Amplitude Gratings Research Articles

Nonlinear amplification of coherent waves in media with soliton-type refractive index pattern

We derive the complex Ginzburg-Landau equation for the dynamical self-diffraction of optical waves in a nonlinear cavity. The case of the reflection geometry of wave interaction as well as a medium that possesses the cubic nonlinearity (including a local and a nonlocal nonlinear responses) and the relaxation is considered. A stable localized spatial structure in the form of a "dark" dissipative soliton is formed in the cavity in the steady state. The envelope of the intensity pattern, as well as of the dynamical grating amplitude, takes the shape of a tanh function. The obtained complex Ginzburg-Landau equation describes the dynamics of this envelope; at the same time, the evolution of this spatial structure changes the parameters of the output waves. New effects are predicted in this system due to the transformation of the dissipative soliton which takes place during the interaction of a pulse with a continuous wave, such as retention of the pulse shape during the transmission of impulses in a long nonlinear cavity, and giant amplification of a seed pulse, which takes energy due to redistribution of the pump continuous energy into the signal.

Perturbed Talbot patterns for the measurement of low particle concentrations in fluids

Behind periodic amplitude or phase objects, the object transmittance is repeated at the so-called Talbot distances. In these planes perpendicular to the propagation direction, Talbot self-images are formed. In the case of plane wave illumination, the distances between the self-images are equally spaced. A periodic pattern called optical carpet or Talbot carpet is formed along the propagation direction. We show theoretically how the presence of spherical particles (10 to 100 μm in diameter) behind gratings of 20 and 50 μm period affects the formation of Talbot carpets and Talbot self-images at 633 nm illumination wavelength. The scattering of the particles is modeled by the Fresnel diffraction of its geometrical shadow. We analytically calculate the interference of the diffraction orders of rectangular and sinusoidal amplitude gratings disturbed by the presence of particles. To verify our model, we present measurements of Talbot carpets perturbed with both opaque disks and transparent spheres, and discuss the effects for various size parameters. We present an approach to simulate the movement of particles within the Talbot pattern in real time. We simulate and measure axial and lateral particle movements within a probe volume and evaluate the effect on the signal formation in a Talbot interferometric setup. We evaluate the best system parameters in terms of grating period and particle-detector-distance for a prospective measuring setup to determine characteristics of flowing suspensions, such as particle volume concentration or particle size distribution.

Talbot images of wavelength-scale amplitude gratings

By means of experiment and simulation, we achieve unprecedented insights into the formation of Talbot images to be observed in transmission for light diffracted at wavelength-scale amplitude gratings. Emphasis is put on disclosing the impact and the interplay of various diffraction orders to the formation of Talbot images. They can be manipulated by selective filtering in the Fourier plane. Experiments are performed with a high-resolution interference microscope that measures the amplitude and phase of fields in real-space. Simulations have been performed using rigorous diffraction theory. Specific phase features, such as singularities found in the Talbot images, are discussed. This detailed analysis helps to understand the response of fine gratings. It provides moreover new insights into the fundamental properties of gratings that often find use in applications such as, e.g., lithography, sensing, and imaging.

Four-mode plasmonic structure based on a prism-grating anticrossing bandgap

We have developed a plasmonic structure based on an anticrossing bandgap prism-grating coupling technique. We observe that up to four surface plasmons can be excited simultaneously in this plasmonic structure. Initial experiments confirm that such a plasmonic structure can improve sensor performance by tuning the amplitude of the grating. From numerical simulations, we conclude that plasmon modes with equal propagation constants at a different wavelength can only be excited at different grating amplitudes of our plasmonic structure, in such a way that the increase of wavelength implies the increase of the amplitude for a fixed propagation constant.

Talbot effect by a photorefractive volume phase grating

In our proposal a light intensity distribution generated by an incoherently illuminated planar amplitude grating is projected into a photorefractive crystal. This 3D distribution is mapped as an index refractive perturbation via the photorefractive effect thereby generating a volume phase grating. The self-imaging phenomenon in the Fresnel field of this volume phase grating coherently illuminated is theoretically and experimentally analyzed. A model to simulate this volume grating that considers the 3D light intensity distribution formed in the crystal combined with the photorefractive grating formation theory is proposed. A path-integral approach to calculate the self-image patterns which account for the inhomogeneous propagation through the photorefractive grating is employed. The experimental and theoretical results show that the self-images location coincides with that of the self-images generated by planar phase grating of the same period. Moreover, the self-images visibility depends on three parameters: the exit pupil diameter of the incoherent recording optical system, the external electric field applied on the crystal, and the crystal thickness. To study the visibility behavior, a phase parameter which includes the three mentioned parameters is proposed. The self-images visibility shows the typical sinusoidal dependence found in planar phase grating. A good agreement between theoretical and experimental results is observed.

