Digital volume gratings

An optical element constructed by stacking a set of binary-phase grating sheets can simulate the functions of optically recorded volume gratings. Our electromagnetic numerical study also shows that if one of the grating sheets is replaced by another one with different grating period, power spectrum of the diffracted wave changes completely with extra diffraction orders. This property will claim strong advantage in security document applications. Analysis of alignment error reveals interesting phenomena concerning to how misalignment affects diffraction efficiency.     

Phase interpretation for polarization-dependent near-field images of high-density gratings

It has been described that the near-field images of a high-density grating at the half self-imaging distance could be different for TE and TM polarization states. We propose that the phases of the diffraction orders play an important role in such polarization dependence. The view is verified through the coincidence of the numerical result of finite-difference time-domain method and the reconstructed results from the rigorous coupled-wave analysis. Field distributions of TE and TM polarizations are given numerically for a grating with period d = 2.3λ, which are verified through experiments with the scanning near-field optical microscopy technique. The concept of phase interpretation not only explains the polarization dependence at the half self-imaging distance of gratings with a physical view, but also, it could be widely used to describe the near-field diffraction of a variety of periodic diffractive optical elements whose feature size comparable to the wavelength.     

Shape resonances in nested diffraction gratings

The diffraction problem of a plane wave impinging on a grating formed by nested cavities is solved by means of the modal method, for s and p polarization modes. The cavities are formed by perfectly conducting sheets that describe rectangular profiles. The electromagnetic response of the grating is analyzed, paying particular attention to the generation of resonances within the structure. The dependence of the resonances on the geometrical parameters of the grating is studied, and results of far and near field are shown. The results are checked and compared with those available in the literature for certain limit cases.     

Self-imaging with curved gratings

We analyze the near field behavior of binary amplitude gratings which present a curved profile. This configuration has an important application in rotary optical encoders. This kind of encoders is used to measure the angular displacement between two different parts of the devices. To our knowledge, its behavior in the near field has not been analyzed yet. We have found that Talbot effect is produced but the period of the self-images and Talbot distances change as we separate from the grating. We have fabricated a curved grating and have performed the experiment to corroborate the behavior theoretically found. This fact could be useful in systems that use Talbot effect to measure displacements, since the mechanical tolerances grow.     

Inverse symmetric Dammann gratings

Inverse symmetric Dammann grating is a special grating, whose transition points are reflection symmetric about the midpoint with inverse phase offset in one period. It can produce even-numbered or odd-numbered array illumination when the phase modulations are π or a specific value. Numerical solutions optimized by the steepest-descent algorithm for binary phase and multilevel phases with splitting ratio from 1 × 4 to 1 × 14 are given. Fabrication of 1 × 6 array without the zero-order intensity and 1 × 7 array with the zero-order intensity are made from the same amplitude mask. A 6 × 6 output without the crossed zero-orders was achieved by crossing two one-dimensional 1 × 6 inverse symmetric Dammann gratings. This grating may have potential value for practical applications.     

Power penalty of cascaded Bragg gratings in the presence of PMD and PDL

Considering the presence of birefringence in Bragg gratings, the spectral polarization mode dispersion (PMD) and polarization dependent loss (PDL) induced power penalty of eye opening is examined for a network with cascaded Bragg gratings. It is shown that when the birefringence in the grating is less than 10⁻⁵, the induced power penalty is less than 0.1 dB for a network with up to 30 cascaded Bragg gratings. However, when the grating birefringence is on the order of 10⁻⁴, the induced power penalty can be as high as 5.6 dB for a network with 14 cascaded Bragg gratings.     

Varied laser induced damage phenomena of gold coated gratings for pulse compression

In this paper, gold-coated gratings for pulse compression have been prepared and their laser damage experiments have been performed. Varied laser damage morphologies have been observed: when a 60 fs-pulsed laser with energy density slightly higher than the damage threshold was used, damage morphology with a characteristic of discrete distribution of small pits was appeared. These damage pits are linearly distributed at the junction of ridges and grooves. If the laser energy density is much higher than the damage threshold, the gold films was overall ablated and the grating structure disappeared. Besides, if the gold film has poor adhesion, it was peeled off. When a 450 ps-pulsed laser with energy density slightly higher than the damage threshold was used, part of grating ridges will be ablated and an obvious line exists between the ablated area and the unchanged area. In theory, the laser induced temperature field and stress field in gold-coated gratings were calculated based on the electromagnetic field using the finite element method. It is demonstrated that the temperature and thermal stress distribution characteristics are affected by the laser heating rate and the heat diffusion time (the calculated diffusion time ranges from 6 fs to 450 ps), which determines the laser damage characteristics. The possible damage drivers have electron hydrodynamic pressure, thermal ablation and thermal stress.     

Effect of recording conditions on the anisotropic diffraction of volume holographic gratings

The anisotropic Bragg diffraction of the volume holographic gratings in photorefractive crystals are investigated based on the model of anisotropic coupled-wave theory. The effect of the initial intensity ratio and the recording angles of the two recording waves on the anisotropic Bragg diffraction properties is discussed. It is shown that both the ratio of the initial intensity and the incident angles of the recording waves are selective action for the anisotropic Bragg diffraction efficiency of the volume holographic gratings, while these two recording conditions are not selective action for the isotropic Bragg diffraction. Furthermore, the Bragg phase matching condition of anisotropic diffraction is analyzed when the recording angles change.     

