Nonlinear optics with structured light Download： 685次
1 Introduction
Structured light^{1} refers to the modernday ability to tailor light in all its degrees of freedom (DoFs), spatial and temporal, to create complex optical fields in both the classical^{25} and quantum^{6, 7} domains. Combining DoFs have given rise to novel and exotic states of light as 2D, 3D and even 4D fields, including optical knots^{8, 9}, skyrmions^{10, 11}, Mobius strips^{12}, spatiotemporal fields^{1316}, raywave structured fields^{17, 18}, quantumlike classical light^{1921} and photonic wheels^{22}. But although the progress has been rapid of late, the topic itself can be dated back to Thomas Young and his double slit experiment, where arguably the first structured light was created. Indeed, the very essence of structured light is the notion of superpositions, where interference (not necessarily in intensity) gives rise to the desired structure. Today one can formulate all of structured light as a linear superposition principle^{1}, giving rise to geometric representations of the superpositions, from the orbital angular momentum (OAM)^{23}, to the total angular momentum^{24} of light, and more recently a generalised framework for multiple DoFs^{25}. For example, even simple plane waves hold the potential for structure: one plane wave may have a phase gradient, two plane waves will give rise to an intensity structure (as done by Young more than 200 years ago), three plane waves can produce an optical phase singularity, while multiple plane waves can give rise to exotic families of structured light, for instance, planes waves travelling on a cone give rise to Bessel beams^{26}. If the interfering plane waves are allowed to hold information in another DoF, say polarization, then just two can create exotic polarization structures^{27} and if focussed, will create synthetic chiral light in 3D^{28}. It is clear that there is a strong link between interference, a linear effect, and structured light. For this reason, the vast bulk of studies involving structured light have considered linear optical elements, with only much more recent progress in nonlinear optics with structured light, the topic of this review.
The invention of the laser^{29} is seen as fundamental to the development of the research field of nonlinear optics, with the first nonlinear optical demonstration of second harmonic generation (SHG)^{30} following quickly, soon after by third harmonic generation^{31} and SHG carrying spin angular momentum (SAM)^{32}. The reason for the strong historical linkage is simple: nonlinear optical phenomena are weak and typically need a coherent high power source to be observed. This knowledge can be dated back as far a Fresnel, who already understood that wave superpositions could transcend the linear regime. With the development of stronger laser sources and more efficient nonlinear materials, we have overcome this requirement. It is only natural then that the study of nonlinear optical phenomena shifts from asking “how much light is there?” based on efficiency concerns (intensity being the key to address this), to “what does the light look like?” (the structure of the light). Seminal works began analysing the structure of the generated light three decades ago^{33} with early work demonstrating the doubling of the number of singularities in the generated field^{34}. Following the link between orbital angular momentum (OAM) and these socalled screw dislocations (see ref.^{35} and references therein), the use of OAM carrying LaguerreGaussian (LG) modes in nonlinear optics was demonstrated^{36} followed a little later by the first production of quantum structured photons by nonlinear optics, demonstrating OAM entangled states^{37}. Although these important works set the scene, further progress has been slow, until only recently.
In this review we follow the progress in the field, from intensity drive processes that serve to alter the frequency of the pump light, to the present day nonlinear toolkit for the creation, manipulation and detection of structured light. We begin with the familiar wave mixing processes of second order, which have been deeply explored and continue to develop to this day, serving to exemplify how counterintuitive these interactions can be with the introduction of structured light. We then move on to show the types of media that allow these process and how they can also be structured, playing a crucial role in recent advances. We expand into higherorder parametric processes, including third harmonic generation and the generation of optical vortex solitons. Finally, we cite recent developments in high harmonic generation, an extreme nonparametric process, and the unusual applications of nonlinear processes in the quantum regime.
