Institute of Fundamental Technological Research

Raport zawiera graficzny zestaw wyników prac prowadzonych w okresie październik 2019 - marzec 2020 w ramach współpracy pomiędzy IPPT PAN i IF PAN. Prace prowadzone w IF PAN dotyczyły nałożenia warstwy złota na płytkę kwarcu i grawerowania w tej warstwie struktury jednowymiarowej soczewki Fresnela. Prace prowadzone w IPPT PAN dotyczyły wyznaczania parametrów geometrycznych wygrawerowanej struktury i charakterystyk jej oddziaływania z padającym polem optycznym. Prace eksperymentalne obu zespołów badawczych pozwoliły na precyzyjne sformowanie jednowymiarowej struktury ogniskującej typu płytki strefowej Fresnela (Fresnel Zone Plate - FZP) o właściwościach zgodnych z wynikami symulacji numerycznych.

Patterning of lines of holes on a layer of positive photoresist SXAR-P3500/6 (Allresist GmbH, Strausberg, Germany) spin-coated on a quartz substrate is carried out by using scanning near-field optical lithography. A green 532 nm-wavelength laser, focused on a backside of a nanoprobe of 90 nm diameter, is used as a light source. As a result, after optimization of parameters like laser power, exposure time, or sleep time, it is confirmed that it is possible to obtain a uniform nanopattern structure in the photoresist layer. In addition, the lines of holes are characterized by a uniform depth (71–87nm) and relatively high aspect ratio ranging from 0.22 to 0.26. Numerical modelling performed with a rigorous method shows that such a structure can be potentially used as a phase zone plate.

optical lithography, photoresist, quartz, hole nanopatterning

In photonic applications of optical beams, their transverse cross-section should be often narrow, with a diameter in their waist of the order of one wavelength or even less. Within this range, the paraxial approximation of beam fields is not valid and standard corrections by field expansions with respect to a small parameter are not efficient as well. Thus, still there is a need for more accurate beam field description. In this report, an exact vector solution for free-space propagation is given in terms of elegant Laguerre–Gaussian beams. The analysis starts from the known paraxial field approximation and next, through bidirectional field transformation and application of a Hertz potential leads to an exact vector solution. The role of the paraxial solution in construction of the exact solution is elucidated. The method works well not only in cases of free-space propagation but also in description of beam interactions with planar interfaces and multilayers.

elegant Laguerre–Gaussian beams, paraxial and nonparaxial solutions, bidirectional transformation, Hertz potentials

Optical characteristics of a finite two-dimensional silver stripe photonic crystal of a square lattice are numerically analysed with use of multilayer Rigorous Coupled Wave Analysis. Qualitative changes in optical response of the crystal originated from modifications of the thickness and filling factors of each layer and the polarization direction of the incident wave are shown. The crystal manifests its various characteristics in wideband or narrowband reflection and transmission, while absorption remains low. The behaviour of the crystal is determined by its structure geometry yielding excitation of localized plasmons and collective modes together with interactions between them. The optical response of the square lattice structure is also compared with the response of a triangular lattice crystal.

The interactions of first-order elegant Laguerre–Gaussian beams (ELG) with a two-dimensional periodic array are analysed theoretically and numerically. The structure consists of a periodic composition of two-zone Fresnel plates engraved in a silver film. The beam field is composed of periodic sequences of beams of circular or polar polarization incidence upon the structure. The beam axes coincide with the symmetry axes of every fourth Fresnel zone plate placed periodically along two orthogonal coordinates of a horizontal plane of the structure. It is shown that the beam-structure interaction results in substantial cross-polarization coupling, higher-order mode excitation, strong focussing and the extraordinary transmission of the optical field. An interpretation of the results is given per an analogy to the beam-structure interactions observed at planar, homogeneous and isotropic dielectric interfaces and layers.

Reformulation of conventional beam definitions into their bidirectional versions and use of Hertz potentials make beam fields exact vector solutions to Maxwell’s equations. This procedure is applied to higher-order elegant Laguerre–Gaussian beams of transverse magnetic and transverse electric polarization. Their vortex and anti-vortex co-axial compositions of equal and opposite topological charges are given in a closed analytic form. Polarization components of the composed beams are specified by their radial and azimuthal indices. The longitudinal components are common for beam compositions of both types; meanwhile, their transverse components are different and comprise two—nonparaxial and paraxial—separate parts distinguished by a paraxial parameter and its inverse, respectively. The new solutions may appear useful in modeling and tailoring of arbitrary vector beams.

