1st Order Diffraction Research Articles

Femtosecond laser direct writing of diffraction grating and its refractive index change in chalcogenide As2Se3 film.

Chalcogenide glasses possess novel optical property in infrared range, which make them ideal candidates for photonic devices by laser direct writing. Precisely control of the refractive index manipulation in the material is the key to achieve high quality optical devices. In this work, diffraction gratings in chalcogenide As2Se3 thin films were fabricated with femtosecond laser direct writing and its refractive index change was carefully studied. Grating diffraction efficiency was measured from visible to near-infrared light by using multiple single-wavelength lasers and a supercontinuum laser. Clear diffraction patterns and high diffraction efficiency indicated the good optical quality of the prepared gratings. Results show that the grating with period of 5 µm inscribed under pulse energy of 30 nJ demonstrated a 1st-order diffraction efficiency of 30% at 808 nm testing wavelength, due to the changes of refractive index and absorption. The relationship of the change of refractive index and absorption coefficient of film under different laser irradiation intensity is carefully studied. The maximum refractive index change was estimated to be 0.087 at 808 nm.

Lossless 0th and −1st order switching by dual-excitation of grating waveguide mode

The reflected 0th and −1st diffraction orders of a waveguide grating can be switched between 0 and 1 diffraction efficiency upon the excitation of a forward- and backward-propagating waveguide mode by means of the +1st and −2nd orders. Such mode-coupling trigger of high isolation switching is found to be in the neighborhood of the −1st order Littrow condition under the condition that no transmitted order can propagate; the condition is here fulfilled without loss penalty by reflecting them under total internal reflection. This requires a waveguide refractive index larger than 3, and resorting to a semiconductor in the near infrared. This non-Fano phenomenon is yet another feature of resonant gratings. The reflective switching effect lends itself to a stable monolithic implementation, and can be used for wavelength control, or for the evanescent wave sensing of measurands in the transmission medium.

Terahertz dispersion using multi-depth phase modulation grating.

We present a multi-depth phase modulation grating (MPMG) in the terahertz range making real-time multichannel Fourier-transform spectroscopy available in a stationary manner. The calculation of the Fraunhofer diffraction field distribution and diffraction efficiency of an MPMG indicates that the zeroth-order diffraction light of an MPMG carries phase information and its diffraction intensity is modulated by the groove depth. A good agreement is found between the measurements of the 0th- and ±1st-order diffraction efficiency at 0.5 and 0.34 THz and the simulation. The frequencies of the terahertz source retrieved from the zeroth-order diffraction intensity at 0.5, 0.4, and 0.34 THz are identical to the actual frequencies.

Fabrication of Dynamic Holograms on Polymer Surface by Direct Laser Writing for High-Security Anti-Counterfeit Applications

Anti-counterfeit technology has attracted much attention with the development of economy, because many counterfeit products that are difficult for identification have been produced, which extremely damage the interests of consumers. Here, a high-resolution ultraviolet direct laser writer is applied to fabricate computer-generated holograms (CGH) with laser spot size of 300 nm for anti-counterfeit applications. The characteristics of the reconstructed images illuminated by monochromatic light are demonstrated in details. Additionally, colorful reconstructed images are observed with white light illumination in the high-security holograms samples. Furthermore, a kinematic effect of colorful reconstructed images are also observed by modifying focus depth and object size in the algorithm. The normal first (+1st) order diffraction and negative first (-1st) order diffraction in the high-security holograms exhibit different sizes due to distinguishing magnifications. The kinematic effect of white-light holograms shows great potential in anti-counterfeit applications due to its simplicity for recognition and high security since they are hard to duplicate.

