Temporal superresolution: An application of frequency filtering by a grating in the resonance domain

Abstract

A diffraction grating in the resonance domain is known to exhibit significant change in diffraction efficiencies with a small change of the grating parameters. It is proposed that this property can be utilized for frequency filtering, when polychromatic light illuminates the grating. As an example, compression of a femtosecond optical pulse is numerically demonstrated with the concept of superresolution. Suppression of zeroth diffraction order by suitably optimized grating structure induces the pulse width to narrow. This scheme considerably simplifies existing optical pulse shaping systems.     

Temporal evaluation of fringe patterns with spatial carrier with an improved asynchronous phase demodulation algorithm

Abstract

A method for temporal evaluation of fringe patterns with a spatial carrier is presented. The proposed technique consists in the recording of the temporal irradiance fluctuations obtained when a linear variation of the set-up sensitivity is introduced. In this way, the use of a spatial carrier introduces a linear temporal carrier frequency. This allows the use of fast and low time consuming temporal asynchronous demodulation algorithms, similar to those employed in spatial phase shifting techniques. An existing five-step algorithm has been corrected for asynchronous demodulation. It is shown that it is possible to fix the sensitivity variation in such a way that the algorithm presents optimum behaviour against noise and nonlinearities presented by the temporal irradiance signal. Finally, the technique has been applied to measure the shape of an object, using a fringe projection set-up.     

Temporal phase evaluation by fourier analysis of fringe patterns with spatial carrier

Abstract

A new method is presented for the temporal evaluation of fringe patterns with spatial carrier. The proposed technique involves recording the irradiance fluctuations obtained when a linear variation of the set-up sensitivity is introduced. In this condition, the use of a spatial carrier introduces a linear temporal carrier frequency. In this way, Fourier analysis can be performed to obtain the phase and, finally, the quantity to be measured. The optimum conditions for the sensitivity variation have been studied in order to minimize the errors associated with the Fourier analysis. The technique has been applied to measure the distribution of ray deflections on the surface of two ophthalmic lenses using a deflectometric set-up.     

Shift and shape of grating diffracted beams

Abstract

The grating diffraction of beams is theoretically investigated by applying an electromagnetic method (the Integral Equation System Method with Parametrization of the grating profile = IESMP) to their plane wave components. For the first time, explicit values for the displacement of grating diffracted Gaussian beams are calculated with this method. For total reflection this displacement of beams is known as the Goos-Hänchen shift. A maximum shift of 36 μm has been found for the investigated sinusoidal grating near an anomaly which is much greater than the known Goos–Hänchen shift of about 1 μm for the total reflection case. The replacement of the angular spectrum of plane waves with constant wavelength by a wavelength spectrum of plane waves of constant direction allows an analogous treatment of short-time pulses. Surprisingly, the above anomaly causes a maximum temporal shift of 80 fs for the pulse diffraction. These temporal shifts and additional effects like pulse deformations can influence ultra short-time pulse experiments. Furthermore, the behaviour of temporally and spatially Gaussian shaped light pulses (TSG pulses) by grating diffraction are studied considering the diffraction of an angular and wavelength dependent spectrum of plane waves. The diffraction of a short TSG pulse at the above grating deforms the pulse and creates an additional smaller satellite pulse. All described effects occur only at positions of the space–time complex filtering function in the angular-wavelength frequency space with high gradient of the phase.     

Self-reconstruction of wave packets due to spatio-temporal couplings

Abstract

The spatio-temporal self-reconstruction of the wave function fulfilling the wave equation is examined. The effect is based on the sampling of the spatial spectrum of the wave function in the cylindrical coordinates and on its coupling to the temporal frequency spectrum. The predetermined spatio-temporal profile of the wave function is approximately reconstructed at the periodic spatial intervals along the propagation direction for the continuous temporal spectrum. The periodicity appearing in both the spatial and temporal evolutions are examined for wavefields with the discrete temporal spectrum. The reconstructed field then simultaneously exhibits propagation properties known as the self-imaging and the mode-locking.     

Visual sensitivity in the presence of a patterned background

The sensitivity of the visual system depends on ambient illumination: Sensitivity is reduced in the presence of a bright, uniform background. We asked how sensitivity is adjusted when the background is spatially detailed and therefore contains both luminance peaks and troughs in the neighborhood of a foreground object. A test flash was superimposed on a static sinusoidal grating. As the grating's spatial frequency increased, sensitivity for flash detection declined, regardless of whether the flash was superimposed on a peak or a trough of the grating. We studied the mechanisms underlying this loss of sensitivity by delivering the test stimulus through one eye and the background through the other. The conclusion is that three mechanisms are involved. Luminance adaptation and a masking process adjust sensitivity at low- and mid-range spatial frequencies, respectively. The third mechanism, a contrast gain control, is localized (it occurs at spatial frequencies approaching the limit for resolution) and fast (complete in half a second), and it results from early processing in the visual pathway (it is absent during dichoptic viewing). This local adjustment of sensitivity may help to protect the clarity of even the smallest details in the visual scene.     

