Geometrical phase image encryption obtained with space-variant subwavelength gratings

An optical encryption method based on a geometrical phase produced by space-variant polarization manipulation is presented. The decrypted picture is retrieved either by a polarization measurement of the beam emerging from the encrypted element or by a single intensity measurement of the beam transmitted through the encrypted element followed by an optical key element. Both elements are realized by use of computer-generated space-variant subwavelength dielectric gratings. Theoretical analyses of the optical concept are presented along with experimental results.     

Propagation-invariant vectorial Bessel beams obtained by use of quantized Pancharatnam-Berry phase optical elements

Propagation-invariant vectorial Bessel beams with linearly polarized axial symmetry based on quantized Pancharatnam-Berry phase optical elements are described. The geometric phase is formed through the use of discrete computer-generated space-variant subwavelength dielectric gratings. We have verified the polarization properties of our elements for laser radiation at 10.6-microm wavelength and also demonstrated propagation-invariant, controlled rotation of a propeller-shaped intensity pattern through the simple rotation of a polarizer.     

Polychromatic vectorial vortex formed by geometric phase elements

We propose the use of a geometric phase, obtained by spatial polarization state manipulations, for the formation of polychromatic vectorial vortices. Experimental demonstration is obtained by using Pancharatnam-Berry phase optical elements formed by a space-variant subwavelength grating etched on a GaAs wafer. We further demonstrate formation of scalar and unpolarized polychromatic vortices.     

Optical properties of polarization-dependent geometric phase elements with partially polarized light

The behavior of geometric phase elements illuminated with partially polarized monochromatic beams is investigated both theoretically and experimentally. The element discussed in this paper is composed of wave plates with π-retardation and a space-variant orientation angle. We found that a beam emerging from such an element comprises two polarization orders; right-and left-handed circularly polarized states with conjugate geometric phase modification. This phase equals twice the orientation angle of the space-variant wave plate comprising the element. Apart from the two polarization orders, the emerging beam coherence polarization matrix includes a “vectorial interference matrix” which contains information concerning the correlation between the two orthogonal, circularly polarized portions of the incident beam. In this paper we measure this correlation by a simple interference experiment. In addition, we found that the equivalent mutual intensity of the emerging beam is modulated according to the geometric phase induced by the element. Other interesting phenomena concerning propagation will be discussed theoretically and demonstrated experimentally. The experiment made use of a spherical geometric phase element that was realized by use of a space-variant subwavelength grating illuminated with CO₂ laser radiation of 10.6 μm wavelength.     

Computer-generated space-variant polarization elements with subwavelength metal stripes

A novel method of performing two-dimensional space-variant polarization operations is presented. The method is based on determining the local direction and period of subwavelength metal-stripe gratings by use of vectorial optics to obtain any desired continuous polarization change. We demonstrate our approach with specific computer-generated space-variant polarization elements for laser radiation at 10.6mum. The polarization properties are verified with complete space-variant polarization analysis and measurement.     

High-efficiency broadband diffractive elements based on polarization gratings

A method is introduced for designing paraxial-domain diffractive elements working over a broad frequency range. The method is based on space-variant manipulation of the state of polarization by form-birefringent binary diffractive structures. It is shown that any scalar phase transmission function can be realized by use of such polarization-modulating structures and that at least in some cases it is even possible to exceed the scalar paraxial-domain upper bounds of diffraction efficiency over a broad frequency band.     

Formation of linearly polarized light with axial symmetry by use of space-variant subwavelength gratings

We present a novel method for forming linearly polarized axially symmetric beams with various polarization orders that is based on computer-generated space-variant subwavelength gratings. We introduce and experimentally demonstrate that our space-variant polarization state manipulations are accompanied by a phase modification of a helical structure that results from the Pancharatnam-Berry phase. We have verified the polarization properties of our gratings for laser radiation at 10.6-microm wavelength.     

Pancharatnam--Berry phase in space-variant polarization-state manipulations with subwavelength gratings

We report the appearance of a geometrical phase in space-variant polarization-state manipulations. This phase is related to the classic Pancharatnam-Berry phase. We show a method with which to calculate it and experimentally demonstrate its effect, using subwavelength metal stripe space-variant gratings. The experiment is based on a unique grating for converting circularly polarized light at a wavelength of 10.6 mum into an azimuthally polarized beam. Our experimental evidence relies on analysis of far-field images of the resultant polarization.     

Generation of vector beam with space-variant distribution of both polarization and phase

We present an idea to generate an arbitrary space-variant vector beam with structured polarization and phase distributions. The vector beams are synthesized from the left- and right-hand polarized light, each carrying different phase distributions. Both the phase and the state of polarization of vector beams can be tailored independently and dynamically by a spatial light modulator.     

Space-variant filtering with holographic multifacet elements

We present a spatial filtering method for space-variant operations. The method is based on the combination of a holographic lenslet array and an appropriate filter array. The lenslets produce local Fourier transforms of the object which are filtered in parallel and independently by the spatial filters. The most obvious space-variant setup based on lenslet arrays would consist of many narrow 4f-setups, arranged side by side. The total object would be partitioned into many small object patches, as many as there are lens elements in the lenslet array. However this setup shows the undesired effect of local inversion. Therefore we choose a setup with only one lenslet array and an imaging lens which avoids the local inversion.     

Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings

We present a novel method for forming radially and azimuthally polarized beams by using computer-generated subwavelength dielectric gratings. The elements were deposited upon GaAs substrates and produced beams with a polarization purity of 99.2% at a wavelength of 10.6 microm . We have verified the polarization properties with full space-variant polarization analysis and measurement, and we show that such beams have certain vortexlike properties and that they carry angular momentum.     

