Higher-order Diffraction Beams Research Articles

Graphic-processable deep neural network for the efficient prediction of 2D diffractive chiral metamaterials.

We propose a novel, to the best of our knowledge, graphic-processable deep neural network (DNN) to automatically predict and elucidate the optical chirality of two-dimensional (2D) diffractive chiral metamaterials. Four classes of 2D chiral metamaterials are studied here, with material components changing among Au, Ag, Al, and Cu. The graphic-processable DNN algorithm can not only handle arbitrary 2D images representing any metamaterials that may even go beyond human intuition, but also capture the influence of other parameters such as thickness and material composition, which are rarely explored in the field of metamaterials, laying the groundwork for future research into more complicated nanostructures and nonlinear optical devices. Notably, the rigorous coupled wave analysis (RCWA) algorithm is first deployed to calculate circular dichroism (CD) in the higher-order diffraction beams and simultaneously promote the training of DNN. For the first time we creatively encode the material component and thickness of the metamaterials into the color images serving as input of the graphic-processable DNN, in addition to arbitrary graphical parameters. Especially, the smallest intensity is found in the third-order diffraction beams of E-like metamaterials, whose CD response turns out to be the largest. A comprehensive study is conducted to capture the influence of shape, unit period, thickness, and material component of arrays on chiroptical response. As expected, a satisfied precision and an accelerated computing speed that is 4 orders of magnitude quicker than RCWA are both achieved using DNN. This work belongs to one of the first attempts to thoroughly examine the generalization ability of the graphic-processable DNN for the study of arbitrary-shaped nanostructures and hypersensitive nanodevices.

Exploiting deep learning network in optical chirality tuning and manipulation of diffractive chiral metamaterials

Abstract Deep-learning (DL) network has emerged as an important prototyping technology for the advancements of big data analytics, intelligent systems, biochemistry, physics, and nanoscience. Here, we used a DL model whose key algorithm relies on deep neural network to efficiently predict circular dichroism (CD) response in higher-order diffracted beams of two-dimensional chiral metamaterials with different parameters. To facilitate the training process of DL network in predicting chiroptical response, the traditional rigorous coupled wave analysis (RCWA) method is utilized. Notably, these T-like shaped chiral metamaterials all exhibit the strongest CD response in the third-order diffracted beams whose intensities are the smallest, when comparing up to four diffraction orders. Our comprehensive results reveal that by means of DL network, the complex and nonintuitive relations between T-like metamaterials with different chiral parameters (i. e., unit period, width, bridge length, and separation length) and their CD performances are acquired, which owns an ultrafast computational speed that is four orders of magnitude faster than RCWA and a high accuracy. The insights gained from this study may be of assistance to the applications of DL network in investigating different optical chirality in low-dimensional metamaterials and expediting the design and optimization processes for hyper-sensitive ultrathin devices and systems.

Optical circular dichroism engineering in chiral metamaterials utilizing a deep learning network.

Here, a deep learning (DL) algorithm based on deep neural networks is proposed and employed to predict the chiroptical response of two-dimensional (2D) chiral metamaterials. Specifically, these 2D metamaterials contain nine types of left-handed nanostructure arrays, including U-like, T-like, and I-like shapes. Both the traditional rigorous coupled wave analysis (RCWA) method and DL approach are utilized to study the circular dichroism (CD) in higher-order diffraction beams. One common feature of these chiral metamaterials is that they all exhibit the weakest intensity but the strongest CD response in the third-order diffracted beams. Our work suggests that the DL model can predict CD performance of a 2D chiral nanostructure with a computational speed that is four orders of magnitude faster than RCWA but preserves high accuracy. The DL modelintroduced in this work shows great potentials in exploring various chiroptical interactions in metamaterials and accelerating the design of hypersensitive photonic devices.

Analysis of output beam polarization in higher-order self diffraction via two-wave mixing in BSO crystal

Generation of two higher-order diffraction beams in two-wave mixing in transmission geometry have been analyzed theoretically in photorefractive cubic crystal of 23 symmetry, BSO (Bismuth Silicon Oxide) and considering its optical activity as one of the important parameter. Results are shown graphically by solving coupled wave equations using fourth-order Runge–Kutta method. The effect of polarization state of pump beam, optical activity, off-Bragg parameter, coupling coefficients, absorption and thickness of crystal has been analyzed on the beam intensities and their respective polarizations. It has been observed that as the value of the off-Bragg parameter reduces the transfer of energy to the higher-order beams increases. It has been also observed that by selecting proper input beam polarization and crystal thickness, diffracted beam intensity and its polarization could be controlled considerably. It has also been seen that by controlling input pump beam polarization, particular higher-order beam can be selectively amplified.