2 Theoretical background
The field of nonlinear optics is a venerable topic, and the reader is referred to excellent textbooks on the topic^{3840}. For the benefit of the reader, We begin by briefly outlining the core theory needed for the review, and to this end we begin with Maxwell's equations in the presence of a medium. If condensed and rewritten in terms of a wave equation, one finds,
where
where
But what are the governing principles when the light has internal structure? In this review we will often use scalar and vectorial combinations of light that carries OAM, a highly topical example. Such modes of light have an azimuthal phase profile given by
With suitable approximations (such as the slowly varying envelope approximation and lossless media) the generated field in three wave mixing can take the form
Similar differential equations are also derived for each frequency, initially obtaining three coupled differential equations. While these equations were initally derived as plane waves, structured light reveals more intricate interactions. For example, the phases and intensities are all intertwined: reshaping one field can mean completely new dynamics and new structures in all three involved fields. Due to the low conversion efficiency, a characteristic of nonlinear processes, in singlepass geometry we can make use of the nondepletion approximation, where the input fields can be regarded as static and therefore do not change on propagation. These equations show one remarkable feature of nonlinear optics: the nontriviality of the superposition principle. For example, let us associate the generated field
The expansion of these fields into propagating waves in different directions gives us the phasematching quantity
That ensures that the light generated is through a coherent process and interferes constructively at each wavefront generation. When
Fig. 1. Linear and nonlinear processes. Using second harmonic generation (SHG), we illustrate the differences between linear and nonlinear processes. (a ) Linear processes produce an output mode that is the addition of two input spatial modes of light, while SHG produces the product of the two modes. The linear superposition of two different modes with orthogonal polarization states generates a vector beam, which has a inhomogeneous polarization state. The polarization profile is represented as yellow lines across the transverse profile. In SHG, and wave mixing in general, the polarization profile will dictate where wave mixing happens and thus alter directly the spatial profile. In (b ) we show exemplify how path can also be controlled via polarization and the different phase matching conditions of crystals, including the periodic poling of type0. The mechanism which allows these interactions is sketched in (c ). Phasematching is the condition necessary for wave mixing to occur and exploits birefringence (types I and II) or periodical polling (type0) to achieve it.
Polarization also has a nonimmediate role. In the linear regime, optical beams with orthogonal polarization states do not interfere to produce fringes (but they do produce fringes in polarization^{27, 41}). In contrast, in nonlinear media, they do interact through the coupled interactions with the medium. If the input beam has a inhomogenous polarization profile, i.e. vector beam, then this interaction is different in every point of the transverse profile. We illustrate this in
The combination of
3 Structured dofs and their nonlinear coupling
By choosing sumfrequency generation and breaking wavelength degeneracy, it is possible to encode different structures in each frequency. If one of the fields is physically expanded and thus approximated to be a plane wave, we see the directly transfer and manipulation of the spatial profile of a beam across wavelengths^{4244}. In this case, the lack of structure of one field enables the generated beam to completely inherit the structure from the other. By using different spatial modes in each frequency, it was possible to perform OAM algebra^{45}. This creates an interesting interaction where the wavelength is used as a control parameter for the spatial structure.
In initial works with SHG it was observed that the generated field would be proportional to the square of the fundamental frequency^{36}, as it is possible to see in
The path degree of freedom can also be used: in
Fig. 2. Wave mixing with different degrees of freedom. In (a ), the authors show OAM algebra in noncollinear SHG. When typeII phasematching is used, the same noncollinear geometry allows for polarization switching, shown in (b ). This effectively couples multiple degrees of freedom in a single process: path, polarization, radial and angular transverse structures. The radial selection rules of LG modes in wave mixing are demonstrated in (c ). There is a intrinsic relation between the radial and angular degrees of freedom, which is manifested in the propagation dependence of the spatial profiles. In (d ), a experimental scheme using a Sagnac interferometer achieves faithful frequency conversion of vector light. Spin and orbital angular momentum are combined in second harmonic generation in (e ). Figure repoduced with permission from: (a) ref.^{48}, Springer Nature; (b) ref.^{50}, © Optica Publishing Group; (c) ref.^{54}, © American Physical Society; (d) ref.^{69}, American Physical Society; (e) ref.^{70}, under aCreative Commons Attribution 4.0 International License
The three process depicted above are independent and do not interfere with each other. Interestingly, not all nonlinear process are independent. Using polarization as a control parameter in typeII SHG, the authors realized that nonlinear process can interfere destructively^{50}. As illustrated in
3.6 Scalar structured light
The fields in
Interestingly, the coupling is not only between light and matter, but between differences in structure of the fields themselves, particularly within a given family. For instance, the “untwisting” of the azimuthal phase of an OAM LaguerreGaussian (LG) mode in turn altered the radial index^{52, 53}, with the rules governing this interaction only recently unveiled^{54}, and shown to be true for wave mixing processes of any order^{55}. This intricate relation is illustrated in
Table 1. Behaviour of various structures of light in second order nonlinear wave mixing. Here, n_{x}/n_{y} are the indices for HG modes, ℓ, p are the azimuthal/radial indices for LG modes and p/m are the parameters for InceGaussian modes. Indices with primes, such as ℓ′′ are of fundamental field modes and the ones without are of the frequency generated.