An exact closed-form representation is derived of a vector elegant Laguerre–Gaussian wave packet. Its space–time representation consists of three mutually orthogonal field components—of a common azimuthal index and different radial indices—uniquely distinguished by first three powers of the paraxial parameter. The transverse components are of tm-radial and te-azimuthal polarization and appear, under their normal incidence, to be eigenmodes of any horizontally planar, homogeneous and isotropic structure, with eigenvalues given by the reflection and transmission coefficients. In this context, the interrelations between the cross-polarization symmetries of wave packets in free space and at medium planar interfaces are discussed.

An analysis of phenomena leading to high transmission at a one-dimensional metal grating is presented. It is shown that high resonant transmission can be obtained either for thick or thin gratings for a wide range of filling factors and that the origins of the enhanced transmission are different in each case. We analyse the optical response of structures with subwavelength slits and of various thicknesses. The role of different pure (dielectric cavity modes, surface plasmon polaritons) and coupled resonances on the enhanced transmission is presented.

Extraordinary optical transmission and good focusing properties of a two-dimensional scattering structure is presented. The structure is made of Fresnel zone plates periodically arranged along two orthogonal directions. Each plate consists of two ring-shaped waveguides supporting modes that match the symmetry of a circularly polarized incident plane wave. High field concentration at the focal plane is obtained with the short transverse and long longitudinal foci diameters. Optical vortex excitation in a paraxial region of the transmitted field is also observed and analysed in terms of cross-polarisation coupling. The structure presented may appear useful in visualization, trapping and precise manipulations of nanoparticles.

Fresnel zone plates, focusing, cross-polarisation coupling, optical vortices

The phenomenon of excitation and cancellation of higher-order elegant Hermite–Gaussian and Laguerre–Gaussian three-dimensional beams, induced at a dielectric isotropic interface by cross-polarization coupling, is analysed. The cross-polarization effect depends quantitatively on interrelations between beam field spatial distribution and beam polarization. These relations are derived for two basic cases of linear and circular polarization and confirmed by numerical simulations.

Three-dimensional optical beams incident on a dielectric interface undergo deformations upon reflection and refraction. Within first-order optics these deformations may be interpreted as longitudinal and transverse displacements and deflections of beam axes. In general, these effects are different for TE and TM components of the beam field. The problem of beam reflection and refraction at the interface is formulated and solved in such a manner that the beams are obtained with uniquely defined uniform displacements of their axes in a spatial domain and their spectrum centres in a spectral domain. Additional modifications of the beam polarization state remain generally small and non-uniform throughout the entire beam spectrum. In this context, a special role of polarization states diagonal in the interface plane is indicated.

Beam optics, polarization optics, reflection, refraction, Lorentz group

Beam reflection at a focusing nonlinear-linear interface near critical incidence of total internal reflection is analysed.
Basics of the three-dimensional formulation of the problem are outlined. Numerical simulations of the beam reflection are presented.
It is shown that owing to cross focusing and deformations of incident and reflected beams, a bistable switch is possible to achieve.
Characteristic features of this switch are discussed.

nonspecular reflection, nonlinear interfaces, beam switching, optical bistability

Polarisation, amplitude and beam shape aspects of the three-dimensional optical beam reflection at dielectric interfaces are analysed within a framework of the aberrationless approach. Roles of the paraxial approximation, the cross-dimensional coupling and the nonparaxial cross-polarisation coupling in the beam description are discussed. It is shown that the substantial first-order transverse beam modifications exist for both – linear and circular – beam polarisation states. Characteristic features of the single beam bistable switch at nonlinear interfaces are also discussed and numerical examples of the reflected beam field reshaping are presented.

