The application of reciprocity principles in optics has a long history that goes back to Stokes, Lorentz, Helmholtz and others. Moreover, optical applications need to be seen in the context of applications of reciprocity in particle scattering, acoustics, seismology and the solution of inverse problems, generally. In some of these other fields vector wave propagation is, as it is in optics, of the essence. For this reason the simplified approach to light wave polarization developed by, and named for, Jones is explored initially to see how and to what extent it encompasses reciprocity. The characteristic matrix of a uniform dielectric layer, used in the analysis of interference filters and mirrors, is reciprocal except when the layer is magneto-optical. The way in which the reciprocal nature of a characteristic matrix can be recognized is discussed next. After this, work on the influence of more realistic attributes of a dielectric stack on reciprocity is reviewed. Some of the numerous technological applications of magneto-optic non-reciprocal media are identified and the potential of a new class of non-reciprocal components is briefly introduced. Finally, the extension of the classical reciprocity concept to systems containing components that have nonlinear optical response is briefly mentioned.

https://iopscience.iop.org/article/10.1088/0034-4885/67/5/R03/pdf

Reciprocity in optics

Solitons, nonlinear self-trapped wavepackets, have been extensively studied in many and diverse branches of physics such as optics, plasmas, condensed matter physics, fluid mechanics, particle physics and even astrophysics. Interestingly, over the past two decades, the field of solitons and related nonlinear phenomena has been substantially advanced and enriched by research and discoveries in nonlinear optics. While optical solitons have been vigorously investigated in both spatial and temporal domains, it is now fair to say that much soliton research has been mainly driven by the work on optical spatial solitons. This is partly due to the fact that although temporal solitons as realized in fiber optic systems are fundamentally one-dimensional entities, the high dimensionality associated with their spatial counterparts has opened up altogether new scientific possibilities in soliton research. Another reason is related to the response time of the nonlinearity. Unlike temporal optical solitons, spatial solitons have been realized by employing a variety of noninstantaneous nonlinearities, ranging from the nonlinearities in photorefractive materials and liquid crystals to the nonlinearities mediated by the thermal effect, thermophoresis and the gradient force in colloidal suspensions. Such a diversity of nonlinear effects has given rise to numerous soliton phenomena that could otherwise not be envisioned, because for decades scientists were of the mindset that solitons must strictly be the exact solutions of the cubic nonlinear Schrodinger equation as established for ideal Kerr nonlinear media. As such, the discoveries of optical spatial solitons in different systems and associated new phenomena have stimulated broad interest in soliton research. In particular, the study of incoherent solitons and discrete spatial solitons in optical periodic media not only led to advances in our understanding of fundamental processes in nonlinear optics and photonics, but also had a very important impact on a variety of other disciplines in nonlinear science. In this paper, we provide a brief overview of optical spatial solitons. This review will cover a variety of issues pertaining to self-trapped waves supported by different types of nonlinearities, as well as various families of spatial solitons such as optical lattice solitons and surface solitons. Recent developments in the area of optical spatial solitons, such as 3D light bullets, subwavelength solitons, self-trapping in soft condensed matter and spatial solitons in systems with parity-time symmetry will also be discussed briefly.

http://www.physics.sfsu.edu/~laser/pdf/rop347172p20.pdf

Optical spatial solitons: historical overview and recent advances

Over the last dozen years, the area of accelerating waves has made considerable advances not only in terms of fundamentals and experimental demonstrations, but also in connection to a wide range of applications. Starting from the prototypical Airy beam that was proposed and observed in 2007, new families of accelerating waves have been identified in the paraxial and nonparaxial domains in space and/or time, with different methods developed to control at will their trajectory, amplitude, and beam width. Accelerating optical waves exhibit a number of highly desirable attributes. They move along a curved or accelerating trajectory while being resilient to perturbations (self-healing) and are diffraction-free. It is because of these particular features that accelerating waves have been utilized in a variety of applications in the areas of filamentation, beam focusing, particle manipulation, biomedical imaging, plasmons, and material processing, among others.

Airy beams and accelerating waves: an overview of recent advances

During femtosecond laser fabrication, photons are mainly absorbed by electrons, and the subsequent energy transfer from electrons to ions is of picosecond order. Hence, lattice motion is negligible within the femtosecond pulse duration, whereas femtosecond photon-electron interactions dominate the entire fabrication process. Therefore, femtosecond laser fabrication must be improved by controlling localized transient electron dynamics, which poses a challenge for measuring and controlling at the electron level during fabrication processes. Pump-probe spectroscopy presents a viable solution, which can be used to observe electron dynamics during a chemical reaction. In fact, femtosecond pulse durations are shorter than many physical/chemical characteristic times, which permits manipulating, adjusting, or interfering with electron dynamics. Hence, we proposed to control localized transient electron dynamics by temporally or spatially shaping femtosecond pulses, and further to modify localized transient materials properties, and then to adjust material phase change, and eventually to implement a novel fabrication method. This review covers our progresses over the past decade regarding electrons dynamics control (EDC) by shaping femtosecond laser pulses in micro/nanomanufacturing: (1) Theoretical models were developed to prove EDC feasibility and reveal its mechanisms; (2) on the basis of the theoretical predictions, many experiments are conducted to validate our EDC-based femtosecond laser fabrication method. Seven examples are reported, which proves that the proposed method can significantly improve fabrication precision, quality, throughput and repeatability and effectively control micro/nanoscale structures; (3) a multiscale measurement system was proposed and developed to study the fundamentals of EDC from the femtosecond scale to the nanosecond scale and to the millisecond scale; and (4) As an example of practical applications, our method was employed to fabricate some key structures in one of the 16 Chinese National S&T Major Projects, for which electron dynamics were measured using our multiscale measurement system.

