Showing papers on "Diffraction efficiency published in 2016"

Diffraction gratings: from principles to applications in high-intensity lasers

Abstract: Diffraction gratings were discovered during the 18th century, and they are now widely used in spectrometry analysis, with outstanding achievements spanning from the probing of single molecules in biological samples to the analysis of solar systems in astronomy. The fabrication of high-quality diffraction gratings requires precise control of the period at a nanometer scale. The discovery of lasers in the 1960s gave birth to optical beam lithography in the 1970s. This technology revolutionized the fabrication of diffraction gratings by offering highly precise control of the grating period over very large scales. It is surprising to see that a few years after, the unique spectral properties of diffraction gratings revolutionized, in turn, the field of high-energy lasers. We review in this paper the physics of diffraction gratings and detail the interest in them for pulse compression of high-power laser systems.

3D printed diffractive terahertz lenses

Abstract: A 3D printer was used to realize custom-made diffractive THz lenses. After testing several materials, phase binary lenses with periodic and aperiodic radial profiles were designed and constructed in polyamide material to work at 0.625 THz. The nonconventional focusing properties of such lenses were assessed by computing and measuring their axial point spread function (PSF). Our results demonstrate that inexpensive 3D printed THz diffractive lenses can be reliably used in focusing and imaging THz systems. Diffractive THz lenses with unprecedented features, such as extended depth of focus or bifocalization, have been demonstrated.

Beam steering for virtual/augmented reality displays with a cycloidal diffractive waveplate.

Abstract: We proposed a switchable beam steering device with cycloidal diffractive waveplate (CDW) for eye tracking in a virtual reality (VR) or augmented reality (AR) display system. Such a CDW diffracts the incident circularly polarized light to the first order with over 95% efficiency. To convert the input linearly polarized light to right-handed or left-handed circular polarization, we developed a broadband polarization switch consisting of a twisted nematic liquid crystal cell and an achromatic quarter-wave retardation film. By cascading 2-3 CDWs together, multiple diffraction angles can be achieved. To suppress the color dispersion, we proposed two approaches to obtain the same diffraction angle for red, green, and blue LEDs-based full color displays. Our device exhibits several advantages, such as high diffraction efficiency, fast response time, low power consumption, and low cost. It holds promise for the emerging VR/AR displays.

Digital polarization holography advancing geometrical phase optics.

Abstract: Geometrical phase or the fourth generation (4G) optics enables realization of optical components (lenses, prisms, gratings, spiral phase plates, etc.) by patterning the optical axis orientation in the plane of thin anisotropic films. Such components exhibit near 100% diffraction efficiency over a broadband of wavelengths. The films are obtained by coating liquid crystalline (LC) materials over substrates with patterned alignment conditions. Photo-anisotropic materials are used for producing desired alignment conditions at the substrate surface. We present and discuss here an opportunity of producing the widest variety of "free-form" 4G optical components with arbitrary spatial patterns of the optical anisotropy axis orientation with the aid of a digital spatial light polarization converter (DSLPC). The DSLPC is based on a reflective, high resolution spatial light modulator (SLM) combined with an "ad hoc" optical setup. The most attractive feature of the use of a DSLPC for photoalignment of nanometer thin photo-anisotropic coatings is that the orientation of the alignment layer, and therefore of the fabricated LC or LC polymer (LCP) components can be specified on a pixel-by-pixel basis with high spatial resolution. By varying the optical magnification or de-magnification the spatial resolution of the photoaligned layer can be adjusted to an optimum for each application. With a simple "click" it is possible to record different optical components as well as arbitrary patterns ranging from lenses to invisible labels and other transparent labels that reveal different images depending on the side from which they are viewed.

Polarization volume grating with high efficiency and large diffraction angle.

Abstract: We propose a polarization volume grating (PVG), which exhibits nearly 100% diffraction efficiency and large diffraction angle. Both reflective and transmissive PVGs can be configured depending on application preference. Such a PVG is polarization-sensitive so that it can split an incident unpolarized beam into two well-separated yet polarized beams. These outstanding features make PVG a strong candidate for photonic and display applications. To investigate and optimize the diffraction properties, we build a rigorous simulation model based on finite element method. To illustrate its potential applications, we propose a simple 2D/3D wearable display using a planar waveguide comprising of two reflective PVGs.