A study on the output beam profile of a ring resonator type diplexer

A ring resonator type diplexer was tested for fast switching device for ECCD system. The ring resonator was composed by circular corrugated waveguides with 63.5 mm diameter. Four in/output ports were separated from the resonator by half mirrors. The resonance frequency and its interval were designed as 170 GHz and 460 MHz, respectively. The mock-up diplexer which utilizes slotted planes with 2 mm period or sapphire disk with 1 mm thickness as half mirrors were examined at using 170 GHz-band low power oscillator. RF beam with 95% of the fundamental mode (LP01 mode) was provided into the input port of the diplexer using a mode generator. Beam profiles from output ports were measured and mode contents in output ports were deduced. When the slotted mirrors were utilized, the LP01 mode purity was decreased as 85% at the resonance frequency, 170 GHz. This was because higher order modes were induced by the higher order diffraction beams from the slotted half mirror. On the other hand, mode purity was increased higher than 98% at 170 GHz when sapphire mirrors were utilized.

Abnormal optical characteristics of the waveguide-grating structures

In this paper we investigate the optical property of the waveguide-grating structures (WGS) with the grating period in the scale of micrometer, which is larger than the wavelength of the incident light. In such structures, the higher-order diffracted beams can also couple into the waveguide, while in the structure that the period of grating is much smaller than the wavelength of incident light, only the ± 1 orders of diffraction can excite the propagation modes of the waveguide. Numerical calculations of extinction of the higher-order structure show that except for the extinction peaks, enhanced transmission can also be obtained, which is also observed in experiment. Further simulations indicate that the enhancement can be tuned by changing the structural and the geometric parameters of the WGS device. In addition, the wavelength that extraordinary transmit is decided by the duty cycles of the gratings, so, the enhancement might be attributed to the phenomena of missing order in gratings with large period.

Two-wave and induced three-wave mixing in thin holograms

The results of investigations of two- and three-wave mixing in thin holograms are presented. A spatial light modulator fabricated from a Bi12SiO20 (or BSO) crystal was used as a photosensitive medium for holographic recording. It was found experimentally that mixing can take place between higher-order diffracted beams, a phenomenon which uniquely characterizes thin holograms. The necessary theoretical analysis underlying the wave mixing for two specific orientations of the BSO crystal has been developed. We have found qualitative agreement between theory and experiments and concluded that the modulator can be used as an efficient medium for adaptive interferometric techniques.

Effects of Arbitrary Phase Shift on the Higher-order Self-diffraction in Absorptive Photorefractive Medium

Abstract Interactions between optical beams incident upon and two higher-order self-diffracted beams generated within an absorptive photorefractive material are investigated by solving a set of coupled differential equations. The medium is assumed to be free of linear and circular birefringence. Arbitrary phase shift between the light grating and the refractive index grating is considered. It is shown that under favourable conditions, a significant amount of power may be transferred to the newly generated waves. Investigated are the effects of phase shift, thickness and absorption of the crystal, coupling constant and off-Bragg parameter on energy transfer to the higher-order diffracted beams. It is shown that in the case of phase-shift other than π/2, higher-order self-diffracted beams can be generated on both sides of the input beams. Coupled wave equations are solved numerically by a fourth-order Runge-Kutta method and results are presented in graphical form. This analysis is valid for the near colline...

Holographic optical element for an optical disk head with spot-size detection servo optics

A CGH construction of a holographic optical element (HOE) for an optical disk head with spot-size detection by means of superimposing two Fresnel zone plates is studied. Optimum parameter values for the ratio of segment to grating pitch (duty) and grating height are clarified from the viewpoint of total light power efficiency in the round trip optical system. The influences of higher-order diffracted beams near the first-order diffracted beams used to get signals on signal detection are shown to be small. The HOEs with almost optimum parameter values are fabricated and the desired diffracted spots, the expected total light power efficiency, and the small influence of higher-order diffracted beams are observed.

The diffraction grating under nonuniform illumination

A grating illuminated by a beam with a spatial distribution of intensity produces a diffraction pattern that appears to consist of copies of the incident beam. The copies are centered at the classical diffraction angles given by nλ=d sin φ. In this article, this is indeed shown to be the case if the incident beam has a very narrow spread in wavelength and direction. If the incident beam has a very narrow spread in direction, but not in wavelength, only the zeroth-order diffracted beam is a copy of the incident beam. The higher-order diffracted beams are spread out in wavelength. A black-and-white lantern slide projected through a grating shows the picture in black and white in zeroth-order and as colored images in higher orders.

