Depth Of Gratings Research Articles

Design of the Single Heterogeneous Quantum Dot Lasers Emitting 4 Wavelengths Using Combination‐Grating Technology

AbstractMulti‐wavelength light sources are crucial for high‐bandwidth silicon photonic chips. In this paper, a single heterogeneous quantum dot distributed feedback (DFB) laser emitting 4 wavelengths using the combination‐grating technology is designed. To the best of the knowledge, this is the first heterogeneously integrated quantum dot DFB laser that lases stable multi‐wavelength in a single cavity. When the etching depth, etching width, and total length of gratings are 100 , 550 nm, and 1 000 µm, respectively, 4‐wavelength with 1297.01 , 1303.38 , 1309.74 , and 1316.11 nm are obtained by varying the grating period from 196 to 199 nm with the spacing of 1 nm. Compared to the conventional DFB laser arrays, the DFB laser units are significantly reduced by 3/4 while maintaining the same number of output wavelengths. Additionally, by optimizing the λ/4 phase‐shift position and the duty cycle of gratings, the output power at the front‐end of the 4‐wavelength laser is significantly improved. Specifically, the ratio of the output power from the front‐end and rear‐end of the laser increases from the conventional 1.00 to 2.51. This work provides a competitive candidate for multi‐wavelength, high‐performance, and large‐scale silicon‐based light sources used in data centers, lidar, and component detection.

Photonic-grating-enabled selective manipulation of surface waves within the Reststrahlen band

Due to the favorable ability of strong field confinement and long lifetimes, mid-infrared (MIR) surface phonon polariton (SPhP) resonances hold great promise for advanced nanophotonic applications. Here, we report an approach to manipulate phononic surface waves by constructing a germanium (Ge) grating on a bulk polar silicon carbide (SiC) surface. The fabricated samples are characterized via the polarization- and angle-dependent reflection spectroscopy, and the experimental results reveal that the grating coupling to SPhPs takes place within the SiC Reststrahlen band, which is dominated by the depth and period of gratings. This work not only provides a better understanding for grating coupling to SPhP, but also enables potential applications in developing photonic-phononic hybrid structures with other polar dielectrics operating at Reststrahlen band.

Subwavelength diffraction gratings with macroscopic moiré patterns generated via laser interference lithography.

We propose a simple and flexible fabrication approach based on the moiré effect of photoresist gratings for rapid synthesis of apodized structures with continuously varying depth. Minor modifications in a standard laser interference lithography setup allow creating macroscopic, visible by naked eye moiré patterns that modulate the depth of subwavelength diffraction gratings. The spatial frequency of this modulation is easily controlled in a wide range, allowing to create a quasicrystal in extreme cases. Experimental results are confirmed by a theory with clear graphical solutions and numerical modeling. The method is universal and does not depend on a specific choice of photoresist and/or substrate materials, making it a promising choice for structured light applications, optical security elements or as a basic structuring method of complex optical devices.

Analysis of diffraction efficiency of phase gratings in dependence of duty cycle and depth

The analysis of dependence of diffraction efficiency on duty cycle and modulation depth of phase gratings with rectangular and Gaussian profile was performed by means of specially designed program. An Angular Spectrum method applied for monochromatic light propagation in far field through phase grating was used for calculation of diffraction efficiency of gratings. Diffraction efficiency maps of 0-5th diffraction orders were obtained for different grating profiles. It is shown that changing the duty cycle of grating makes it possible to tune smoothly the diffraction efficiency and to redirect the light intensity in required orders.

Superlens-enhanced laser interference lithography

A one-step lithography method based on a superlens is proposed to fabricate diffraction-unlimited metallic patterns. By controlling the material parameters and the distribution of the impinging energy, various phenomena, such as periodic nanonetworks, ultrathin nanowires (sub-50-nm feature size), and variable-sized nanoparticles (ranging from sub-10 nm to several hundreds of nanometers), are fabricated using a 1,064-nm nanosecond laser. The evolution pathway of such phenomena is explained by the dewetting process of metallic films. The direct-writing performance of a transparent material with a superlens is studied, and the maximum etching depth of Si gratings can reach 2 µm under a single laser pulse, with fine profiles.