High-efficiency V-shaped phase gratings to suppress high order diffractions

We propose a V-shaped phase grating to simultaneously improve the diffraction efficiency of the 1st order diffraction mode and suppression of high order modes. An analytic description is given that indicates the 0th, 2nd, 3rd, and 4th order diffractions can be completely suppressed while the 1st order absolute diffraction efficiency can reach a theoretical maximum of 27.72%, which is much higher than that reported from single order gratings, such as sinusoidal amplitude transmission gratings. The dependencies of the 1st order diffraction efficiency on the wavelength and depth deviations are also discussed. The experimental results show that the absolute efficiency of the 1st order diffraction is 25.85% while the 2nd, 3rd, and 4th order diffractions disappear completely, confirming the theoretical predictions. The diffraction patterns of a xenon lamp demonstrate the suppression of the high order diffractions from our quartz phase grating. The unique dispersive properties of the V-shaped phase grating make it attractive for broad spectroscopy and high-accuracy monochromatization applications.

High-performance switchable grating based on pre-transitional effect of antiferroelectric liquid crystals.

An optical phase grating prototype based on the homeotropic aligned antiferroelectric liquid crystal (AFLC) is demonstrated. By applying an in-plane electric field using comb-like electrodes, the helical structure of AFLC is deformed with the molecules rotating parallel to the electric field because of dielectric anisotropy. This deformation is called the pre-transitional effect of AFLC and induces biaxiality. By using this effect, a switchable phase grating is constructed using a 40μm thick cell filled with (S)-MHPOBC at 85°C. For 532nm TM polarized incident light, the maximum diffraction efficiency of 37.0% is achieved at the electric field of 1.8V/μm for the ± 1st order diffraction. The rise and decay times for the 1st order diffraction pattern are 510μs and 210μs, respectively. The high diffraction efficiency achieved under low field makes it promising for future electro-optical applications.

Modal analysis of resonant and non-resonant optical response in semiconductor nanowire arrays

Nanowire array solar cells have reached efficiencies where it becomes feasible to talk about creating tandem solar cells in order to achieve even higher efficiencies. An example of such a tandem solar cell could be a nanowire array embedded in a membrane and integrated on top of a Si bottom cell. Such a system, however, requires understanding and control of its interaction with light, especially to make sure that the low energy photons are transmitted to the bottom cell. The dependence of the optical response of a nanowire array on the nanowire length, diameter, array pitch, materials surrounding the nanowires, and absorption coefficient of the nanowire material is very strong and possibly resonant, indicating the complexity of the optical response. In this work, we use an eigenmode-based analysis to reveal underlying physics that gives rise to observed resonant and non-resonant behavior. First, we show that an effective refractive index can be defined at long wavelengths, where only a single mode propagates. Second, we analyze the origin of the resonant reflection when the next optical mode becomes propagating and can be ‘trapped’ in the array and interact with the fundamental mode. Additionally, we define two simple boundaries for the wavelength range of the resonant response: the resonances can only occur if there is more than 1 propagating mode in the array, and they disappear if the 1st diffracted order is propagating in the top or bottom material. Such resonance effects could be detrimental for tandem solar cells. We thus provide recommendations for tuning the geometry of the array and the nanowire materials in order to push the resonant regime to the absorbing regime of the nanowire, where absorption in the nanowires dampens the resonances. Finally, this work demonstrates the strength of an eigenmode-based analysis of the optical response of periodic nanostructures in terms of simplifying the analysis of a complex system.

Trimming method for a high-yield manufacturing of high-efficiency diffraction gratings.

The tolerances in manufacturing of fully dielectric diffraction gratings based on the leaky-mode resonance in the -1st diffraction order can be challenging, especially if the grating design exhibits high diffraction efficiency (DE) only within a comparatively narrow spectral bandwidth. To gain improved control on the spectral bandwidth exhibiting high DE, we implemented a two-step etching approach within the fabrication process of the grating. First, a dry and anisotropic etching step was used for pre-shaping the grating, followed by iterative isotropic wet-etching steps using an alkaline solution (KOH) at a temperature of 90°C to adjust the maximum efficiency around the desired wavelength with high precision. This straightforward method gave us very good control on tailoring the DE as a function of the wavelength and led to the demonstration of DEs as high as 99.7±0.2% in the -1st diffraction order at a wavelength of 1030nm and of >99% in the wavelength range between 1020 and 1070nm. The gratings were used as cavity end mirrors of an Yb:YAG thin-disk laser, generating an output power of 145W in fundamental mode operation (M2<1.1).

