Response Of Gratings Research Articles

Complex method for angular-spectral analysis of volume phase diffraction gratings recorded in photopolymers

Photopolymer recording materials are nowadays widely used for recording of diffraction gratings and other diffraction elements. For obtaining the best performance of these diffraction gratings for desired applications, it is important to assess these gratings from many different perspectives. In this contribution, we present an experimental and characterization approach to an analysis of diffraction gratings recorded into photopolymer materials. This approach is able to provide a complex and very illustrative description of these gratings response and, with accordance to the theory, information about some important grating parameters, such as a spatial period, slant angle, etc., as well. This approach is based on the measurement of a grating response for a wide range of angles and wavelengths and then on the construction and subsequent analysis of maps in the angular-spectral plane. It is shown that the measurements are in a good agreement with the theoretical predictions based on either approximate (Kogelnik’s coupled wave theory) or rigorous (RCWA) techniques and that this approach provides complex and detailed characterization of the grating response which can be used for additional optimization or decision of applicability of measured sample gratings.

Spectral response of long-period fiber gratings to cladding refractive index perturbation

The spectral response of long-period fiber gratings can be tailored by the cladding index perturbation (C-LPFGs) induced by written methods. Here, we investigate theoretically the effects of radial dependence and the magnitude of the cladding index modulation on the transmission spectra of C-LPFGs. Simple analytical expressions that describe the dispersion characteristics of the guided core mode and cladding modes are derived from a multilayer cylindrical waveguide. As the radial depth increases, we demonstrate that transition points exist for the resonances of lower cladding modes, i.e., LP06 and LP15 modes, by comparing the mode-coupling phase to the value π/2. In addition, we show that resonant wavelength shifts of all cladding modes follow the same trend. For the LPvj (v≠0) modes with two polarizations, the cross talk weakens the power exchanges between core mode LP01 and LPvj (v≠0) modes. Moreover, the coupling mechanism relating to cladding index modulation is explained by the presence of the interaction between the evanescent field of the core mode and cladding modes. This work is promising in terms of providing sufficient guidelines to understand and explore design and application of LPFGs.

Holographic humidity response of slanted gratings in moisture-absorbing acrylamide photopolymer.

Holographic humidity response is characterized in detail using transmission and reflection geometry in moisture-absorbing acrylamide photopolymer. The diffraction spectrum and its temporal evolution at various relative humidity are measured and analyzed. The quantitative relations between relative humidity and holographic properties of slanted gratings are determined. The responsibility of holographic gratings for various relative humidity is observed by the spectrum response of gratings. The extracted humidity constants reflect the applicability of reflection and transmission gratings at different humidity regions. The humidity reversibility experiment is achieved for confirming repeatability of the sensor. These experiments provide a probability for improving the applicability of a holographic humidity sensor. Finally, the extended diffusion model is derived by introducing the expansion coefficient to describe the dynamic swelling process. This work can accelerate development of the holographic sensor and provide a novel strategy for exploring the swelling mechanism of photopolymer.

Enhanced photorefractive performance of the nematic liquid crystal cell containing photoconductive polymer film

Photorefractive (PR) nematic liquid crystals (NLCs) possess large optical non-linearity but coarse grating spacings (tens of microns) and slow response time (generally in the order of 1 s). Here we presented a great improvement in PR performance of NLC cells containing photoconductive films as aligning layers by varying the thickness and the sensitizer concentration of the photoconductive layer to enhance the surface electric field modulation. As a result of optimising, considerable diffraction efficiencies and the response time as fast as tens of milliseconds were obtained from steady-state PR gratings within a wide range of grating spacings from 30 to 0.7 μm. Besides, the grating response was enhanced significantly compared with the previous reports under similar experimental conditions.