/pdf/electrons-dynamics-control-by-shaping-femtosecond-laser-535kqykqpo.pdf

Electrons dynamics control by shaping femtosecond laser pulses in micro/nanofabrication: modeling, method, measurement and application

We report femtosecond laser micromachining of micron-size curved structures using tailored accelerating beams. We report surface curvatures as small as 70 μm in both diamond and silicon, which demonstrates the wide applicability of the technique to materials that are optically transparent or opaque at the pump laser wavelength. We also report the machining of curved trenches in silicon. Our results are consistent with an ablation-threshold model based on calculated local beam intensity, and we also observe asymmetric debris deposition which is interpreted in terms of the optical properties of the incident accelerating beam.

/pdf/micromachining-along-a-curve-femtosecond-laser-1lxqlctwe3.pdf

Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams

We use caustic beam shaping on 100 fs pulses to experimentally generate non-paraxial accelerating beams along a 60 degree circular arc, moving laterally by 14 \mum over a 28 \mum propagation length. This is the highest degree of transverse acceleration reported to our knowledge. Using diffraction integral theory and numerical beam propagation simulations, we show that circular acceleration trajectories represent a unique class of non-paraxial diffraction-free beam profile which also preserves the femtosecond temporal structure in the vicinity of the caustic.

/pdf/sending-femtosecond-pulses-in-circles-highly-non-paraxial-2xs10k4eda.pdf

Sending femtosecond pulses in circles: highly non-paraxial accelerating beams

Femtosecond pulses provide an extreme degree of confinement of light matter-interactions in high-bandgap materials because of the nonlinear nature of ionization. It was recognized very early on that a highly focused single pulse of only nanojoule energy could generate spherical voids in fused silica and sapphire crystal as the nanometric scale plasma generated has energy sufficient to compress the material around it and to generate new material phases. But the volumes of the nanometric void and of the compressed material are extremely small. Here we use single femtosecond pulses shaped into high-angle Bessel beams at microjoule energy, allowing for the creation of very high 100:1 aspect ratio voids in sapphire crystal, which is one of the hardest materials, twice as dense as glass. The void volume is 2 orders of magnitude higher than those created with Gaussian beams. Femtosecond and picosecond illumination regimes yield qualitatively different damage morphologies. These results open novel perspectives for laser processing and new materials synthesis by laser-induced compression.

/pdf/high-aspect-ratio-micro-explosions-in-the-bulk-of-sapphire-1ba48dufvl.pdf

High aspect ratio micro-explosions in the bulk of sapphire generated by femtosecond Bessel beams.

Arbitrary shaping of the on-axis intensity of Bessel beams requires spatial modulation of both amplitude and phase. We develop a non-iterative direct space beam shaping method to generate Bessel beams with high energy throughput from direct space with a single phase-only spatial light modulator. For this purpose, we generalize the approach of Bolduc et al. to non-uniform input beams. We point out the physical limitations imposed on the on-axis intensity profile for unidirectional beams. Analytical, numerical and experimental results are provided.

Arbitrary shaping of on-axis amplitude of femtosecond Bessel beams with a single phase-only spatial light modulator

We report the observation of arbitrary accelerating beams designed using a non-paraxial description of optical caustics. We use a spatial light modulator-based setup and techniques of Fourier optics to generate circular and Weber beams subtending over 95 degrees of arc. Applying a complementary binary mask also allows the generation of periodic accelerating beams taking the forms of snake-like trajectories, and the application of a rotation to the caustic allows the first experimental synthesis of optical accelerating beams upon the surface of a sphere in three dimensions.

Arbitrary non-paraxial accelerating periodic beams and spherical shaping of light

The material processing technique of “stealth” nanomachining is based on translating a longitudinally extended beam such as a Bessel beam into a transparent sample to generate extended nanochannels, which leads to subsequent internal stress that facilitates high quality cleaving. In this letter, we compare the quality of such cleaving in glass samples obtained using Bessel beams with both circularly symmetric and elliptical transverse profiles. We find that the use of an elliptical Bessel beam generates elliptical nanochannels, which greatly improves the cleavage quality and cuts material strength by aligning the centre of the cleavage plane with the centre of the machined channels. These results are interpreted using numerical simulations that show how elliptical nanochannels enhance the intensity and localization of the tensile stress distribution in glass under bending when compared to channels with circular cross-sections.

Remo Giust

Papers

Sending femtosecond pulses in circles: highly non-paraxial accelerating beams

High aspect ratio micro-explosions in the bulk of sapphire generated by femtosecond Bessel beams.

Arbitrary shaping of on-axis amplitude of femtosecond Bessel beams with a single phase-only spatial light modulator

Arbitrary non-paraxial accelerating periodic beams and spherical shaping of light

Submicron-quality cleaving of glass with elliptical ultrafast Bessel beams