Multifunctional metasurface: from extraordinary optical transmission to extraordinary optical diffraction in a single structure

We show that, a metasurface composed of subwavelength metallic slit array embedded in an asymmetric environment can exhibit either extraordinary optical transmission (EOT) or extraordinary optical diffraction (EOD). By employing an analytical model expansion method and the diffraction order chart in k-vector space, we found that the resonance decaying pathway of the local slit cavity mode can be tuned to either 0th or -1st diffraction order by changing the parallel wavevector, which gives rise to enhanced 0th transmission (EOT) of the structure for small incident angles, and enhanced -1st diffraction (EOD) for large incident angles. Based on this appealing feature, a multifunctional metasurface that can switch its functionality between transmission filter, mirror and off-axis lens is demonstrated. Our findings provide a convenient way to construct multifunctional integrated optical devices on a single planar device.

Improvement of contact grating device for efficient terahertz wave generation using bi-angular filter

We have proposed an improved contact grating device for generating terahertz waves efficiently and have succeeded in developing the device with a very high diffraction efficiency and a wide spectral width. This device has a bi-angular filter and a Fabry–Perot-type structure, which are composed of dielectric multilayers. The bi-angular filter is designed to reflect the 0th-order wave and transmit the–1st-order diffraction wave. Numerical calculations indicate that the new device has a maximum diffraction efficiency over 99% and a spectral width of approximately 20 nm. We measured a high efficiency of 90% over a broad spectral range using a fabricated device.

Effects of structure parameters on high-order diffraction suppression of quasi-periodic gratings

We introduce the design and implementation of quasi-periodic gratings for high-order diffraction suppression. The effects of hole shape (circle, rectangle, diamond, and hexagon) and location distribution on the diffraction properties are investigated. We theoretically and experimentally demonstrate that the quasi-triangle array with hexagonal holes is highly advantageous for suppressing high-order diffractions. Additionally, the quasi-periodic location distribution also helps to suppress high-order diffraction. Remarkably, the analytical results show that the 1st, 2nd, 3rd, 4th, 5th, and 6th order diffractions can be completely suppressed for the special structure parameters of the quasi-periodic gratings, and the 7th order diffraction intensity is as low as 2.2&#x00D7;10&#x2212;5 of the 1st order. The experimental results show there exist only 0th and &#x00B1;1st order diffraction peaks along the &#x03BE; axis, which qualitatively agree with the theoretical and numerical predictions. Compared with the traditional 1&#x2236;1 grating, the quasi-triangle array with hexagonal holes can effectively suppress high-order diffractions. We except the quasi-periodic gratings may find significant applications in high-accuracy wide spectral measurement ranging from the far infrared to the x-ray regions.

Micro-Grating Array-Enabled Power Efficiency Improvement for a DMD-Based Optical Switch

Digital micro-mirror device (DMD)-based optical switch can dynamically change the channels reallocation and provide flexibility in optical networking with the advantages of fast time response and scalable port number. However, the DMD as a binary diffraction device has a limited efficiency of 10.1% at the +1st diffraction order. Here we propose and demonstrate a DMD-based optical switch with improved efficiency enabled by a blazed micro-grating array. The blazed micro-grating array is designed and fabricated to diffract and make use of the wasted −1st order beams of the DMD. Using this device, we achieve ~2 dB efficiency improvements for a $2\times 2$ optical switch with all switching states. We experimentally demonstrate high speed switching of channels carrying 15 and 30 Gb/s ON-OFF keying signals. The micro-grating array has the potential to develop for the DMD-based optical switch with multiple channels.

Fabrication of optical vortex lattices based on holographic polymer-dispersed liquid crystal films.