Couplings in GaAs/AlGaAs/Metal Photonic Waveguides with Metallic Variations

ABSTRACTTo have better light-emitting performance, semiconductor-metal periodic photonic waveguides can generate stable wavelengths. This work constructs a multi-parameter model to compute the backward-wave mode-coupling coefficients, which are important to the analysis and performance of photonic devices. For such a semiconductor-metal hybrid structure, a proper photonic technique needs to be utilized to solve this computational complexity.Numerical results demonstrate how the materials of metal gratings, the corrugation amplitudes of metal gratings, and the metallic aluminum mole fraction can affect the coupling coefficients. Further physical interpretation and discussion can support and explain the above results. The results can help engineers decide the values of parameters used in fabrication. Future work and applications will be proposed.

Modeling Silicon-Based Periodic Waveguides for Optical Interconnects

ABSTRACTTo assist the precision and stability of wavelength at 1550 nm and 1300 nm in planar optical waveguides, hybrid semiconductor-metal corrugated gratings with nanometer period are integrated into silicon-based optical interconnects. This work utilizes multi-parametric optical waveguide models to compute the mode-coupling coefficients in the silicon photonic devices. For such a semiconductor-metal hybrid structure, a proper photonic technique needs to be utilized to solve this computational complexity. The optical method and the photonic method are used to compute coupling coefficients. Both methods have close numerical values shown in figures. Numerical results demonstrate how the normalized corrugation amplitudes of metal gratings can affect the coupling coefficients. Further physical interpretation and discussion can support and explain the above results. The modeling results can help engineers decide the values of parameters used in the design and fabrication of optical waveguides.

Experimental study of 8-bits information transmission system based on orbital angular momentum of light beams

An experimental setup is built to realize 8-bits information transmission based on orbital angular momentum (OAM) of light beams. In the modulation section, a controllable laser diode array and a stable phase modulator are used to superpose and encode the OAM states. A binary amplitude grating is used to detect the OAM states in the demodulation part. This system transmits 8-bits data successfully.

Grating amplitude effect on electroluminescence enhancement of corrugated organic light-emitting devices

We report grating amplitude dependence of electroluminescence (EL) in organic light-emitting devices with one-dimensional corrugated structure. Our proposed devices can emit light from both the top silver and bottom quartz side, and both exhibit amplitude-dependence EL enhancement. The effect of grating amplitude on the EL intensity has been studied experimentally and numerically to find out the optimal grating amplitude for the greatest EL enhancement. We deduce from the numerical simulations and experimental results that surface plasmon-polariton modes and waveguide modes are coupled out of the corrugated devices efficiently at the optimal amplitude; therefore, higher efficiency of light extraction could be realized.

Self-imaging of gratings with two roughness levels

In previous works, the authors have analyzed diffraction gratings with surface roughness on their strips. Appl. Opt. 46 (2007) 3668 determined the near field of a grating whose strips present two kinds of roughness, one of them so rough that the grating acts as an amplitude grating. On the other hand, in J. Opt. Soc. Am. A 25 (2008) 2390, a grating with roughness only in one of the grating levels is studied. In the present work, we extend our analysis to the general case where the strips of the grating present two finite roughness levels. As a consequence, the periodic modulation is only generated by random micro-topography of the strips. A statistical analysis is developed to obtain equations that predict the average intensity distribution after the grating. This general case presents differences with the previous works. For example, the maximum contrast of the self-images is given at a certain distance from the grating, that is, the contrast of the self images firstly increases with the distance of the observation plane and after, it decreases. Numerical simulations, based on Rayleigh–Sommerfeld approach, are performed which confirm the theoretical predictions.

Point-by-point inscription of apodized fiber Bragg gratings

We demonstrate apodized fiber Bragg gratings (FBGs) inscribed with a point-by-point (PbP) technique. We tailor the grating phase and coupling amplitude through precise control over the longitudinal and transverse positions of each laser-inscribed modification. This method of apodization is facilitated by the highly localized, high-contrast modifications generated by focused IR femtosecond laser inscription. Our technique provides a simple method for the design and implementation of PbP FBGs with complex apodization profiles.

Dipole-induced grating in a waveguide-coupled photonic crystal microcavity embedding a driven three-level emitter

We study optical transmission characteristics of a waveguide-coupled photonic crystal microcavity embedding a driven three-level dipole emitter. By spatially modulating the control field, alternating regions of high transmission and absorption can be produced in two waveguide channels which can be used for an amplitude grating.

Magnetic field sensing using polarization properties in magneto-optical fiber Bragg gratings

Fiber Bragg gratings have has been widely used in sensors. We analyze the transmission and polarization properties of magneto-optical fiber Bragg gratings based on coordinate conversion. The simulations demonstrate the influence of magnetic field intensity on the transmission spectrum, the polarization properties by the coupled mode theory, and the Jones formalism. The results show that while a small magnetic field can hardly be detected in the grating amplitude response, it leads to significant polarization properties such as the third normalized Stokes parameter, polarization dependent loss, and ellipticity. We demonstrate that these polarization properties contain information about the magnetic field and can thus be used for magnetic field sensing purposes. The sensitivity and dynamic range depend on the physical parameters of the grating.

