Research Scientist Emeritus at Czech Academy of Sciences
SPIE Involvement:
Author
Area of Expertise:
Diffractive Optics and Diffraction ,
Optical Physics and Spectroscopy ,
Optical Holography and Interferometry ,
Optical Properties and Negative Refraction ,
Electromagnetism and Guided Waves
Publications (31)
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Nonparaxial diffractive lenses are without the “spherical” (aperture) aberration for two prespecified conjugate points on the axis. The distribution of zones is characteristic for each location of conjugate points. The existing relations for calculation of zone distribution by the relation for two prespecified conjugate points located in finite distances and the spherically curved substrate of the lens is completed. The relation has been reduced to a compact and simple form.
Off-axis holographic diffractive optics creates beams with an elliptic cross section. Focusing properties of that beams
differ from beams having a circular aperture. Axial intensity distributions of converging spherical waves behind elliptic
apertures are analyzed. Similarly to behaviour of circular cross section beams, main maxima move from the geometric
focus to the location of the aperture with decreasing the Fresnel number. However, their displacements and values are
higher than for the circumscribed circular aperture. Minima of curves do not achieve zero values as expected. All results
can not be given in closed form; only numerical results for specific parameters can be computed.
Devices for document security consisting of a thin metallic film the boundaries of which are undulated with a relief of a
rainbow hologram, with the lower boundary facing to a lossless medium and the upper one facing (i) to a lossless
medium with the same refractive index or (ii) to a thin dielectric film with a higher refractive index, are proposed. When
viewed through in collimated and monochromatic light, they exhibit unique angular variation of appearance - a marked
succession of dark and bright areas if the incident beam is polarized in the plane of recording of the hologram (the s-polarization).
The devices are modelled as single-film and double-film structures that are composed either of a 30 nm
thick silver film, which is sandwiched between two photoresist layers, or of a 30 nm thick silver film, which is deposited
on a photoresist layer, and a 60 nm thick overlay film of titanium dioxide. Sensitivity to the polarization and the unique
angular variation for the s-polarization follow from theoretical calculations, assuming a sinusoidal modulation of the
surface relief, and they are demonstrated experimentally by capturing intensity distributions of light transmitted through
realized samples in the zero diffraction order.
Off-axis holographic optical elements can be used for collimation of optical beams from edge emitting diode lasers.
Such a single element collimator can simultaneously compensate large elliptic cross-section and considerable
astigmatism of that beams and also reduce two selected lower aberrations. Beside a current transverse diffraction pattern
in the focus also patterns in the vicinity of the focus should take attention. Diffraction patterns due to an elliptic aperture
of such a collimator are very complicated and for their theoretical description sophisticated methods must be used. This
contribution involves some preliminary results of the study. Theoretical transverse diffraction patterns in the vicinity of
the focus have been mainly presented and their description analyzed.
Diffraction is analyzed for oblique propagation of light beam under a large angle. Fresnel diffraction approximation is
valid provided the beam is deflected into the direction of oblique propagation, the structure of the diffraction screen is
projected onto the plane perpendicular to the propagation direction, and the diffraction pattern is observed in the plane
perpendicular to the propagation. The task is illustrated by the diffraction due to a circular aperture.
Holographic gratings that are recorded as a whole in a single exposition are limited in size because of the available power of suitable laser sources and nonlinear response of and/or reciprocity effects in a recording medium. A sequential-illumination technique can help in this case. This technique relies on piecewise grating recording that consists in scanning with a relatively narrow laser beam, a pencil, across the grating surface employing an appropriate optical set up. The contribution describes a method utilizing a small parallel displacement of the laser pencil by turning a plane-parallel
plate, which is then transferred to a larger angular deflection by a short focus lens. Simultaneously, the beam is expanded angularly. This all can take place either before light enters the beam-splitter or along paths of both the interfering beams. In this way, uniform diffraction efficiency gratings that are much larger than the cross-section of the beam can be achieved. The laser pencil can be moved in polar or rectangular coordinates. Recording of larger gratings supposes large precise collimating mirrors. If they are not available e.g. due to their high price, they can be replaced by long propagating homocentric beams with their origins in the same distance from the recording plate.
Ellipticity of optical beams can be compensated by means of diffraction gratings. Holographic gratings are a simple alternative, which is noted for the possibility of recording gratings with curved and non-equidistant grooves. Using spherical wave fronts off-axis diffractive imaging elements can be recorded. They can be used for a beam transformation. The usual transformation task is to collimate beams emitted by edge-emitting diode lasers. Holographic recording and reconstruction, taking into account aberrations of the third order and assuming a recording layer to be on a spherical substrate, are described. Experiments verifying theoretical presumptions were carried out. Fraunhofer diffraction pattern with a very narrow central maximum was obtained.