One might ask if there is there a recipe for the input to the nonlinear process in order to obtain a desired output structured field? The answer can be trivial, where one or more of the input profiles are plane waves and one of them contains the desired structure. By this approach, LG and HG structured modes have been created, as well as general structured images^{71}. When this is not possible, the HG basis is suggested to be optimal^{72}, and has been used for high fidelity mode generation^{73}. Because wave mixing allows for light modulation by light, the process can be adapted to be used as a detector of structured light^{71, 74, 75}, and has been used to detect LG and HG modes with very little modal crosstalk, in a manner analogous to modal decomposition^{76}. Even complex images can be handled in this manner, with the benefit of noise reduction (squaring a signal will amplify the strong and the decrease weak). For this reason, this has been an emerging application of SHG, with demonstrations including augmented edge contrast^{77, 78} and contrast enhancement to improve recognition of human faces and QR codes^{79}.
3.7 Vectorial structured light
So far we have considered the case where the structured light is scalar, so that the polarization is homogenous across the field. A complex vectorial structure is achieved by combining orthogonally polarized states such that each has its own unique spatial mode. If the spatial modes are also orthogonal, then the polarization structure of the field will be maximally inhomogeous^{3}. On the righthand side of
A peculiar effect observed in the nonlinear regime is phase conjugation, where the generated beam has the conjugate (negative) phase of a impinging beam. The allure of the nonlinear approach is that no knowledge of the initial phase is required for the process, unlike linear phase conjugation that always requires some wavefront sensing and adaptive control. In nonlinear optics this effect was first achieved and historically associated with fourwave mixing, but it has been shown that a second order effect, Stimulated Parametric Down Conversion, can partially achieve it, conjugating the transverse phase structure^{88} but not the propagation direction. It has been demonstrated with scalar^{89} and as well as vector^{9092} beams.
3.8 Spinorbit coupling
In paraxial optics, the spin angular momentum and the orbital angular momentum of a photon are treated as independent degrees of freedom. But even in this regime, we can find instances of these two quantities coupled. A notable example is a special group of vectorial inhomogeneous beams made of spatial modes carrying different OAM in polarization components carrying SAM. Besides these vector vortex beams, conical diffraction^{93} has been shown to produce optical vortices in the linear regime depending on the input SAM, effectively coupling them. Conical diffraction is a consequence of birefringence and has been reported to excite second harmonic generation in biaxial crystals^{9496}. The combination of conical diffraction with nonlinear process such as second harmonic generation can be combined to create cascaded processes that operate both on OAM and SAM^{97}. In this interesting example, the SAM is converted into OAM by conical diffraction, but only partially. The two parts (converted and unconverted) then act as fundamental fields for a SHG process of each state. The resulting beams from this conversion also suffer conical diffraction, having their OAM altered according to their SAM. By starting with a simple Gaussian beam with SAM, the authors show these two DoFs can be strongly coupled even in a simple material. However, these two degrees of freedom, while independent and possibly coupled, can interact in a nonlinear process^{70}, as depicted in
3.9 Intracavity dynamics
Lasers are a well known nonlinear device, and here too structured light laser cavities have a long history (see ref.^{98} for a review), with internal frequency generation used extensively for OAM generation^{99} and even with wavelength tuneability^{100}. While a full review is beyond the scope of this article (see refs.^{98100} for good reviews), we briefly highlight some interesting advances. These include intracavity geometric phase^{101} for helicity control, spinorbit effects^{102} with high purity, vortex OPOs^{103} to move into the midinfrared, wavelength and OAM tuneable lasers^{104} based on fibre geometries. Most of these solutions have been at low power. Nonlinear laser amplifiers have been used to raise the power levels, both in bulk crystals^{105} and disks^{106} with vectorial light, including parameteric amplification of ultrafast structured light^{107}, and with scalar structured light in Erbium fibre amplifiers^{108} as well as by Raman amplification^{109}.