Controlling Light with Geometric-Phase Holograms

Abstract: Improved fabrication techniques are creating a new generation of gratings, lenses, and other elements that are physically thin and optically thick.

Wide-angled off-axis achromatic metasurfaces for visible light.

Abstract: We present an approach to build multiwavelength achromatic metasurface that can work in off-axis configuration with an ultra-wide applicable incident angle range for visible light. The metasurface is constructed by combining multiple metallic nano-groove gratings, which support enhanced diffractions for transverse magnetic polarization in an ultrawide incident angle range from 10° to 80° due to the excitations of localized gap plasmon modes at different resonance wavelengths. To achieve the achromatic diffraction, the ratio between the resonance wavelength and the period of each elementary grating is fixed. Incident light at those multiple resonance wavelengths can be efficiently diffracted into the same direction with near-complete suppression of the specular reflection. Based on the similar approach, we also design a wide-angled off-axis achromatic flat lens for focusing light of different wavelengths into the same position. Our findings provide an alternative simple way to design various off-axis achromatic flat optical elements without stringent angle requirement for imaging and display applications.

Low-Toxicity Photopolymer for Reflection Holography

Abstract: A novel composition for a low-toxicity, water-soluble, holographic photopolymer capable of recording bright reflection gratings with diffraction efficiency of up to 50% is reported. The unique combination of two chemical components, namely, a chain transfer agent and a free radical scavenger, is reported to enhance the holographic recording ability of a diacetone acrylamide (DA)-based photopolymer in reflection mode by 3-fold. Characterization of the dependence of diffraction efficiency of the reflection gratings on spatial frequency, recording intensity, exposure energy, and recording wavelength has been carried out for the new low-toxicity material. The use of UV postexposure as a method of improving the stability of the photopolymer-based reflection holograms is reported. The ability of the modified DA photopolymer to record bright Denisyuk holograms which are viewable in different lighting conditions is demonstrated.

3D-printed diffractive elements induced accelerating terahertz Airy beam

Abstract: We first demonstrate the accelerating terahertz (THz) Airy beam with a 0.3-THz continuous wave. Two diffractive elements are designed and 3D-printed to form the generation system, which cannot only imprint the desired complex phase pattern but also perform the required Fourier transform (FT). We both numerically and experimentally demonstrate the propagation dynamics of the accelerating THz Airy beam and investigate its self-healing property during propagation in the free space. Our observations are in good agreement with the numerical simulations. Such an accelerating THz Airy beam could be able to develop novel THz imaging systems and robust THz communication links.

Fast-response and high-efficiency optical switch based on dual-frequency liquid crystal polarization grating

Abstract: A dual-frequency liquid crystal polarization grating is fabricated by photoalignment and demonstrated as an optical switch. A high diffraction efficiency up to 95% is obtained for a single first order with circular incident polarization. Via merely alternating the frequency of applied electric field, the switch On and Off time reach 350 μs and 550 μs, respectively. This work supplies a new design for fast-response and high-efficiency optical switch with the merits of easy fabrication and low power consumption.

Capturing Structural Dynamics in Crystalline Silicon Using Chirped Electrons from a Laser Wakefield Accelerator

Abstract: Recent progress in laser wakefield acceleration has led to the emergence of a new generation of electron and X-ray sources that may have enormous benefits for ultrafast science. These novel sources promise to become indispensable tools for the investigation of structural dynamics on the femtosecond time scale, with spatial resolution on the atomic scale. Here, we demonstrate the use of laser-wakefield-accelerated electron bunches for time-resolved electron diffraction measurements of the structural dynamics of single-crystal silicon nano-membranes pumped by an ultrafast laser pulse. In our proof-of-concept study, we resolve the silicon lattice dynamics on a picosecond time scale by deflecting the momentum-time correlated electrons in the diffraction peaks with a static magnetic field to obtain the time-dependent diffraction efficiency. Further improvements may lead to femtosecond temporal resolution, with negligible pump-probe jitter being possible with future laser-wakefield-accelerator ultrafast-electron-diffraction schemes.