Total internal reflection, Effects of nonspecular reflection, Beam shaping, Nonlinear interfaces, Optical bistability

An analytic model of beam reflection at a nonlinear–linear interface is presented.
An incident field approaches a nonlinear side of the interface at an angle close to a critical
angle of total internal reflection. A nonlinearity of the plain Kerr focusing type is considered.
A beam field at the interface is described by changes of the beam parameters during
propagation and reflection, that is, by aberrationless effects of nonlinear propagation and
nonspecular effects of reflection. Numerical iteration of the analytic solution indicates that,
for certain sets of incident beam and interface parameters, a bistable switch of the reflected
beam can be obtained. Characteristic features of this switch appear to be different from those
of a plane wave reflection.

nonlinear interfaces, optical bistability, nonspecular reflection

Nonspecular reflection at a nonlinear–linear dielectric interface with local Kerr nonlinearity is analyzed. The Fresnel reflectivity and the variational solution are explicitly given in a closed form. Bistable switching of the interface is demonstrated by numerical simulations based on the monotonic iteration procedure.

Bounded beams reflected at the interface between two dielectric media can undergo lateral displacements, focal shifts, angular deviations, changes in the beam waist size and complex amplitude. These effects are examined for beams incident from a linear medium onto a nonlinear defocusing Kerr-type material, where the nonlinear medium changes are supposed to be homogeneously non-local. An exact solution to the reflection problem is numerically iterated by a sequence of solutions to the respective linear problems and a rigorous first-order analysis of the non-specular phenomena is also given. The beam-interface interaction is described in terms of the Wigner distribution function invariant with respect to the nonspecular ABCD transformation. The results show that, for some specified beam parameters, the beam reflection may exhibit bistable switching, which is accompanied by bistable changes in all the non-specular effects.

Non-linear interface, Gaussian-Beam, NonspecularPhenomena, Dielectric Interface, Reflection, MediaLight, Displacement, Propagation, Shift

Multidimensional propagation of a light pulse or beam in a nonlinear sample of a Kerr type is described within the first-order optics formalism. A scale transformation that relates the nonlinear and linear propagation processes is defined by use of the nonlinear aberrationless effects. The nonlinear ray transfer matrix and Wigner distribution function are explicitly given in a factored form for the propagation of a symmetric Gaussian optical signal. An on-axis phase correction to the nonlinear first-order formalism is also specified.

For nonlinear propagation, scaled complex ray tracing [Opt. Commun. 119, 218 (1995)] in samples of Kerr media is accomplished in terms of four independent aberrationless effects: optical self-shortening, beam waist shift, waist width modification, and on-axis phase shift. A complex amplitude nonlinear modification is also introduced, and a symplectic nonlinear ABCDmatrix is determined. All the aberrationless effects are self-consistently defined, and their dynamics are shown for focusing and defocusing nonlinearities, beam powers up to the self-trapped soliton or critical levels, and propagation ranges including those that contain a self-collapse point. The multidimensional nature of the analysis is indicated, and its relevance to pulse compression, Z-scan measurements, and higher-order mode propagation is outlined.

A rigorous spectral analysis is given for the nonspecular reflection of a three-dimensional Gaussian beam at a dielectric isotropic planar structure. For the first time all independent nonspecular effects are derived in a self-consistent manner for the three-dimensional case. It is shown that the longitudinal nonspecular effects in the incidence plane, that is, the lateral and focal shifts of the beam waist position, the angular rotation of the reflected-beam axis, and the modifications of the beam waist width and complex amplitude, have their direct analogies in the plane transverse to the incidence and interface planes that gives transverse nonspecular effects. Moreover, the existence of the other, not yet reported, effect of nonspecular modification of the beam polarization is also proved. A role for TM and TE polarizations in reflected-beam formation is indicated. The results show that, up to the symmetric second-order terms in approximation of Fresnel coefficients, each of the longitudinal and transverse beam factors independently preserves its shape under reflection at the expense of changes of the beam reference frame, width, amplitude, and polarization parameters

A new scale transformation of complex ray parameters is introduced in an unified manner to treat the nonlinear propagation in Kerr media. It is shown that the nonlinear propagation, including soliton propagation, can be consistently traced by complex rays specific to the linear propagation with the imposed scale effects of self-shortening, self-focusing and phase self-modification. The solution obtained is explicitly described as the propagation in a free-space modified by three propagation effects, namely, the nonlinear changes of the beam or pulse waist position, waist width and on-axis phase. A field of cylindrical symmetry and arbitrary transverse dimension is analyzed for power levels ranging from the linear propagation to the soliton self-trapping. It is shown that the method can be formulated within a frame of the nonlinear ABCD matrix formalism and specified to comply with the variational analysis of the problem.