Study of the formation of a microrelief on ZnSe- and CdSe-crystal surfaces ablated by excimer KrF-laser radiaton

One-dimensional gratings with a period of are formed on the surfaces of CdSe and ZnSe crystals ablated by two interfering radiation beams of a nanosecond excimer KrF laser. Investigated are the dependences of the shape and depth of gratings on the energy density under irradiation by a single pulse, and on the number of pulses at a given energy density. The maximum grating depth is estimated as of the period. By forming a one-dimensional grating with a period of and a depth of on the CdSe-crystal surface, this surface becomes antireflective at a wavelength of . The surface reflectivity is reduced by 88 %. A possibility of forming two-dimensional gratings having periods of 1 and is demonstrated.

Coupling coefficient calculation for GaSb-based quantum well distributed feedback lasers with laterally coupled gratings

We calculated the coupling coefficient of different types of laterally coupled distributed feedback (LC-DFB) structures with coupled-wave theory and the two-dimensional semivectorial finite difference method. Effects neglected in previous studies such as other partial waves, the ohmic contact and metal contact layers are taken into account in this calculation. The LC-DFB structure with metal gratings is especially studied due to its advantage over index-coupled structures. The dependence of coupling coefficient on structure parameters is theoretically calculated such as grating order, ridge width, thickness of the residual cladding layer, grating depth and lateral proximity of gratings to the ridge waveguide. A complex-coupled GaSb-based 2 µm LC-DFB structure is optimized to achieve a high coupling coefficient of 14.5 cm−1.

Modeling adapted to manufacturing of holographic super Gaussian gratings

A few holographic metallic (gold and silver) gratings with maximum diffraction efficiency (DE) in the 700 to 1100 nm wavelength range were designed. These designed diffraction gratings can be attractive for stretching and compressing pulses in chirped pulse amplification (CPA) technology. They were optimized for transverse magnetic polarized light in the first order (littrow mount). KPP1206 photoresist was used to model the final pattern on photoresist thin film. To obtain super Gaussian profiles, approximately identical exposure energy density intervals were used for optimizing grating profile. The optimized gold and silver gratings were compared in terms of DE, bandwidth and incidence angle range. Dependence of DE on the depth and duty cycle of super Gaussian gold and silver gratings showed that the silver grating had higher DE than the gold grating in 1064 nm. Fabricated silver grating based on modeling results had good agreement with experimental results.

Influence of surface relief depth on diffraction efficiency of phase gratings recorded in Slavich PFG-01

The diffraction efficiencies of surface relief gratings formed in Slavich PFG-01 silver halide emulsion have been studied in the frequency range 300–1200grooves/mm in terms of relief depths and periods of the gratings. The relief depths generated in the gratings show a sudden decrease up to a certain frequency, then a slight increase and finally decrease with increasing grating frequency for a symmetrical geometry of holographic recording. Effect of grating period variation on the relief depth of the phase gratings is found to be similar to the correlation of diffraction efficiency and grating aspect ratio. Diffraction efficiency response of a grating with a fixed groove frequency has also been investigated in terms of relief depths.

Spectrophotometric method for measuring the groove depth of calibration reflection gratings

A method for measuring the groove depth of calibration gratings is proposed which is based on measuring the spectral dependence of the the zero-order reflection diffraction efficiency. The errors of the method are determined by three main factors: the shift of the maxima of the spectrum due to the wall slope of the grating grooves, the error in setting the wavelength of the spectrophotometer, and the divergence of the light beam in the setup. It is shown theoretically that the measurement error is in the range of 0.25–1%, depending on the fabrication technology of the grating and measuring equipment. The method was tested experimentally using commercial calibration gratings. The range of applicability of the method is discussed in terms of the geometrical parameters of the microstructure of reflection gratings and the characteristics of the spectrophotometer used.

Optically Induced Surface Relief Gratings in Polymer Films Doped With Sulphonyl Group Containing Azobenzene

In holography, more attractive have become azobenzene compounds doped in a polymer matrix (host-guest polymer film) or chemically attached to the polymer. Azobenzene molecules exhibit reversible photoisomerization between trans- and cisisomers which can form a surface relief grating in the films. The authors investigate the holographic recording and formation of surface relief gratings in a host-guest polymer film with two original azobenzene compounds. Holographic recording with 325 nm laser light was performed in host-guest polymer films with the host being polymethylmetacrylate (PMMA) and the guest – 15 wt% azobenzene molecules (A-45 or A-48). In both cases an increase in the diffraction efficiency at the beginning of the process could be related to the trans-cis-photoisomerization, while the second increase − to the formation of surface relief gratings. The systems with A-45 molecules reach a diffraction efficiency of 0.7%, and with A-48 molecules − of 0.24%. Also, the depth of surface relief gratings is greater in the films with A-45 (35 to 45 nm) than in those with A-48 (4 to 6 nm) molecules.