Highly efficient spectrally encoded imaging using a 45° tilted fiber grating

Abstract: A novel highly efficient, fiber-compatible spectrally encoded imaging (SEI) system using a 45° tilted fiber grating (TFG) is proposed and experimentally demonstrated for the first time, to the best of our knowledge The TFG serves as an in-fiber lateral diffraction element, eliminating the need for bulky and lossy free-space diffraction gratings in conventional SEI systems Under proper polarization control, due to the strong tilted reflection, the 45° TFG offers a diffraction efficiency as high as 935% Our new design significantly reduces the volume of the SEI system and improves energy efficiency and system stability As a proof-ofprinciple experiment, spectrally encoded imaging of a customer-designed sample (96 mm x 30 mm) using the TFG-based system is demonstrated The lateral resolution of the SEI system is measured to be 42 μm in our experiment

Diffraction grating characterisation for cold-atom experiments

Abstract: We have studied the optical properties of gratings microfabricated into semiconductor wafers, which can be used for simplifying cold-atom experiments. The study entailed the characterization of the diffraction efficiency as a function of the coating, periodicity, duty cycle, and geometry using over 100 distinct gratings. The critical parameters of experimental use, such as the diffraction angle and wavelength, are also discussed, with an outlook to achieving optimal ultracold experimental conditions.

Nanoparticle-polymer composite volume holographic gratings dispersed with ultrahigh-refractive-index hyperbranched polymer as organic nanoparticles.

Abstract: We report on volume holographic recording at a wavelength of 532 nm in photopolymerizable polymer nanocomposites that are incorporated with new hyperbranched polymers (HBPs) acting as transporting organic nanoparticles. Since HBPs possess an ultrahigh index of refraction of 1.82 due to the inclusion of triazine and aromatic ring units, high-contrast transmission volume holographic gratings with refractive index modulation amplitudes as large as 2.2×10(-2) are recorded. This value enables us to realize a 10 μm thick transmission volume grating with the diffraction efficiency near 100% in the green.

Enhanced light extraction efficiency of OLEDs with quasiperiodic diffraction grating layer

Abstract: We presented enhanced light extraction efficiency of organic light emitting diodes (OLEDs) cells with a nano-sized diffraction grating layer. Various diffraction gratings of different morphologies including linear, cubic, hexagonal and quasiperiodic patterns were fabricated by multiplexing light interference exposure on an azobenzene thin film. The effect of diffraction grating layer on device performances including luminous properties and quantum efficiency was investigated. In contrast to periodic grating patterns, the quasiperiodic structures leading broadband light extraction resulted in improved external quantum efficiency and power efficiency by 73% and 63%, respectively, compared to conventional OLED with flat surface of glass substrate.

Highly efficient blazed grating with multilayer coating for tender X-ray energies.

Abstract: For photon energies of 1 – 5 keV, blazed gratings with multilayer coating are ideally suited for the suppression of stray and higher orders light in grating monochromators. We developed and characterized a blazed 2000 lines/mm grating coated with a 20 period Cr/C- multilayer. The multilayer d-spacing of 7.3 nm has been adapted to the line distance of 500 nm and the blaze angle of 0.84° in order to provide highest efficiency in the photon energy range between 1.5 keV and 3 keV. Efficiency of the multilayer grating as well as the reflectance of a witness multilayer which were coated simultaneously have been measured. An efficiency of 35% was measured at 2 keV while a maximum efficiency of 55% was achieved at 4 keV. In addition, a strong suppression of higher orders was observed which makes blazed multilayer gratings a favorable dispersing element also for the low X-ray energy range.

Novel Effective Approach for the Fabrication of PDMS-Based Elastic Volume Gratings

Abstract: All-optical fabrication of elastic volume diffraction gratings in polydimethylsiloxane (PDMS) is presented. Novel material based on the commercially available PDMS with incorporated benzophenone (BPh) photoactive molecules is developed. The gratings are formed by a holographic technique and UV irradiation through an amplitude mask. New material permits to obtain efficient volume gratings with periods ranging from hundreds nanometers to dozens of micrometers in elastic films of different thicknesses. Besides symmetric transmission 1D gratings, slanted and 2D gratings have been fabricated as well. Photoattachment of BPh molecules and their real-time diffusion within elastic PDMS matrix in accordance with the spatially modulated light is considered as a mechanism of the gratings formation. The refractive index modulation amplitude of about 7.0 × 10−4 is achieved. It is shown that mechanical strain of the elastic volume gratings allows fully reproducible alteration of the gratings parameters. In order to tune the diffracted wavelength over the whole visible spectral range (from 410 up to 700 nm), a strain of about 75% is required. New volume diffraction PDMS gratings represent very successful combination of cheap and widely known materials with one-step optical fabrication techniques providing high-performance tunable diffraction elements that can be applied in photonics, sensing, and spectroscopy.