Response of fiber Bragg gratings bonded on a glass/epoxy laminate subjected to static loadings

Fiber Bragg gratings (FBG) may be used to monitor strain over the surface of a structure as an alternative technology to conventional strain gauges. However, FBG bonding techniques have still not been established to yield satisfactory surface measurements. Here, two adhesives were investigated, one with low viscosity and the other with high viscosity for bonding FBGs on glass/epoxy sandwich skins. First, instrumented elementary specimens were tested under tension. FBG strain results were analyzed together with digital image correlation (DIC) measurements. The influence of the bonding layer on the measured strain and on the integrity of the sensor was investigated by considering different regions of interest. Next, an instrumented structural sandwich beam was tested under four-point bending. FBG rosettes were compared to conventional strain gauge rosettes. The high viscosity adhesive demonstrated behaviors that affected FBG accuracy. Brittleness of the bonding layer and poor interface adhesion were observed using DIC and X-ray tomography. By contrast, the low viscosity adhesive demonstrated satisfactory results. The FBG strain measurements appeared to be consistent with those of DIC. The accuracy is also adequate as the FBGs and the conventional strain gauges had similar results in three directions, under tension and under compression.

Dynamic interrogator for elastic wave sensing using Fabry Perot filters based on fiber Bragg gratings

Use of in-fiber Fabry–Perot (FP) filters based on fiber Bragg gratings as both sensor as well as an interrogator for enhancing the detection limit of elastic wave sensing is investigated in this paper. The sensitivity of such a demodulation scheme depends on the spectral discrimination of the sensor and interrogator gratings. Simulations have shown that the use of in-fiber FP filters with high finesse provide better performance in terms of sensitivity compared to the demodulation using fiber Bragg gratings. Based on these results, a dynamic interrogator capable of sensing acoustic waves with amplitude of less than 1 micro-strain over frequencies of 10kHz to several 100kHz has been implemented. Frequency response of the fiber Bragg gratings in the given experimental setup has been compared to that of the conventional piezo sensors demonstrating that fiber Bragg gratings can be used over a relatively broad frequency range. Dynamic interrogator has been packaged in a compact box without any degradation in its performance.

Sum-frequency generation echo and grating from interface.

The work addresses spectroscopy of fourth-order Sum Frequency Generation Echo and Grating responses as an experimental tool to study structure and dynamics at interfaces. First, it addresses experimental geometry to extract background-free fourth-order Echo and Grating responses. Further, the article provides the analytical expressions of the response functions for these nonlinearities. The derived expressions are used to model the χ((4)) two-dimensional spectral responses of a hydrated methyl acetate, which resembles a hydrated carbonyl moiety at the polar outer side of a phospholipid membrane. Orientation, transition dipole moments, and Raman tensors are obtained from the results of classical and quantum calculations, respectively. The numerical studies for the nonlinear responses under different polarization schemes and timings suggest the possibility of securely factoring of spectral contributions of χ(YYYZX) and χ(YYYZY) macroscopic susceptibilities. As such, the nonlinearities provide an experimental perspective on orientation of a generic (low-symmetry) molecular system at interfaces. Besides, the spectral properties of the tensors may reflect correlations of the in-plane and out-of-plane field components specific to the interface. For the case of a phospholipid membrane, the experiment would address in-plane and out-of-plane anisotropy of hydrogen bonding and related dynamics.

Investigation of the sensitivity to humidity of an acrylamide-based photopolymer containing N-phenylglycine as a photoinitiator

Sensitivity of holographic recording materials to the relative humidity (RH) of the environment often restricts their use in fabrication of holographic optical elements and other applications. It is important to develop materials with little or no sensitivity to humidity. In this paper the humidity response of transmission gratings recorded in an acrylamide-based photopolymer containing N-phenylglycine (NPG) as a photoinitiator is studied at RH=20–90%. The hologram is found to be completely insensitive to humidity at RH below 70% and its diffraction efficiency remains constant. A decrease in diffraction efficiency is observed at RH=80–90% but this decrease is fully reversible, demonstrating quantitatively the NPG photopolymer’s excellent resistance to humidity.

Degradation of swept-parameter VEP responses by neutral density filters in amblyopic and normal subjects.