Gaussian beam nonspecular scattering is analysed in a framework of the complex-ray geometrical optics with a planar dielectric interface or multilayered configuration assumed as a model of the scattering structure. The deformation parameters of the beam are rederived and the appropriate eikonal function is defined for the regular case, i.e., excluding the angles of incidence close to any singularity of the scattering coefficient. A canonical transformation of complex-ray data is described and the three-dimensional complex-valued ray-transfer matrix of the structure is given. The interrelations between the matrix elements and the deformation parameters are described.

A gaussian beam reflection at a single interface between a linear medium and the nonlinear medium driven by electro-optical feedback is analysed by the method of the monotone iteration of gaussians. The field is described completely in terms of six independent amplitude and geometrical distortions of the reflected beam. Under certain conditions all these nonspecular reflection effects exhibit significant bistable behaviour. The limitations imposed on the nonspecular bistability by diffraction is discussed and the existence of the strong bistability in the diffusive and coupled-cavity configurations is indicated.

The net displacement of the intensity peak in relatively narrow Gaussian beams reflected at a dielectric interface is shown to be produced by a combination of four distinct nonspecular effects, namely, lateral, focal, and angular shifts and a modification of the beam-waist magnitude. We also find that these effects cause the axis of the reflected beam to follow a trajectory that depends on the beam width and on the distance from the waist of the geometric-optical reflected beams. To determine all the details of this nonspecular behavior, we derive a new expression for the reflected field; in contrast to previously reported results, this expression also holds for small beam widths and for incidence angles equal or close to the critical angle of total reflection. Our derivation yields accurate results for the four distinct nonspecular effects and provides a consistent explanation of the available experimental data on the net displacement of the beam peak.

A new configuration of the one-dimensional reflective asymmetrical metallodielectric grating structure for unidirectional excitation of surface plasmon polaritons (SPPs) is proposed. The structure is embedded between two different dielectric media and composed of two 1D metallic gratings each of the two consisted of periodically placed rectangular metal stripes. The case of normal incidence is analysed. It is shown that even a small horizontal shift between these two layers or a change in dielectric contrast of the grating fillings, the structure may redirect an energy flow of the SPP in the near field. An explanation of this unidirectional SPP excitation is given. Besides the SPP excitation by a plane wave, the excitation by a finite-diameter 3D Gaussian beam is analysed as well, as the beam facilitates visualisation of the SPP finite propagation length and efficiency of the directivity switch. It is shown that the switching phenomenon exists together with a high concentration of the electromagnetic field at the structure, the feature especially desirable in techniques of subwavelength nanovisualisation. The configurations analysed may be also useful in designing optical devices as optical switches, VLSI devices, light harvesting photodetector structures or, in general, in any case where efficient control of energy propagation directivity is of primary importance.

Surface plasmon polaritons, planar metallic gratings, plasmonic structures, unidirectional excitation and propagation

Behaviour of Laguerre{Gaussian beams (optical vortices are their attributes) impinged at a dielectric interface under distinct angles is discussed. For different incident angles the beams interact with the interface differently. Two ranges of incident angles, specified by diverse optical vortices excitation which is caused by cross-polarization effect, is analyzed. „Significant” boundary between these two ranges is defined. Theoretical analyses are confirmed by numerical simulations.

Excitation and cancellation of higher-order elegant Hermite-Gaussian and Laguerre-Gaussian beams under normal incidence at isotropic, lossless, dielectric interfaces are analysed. It is shown that such phenomena are originated in the cross-polarization coupling between orthogonal polarization components of the beams and depend qualitatively on interrelations between beam field spatial distribution and beam polarization. For Lagueffe-Gaussian beams these interrelations associate beam orbital and spin angular momenta. Analytic description confirmed by numerical simulations is given for transmission of two types of beams: Hermite-Gaussians of linear polarization and LagueffeGaussians of circular polarization.

refraction, reflection, cross-polarization, elegant Hermite-Gaussian and Laguerre-Gaussian beams