Modeling spatially localized photonic nanojets from phase diffraction gratings

Abstract: We investigated numerically the specific spatially localized intense optical structure, a photonic nanojet (PNJ), formed in the near-field scattering of optical radiation at phase diffraction gratings. The finite-difference time-domain technique was employed to study the PNJ key parameters (length, width, focal distance, and intensity) produced by diffraction gratings with the saw-tooth, rectangle, and hemispheric line profiles. Our analysis showed that each type of diffraction gratings produces a photonic jet with unique characteristics. Based on the numerical calculations, we demonstrate that the PNJ could be manipulated in a wide range through the variation of period, duty cycle, and shape of diffraction grating rulings.

Diffraction gratings generating orders with selective states of polarization.

Abstract: We propose specially designed double anisotropic polarization diffraction gratings capable of producing a selective number of diffraction orders and with selective different states of polarization. Different polarization diffraction gratings are demonstrated, including linear polarization with horizontal, vertical and ± 45° orientations, and circular R and L polarization outputs. When illuminated with an arbitrary state of polarization, the system acts as a complete polarimeter where the intensities of the diffraction orders allow measurement of the Stokes parameters with a single shot. Experimental proof-of-concept is presented using a parallel-aligned liquid crystal display operating in a double pass architecture.

Stretchable Hexagonal Diffraction Gratings as Optical Diffusers for In Situ Tunable Broadband Photon Management

Abstract: A stretchable transmissive hexagonal diffraction grating, which has the potential to act as an optical diffuser, is demonstrated. Leveraging the simplicity of the self-assembly fabrication process, the photon manipulation capability of polystyrene nanosphere arrays, and elastomeric properties of polydimethylsiloxane, the proposed device is capable of reproducible in situ tuning of both diffraction efficiency and spectral range. While being able to achieve maximum diffraction efficiencies of about 80%, the device displays highly efficient and broadband light diffusion fairly independent of incident light polarization and angle of incidence. Due to its efficient and tunable diffraction capabilities, one potential application of the reported device can be broadband photon management in solar cells and photodetectors by significant increase of the light path length inside the light-absorbing thin films of these devices. As a proof of concept, the proposed optical diffuser is utilized for light absorption enhancement in colloidal quantum dot semiconductor thin films. The demonstrated devices enable integration of cheap and widely used materials with simple cost-effective fabrication for photon management in optics, photonics, and optoelectronics.

Off-axis holographic lens spectrum-splitting photovoltaic system for direct and diffuse solar energy conversion

Abstract: This paper describes a high-efficiency, spectrum-splitting photovoltaic module that uses an off-axis volume holographic lens to focus and disperse incident solar illumination to a rectangular shaped high-bandgap indium gallium phosphide cell surrounded by strips of silicon cells. The holographic lens design allows efficient collection of both direct and diffuse illumination to maximize energy yield. We modeled the volume diffraction characteristics using rigorous coupled-wave analysis, and simulated system performance using nonsequential ray tracing and PV cell data from the literature. Under AM 1.5 illumination conditions the simulated module obtained a 30.6% conversion efficiency. This efficiency is a 19.7% relative improvement compared to the more efficient cell in the system (silicon). The module was also simulated under a typical meteorological year of direct and diffuse irradiance in Tucson, Arizona, and Seattle, Washington. Compared to a flat panel silicon module, the holographic spectrum splitting module obtained a relative improvement in energy yield of 17.1% in Tucson and 14.0% in Seattle. An experimental proof-of-concept volume holographic lens was also fabricated in dichromated gelatin to verify the main characteristics of the system. The lens obtained an average first-order diffraction efficiency of 85.4% across the aperture at 532 nm.