Frequency converting cavities for structured light at the source include the use of exotic intracavity elements such as spatial light modulators for radial modes^{110} and metasurfaces for superchiral OAM modes^{111}, with recent work extending to vortex lattices^{112} and Poincaré beams^{113}. Nonlinear optical elements are often placed in cavities to enhance the efficiency, but this too can influence modal structure. Nonlinear cavities such as Optical Parametric Oscillators (OPOs) show rich behaviour not seen in freespace propagation. For example, controlling the spatial properties of a Gaussian pumped triple resonant OPO changes its threshold and allows for simultaneous oscillation of several mode pairs with fixed relative phases^{46}, and can result in multiple complex patterns^{114, 115}. A thorough study on the influence of the geometrical properties of the OPO on the generated spatial modes can be seen in^{116} and their applications in continuous variable entanglement in^{117}. The structured output can be tailored by structuring the pump^{56, 118}, as can the geometry of the cavity itself^{119}, making the cavity selective to specific modes.
4 Structured matter for structured light
The nonlinearity we are discussing refers to the interaction of light and matter. The structure of the output light (created or detected) is therefore tailored by both the input light and the medium, allowing the latter to be tailored. This is achieved when the medium higherorder susceptibility is no longer a constant but instead has a space dependency, e.g.,
4.2 Crystals
In the past this structuring of crystals has been done through acoustooptic modulators, giving rise to effects such as Bragg and RamanNath scattering, modulating the refractive index hence the phase matching conditions as well. The modern toolkit includes more direct manipulation of materials (e.g., structured photonic crystal). Phase matching in nonlinear photonic crystals has been well explained and explored^{123125} with periodic poling playing a important role in the past decade^{126}, branching into many applications, including a nonlinear version of the Talbot effect^{127}. By introducing a carefully crafted spatial modulation in a nonlinear crystal, it was shown to be possible to control the amplitude and phase of the generated fields^{128130}. One highlight is the work illustrated in
Fig. 4. Nonlinear optics enabled metasurfaces. These devices were shown to enable nontrivial interactions while frequency converting beams. In (a ) a SHG process coupling SAM and OAM. The combination of frequency conversion with holography creates metasurfaces with metalensing properties in (b )^{144}. An application taking advantage of the high damage threshold of these materials can be seen in (c )^{111} where the inclusion of a metasurface inside an optical cavity creates a laser with OAM from the source. Figure repoduced with permission from: (a) ref.^{143}, © American Chemical Society; (b) ref.^{144}, under a Creative Commons NonCommercial No Derivative Works (CCBYNCND) Attribution License; (c) ref.^{111}, Springer Nature.
The phasematching conditions involves not only material but also energy constrains. The periodic polling can not only enable frequency control^{131, 132} but when multiplexed it achieves phasematching for multiple wavelengths in the same crystal^{133}. Recently, a novel pattern in the periodic polling named quasiperiodic polling achieved simultaneous second and third harmonic generation^{134}. Further, the structuring of the media is not restricted to one dimension: by using oblique incidence on a periodically polled crystal it was possible to couple mode selection with phase matching^{135}, coupling DoFs of light and matter. Photonic crystals can be structured so that phasematching is crafted in both longitudinal and transverse directions^{136138} so that light is structured as it is generated. A thorough review on this emerging area can be seen in ref.^{139}.
An interesting combination of birefringence and periodic polling can be seen in ref.^{140}, where the spatial macroscopic structure complements the unit cell structure to achieve both type0 and typeII phasematching simultaneously. Besides changing the structure itself, changing the orientation of the medium can achieve interesting results. The sandwich crystal configuration (a combination of two identical crystals optically joined but oriented at 90°) has been employed for the frequency conversion of vector light^{82}.
As much as the structured of the medium dictates phasematching, the other way around also happens: we can use this property of the medium from a material analysis perspective^{141} and use these nonlinear process to characterize crystals according to their symmetry groups^{142}.