To determine whether objective visual function, measured by swept-parameter visual evoked potential (sVEP), is preferentially degraded by neutral density filtration (NDF) in normal control and fellow eyes compared to amblyopic eyes, and to determine whether the response to NDF is a function of stimulus type, using grating and vernier stimuli. Monocular Snellen acuity and both grating and vernier sVEP responses were measured in each eye of 23 children or adolescents with amblyopia and 21 visually and neurologically normal children or adolescents. Acuity and sVEP responses were measured with and without a 2.0 log unit neutral density filter before the viewing eye. Suprathreshold sVEP grating responses were more sensitive than vernier to degradation by amblyopia in the unfiltered state and to NDF-induced preferential degradation of responses from fellow and normal control eyes. For threshold measurements, on the other hand, vernier responses were more sensitive to degradation by amblyopia in the unfiltered state and to NDF-induced preferential depression. Threshold vernier responses of amblyopic eyes were paradoxically enhanced by NDF. Neutral density filtration causes preferential degradation of both threshold and suprathreshold sVEP responses in normal control eyes and fellow eyes of amblyopes, compared to amblyopic eyes. The degradation is stimulus specific and dependent upon whether threshold or suprathreshold responses are measured. Grating responses are more likely to identify suprathreshold abnormalities, while vernier stimuli are more likely to detect threshold abnormalities. These findings may be used to optimize the stimulus parameters and design of future studies utilizing evoked potential techniques in amblyopic subjects.

Application of the Hilbert Transform Method for the Retrieval of the Phase Characteristics of Plasmonic Metal Bragg Gratings

We demonstrate, with detailed examples, a method to retrieve the phase and group-delay responses of plasmonic metal Bragg gratings (MBGs) from their reflection and transmission spectra. The method is based on the Hilbert transform (HT) that relates the phase and the amplitude spectrum of a minimum-phase system. For the retrieval of the reflection phase, if the propagation loss of the grating is negligible, the method cannot tolerate any asymmetry in the grating profile and thus fails to operate for practical low-loss fiber or dielectric-waveguide Bragg gratings, where the fabrication errors are sufficient to destroy the symmetry requirement. The large propagation loss of the surface plasmon mode, however, makes possible the retrieval of the reflection phase of an MBG that contains a certain degree of asymmetry in the grating profile. For the retrieval of the transmission phase, the symmetry requirement is not an issue, while a large propagation loss can introduce significant errors in the retrieved phase spectrum. It is possible, however, to largely reduce such errors by applying the HT method to the spectrum with the background propagation loss artificially removed. The HT method provides a simple and effective way to obtain the phase and group-delay characteristics of MBGs, which are difficult to measure directly, and can find applications in the development of grating-based plasmonic devices.

Optimization of the Rayleigh anomaly of metallic gratings for terahertz sensor applications

The frequency of the Rayleigh anomaly of a metallic grating varies with the refractive index of the surrounding medium. To employ this phenomenon in optical sensors it is essential that the feature, due to the Raleigh anomaly in the sensor’s optical response, is very distinct and stable. We study the reflectance of optical structures consisting of a metallic grating with a thin dielectric film on highly reflective silicon substrates in the terahertz (THz) range between 0.6 and 2 THz. A distinct reflectance peak due to the Rayleigh anomaly can only be observed if a dielectric spacer layer is inserted between the metallic grating and silicon substrate. The dielectric layer between the grating and substrate acts as a Fabry–Pérot resonator with a low quality factor. Thus, the corresponding Fabry–Pérot modes only couple weakly to the Rayleigh anomaly. At the frequency of the Rayleigh anomaly, the combined structure exhibits a distinct peak due to the Rayleigh anomaly, no matter whether there is a Fabry–Pérot low or high reflection band at this frequency. In particular, the reflection background in the vicinity of the frequency of the Rayleigh anomaly is suppressed when the Rayleigh anomaly is in resonance with a Fabry–Pérot low reflection band, whilst the Rayleigh reflectance peak itself is retained. The underlying physics is confirmed by a simple analytic model and by numerical calculations. This approach of optimizing the optical response of metallic gratings is important for the design of THz sensing devices based on Rayleigh anomalies.