Critical-angle x-ray transmission grating spectrometer with extended bandpass and resolving power > 10,000

Abstract: A number of high priority subjects in astrophysics can be addressed by a state-of-the-art soft x-ray grating spectrometer, such as the role of Active Galactic Nuclei in galaxy and star formation, characterization of the Warm-Hot Intergalactic Medium and the missing baryon problem, characterization of halos around the Milky Way and nearby galaxies, as well as stellar coronae and surrounding winds and disks. An Explorer-scale, largearea (> 1,000 cm2), high resolving power (R =λ/Δλ > 3,000) soft x-ray grating spectrometer is highly feasible based on Critical-Angle Transmission (CAT) grating technology, even for telescopes with angular resolution of 5-10 arcsec. Still, significantly higher performance can be provided by a CAT grating spectrometer on an X-ray- Surveyor-type mission. CAT gratings combine the advantages of blazed reflection gratings (high efficiency, use of higher diffraction orders) with those of conventional transmission gratings (lowmass, relaxed alignment tolerances and temperature requirements, transparent at higher energies) with minimalmission resource requirements. They are high-efficiency blazed transmission gratings that consist of freestanding, ultra-high aspect-ratio grating bars fabricated from silicon-on-insulator (SOI) wafers using advanced anisotropic dry and wet etch techniques. Blazing is achieved through grazing-incidence reflection off the smooth grating bar sidewalls. The reflection properties of silicon are well matched to the soft x-ray band, and existing silicon CAT gratings can exceed 30% absolute diffraction efficiency, with clear paths for further improvement. Nevertheless, CAT gratings with sidewalls made of higher atomic number elements allow extension of the CAT grating principle to higher energies and larger dispersion angles, thus enabling higher resolving power at shorter wavelengths. We show x-ray data from CAT gratings coated with a thin layer of platinum using atomic layer deposition, and demonstrate efficient blazing to higher energies and much larger blaze angles than possible with silicon alone. We also report on measurements of the resolving power of a breadboard CAT grating spectrometer consisting of a Wolter-I slumped-glass focusing mirror pair from Goddard Space Flight Center and CAT gratings, performed at the Marshall Space Flight Center Stray Light Facility. Measurement of the Al Kα doublet in 18th diffraction order shows resolving power > 10,000, based on conservative preliminary analysis. This demonstrates that currently fabricated CAT gratings are compatible with the most advanced grating spectrometer instrument designs for future soft x-ray spectroscopy missions.

Fabrication process for 200 nm-pitch polished freestanding ultrahigh aspect ratio gratings

Abstract: A fully integrated fabrication process has been developed to fabricate freestanding, ultrahigh aspect ratio silicon gratings with potassium hydroxide (KOH)-polished sidewalls. The gratings are being developed for wavelength-dispersive, soft x-ray spectroscopy on future space telescopes. For this application, the grating needs to have a large open-area fraction and smooth sidewalls (roughness < 1 nm) to maximize efficiency. The prototype gratings fabricated with the process presented here have been tested on a synchrotron beamline and have demonstrated an absolute diffraction efficiency greater than 30% for 2 nm-wavelength x-rays in blazed orders. This efficiency is greater than twice the efficiency of previously fabricated gratings. The fabrication process utilizes silicon-on-insulator wafers where the grating and a cross support are etched in the device layer, and an additional structural support is etched in the handle layer. The device layer and handle layer are both etched via deep reactive-ion etchin...

Diffractive optical devices produced by light-assisted trapping of nanoparticles.

Abstract: One- and two-dimensional diffractive optical devices have been fabricated by light-assisted trapping and patterning of nanoparticles. The method is based on the dielectrophoretic forces appearing in the vicinity of a photovoltaic crystal, such as Fe:LiNbO3, during or after illumination. By illumination with the appropriate light distribution, the nanoparticles are organized along patterns designed at will. One- and two-dimensional diffractive components have been achieved on X- and Z-cut Fe:LiNbO3 crystals, with their polar axes parallel and perpendicular to the crystal surface, respectively. Diffraction gratings with periods down to around a few micrometers have been produced using metal (Al, Ag) nanoparticles with radii in the range of 70-100 nm. Moreover, several 2D devices, such as Fresnel zone plates, have been also produced showing the potential of the method. The diffractive particle patterns remain stable when light is removed. A method to transfer the diffractive patterns to other nonphotovoltaic substrates, such as silica glass, has been also reported.