Motion transparency from opposing luminance modulated and contrast modulated gratings

Two luminance gratings of identical orientation and opposite directions of motion are seen as moving across one another (i.e. moving transparently) only if they differ in spatial frequency (SF) by a factor of four or more. Identical SF gratings produce counter-phase flicker. This suggests that opposite motions cancel each other at the level of motion detection. Here we show that motion transparency is perceived with two gratings of the same SF and orientation moving in opposite directions, when one grating is a first-order, luminance modulated (LM) stimulus and the other is a second-order, contrast modulated (CM) stimulus. Participants were presented with various combinations of LM and CM gratings. In experiment 1, the test stimulus contained the summation of oppositely moving LM and CM gratings. In order to assess the simultaneous perception of both motions, we used a paradigm where observers were required to discriminate the direction of motion of each component from counter-phase flicker. Results show that observers can accurately discriminate both LM and CM directions of motion in a transparent configuration. We next measured the effect of varying the contrast/modulation depth of LM and CM gratings on the perception of transparency. The perception of motion transparency depends upon the relative contrast/modulation depth of the component gratings: raising the contrast of the LM component necessitates a greater modulation depth for the CM component if motion transparency is to be perceived. Our results are consistent with a motion system comprised of two separate, but not wholly independent, pathways for the encoding of LM and CM signals. We hypothesise that the observed contrast dependence is the result of contrast gain control mechanisms that receive inputs from separate motion systems.

Correlation of anisotropic cell behaviors with topographic aspect ratio

In this study, we have used nanoimprinting to create a range of micro- and nanoscale gratings, or their combination, in bulk polystyrene plates to investigate anisotropic cell behaviors of human dermal fibroblasts with respect to the aspect ratio (depth/width) of gratings. The depth and width of the polystyrene gratings both show strong effects individually on cell alignment and elongation that are qualitatively similar to the results of other studies. However, consistent quantitative comparison of these individual parameters with different studies is complicated by the diversity of combinations of width and depth that have been tested. Instead, the aspect ratio of the gratings as a unified description of grating topography is a more consistent parameter to interpret topographic dependence of cell morphology. Both cell alignment and elongation increase with increasing aspect ratio, and even a shallow grating (aspect ratio of ∼0.05) is sufficient to induce 80% cell alignment. Re-plotting data recently published by other groups vs. aspect ratio shows a similar dependence, despite differences in cell types and surface structures. This consistency indicates that aspect ratio is a general factor to characterize cell behaviors. The relationship of cell elongation and alignment with topographic aspect ratio is interpreted in terms of the theory of contact guidance. This model provides simplicity and flexibility in geometry design for devices and materials that interface with cells.

Silicon thin-film solar cells with rectangular-shaped grating couplers

As an alternative to randomly textured transparent conductive oxides as front contact for thin-film silicon solar cells the application of transparent grating couplers was studied. The grating couplers were prepared by sputtering of aluminium-doped zinc oxide (ZnO) on glass substrate, a photolithography and a lift-off process and were used as periodically textured substrates. The period size and groove depth of these transparent gratings were tuned independently from each other and varied between 1 and 4 μm and 100–600 nm. The optical properties of rectangular-shaped gratings and the opto-electronic behaviour of amorphous and microcrystalline silicon solar cells with integrated grating couplers as a function of the grating parameters (period size P and groove depth hg) are presented. The optical properties of the gratings are discussed with respect to randomly textured substrates and the achieved solar cell results are compared with the opto-electronic properties of solar cells deposited on untextured (flat) and randomly textured substrates. Copyright © 2005 John Wiley & Sons, Ltd.

Reduction of Birefringence and Polarization- Dependent Loss of Long-Period Fiber Gratings Fabricated with a KrF Excimer Laser

We discuss the effect of UV laser exposure time, repetition rate, and heating by a heating coil on the resonance peak depth and polarization-dependent loss (PDL) of long-period fiber gratings (LPFGs). The LPFGs were fabricated with a KrF excimer laser and an amplitude mask. We observed an initial increase of the resonance peak depth and PDL as the UV exposure time was increased, which eventually decreased in response to over-coupling. With the total UV fluence kept constant, the peak depth continued to increase as the repetition rate was increased beyond 10 Hz, whereas the maximum PDL decreased when the repetition rate was higher than 17 Hz. This is believed to be a thermal effect caused by the rapid delivery of UV laser pulses. We observed a similar reduction of the maximum PDL from 1.35 to 0.25 dB when the fiber was heated by an adjacent heating coil.