Propagation of optical pulses with spatial and temporal dependence

A convenient approximate formula is proposed for the study of free-space propagation of spatial and temporal pulses with an identifiable carrier frequency. It does not contain a time derivative operation on the pulse's temporal envelope explicitly. It is shown that once a short (for example, picosecond or subpicosecond) pulse is created with a spatial and a temporal structure, it does not last forever. The approximation discussed is valid over a certain distance as dictated by the wave equation. Beyond this distance, the spatial and temporal characteristics begin to influence each other significantly. Two examples are presented. The first example is that of a pulse with a factored form of a spatial envelope times a temporal envelope. The second example is that of a clear aperture with a grating, by which pulse stretching or temporal distortion is examined and the result is in agreement with that found in the literature.     

High-sensitivity Diffraction-compensated Moiré Deflectometry

Abstract

The spatial resolution and angular sensitivity of conventional moiré deflectometry are known to obey a conjugate relationship reminiscent of the uncertainty principle so that one cannot be improved without deteriorating the other. This paper looks at the origin of this relationship and suggests ways by which this ‘uncertainty principle’ can be violated. It is shown that a ‘projection’ of the grating which is free from diffraction effects and which, at the same time, contains the deflection information amplified by the ‘optical lever’ distance D between the gratings can be formed if the diffracted beams of order + 1 and ? 1 are separated from other orders and are recombined in certain ways. As a result, the angular sensitivity, which depends on the ratio of the pitch d of the grating to the distance D between the two gratings, can be improved without losing the spatial resolution by multiple diffraction orders. One of the diffraction compensation schemes is experimentally illustrated. It is shown that the ‘uncertainty product’ is improved by more than two orders of magnitude.     

Necessary Condition for Temporal Self Imaging in a Linear Dispersive Medium

Abstract

It was recently shown that a periodic pulse train will reproduce itself at periodic distances upon propagation in a linear dispersive medium. By drawing an analogy between this temporal self-imaging problem and the well known spatial self-imaging phenomenon, we derive the necessary condition for temporal self-imaging and show that the class of temporally self-reproducing signals is much broader than the subset of periodic signals.     

Computation of the near-field pattern with the coupled-wave method for transverse magnetic polarization

Abstract

In this paper, an accurate method for computing the elecromagnetic field distribution in lamellar gratings is proposed. The method that relies on the rigorous coupled-wave analysis provides accurate numerical results and avoids possible sources of artefacts due to permittivity discontinuities. Its performance is analysed through various lamellar grating cases, including dielectric and metallic materials, the visible and near-infrared (1–10 μm) regions of the spectrum. Special attention is placed on field singularities which are in general present at the grating wedges for transverse magnetic polarization.     

A surface plasmon study of the optical dielectric function of indium

Abstract

The optical dielectric function of indium is measured by optical excitation of surface plasmon polaritons on an indium-coated silica grating for a range of wavelengths in the visible region of the spectrum. By exciting the surface plasmon polariton at the buried indium-grating interface, the indium surface that supports the surface plasmon polariton is kept free from oxidation. Comparison of angle-dependent reflectivities with a grating modelling theory gives both the real and imaginary parts of the dielectric function of indium. These results are compared with free-electron models to obtain an estimate of the plasma frequency and relaxation time.     

Polarization separation of light in holographic grating reflection in conical mounting

Abstract

We experimentally investigate the interaction of linearly polarized light with a holographic grating in a conical mounting. Due to the periodic structure, the polarization properties of the reflected zeroth-order beam are highly sensitive to the conical angle. When a focused Gaussian beam with linear polarization impinges on an air–grating interface at an exceptional conical angle, a spatial splitting of the reflected beam is observed behind a polarizer. We find that it can be interpreted using the anisotropy of the polarization distribution in holographic grating reflection.     

Interference Phenomena in Waveguides with Two Corrugated Boundaries

Abstract

Waveguide structures with two corrugated interfaces are considered. It is shown theoretically and experimentally that these structures can form the basis for a highly-efficient unidirectional grating coupler for slab waveguides. The anomalous light reflection from waveguides with two corrugated boundaries is also considered. The possibility of using corrugated waveguides for frequency stabilization of a semiconductor laser is demonstrated.     

Characterization of a grating-coupled liquid crystal cell using a rigorous theoretical model

Abstract

We use a rigorous differential formalism to model the optical response of a multilayer structure having both a surface-relief grating and containing uniaxial materials. The uniaxial material is, in this case, a layer of liquid crystal that has its uniaxial axis defined by its director. By fitting experimental angle dependent reflectivity data to a multilayer grating model we are able to determine the spatial profile of the liquid crystal director, and show how accurately the optical response of such a system may be modelled.     