This Letter demonstrates optical vortex lattices based on holographic polymer-dispersed liquid crystal (HPDLC) films. The fabrication method uses a phase-only reflective spatial light modulator with numerically calculated phase profiles loaded on it to simplify multi-helical-wave interference. The beam profiles of the diffraction beams are simulated using the Fourier transform and compared with experimental results. The topological charges of the 1st-order diffraction beams reconstructed from the HPDLC films are examined using a Michelson interferometer.

Reverse design for diffraction gratings by modal method

A novel method for reverse design of the rectangular-groove dielectric surface-relief grating by modal method is presented. The principle of the reverse design method is the excitation and coupling between the propagating modes in grating. When the modes 0 and 1 are transmission through the grating, the phase difference is accumulated. By adjusting the cumulative phase difference between the modes 0 and 1, the energy can be reallocated between the − 1st and 0th order diffraction light. Thereby the diffraction efficiency of the grating − 1st and 0th order are adjusted. By using these reverse design method, we analyze the design of the beam splitter and blazed grating. As an example, a − 1st transmitted order blazed grating has been designed by reverse design method. The comparative results have shown that the geometrical parameters of the grating calculated by modal method agree well with the results simulated by the rigorous couple-wave analysis (RCWA).

Versatile and compact wide-range VUV spectrometer for quantitative measurements

Main parameters of a new scheme of a compact VUV grazing incidence spectrometer based on a plane amplitude diffraction grating are considered. The spectrometer will allow simultaneous detection of spectra at the +1st order diffraction edge with a sufficiently high (λ/δ λ ∼ 150) spectral resolution and in the –1st order with a moderate resolution (λ/δ λ ∼ 15 – 30), but in a very wide (5 – 200 nm) spectral range. The use of such a spectrometer is promising for measuring the absolute radiation yield in these spectral regions, which is necessary for the diagnostics and control of plasma radiation sources, including those intended for projection EUV nanolithography.

Analysis of spurious diffraction orders of computer-generated hologram in symmetric aspheric metrology.

Computer-generated hologram (CGH) has been widely used as a wavefront compensator in symmetric aspheric metrology. As a diffractive element, it generates different diffraction orders, but only the 1st-order diffraction is used to test aspheric surface. The light from spurious diffraction orders (SDO) will produce many high-frequency fringes in interferogram and reduce measurement accuracy. In this paper, we regard the CGH null system as an imaging system and develop an aberration model in Seidel formalism to analyze the SDO. This model has the advantage to address the difference between the SDO (k1, k2) and (k2, k1). We consider the effect of the pupil distortion so that our model can analyze the SDO with a large pupil distortion. We derive the condition to ensure the 2nd-order and 4th-order aberrations have the same sign and calculate the minimum defocused distance (power carrier frequency) of CGH. According to the marginal-ray heights (h1andh3) on the CGH in the first and second passes, we determine the condition that the SDO covers the whole CGH in the second pass. We analyze the SDO of 4 CGH designs and compare the results from our aberration model with these from real ray trace. These results validate that our aberration model is feasible whether the aspheric part is convex or concave and whether CGH is inside or outside the focus of the transmission sphere.

Femtosecond laser induced damage of pulse compression gratings

Laser induced damage of Au-coated gratings (ACG) and metal multilayer dielectric gratings (MMDG) for pulse compression were measured using 800±35nm femto-laser with pulse width of 30.2fs. The -1st order diffraction efficiency of the ACG is over 90% in wavelength range from 700 to 1000nm. The MMDG has a 148nm bandwidth (750–897nm) with -1st order diffraction efficiency greater than 90%. The laser damage experiment on grating samples was performed in air for single-shot damage. The single-shot damage threshold of the ACG and MMDG was determined to be 0.32±0.02J/cm2 and 0.31±0.02J/cm2, respectively. The damage morphologies of the ACG revealed that the damage was attributed to the pinholes at the base of the grating pillars and theweak adhesion between metal layer and photoresist gratings layer. The damage feature combined with near field distribution of MMDG indicated that the damage was due to the nonlinear ionization process of the valence electrons in HfO2 film. According to analysis results, the laser damage resistance of the ACG can be enhanced through avoiding the appearance of pinholes and increasing adhesion between metal layer and photoresist layer. And for the MMDG, good performance of HfO2 film, low near field enhancement and single HfO2 grating structures may increase its laser damage resistance.