Optical measurement of depth and duty cycle for binary diffraction gratings with subwavelength features.

We describe a new and unique method for simultaneous determination of the groove depth and duty cycle of binary diffraction gratings. For a near-normal angle of incidence, the +1 and -1 diffracted orders will behave nearly the same as the duty cycle is varied for a fixed grating depth. The difference in their behavior, quantified as the ratio of their respective diffraction efficiencies, is compared to a look-up table generated by rigorous coupled-wave theory, and the duty cycle of the grating is thus obtained as a function of grating depth. Performing the same analysis for the orthogonal probe-light polarization results in a different functional dependence of the duty cycle on the grating depth. By use of both TE and TM polarizations, the depth and duty cycle for the grating are obtained by the intersection of the functions generated by the individual polarizations. These measurements can also be used to assess qualitatively both the uniformity of the grating and the symmetry of the grating profile. Comparison with scanning electron microscope images shows excellent agreement. This method is advantageous since it can be carried out rapidly, is accurate and repeatable, does not damage the sample, and uses low-cost, commonly available equipment. Since this method consists of only four fixed simple measurements, it is highly suitable for quality control in a manufacturing environment.

Shading and texture: separate information channels with a common adaptation mechanism?

We outline a scheme for the way in which early vision may handle information about shading (luminance modulation, LM) and texture (contrast modulation, CM). Previous work on the detection of gratings has found no sub-threshold summation, and no cross-adaptation, between LM and CM patterns. This strongly implied separate channels for the detection of LM and CM structure. However, we now report experiments in which adapting to LM (or CM) gratings creates tilt aftereffects of similar magnitude on both LM and CM test gratings, and reduces the perceived strength (modulation depth) of LM and CM gratings to a similar extent. This transfer of aftereffects between LM and CM might suggest a second stage of processing at which LM and CM information is integrated. The nature of this integration, however, is unclear and several simple predictions are not fulfilled. Firstly, one might expect the integration stage to lose identity information about whether the pattern was LM or CM. We show instead that the identity of barely detectable LM and CM patterns is not lost. Secondly, when LM and CM gratings are combined in-phase or out-of-phase we find no evidence for cancellation, nor for 'phase-blindness'. These results suggest that information about LM and CM is not pooled or merged--shading is not confused with texture variation. We suggest that LM and CM signals are carried by separate channels, but they share a common adaptation mechanism that accounts for the almost complete transfer of perceptual aftereffects.

A non-contact technique for determining the depth of zero-order gratings

A non-contact technique for determining the depth of zero-order gratings

A non-contact technique for determining the depth of zero-order gratings

In this work we present a simple, non-contact method for characterizing the depth of deep zero-order diffraction gratings using standard visible optics. Form birefringence exhibited by zero-order structures alters the polarization state of light transmitted through them. The amount of change is dependent on several factors including the depth of the grating grooves. By recording the polarization changes of laser light transmitted through the sample we demonstrate how the depth of any grating with a known pitch may be determined. Results for many different gratings have been analysed and show good agreement with groove depths measured from scanning electron micrographs. From these results a universal relationship between the amount of polarization change and the depth of the grating grooves has been determined.

The interaction between stereoscopic and luminance motion

An interaction in apparent motion between perceived three-dimensional forms defined by stereopsis and local luminous elements is reported. Vertical stripes of cyclopean square gratings were simulated by random-dot stereograms. Alternation of two-frame stereograms whose phases differed by 90 deg caused two kinds of percepts, planes' motion in depth (first-order stereoscopic motion, first-order SM) or lateral motion of gratings (higher-order stereoscopic motion, higher-order SM). Experiment 1 explored the conditions under which higher-order SM frequently arose, as opposed to local luminance-based in-depth motion (first-order SM). The results show that, when the spatial arrangements of two-frame random dots were correlated, higher-order SM dominated for long ISI conditions (ISI > 73 msec). When they were uncorrelated, higher-order SM dominated even under zero ISI conditions. Subjects reported that, when higher-order SM was seen, dots were attached to the surfaces of the moving cyclopean figure (motion capture). Experiment 2 tested which factor caused the domination of higher-order SM under uncorrelated conditions in Experiment 1, the larger distance of dot jump or the varied directions of the dots' motion. The results show that, when the distance of dot jump is large or when the directions of dots' motion are incoherent, higher-order SM arises more frequently. When local first-order motion signals are weakened by appropriate temporal and spatial conditions or by incoherent motion directions, higher-order SM dominates and it captures the motion of dots.