralay-IIA equation is first converted into an ODE by using wave transformations. These solutions are extracted by using the modified exponential rational function (MERF) method which provided us with the different types of solitons such as dark, singular, complex dark-singular, solitary wave, and exponential function solutions. To provide insight into the physical behaviors of the nonlinear Kuralay IIA equation, some of the selected solutions are visualized through 3-D surface plots, line graphs, and contour plots.