Broadband RF response of sine wave gratings

ABSTRACTWe experimentally investigate the reflection and transmission of microwaves through grating structures comprised of sinusoidal corrugations. The gratings were fabricated onto dielectric (FR4) circuit board substrates and etched into both sides of the surrounding copper media, where each side is out of phase by 180°. We considered a variety of grating profiles, where each sine wave in a series had the same amplitude but differing frequency. The microwave response of the fabricated gratings was experimentally measured and numerical simulations were conducted and compared to those collected from the fabricated samples. The measured results suggest that such structures can be used potentially as broadband absorbers and polarization filters. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:1982–1984, 2014

Numerical analysis of GeO2-concentration effects in arc-induced long-period fiber gratings under external refractive-index changes

We present a numerical analysis of the response of arc-induced long-period fiber gratings (LPFGs) under ambient refractive-index changes using standard fibers with SiO2 as cladding material and different GeO2 concentration in the SiO2-GeO2 doped core. We obtain that the LPFG-sensitivity is increased using lower GeO2 concentrations and it follows a parabolic behavior. Also, we identify two linear regimes using an external index of 1.37: for GeO2 concentrations between 2 and 3.5 mol %, the LPFG-sensitivity changes with a rate of 3.614 nm per mole fraction of GeO2, while for higher concentrations the sensitivity changes with a rate of 1.39 nm/mol %. Additionally, for fibers with 2 mol% of GeO2, the sensitivity calculated is comparable to this obtained in previous works using corrugated and tapered LPFGs in SMF28 fibers. These results are of interest for the design of improved LPFG-sensors.

Theoretical and Experimental Study of Long-Period Grating Refractive Index Sensor

This article presents the theoretical and experimental investigation of the response of long-period gratings as a refractive index sensor. Cladding modes are calculated, and results are compared with Optigrating 4.2.2 (Optiwave Systems Inc., Ottawa, Canada). The response has been checked for refractive indices ranging from 1 to 1.458. Theoretically simulated results are in accordance with the experimental results. It was found that the software package calculated values correctly up to the seventh decimal point. The ambient refractive index response of a long-period grating over a much wider index range has been modeled for values both less and more than the cladding refractive index.

Magneto-optical Kerr effect in resonant subwavelength nanowire gratings

Periodic arrays of nanorods can present a resonant response at specific geometric conditions. We use a multiple scattering approach to analyze the optical response of subwavelength nanowire gratings made of arbitrary anisotropic materials. When the rods are made of magneto-optical dielectrics we show that there is a complex interplay between the geometric resonances of the grating and the magneto-optical Kerr effects (MOKE) response. As we will show, for a given polarization of the incident light, a resonant magneto-optical response can be obtained by tuning the incidence angle and grating parameters to operate near the resonance condition for the opposite polarization. Our results could be important to understand and optimize MOKE structures and devices based on resonant subwavelength gratings and could open new perspectives in sensing applications.

Effects of cladding radius on the optical characteristics of long-period fiber gratings

Using three-layer vector field model, the dispersion characteristics and spectral response of long-period fiber gratings (LPFGs) with different cladding radii are analyzed. Both the numerical and experimental results demonstrate that LPFG’s resonant wavelengths shift towards much longer wavelength and the transmission depth is strengthened significantly by decreasing cladding radius. When the cladding radius is less than 20 μm, only a single resonant peak over a wavelength range of 600 nm (from 1200 nm to 1800 nm) is achieved, and the sensitivity of LPFG to external refractive index is enhanced significantly.