4.3 Metasurfaces
The structuring of the medium is not exclusive to crystals, as metasurfaces have been employed in many areas and nonlinear optics is no exception. They have seen a lot of atention recently by achieving high conversion efficiencies. The nanostructures composing these crafted surfaces are capable of confining light in volumes smaller than the diffraction limit^{145, 146}, greatly enhancing nonlinear effects. Excellent reviews can be found in ref.^{145, 147, 148}. They are structured by definition and can combine wavelength conversion with wavefront control^{149151}, spinorbit interactions^{152}, OAM operations involving SAM^{143}, image encoding^{153} and optical activity^{154}. Two illustrative cases can be highlighted: OAMSAM interactions^{143} and metalensing^{144}. By creating gold metaatoms with threefold symmetry, the authors in ref.^{143} arranged the metasurface to enable azimuthal geometric phase and frequency conversion at the same time, creating devices depicted in
Fig. 3. Nonlinear Holography. In (a ) the structuring of the medium is illustrated: the fundamental field is always the same, but the medium is not. The selective inversion of the electric domain across the transverse plane creates different spatial structures in the second harmonic field. The periodical transverse structure is responsible for multiple phase matching mechanisms, both longitudinally and transversely. In (b ) it is shown how noncollinear SHG can transfer a specific intensity pattern from one wavelength to the other. First row shows the imaging arrangement and the second column shows the phasematching conditions and an example of output modes. Right below is a experimental demonstration that this can be used for realtime frequency conversion of computer generated holograms. Figure repoduced from: (a) ref.^{130}, © American Physical Society; (b) ref.^{158}, © Optica Publishing Group.
5 Nonlinear holography
Since very early in the study of nonlinear optics, it was understood that wave mixing meant modulation and that this could be used for holography^{155}. In the original version, the counterpropagating fields involved in the fourwave mixing formed a grating that changed the generated field. Nowadays, we have more advanced forms of holography. When looking at
In this sense, by shaping the fundamental beam as a hologram it is possible to modulate the generated beam as it is created^{156}. This process allows for holograms that are self adaptive and depend on the generating fields, being able to copy or regenerate optical modes^{157}, even complex patterns in real time^{158}. In this example, illustrated in
If the interaction happens in more than a single plane, i.e. the medium is longer than a diffraction length, these approaches can be extended to three dimensions for volume holography^{159, 160} in nonlinear crystals, and the reader is referred to refs.^{161163} for excellent reviews on this topic.
6 Fourwave mixing
As we consider higherorder nonlinear effects, wavemixing becomes increasingly complex. For example, OAM conservation in a fourwave mixing (FWM) process with third order nonlinearity was observed in cold cesium gas in ref.^{164} where only one beam was structured with OAM, resulting in the transfer of OAM to the generated beam and similarly with modal superposition^{165}. This was later expanded to include both probe and pump having OAM^{166, 167}, where the phase matching conditions can be fulfilled in more directions than lower order process and this results in the creation of a higher number of states created in different paths, as depicted in
Fig. 5. Higher order process. In the generation of high harmonic orders, it is possible to generate beams of many different OAM from just two different inputs, as depicted in (a ). The process of writting and reading optical memory is depicted in (b ) and the diference in time scales depending on the order of the nonlinear process in (c ). In (d ) it is demonstrated robust selftrapping of a bright vortex beam by exploiting higher order nonlinearities of odd orders. Figure repoduced from: (a) ref.^{209}, Springer Nature; (b) ref.^{191}, © Optica Publishing Group; (c) ref.^{192}, © Optica Publishing Group; (d) ref.^{204}, © American Physical Society.
Using a long medium approximation, radial and angular mode conversion by FWM in a heated Rb vapour was demonstrated, making evident the role of the Gouy phasematching in this regime^{170}. Beyond just spatial DoFs, the spatial and temporal DoFs are not independent in this process^{171}, where frequency control enables selection of various spatial modes as outputs.
Recent developments with dielectric materials have been shown to enable fourwave mixing with high efficiency. These materials have been crafted in the nanoscale as plasmonic nanoantennas^{172, 173}, metasurfaces^{145148}, nanodisks^{174}, enabling not only frequency conversion to a wider range of wavelengths but the intrinsic structure also motivated simultaneous wavefront shaping^{144}.
7 Highharmonic generation
Highharmonic generation (HHG) is an extreme process, not regarded as perturbative process and cannot be represented in
8 Spacetime coupling
The medium cannot interact instantly with light: first, structured light interacts with a medium that inherits this structure momentarily. When the first light source is no longer there, a second light source interacts with the medium and inherits the structure of the first one. This effect is known as optical memory and is regarded as a possibility for storing quantum information in a multidimensional state space. A demonstration of this principle was observed in ref.^{188}, where light interacting with an atomic system (cold cesium gas) induced by a coherence grating lead to OAM conservation, a first step towards the demonstration of optical storage. This spatially dependent coherence transferred to the medium was shown be maintained in time^{189}, reporting storage times of up to 100 μs. It was shown in ref.^{190} that it is possible to store OAM in the same system and also retrieve it by employing Bragg diffraction. The same effect was also achieved in ref.^{191} but exploiting a different effect: coherent population oscilation, which uses the long relaxation time of the ground state of an open twolevel system to store information carried by a light field. This process is depicted in
While the process described above couples a specific structure to another during a time window, there are light structures that are notorious for having its time and space nonseparable: the spatiotemporal optical vortices^{14, 194}. These beams exhibit OAM transverse to propagation direction, instead of usual longitudinal OAM of phase vortex beams. One might wonder if these spacetime structures would hold in the nonlinear regime. Recent works showed that in SHG the spatiotemporal OAM is also conserved^{195, 196}, while also reporting effects such as time astigmatism and singularity splitting due to groupvelocity dispersion.