Stroboscopic holographic interferometry of vibration with space-variant phase

A method employing pulsed illumination for the holographic analysis of vibration with space-variant phase is described. Superimposition of two stroboscopically recorded interference patterns to get the amplitude and the phase of vibration at the intersections of fringes is suggested. Contour maps of these two quantities over the entire object surface can then be prepared by interpolation. Detailed solutions are presented for single and double frequency vibrations.     

Space-variant geometrical phases in focused cylindrical light beams

We show that the depolarization caused when light is focused with a high-numerical-perture lens is accompanied by a space-variant geometrical phase. This phase results in the formation of modes with helicities and phase singularities that differ from those of the original beam. We show that this effect can be explained as a transverse shift of the rays, which is reminiscent of the recently discovered optical Hall-Magnus effect. Our results show that the asymmetric focal spot associated with the focus of linearly polarized light can be explained through geometrical effects.     

Real-time analysis of partially polarized light with a space-variant subwavelength dielectric grating

A novel method for real-time polarization measurement is presented. The method is based on a space-variant wave plate that we realized as a computer-generated space-variant subwavelength dielectric grating. The Stokes parameters of the incident beam are determined by Fourier analysis of the space-variant intensity transmitted through the grating and an analyzer. We discuss the design and realization of such wave plates and demonstrate our technique with polarization measurements of both polarized and partially polarized CO(2)-laser radiation at a wavelength of 10.6 mum.     

Rotating vectorial vortices produced by space-variant subwavelength gratings

A new class of vectorial vortex based on coherent addition of two orthogonal circularly polarized Bessel beams of identical order but with different propagation constants is presented. The transversely space-variant axially symmetric polarization distributions of these vectorial fields rotate as they propagate, while they maintain a propagation-invariant Bessel intensity distribution. These properties were demonstrated by use of discrete space-variant subwavelength gratings for 10.6 microm CO2 laser radiation. The polarization properties were verified by both full space-variant polarization analysis and measurements. Rotating intensity patterns are also demonstrated by transmitting the vectorial vortices through a linear polarizer.     

Spin-induced angular momentum switching

When light is transmitted through optically inhomogeneous and anisotropic media the spatial distribution of light can be modified according to its input polarization state. A complete analysis of this process, based on the paraxial approximation, is presented, and we show how it can be exploited to produce a spin-controlled change in the orbital angular momentum of light beams propagating in patterned space-variant optical axis phase plates. We also unveil a new effect: the development of a strong modulation in the angular momentum change upon variation of the optical path through the phase plates.     

Image restoration for interlaced scan CCD image with space-variant motion blurs

When the speeds of objects in a scene exceed the temporal resolution of the camera shutter, motion blurs will occur. Since objects are often moving in different directions at different speeds, the degradation of a CCD image is often characterized by space-variant motion blurs. Image restoration algorithms for space-variant motion blurs are available for progressive scan CCD images, but not for interlaced scan images. To address the space-variant image restoration for interlaced scan images, a novel three-step image restoration scheme is proposed. Firstly, one interlaced scan image is divided into odd field and even field images. Secondly, these two field images are further segmented into rectangular blocks and the motion vectors are computed based on these rectangular blocks using an efficient block matching algorithm. Thirdly, image restoration is performed using a blind deconvolution algorithm in the odd or even field image. The final restored image is obtained by combining the restored odd and even field images. The scheme is illustrated by restoring a space-variant blurred moving vehicle image and a synthetic blurred image.     

Separation of spin angular momentum in space-variant linearly polarized beam

We show that the spin angular momentum (SAM) flux in a space-variant linearly polarized beam can be separated in the focal plane. Such a beam carries only orbital angular momentum (OAM) and develops a net SAM flux upon focusing. The radial splitting of the SAM flux density is mediated by the phase vortex (or OAM) and can be controlled by the topological charge of the phase vortex. Optical trapping experiments verify the separation of the SAM flux density. The proposed approach enriches the manipulation of the angular momentum of light fields and inspires more designs of focus engineering, which would benefit optical micromanipulation of microscopic particles.     

Space-variant polarization scrambling for image encryption obtained with subwavelength gratings

We present an optical encryption method based on geometrical phase, which is originated from polarization manipulation. The decrypted picture is retrieved by measuring the polarization of the beam emerging from the encrypted element. The encrypted element is achieved by using a computer-generated space-variant subwavelength dielectric grating. Theoretical analyses of the optical concept by use of Jones and Mueller formalisms, as well as experimental results including full optical decryption process are introduced. Digital implementation and the possibility of using watermarking are also discussed.     

Interlaced scan CCD image motion deblur for space-variant motion blurs

Motion blur is caused by camera shakes or object motions during exposure when the shutter speed is relatively slow. As for the object motion blur, the degradation of a CCD image is often characterized by space-variant motion blurs, since objects are often moving in different directions at different speeds. But most image restorations for space-variant motion blurs are addressed only for progressive scan CCD images. To address the space-variant image restorations for interlaced scan images, we propose a novel image restoration scheme. First, one interlaced scan image frame is required, which is divided into the odd field and the even field images. These two field images are further segmented into rectangular blocks. The motion vectors are computed in these rectangular blocks using an efficient block matching algorithm. Second, image restoration is performed in these rectangular blocks using a constrained least square algorithm in the odd or even field image, which can both preserve edge structures and remove noises. Our novel scheme is illustrated by restoring a space-variant blurred moving boat image and a synthetic blurred image.