Experimental Evaluation of a Fibre Raman Oscillator Having Fibre Grating Reflectors

Abstract

We report on the construction and characterization of a novel fibre Raman oscillator which used fibre grating reflectors rather than discrete mirrors to form the Raman resonator. This was synchronously pumped by a c.w. mode-locked Nd : YAG laser operating at 1·06 µm. Spectral and temporal characteristics of such oscillators formed by two gratings and by one grating and a conventional mirror are presented.     

Examination of the +1, −1 Surface Plasmon Mini-gap on a Gold Grating

Abstract

An energy gap in the excitation of surface plasmons is found for light at normal incidence to a gold grating. This gap occurs at the crossing of the plus and minus first order surface plasmons. It arises directly as a consequence of distortion of the grating from sinusoidality, the first harmonic of the grating providing coupling between the plus and minus one orders. Experiments have been performed using both wavelength scans, where at a fixed angle of incidence the wavelength of excitation is varied, and angle of incidence scans, where for a fixed wavelength the angle of incidence is varied a few degrees either side of normal to the grating. By fitting the angular dependent reflectivity scans using grating modelling theory the gold grating is characterized at all wavelengths. This then allows a detailed comparison of the theoretical dispersion curve with that obtained experimentally. The agreement for both p-polarized light (for angle dependence with the plane of incidence normal to the grating grooves) and for s-polarized light (angle dependence with the plane of incidence perpendicular to the grating grooves) is excellent. An apparent momentum gap in the lower energy branch of the dispersion curve, attributed to the loss of coupling strength, is found to move to the upper branch if the grating profile is inverted.     

Femtosecond single-shot correlation system: a time-domain approach

We introduce, analyze, and experimentally demonstrate what to the best of our knowledge is a new pulse correlation technique that is capable of real-time conversion of a femtosecond pulse sequence into its spatial image. Our technique uses a grating at the entrance of the system, thus introducing a transverse time delay (TTD) into the transform-limited reference pulse. The shaped signal pulses and the TTD reference pulse are mixed in a nonlinear optical crystal (LiB(3)O(5)), thus producing a second-harmonic field that carries the spatial image of the temporal shaped signal pulse. We show that the time scaling of the system is set by the magnification of the anamorphic imaging system as well as by the grating frequency and that the time window of the system is set by the size of the grating aperture. Our experimental results show a time window of ~20 ps. We also show that the chirp information of the shaped pulse can be recovered by measurement of the spectrum of the resulting second-harmonic field.     

Waveguide confinement of cerenkov second-harmonic generation through a graded-index grating coupler: Electromagnetic optimization

Abstract

The feasibility of making a frequency doubler for integrated optics is studied with the electromagnetic theory of gratings and graded-index waveguides as a tool. The device consists of a first waveguide filled with a sol-gel nonlinear material doped or grafted with a nonlinear chromophore whose thickness is chosen to generate a second-harmonic Cerenkov radiation in a dispersive glass substrate. The Cerenkov radiation is coupled into a second waveguide through a graded-index layer produced by ion exchange into glass, lying on top of an ion-etched grating coupler. The aim of the study is to optimize the optogeometrical parameters of the device in order to obtain a resonance line of the second waveguide modes that has an angular width large enough to match the experimental constraints, and which leads to a good enough coupling coefficient. The electromagnetic theory of grating couplers is developed into an S-matrix propagation algorithm form in order to be combined with the electromagnetic analysis of the thick graded-index waveguide with a view to analysing the device.     

Spatial and temporal characterization of phase fluctuations in non-Kolmogorov atmospheric turbulence

Abstract

Atmospheric turbulence severely limits the performance of ground-based imaging and laser propagation systems. Some observational results, showing atmospheric turbulence which does not obey Kolmogorov's theory, have prompted the study of optical propagation through non-Kolmogorov turbulence. This paper presents a theoretical approach to analyse the spatial and temporal characterizations of phase fluctuations in non-Kolmogorov turbulence. The spatial structure function, the temporal structure function and the temporal power spectrum of phase fluctuations are derived. The generalized coherence length ρ₀, the characteristic frequency f_R and the characteristic time T_R are expressed as functions of the index structure constant along the propagation path and the wind velocity. The long exposure MTF, the short exposure MTF and the imaging Strehl ratio are computed.     

Lamellar Gratings as Polarization Components for Specularly Reflected Beams

Abstract

High spatial frequency lamellar gratings are shown to function as phase compensators, quarter-wave and half-wave retarders, and polarization rotators that operate on specularly reflected (zeroth-order) beams. These gratings are designed using rigorous coupled-wave and modal grating diffraction theories. Controlling the geometrical parameters of these gratings allows for engineering the phase retardation and polarization conversion introduced to a reflected beam. Fabrication and operational tolerances for these elements are discussed. Wavelength and polar angle of incidence variation affect the performance of these elements more strongly than variations in other geometrical and operational parameters.