Nondiffracting beams have been in the center of interest for the last decade. These beams, however, can be realized in practice only approximately. The simplest scheme for generating such a beam is to use a sufficiently narrow annular source placed in the back focal plane of a lens. Behind the lens, the beam is pseudo-nondiffracting in some length. The inverse problem is detection of Cerenkov radiation. The trace of a charged particle traveling through a dielectric medium faster than light emits this radiation under a certain angle. Generated conical wave front creates in the back
focal plane of a lens a diffraction pattern in form of a ring. The contribution analyses theoretically both mentioned problems.
The curvature of spectral lines in a plane-grating spectrum is much smaller than that in a prismatic spectrum. The effect of curvature need not always be entirely negligible. Our contribution deals with the more exact solution of the curvature based on a propagation vector diagram of incident and diffracted rays.
The system employs a spatial light modulator (SLM), between a pair of crossed polarizers, and an electronic shutter. Transmission of the SLM with the polarizers is controlled by graphical software that defines which pixels are fully transparent and which are fully opaque. While a particular binary graphics is on the SLM the electronic shutter allows light to pass for a certain time. The graphics is imaged, by an objective, onto a photoresist plate. A mercury lamp is used as a light source. The graphics changes after each exposition and the whole sequence of images determines the resultant surface-relief modulation.
Holographic diffractive doublets are optional systems for collimation of highly elliptical light beams, which are emitted from edge of diode-lasers. The first element converts an impinging astigmatic divergent beam into a cylindrical divergent beam, and the second element transforms the cylindrical beam into a collimated beam. In contrast to previous concept of the doublet with perpendicular input and output, another non-parallel scheme is considered, with the cylindrical wave front from the first element perpendicularly impinging upon the second element. A strongly off-axis holographic set-up is used for recording of diffractive elements in photoresists layers deposited on glass substrates.
Mode spectroscopy is a widely used technique for characterizing planar optical waveguides. Prism couplers are mostly used due to their versatility. For higher-index waveguides like SiO2/SiN or GaInAsP/InP, prism coupling is hampered by the lack of suitable high-index material for fabricating coupling prisms. In this case, short-period grating couplers could be used, instead. We describe the fabrication of “exchangeable” grating couplers with 1200, 1800, and 2400 lines/mm into a photo-curable polymer by copying master grating generated holographically. The grating couplers were applied to glass and Si/SiO2/SiN waveguides, and results were compared with those obtained using prism coupling. Fabrication of gratings with shorter periods is under way.
Diffraction efficiency of surface-relief gratings with various shallow profiles is discussed. A general relation for the diffraction efficiency is derived under the assumption of Fraunhofer diffraction. The general relation is applied to several profiles mostly needed in practice. It is pointed out that shallow profiles can provide high diffraction efficiencies.
Cylindrical optical elements play an important role in processing diode laser beams. Alternatively, diffractive elements can be used especially if they are simply holographically recorded. Analysis of the holographic recording process of elements transforming beams with spherical wave fronts into beams with cylindrical wave fronts is presented. Only rotationally symmetric beams can be used for recording. Four equations provide four unknown parameters. Two examples were realized: one for transformation of a divergent beam with a spherical wave front into a cylindrical divergent beam with a cylindrical wave front the focal line of which lies in the meridional plane and the other for transformation of a collimated beam into a convergent beam with a cylindrical wave front with the same property of the focal line.
Helical wavefronts can be created by transmission of coherent waves through spiral phase filters. This kind of wavefronts has in the center of a helicoid a singular point called an optical vortex in optics. According to the number m of transitions of the wavefronts through the plane perpendicular to the direction of propagation in the full angel 360 degrees C the vortex is called m-charged. A usual approach supposes for the final step an integer multiple of wavelengths which fits into the whole path difference. This contribution analyses the case when this proposition is not fulfilled and the final step is not an integer multiple of wavelength. The wave amplitude in the optical vortex is computed as an integral of phases of all nearest rays around the singular point.
Holographic surface-relief diffractive elements with an inclined profile working as transmission grating couplers for backplane interconnects were fabricated and their diffraction efficiency was measured during a step-by-step development process for various orientations with respect to the direction of incident light. The highest diffraction efficiency was achieved for p-polarized light which propagates inside a medium of lower optical density and is outcoupled into a medium of higher optical density.
Diffractive optics makes use of diffraction of light to design otpical elements and systems, which serve for imaging visual objects and transforming coherent optical beams. A diffractive structure can be computed and the pattern written using focused laser or electron beams. Phase nature of diffraction pattern is preferred. Computations involve the first and second order terms and a curvature of the substrate plate, which can be exploited for the element to be aplanatic. Diffraction grooves should have a suitable transversal saw-tooth profile to obtain the highest diffraction efficiency. An alternative method for fabrication of elements of this kind is holographic recording, which can be use mainly for off-axial components.