Quadric wavefront aberrations in phase-type images of binary amplitude gratings with small opening ratios

Abstract We discuss the quadric wavefront aberration of a fractional Talbot imaging ray which distorts the phase-type image of a binary amplitude grating with a small value of the opening ratio. When the opening ratio is equal to 1/2 or 1/3, the imaging rays are shown to have no quadric wavefront aberrations. For the opening ratios of 1/4 and 1/5, two different types of quadric wavefront aberrations are responsible for the three-level phase images. If the opening ratio gets to 1/6, we find that three different types of quadric wavefront aberrations distort the fractional Talbot image. The quadric wavefront aberration formulated here may be used in evaluating the phase-type image of a binary amplitude grating with an arbitrary value of the opening ratio.

Tunable light diffractor associated with liquid crystal molecular reorientation from homogeneous alignment to periodic twist deformation in micrometre scale

We have demonstrated the formation of a transmissive tunable light diffractor with a fine grating period using a fringe-field switching (FFS) device. The presented device operates as a superposed amplitude and phase grating. The phase grating is formed by a thin slab of a nematic liquid crystal (LC) film and the amplitude grating is constructed by the electrode pattern of the FFS device. The electrode-position-dependent periodic deformation of the LC director as a function of the applied electric field is analysed and the respective occurrence of phase difference in monochromatic, coherent, linearly polarized He–Ne (632.8 nm) laser light is also calculated using the Jones matrix method at operating voltage. The same calculation results show that the transmitted beam of the present FFS diffractor is right-handed elliptically polarized. The operation characteristics of the thin diffracting device are investigated using a He–Ne laser source and a photodetector which shows a significantly large angular deviation of the diffracted beam owing to the small periodicity of LC deformation.

Single-shot color digital holography based on the fractional Talbot effect

We present a method for recording on-axis color digital holograms in a single shot. Our system performs parallel phase-shifting interferometry by using the fractional Talbot effect for every chromatic channel simultaneously. A two-dimensional binary amplitude grating is used to generate Talbot periodic phase distributions in the reference beam. The interference patterns corresponding to the three chromatic channels are captured at once at different axial distances. In this scheme, one-shot recording and digital reconstruction allow for real-time measurement. Computer simulations and experimental results confirm the validity of our method.

Self-imaging by a volume grating

The self-image phenomenon by a volume grating is proposed and theoretically analyzed. A theoretical model based on a path integral formulation to describe wave propagation through the grating inhomogeneous medium is applied. A modified version of the scalar diffraction theory Fresnel propagator is obtained which allows calculating the diffracted field amplitude by the grating. The proposed model is applied to amplitude and/or phase volume gratings. Remarkable features appear, in particular at the fractional Talbot distance 0.125 z T. In this case, if an in-phase real and imaginary grating modulation is considered a self-image intensity profile is observed for determined values of the absorptive and refractive parameters. On the other hand, a spatial comb intensity profile for a near half period shift between the real and imaginary grating modulations is found.

Casimir-Polder interaction between an atom and a dielectric grating

We develop the scattering approach to calculate the exact dispersive Casimir-Polder potential between a ground-state atom and a rectangular grating. Our formalism allows, in principle, for arbitrary values of the grating amplitude and period, and of the atom-grating distance. We compute numerically the potential for a Rb atom on top of a Si grating and compare the results with the potential for a flat surface taken at the local atom-surface distance (proximity force approximation). Except for very short separation distances, the potential is nearly sinusoidal along the direction transverse to the grooves.

Amplitude of the dynamic phase gratings in saturable Er-doped fibers

Dynamic population gratings recorded via local saturation of optical absorption/gain in rare-earth (Er, Yb) doped fibers demonstrate contributions of the amplitude and phase components. Quantitative comparison of the experimentally observed amplitude grating efficiency with that evaluated from spatially uniform saturation of the fiber optical absorption usually shows a significant discrepancy. The grating amplitude proves to be significantly weaker than its theoretical evaluation. The first results on quantitative comparison of the recorded phase grating amplitudes with spatially uniform photo-induced refractive index change in Er-doped fibers at three essentially different wavelengths (1485, 1526, and 1568 nm) are reported. As for the amplitude grating component, the experimentally observed phase grating amplitude is inferior to its theoretical evaluation; this discrepancy is spectrally dependent and is also significantly reduced in the short-wavelength region 1480–1490 nm on the Er3+ ion absorption.

Grating translation technique as a tool for monitoring phase shifts during holographic recording in azo-polymers

Grating translation technique, elaborated for photorefractive materials, can be used for determination of amplitude and phase grating contributions to light diffraction efficiency after holographic recording in photochromic polymer films. Here, we report application of this technique to in situ analysis of the formation of light inscribed diffraction gratings in azo-functionalized polymers. This technique allows for monitoring amplitudes and phase shifts between phase and amplitude gratings during holographic recording. For the investigation, we chose two azo-polymers with identical azo-substituents and characterized by qualitatively different temporal evolutions of grating build-up process during holographic recording with light s-s polarization geometry. The observed differences in grating recording kinetics for these polymers are explained by the difference in dynamics of build-up of amplitude and phase gratings including surface relief gratings and the spatial phase shifts between them and light interference pattern. Methodology described in this work could be applied to systems in which complex mechanism of refractive index changes upon light illumination are expected.