High resolution electron microscopy of the triply incommensurate phase of2H-TaSe2

The triply incommensurate phase of 2H-${\mathrm{TaSe}}_{2}$ obtained by cooling from the normal phase was investigated by transmission electron microscopy between 87 and 113 K with the resolution of 3 A\r{}, one order of magnitude better than earlier experiments. Moir\'elike patterns observed in this phase were confirmed to be interference fringes due to the first- and second-order diffraction beams (with small separation and possibly with higher-order diffraction beams) from the incommensurate structure and were not due to the dark-field diffraction contrast of domains of the commensurate structure as interpreted earlier. Lattice fringes (\ensuremath{\sim}9 A\r{}) of this modulated phase do not show any discontinuity across the boundaries of regions of different contrasts of the moir\'elike fringes which is expected from domain boundaries. Instead, a periodic change in the spacing of the lattice fringes (phase-slip region) expected from the superposition of split superlattice spots in forming the lattice image is observed. This is what is believed to be the first direct observation of the existence of the phase-slip region which is also expected from the discommensuration theory. A series of observations presented here thus shows that the triply incommensurate phase is intrinsically incommensurate and suggests the need for a modification of interpretations of this phase in terms of the double honeycomb discommensuration model.

Investigation of the structure of the object wave field reconstructed by a phase hologram

The spatial nonuniformity of a light beam, which carries optical information, causes a number of undesirable effects which worsen the quality of a holographic image: The relationship of the intensity and phases between the spectral-angular components of the object wave field is altered in the reconstruction, i.e., structural distortions arise, and new components appear which were absent in the recording (noise distortions). Theoretical investigations of these effects have been performed in many papers (see [1-3]); however, being based on generalizations of the Kogelnik theory of coupled waves [4], these investigations encompass only the case of volume (three-dimensional) holograms. For plane holograms a calculation of the intensity of distortions of the speckle-nonuniform object field has been carried out in [5]. Moreover, an intermediate case is often realized in practice in which the hologram is not plane but at the same time its thickness is still insufficiently large for one to treat it as a volume hologram. The effectiveness of the diffraction of light by such holograms has been calculated up to now on the basis of special numerical methods [6], and analytic methods have not even been developed for the plane-wave approximation. However, the numerical calculation performed in [6] has shown that the intensity of lower-order diffraction waves is described in the intermediate case by the Kogelnik formulas [4], which provides a basis for generalizing the theory of coupled waves to the case of holograms of arbitrary thickness with additional taking into account of higher-order diffraction beams.

Possibility of a diffracted beam in the absence of the corresponding Fourier component of potential in gas-surface scattering

It is shown, with a simple analytical example, that the intensity of a diffracted beam in atom-surface scattering is not necessarily small if the corresponding Fourier component of potential is small. This result contradicts the predictions of the existing first-order theory. An experimental result that higher-order diffracted beams can dominate the scattering while the specular and other lower-order beams can be relatively small, combined with a theoretical result that the Fourier components of potential decrease strongly with increasing order, leads to the conclusion that first-order theory is invalid in general for an interpretation of gas-surface diffraction.

Lateral Displacement of Optical Beams at Multilayered and Periodic Structures*

Many planar structures, including multilayered media and periodic configurations of the optical-grating type, are capable of supporting an electromagnetic field of the leaky-wave form. By exciting this field, an incident light beam transfers a portion of its energy into the leaky-wave structure; after being guided longitudinally for a certain distance along the structure, this energy is leaked back to form part of the reflected beam. Owing to the longitudinal energy flow, the complete reflected beam exhibits a lateral displacement that appears either as a forward beam shift, similar to the Goos-Hanchen effect along a single dielectric interface, or as a backward beam shift, which has not been identified before. By deriving a general expression for the field excited by a gaussian light beam incident upon a leaky-wave structure, we find that the reflected beam may undergo a lateral displacement of the order of the beam width; the magnitude of this beam shift may therefore be much larger than the maximum shift produced at a single dielectric boundary. In the case of periodic structures, all of the higher-order diffracted beams are shifted laterally whenever the specularly reflected beam is displaced. The dependence of the lateral displacement on the beam width, the angle of incidence, and the leakage distance is examined in detail and the relevance of the beam shift to optical-beam couplers is discussed.