Holographic diffractive optical elements collimating highly divergent, elliptical and astigmatic edge emitted diode laser beams are analyzed. Elements are recorded using only divergent beams with spherical wavefronts while off-axis astigmatism and coma of the holographic recording arrangement are compensated in a narrow beam approximation. Because of the very asymmetrical recording setup, significant blazing properties are present. Two types of the collimators are proposed: one for obliquely and the other for perpendicularly incident laser beam. Astigmatic properties of the output beams were measured in the reverse setup, i.e. when the collimated laser beams impinge on elements from their back side. Comparison of the advantages and drawbacks of both arrangements is presented.
A simple technique of obtaining light spiral (helium) filters in UV exposed photoresist layers consisting in a combined use of binary masks and revolution of the photosensitive layers during exposition is presented. The filters investigated experimentally are inspected by observing intensity distribution in a laser beam reflected from the sample. The filter giving the angular phase shift variation which is close to that needed for the generation of the first order Bessel beam is realized.
A diffractive element which generates annular light source is investigated from the point of view of its area optimization. In the paraxial approximation, the zones distribution of such an element can be described by a double parabola. As the zone areas of this element are not the same, the equalization of first two zone areas is proposed in order to improve the diffraction efficiency.
A decentered Gaussian beam is a recently introduced generalization of an ordinary Gaussian beam, the propagation of both of which through an arbitrary centered paraxial optical elements can be described by ABCD matrices of paraxial optical rays. The paper shows that the M2 beam quality factor of the decentered Gaussian beam is the same as that of the ordinary Gaussian beam -- equal to 1. We further find out general conditions (for elements with pure real ABCD matrices) which must be fulfilled in order to accomplish the transformation of the Gaussian beam into decentered one or vice versa. The particular cases under specific conditions are presented in the work as well.
A theoretical method making it possible to describe scattering form waveguide structures with periodically and randomly perturbed boundary is presented. This method is based on the approximate assumption of single scattering and the geometric-optical approach for the propagation of the optical field in the waveguide. Experimental results for photoresist waveguides with holographically recorded sinusoidal gratings show that the theory can correctly predict fundamental features of the scattered field.
A measurement technique making it possible to obtain dynamical recording characteristics of photopolymer materials, i.e. the diffraction efficiency versus exposure time and irradiance, from a single holographic exposure using Gaussian recording beams is presented. The material under investigation is the DuPont photopolymer solution HRS- 150X001-20-35.
Holographic transmission grating couplers with an inclined surface relief, which are destined for backplane interconnects, were fabricated and their diffraction efficiency was measured during step-by-step development process. The highest efficiency achieved was obtained for p-polarized light which propagates inside a medium of lower optical density and is outcoupled into a medium of higher optical density.
The holographic method provides a possibility of creating not only uniform diffraction gratings but also non-uniform gratings whose relief depth varies over the grating surface. Therefore the diffraction efficiency of such structures varies over the element surface as well. In this paper we deal with shallow relief gratings with Gaussian modulated groove depth. It is shown that these structures can transform an incident Gaussian beam into a super-Gaussian one of low order. On the basis of the simple theory, basic properties of these elements are discussed. The validity of our approach is confirmed by experiments, and some of them are presented in this paper.
A surface relief holographic grating is designed for the transformation of a Gaussian laser beam into a beam with a flattened plateau in its central part. The depth of grating grooves varies over the surface in order to achieve a distribution of diffraction efficiency complementary to the intensity profile of the laser beam to be transformed. The appropriate efficiency distribution over the grating can be obtained by a technological process during the exposure and development. Experiments have proved that produced grating samples can sufficiently flatten the Gaussian beam, and that the degree of the beam flattening can be easily controlled.
An analysis of focusing properties of gratings having a constant period and bent to some curvature is given. It has been found that the focusing distance is proportional to the radius of curvature. The arising coma aberration can be compensated for by the gradient of the curvature along the surface of the grating.
In this paper, a close analogy between the theoretical model of forming the profile of a diffractive relief structure in photoresist during development and equations of geometrical optics is shown. It is used for the investigation of evolution of the grating profile arising in a positive photoresist layer which was exposed to the interference field of two laser beams. Verification of theoretical conclusions is based on comparison of theoretical and experimental time dependences of diffraction efficiencies of many orders during development. A SEM photography of the relief of a produced grating sample is presented as well. A short section is devoted to diffraction properties of the structures under study with emphasis on their possible applicability to multiple beam splitting.
Photoresist, as one of the most important materials for recording holographic diffraction structures, is treated particularly from the point of view of a control of the development of the surface-relief profile of the grating groove. Primary attention is given to the formation of the desirable profile for the grating multiple beam splitter.
Crossed gratings are analyzed from the point of view of their holographic recording. For the theoretical description of the diffraction efficiency, the Rayleigh model of shallow line profile is used. Applications to metrological gratings for determination of position and to antireflection gratings are presented.
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