Hybrid tilted-pulse-front excitation scheme for efficient generation of high-energy terahertz pulses

Abstract: Conception of a hybrid type tilted-pulse-front pumping scheme for the generation of high-energy terahertz pulses is presented. The proposed setup is the combination of the conventional setup containing imaging optics and the contact grating. The solution was developed for nonlinear materials requiring large pulse-front-tilt angle, like LiNbO3. Due to the creation of the pulse-front-tilt in two steps the limitations of imaging errors can be significantly reduced. Furthermore the necessary grating constant of the contact grating can be larger compared to the simple contact grating scheme making possible the fabrication of the grating profile with significantly higher precision. A detailed optimization procedure with respect to the diffraction efficiency on the contact grating is given for LiNbO3. Instructions are also given how to construct the geometry of the setup in order to minimize imaging errors. Examples are given for LiNbO3 based practically realizable, optimized schemes with reduced imaging errors and high diffraction efficiency on the contact grating.

Observation of photorefractive effects in blue-phase liquid crystal containing fullerene-C 60 .

Abstract: Photorefractive effects manifested in two beam coupling and side diffractions are observed in fullerene-C60 doped blue-phase liquid crystals (BPLC−C60) upon application of a DC bias field. The mechanism at work here is attributed to BPLC lattice distortion by the combined DC (Edc)+ photorefractive space-charge (Ephoto) fields, in addition to the DC + optical field induced effects reported in previous studies of dye-doped system. The first order diffraction efficiency of ∼2×10−3 and beam coupling gain of over 2% are observed in a 55 μm thick sample with input laser beam power of 5 mW at an applied DC voltage of 160 V. The effective nonlinear index coefficient n2 of BPLC−C60 is measured to be on the order of 10−2 cm2/W, which is slightly lower than their NLC counterparts. Owing to the isotropy of BPLC optical properties, these effects can be observed with more relaxed requirements on the laser polarizations, directions of incidence, and sample orientations.

Single-order transmission diffraction gratings based on dispersion engineered all-dielectric metasurfaces.

Abstract: A single-order transmission diffraction grating based on dispersion engineered all-dielectric metasurfaces is proposed, and its wavelength discriminating properties have been theoretically described and confirmed using numerical simulations. The metasurface is designed using a 2D array of all-dielectric resonators, which emulates a Huygens’ source configuration to achieve a perfect match to free space in broad bandwidth. Using a holey dielectric nanodisk structure as the unit cell, the resonant wavelength is tapered across the metasurface to engineer the wavelength-dependent spatial phase gradient, to emulate a dispersive prism. Consequently, different wavelengths are steered toward different directions and thus are discriminated on the output image plane. Due to the subwavelength periodicities involved, wavelength discrimination is achieved directly in the zeroth diffraction order of the device, unlike conventional diffraction gratings, thereby providing a high-efficiency wavelength discriminating device.

Broadband, high-efficiency, arbitrary focusing lens by a holographic dielectric meta-reflectarray

Abstract: In this paper, a metalens based on the dielectric meta-reflectarray consisting of silicon nanorods in combination with a gold ground plane is proposed to realize an arbitrary focusing lens. We have demonstrated that the meta-reflectarray is served as a half-waveplate with near-unity reflectance and over 98% polarization conversion efficiency over a wavelength range from 1.5 to 1.6 μm for circularly polarized light incidences. We have also demonstrated that single spot and four-spaced spots focusing with more than 96% diffraction efficiency over 100 nm bandwidth can be realized by this metalens in the near infrared band just by controlling the reflection phases. The spatial phase distributions of the corresponding designed metalens can be determined via a computer-generated hologram method. Meanwhile, the desired phase can be simply obtained by modulating the orientation of the silicon nanorods. The proposed approach demonstrates a high-performance solution for creating low-cost and lightweight beam-shaping and beam-focusing devices at telecommunication wavelengths.

Optimal design of multilayer diffractive optical elements with effective area method.

Abstract: The effective area method is described to design high-efficiency multiplayer diffractive optical elements (MLDOEs) with finite feature sizes for wide wave band. This method is presented with consideration of the shield effect between two elements of MLDOEs, and the optimal surface relief heights of MLDOEs are calculated with the effective area method. Then the comparisons of diffraction efficiency and polychromatic integral diffraction efficiency for MLDOEs with different period widths are described and simulated with the effective area method and scalar diffraction theory (SDT). Finally, the design results of MLDOEs obtained by SDT and the effective area method are compared by a rigorous electromagnetic analysis method, specifically, the finite-difference time-domain method. These results show that the limits of SDT for MLDOEs, ascertain and quantify the greatest sources of the diffraction efficiency loss due to the shield effect. The design results of the effective area method can obtain higher polychromatic integral diffraction efficiency than that of the SDT when the period width of MLDOEs is taken into account.