Highly sensitive compact refractive index sensor based on phase-shifted sidewall Bragg gratings in slot waveguide

The geometrical and physical parameters of phase-shifted sidewall Bragg gratings in a silicon slot waveguide are optimized to possess performance characteristics desirable for integrated optical sensors. By tailoring the spectral response of such phase-shifted sidewall gratings, highly sensitive compact refractive index sensors detecting the resonance wavelength shift or the variation of light intensity are designed with the transfer matrix method. Both refractive index sensors have a minimum detection limit on the order of 10(-6), and a linear response and a compact structure dimension as small as 11.7 μm, offering the capabilities for sensor array and lab-on-a-chip integration. The resonance-shift sensor has a much wider detection range of 1.32 refractive index units than the intensity-measurement sensor. The performance parameters are compared with other refractive index sensors, including Mach-Zehnder interferometers, ring resonators, surface gratings, and phase-shifted gratings in silicon nanowire.

Capability for Fine Tuning of the Refractive Index Sensing Properties of Long-Period Gratings by Atomic Layer Deposited Al2O3 Overlays

This work presents an application of thin aluminum oxide (Al2O3) films obtained using atomic layer deposition (ALD) for fine tuning the spectral response and refractive-index (RI) sensitivity of long-period gratings (LPGs) induced in optical fibers. The technique allows for an efficient and well controlled deposition at monolayer level (resolution ∼ 0.12 nm) of excellent quality nano-films as required for optical sensors. The effect of Al2O3 deposition on the spectral properties of the LPGs is demonstrated experimentally and numerically. We correlated both the increase in Al2O3 thickness and changes in optical properties of the film with the shift of the LPG resonance wavelength and proved that similar films are deposited on fibers and oxidized silicon reference samples in the same process run. Since the thin overlay effectively changes the distribution of the cladding modes and thus also tunes the device's RI sensitivity, the tuning can be simply realized by varying number of cycles, which is proportional to thickness of the high-refractive-index (n > 1.6 in infrared spectral range) Al2O3 film. The advantage of this approach is the precision in determining the film properties resulting in RI sensitivity of the LPGs. To the best of our knowledge, this is the first time that an ultra-precise method for overlay deposition has been applied on LPGs for RI tuning purposes and the results have been compared with numerical simulations based on LP mode approximation.

Near-field numerical analysis of surface plasmon polariton propagation on metallic gratings

Purpose – The purpose of this paper is to simulate and analyze the excitation and propagation of surface plasmon polaritons (SPPs) on sinusoidal metallic gratings in conical mounting. Design/methodology/approach – Chandezon's method has been implemented in MATLAB environment in order to compute the optical response of metallic gratings illuminated under azimuthal rotation. The code allows describing the full optical features both in far- and near-field terms, and the performed analyses highlight the fundamental role of incident polarization on SPP excitation in the conical configuration. Findings – Results of far-field polarization conversion and plasmonic near-field computation clearly show that azimuthally rotated metallic gratings can support propagating surface plasmon with generic polarization. Originality/value – The recent papers experimentally demonstrated the benefits in sensitivity and the polarization phenomenology that are originated by an azimuthal rotation of the grating. In this work, numerical simulations confirm these experimental results and complete the analysis with a study of the excited SPP near-field on the metal surface.

Optical phase front control in a metallic grating with equally spaced alternately tapered slits

A technique capable of focusing and bending electromagnetic (EM) waves through plasmonic gratings with equally spaced alternately tapered slits has been introduced. Phase resonances are observed in the optical response of transmission gratings, and the EM wave passes through the tuning slits in the form of surface plasmon polaritons (SPPs) and obtains the required phase retardation to focus at the focal plane. The bending effect is achieved by constructing an asymmetric phase front which results from the tapered slits and gradient refractive index (GRIN) distribution of the dielectric material. Rigorous electromagnetic analysis by using the two-dimensional (2D) finite difference time domain (FDTD) method is employed to verify our proposed designs. When the EM waves are incident at an angle on the optical axis, the beam splitting effect can also be achieved. These index-modulated slits are demonstrated to have unique advantages in beam manipulation compared with the width-modulated ones. In combination with previous studies, it is expected that our results could lead to the realization of optimum designs for plasmonic nanolenses.