9 Spatial solitons
The selffocusing action of a medium can balance precisely the diffraction of a beam, resulting in the creation of optical solitons. The first observed optical solitons were dark vortex solitons, which are phase vortices that propagate in a selfdefocusing medium with third order nonlinearity
On the other hand, bright phase vortices suffer from azimuthal modulation instability in self focusing media, which results in their splitting and thus, were hard to be observed. This type of instability in the transverse modulation is similar to one responsible on the filamentation of beams and generation on trains of optical solitons^{198}.
However, by using noncentrosymetric metaldielectric nanocomposites, higherorder nonlinear effects such as fifth and seventh order become dominant and cause selfphase modulation^{199, 200}. This ultimately allowed for the observation of stable bright vortex solitons in ref.^{201204}. In
10 Quantum regime
Nonlinear processes have long been associated with quantum optics as the source of entangled photons. The most common source of entangled photons is Spontaneous Parametric Down Conversion (SPDC)^{210}, a nonlinear process at its core. By harnessing entanglement and the transverse structure of the photons it is possible to increase the dimensions of quantum protocols^{6}. This is often achieved by postselecting a particular state, the choice of which affects the biphoton entanglement spectrum in both its shape and dimensionality. This was first realized using OAM^{37} and subsequently many transverse structures were studied^{211215}, as well as inhomogenously polarized beams^{92, 216} and multipath schemes^{217, 218}. Soon after it followed that it was possible to engineer the pump profile to manipulate the biphoton spectrum and generate a entanglement spectrum straight out of the source^{219223}. Beyond nonlinear optics for creation, the detection and control of quantum states by nonlinear processes has been far less studies, and very much in its infancy.
Although quantum technologies have experienced rapid development in recent years, with light playing a key role, this has mostly been restricted to linear optical solutions, e.g., the ubiquitous beam splitter. For optical systems, a photonphoton interaction in vacuum is not possible. While this is partially true in matter as well, we observe in the nonlinear regime a photonphoton interaction mediated by the medium. Unfortunately this interaction is very unlikely to happen, but it does not mean impossible as this mixture have seen important advances recently (see ref.^{224} for a good review), with the building block of single photon wave mixing^{225}. Nonlinear optics have been suggested in various quantum processes^{226229} and even used for Bell filters^{230} for polarization, entanglement swapping^{231} and a quantum repeater device^{232, 233}. Only recently has structured light entered the equation, with a nonlinear version of spatial teleportation demonstrated with up to 10 modes, overcoming the significant hurdle of ancilliary photons and settting a new stateoftheart of 10 dimensional teleportation^{234}.
11 Conclusion
In this review we have touched many topics regarding nonlinear optics with structured light. Unlike linear optics, which generally act on only one degree of freedom, these process have the intriguing feature of coupling many DoFs through the properties of the medium. The possibility is for compact solutions for the creation, control and detection of structured light, yet many open questions remain: what structures can we create? How can we transfer structures within and between DoFs? What is the exact input one would need to generate a specific desired output? These questions are still open even in the lowest order of wave mixing. As new lightmatter interactions are discovered in the nonlinear regime, it is exciting to see how their structures couple and what insights can be deduced.
From real time holographic transmission to optical memory effects, from bulk crystalline media to sparse gas jets, there are many physical phenomena that are nonlinear optical processes. The development of new materials, techniques and interactions, alongside ever more powerful laser sources, all signal an exciting future for nonlinear control of structured light, and structured light control of nonlinear processes.
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Article Outline
Wagner Tavares Buono, Andrew Forbes. Nonlinear optics with structured light[J]. OptoElectronic Advances, 2022, 5(6): 210174.