Evaluation of femtosecond laser damage to gold pulse compression gratings fabricated by magnetron sputtering and e-beam evaporation.

In this study, two kinds of Au-coated gratings (ACGs) with a period of 1740lines/mm were fabricated and evaluated. For these ACG samples, magnetron sputtering and e-beam evaporation were used as the gold deposition process, and the samples had a bandwidth of at least 170nm, with the -1st-order diffraction efficiency exceeding 90% around the center wavelength of 800nm. The one-on-one damage threshold of ACGs fabricated by magnetron sputtering and e-beam evaporation measured at a pulse width of 60fs was 0.59 J/cm2 and 0.43 J/cm2 in the case of the beam normal fluence, respectively. The typical damage morphology of the former type of samples was melting of the gold film, whereas those of the latter type were blisters and peeling off of the gold film. In theory, the electromagnetic field, temperature field, and thermal stress field distribution in the ACGs were calculated using the finite element method. We demonstrated that the adhesion between the gold film and the photoresist played an important role in determining the damage behavior. Thus, the laser resistance of ACG can be improved by enhancing the adhesion between the gold film and the photoresist, and magnetron sputtering was an alternative method to obtain ACGs with much better adhesion.

Two-dimensional gratings of hexagonal holes for high order diffraction suppression.

We propose two-dimensional gratings comprised of a large number of identical and similarly oriented hexagonal holes for the high order diffraction suppression. An analytical study of the diffraction property for such gratings, based on both square and triangle arrays, is described. The dependence of the high order diffraction property on the hole shape and size is investigated. Notably, theoretical calculation reveals that the 2nd, 3rd and 4th order diffractions adjacent to the 1st order diffraction can be completely suppressed, and the 5th order diffraction efficiency is as low as 0.01%, which will be submerged in the background noise for most practical applications. The 1st order diffraction intensity efficiency 6.93% can be achieved as the hexagonal holes along y-axis connect with each other. For the case of b=Py/3, the 1st order diffraction intensity efficiency is 3.08%. The experimental results are also presented, confirming the theoretical predictions. Especially, our two-dimensional gratings have the ability to form free-standing structures which are highly desired for the x-ray region. Comparing with the grating of the square array, the grating of the triangle array is easy to be fabricated by silicon planar process due to the large spacing between any two adjacent holes. Our results should be of great interest in a wide spectrum unscrambling from the infrared to the x-ray region.

High order diffraction suppression by quasi-periodic two-dimensional gratings

We propose quasi-periodic two-dimensional gratings comprised of a large number of circular holes for the high order diffraction suppression. By using Kirchhoff’s diffraction theory, we analytically investigate the diffraction property of the grating and optimize the structure parameters to suppress the high order diffractions. We analyze the dependence of the high order diffractions on the hole location and size. Notably, theoretical analysis reveals that the 3rd and even order diffractions can be completely suppressed, and the 5th order diffraction is as low as 0.02% of the 1st order diffraction, thereby allowing to submerge in the background noise for most practical applications. The desired diffraction pattern containing the 0th and ± 1st order diffractions results from the constructive interference of lights from different holes, which locate according to some statistical law distribution. The experimental results are also presented, confirming the theoretical predictions. Especially, our gratings have two advantages: the ability to form free-standing structures and large tolerance up to ± 10% deviation of the hole size. The former is highly desired for the x-ray and extreme ultraviolet regions, while the latter ease the fabrication difficulties of the current planar silicon technology. Our results should possess broad potential applications in a wide spectrum unscrambling from the infrared to the x-ray region.