Optical filter based on subtractive dispersion planar reflective gratings

We have successfully designed, fabricated, and tested an optical filter based on cascaded planar reflective gratings. The device uses a combination of two grating elements arranged in a subtractive dispersion configuration. The first grating demultiplexes a 300 nm wide band and drops optical channels at 1490 and 1550 nm, commonly used in passive optical networks. The second grating completely counter-balances the dispersion properties of the first grating and ultimately yields zero dispersion in the output waveguide. Such a configuration allows the transmission of optical signals though the device in an ultra-wide band spanning 1250-1410 nm. The filter was manufactured using an industry standard silica-on-silicon process which was augmented with grating facet formation and metallization. In spite of using low refractive index contrast waveguides (0.82%), the device had a remarkably low footprint of only 0.21 cm². Applications of the device in passive optical networks are discussed.     

Configurable coarse wavelength division demultiplexers based on planar reflective gratings

Configurable coarse wavelength division multiplexing filters were realized using a planar reflective grating architecture utilizing small diffraction angles. The novel architecture yielded a 10-fold reduction in the chip size compared to previously reported filter configurations. The proposed design was manufactured using a standard silica-on-silicon process with a waveguide refractive index contrast of 0.82%. Polarization dependent losses of less than 0.2 dB were achieved without any post-processing steps. Fabricated filters showed insertion losses of 2.4 dB and remarkably broad free spectral ranges of more than 500 nm. The combination of single-mode input and multi-mode output guides resulted in box-like passband responses with bandwidth of 14.2 nm. Applications of the filters for integrated coarse wavelength division receivers and monitors are discussed.     

Use of steel substrates in diffractive optics: Near field of high surface quality steel tape gratings

Steel tape is used in optical applications due to its mechanical properties. However, roughness of steel surfaces affects to wave propagation. The effect can be observed using diffraction gratings with low periods. In such a case, self-images of the grating appear at certain periodic distances from the grating (Talbot planes). When standard steel is used, the contrast of Talbot self-images strongly decreases with the distance from the grating. In this work, we prove that controlling the surface quality of steel, it is possible to improve its optical behavior and, as a consequence, high quality surface steel represents a good choice for diffractive optics when the use of chrome-on-glass masks is not indicated. As an example, we have manufactured a diffraction grating over a high quality steel surface by means of an ablation process with a nanosecond pulsed laser. The contrast of the self-images for these gratings decreases very slowly with the distance, in comparison with the self-images obtained with standard steel tape gratings.     

Long-period fiber gratings fabricated with a CO2 laser beam and phase mask

A new holographic technique is proposed for fabricating long-period fiber gratings (LPGs) using a CO₂-laser and a phase mask. A CO₂ laser operating at 10.6 μm is incident normally on the phase mask and the diffracted interfering beams imprint a thermally induced periodic modulation into the cladding of the fiber placed behind the mask. Preliminary results of this technique are presented and discussed. An unusual self-tapered fiber LPG (STFLPG) is also presented.     

Transmission resonances of metallic compound gratings with subwavelength slits

Transmission metallic gratings with subwavelength slits are known to produce enhanced transmitted intensity for certain resonant wavelengths. One of the mechanisms that produce these resonances is the excitation of waveguide modes inside the slits. We show that by adding slits to the period, the transmission maxima are widened and, simultaneously, this generates phase resonances that appear as sharp dips in the transmission response. These resonances are characterized by a significant enhancement of the interior field.     

Investigation of transmission resonances on the one-dimensional metallic cylindrical gratings in THz frequency range

In the experiments of THz wave transmitting through the metallic cylindrical gratings fabricated by sub-wavelength brass wires, this paper reports that the discrepancy in the sharp resonances occurred as the grating perpendicular or parallel to the electric vector are observed. A simulation based on the finite difference time domain (FDTD) indicated that the enhanced transmission through the grating is attributed to the combined effects of surface plasmons and cavity modes in the perpendicular condition, while the cavity modes dominate the resonant transmission under the other conditions. Additional experimental data and calculated results show that ～1 enhanced coupling efficiency can be realized in some THz frequency, which could be applied to the design and improvement of various optoelectronic devices, or detection of biological molecule and powder samples, etc.     

High-power laser beam shaping by inseparable two-dimensional binary-phase gratings for surface modification of stamping dies

For surface modification of stamping dies, an inseparable two-dimensional binary-phase gratings is introduced to implement the wavefront transformation of high-power laser beams. The design and fabrication of the gratings are described in detail. Two-dimensional even sampling encoding scheme is adopted to overcome the limitations of conventional Dammann grating in the design of two-dimensional output patterns. High diffractive efficiency (>70%) can be achieved through the transformation of the Gaussian laser beam into several kinds of two-dimensional arrays in focal plan. The application of the binary-phase gratings in the laser surface modification of ductile iron is investigated, and the results show that the hardness and the wear resistance of the sample surface were improved significantly by using the binary-phase gratings.     

Diffraction of entangled particles by light gratings

We analyze the diffraction regime of the Kapitza–Dirac effect for particles entangled in momentum. The detection patterns show two-particle interferences. In the single-mode case we identify a discontinuity in the set of joint detection probabilities, associated with the disconnected character of the space of non-separable states. For Gaussian multi-mode states we derive the diffraction patterns, providing an example of the dependence of the light–matter interaction on entanglement. When the particles are identical, we can explore the relation between exchange and entanglement effects. We find a complementary behavior between overlapping and Schmidt’s number. In particular, symmetric entanglement can cancel the exchange effects.     

Design of high-efficiency diffraction gratings based on total internal reflection for pulse compressor

We present designs of high-efficiency compression grating based on total internal reflection (TIR) for picosecond pulse laser at 1053 nm. The setup is devised by directly etching gratings into the bottom side of a prism so that light can successfully enter (or exit) the compression grating. Dependence of the −1 order diffraction efficiencies on the constructive parameters is analyzed for TE- and TM-polarized incident light at Littrow angle by using Fourier modal method in order to obtain optimal grating structure. The electric field enhancement within the high-efficiency TIR gratings is regarded as another criterion to optimize the structure of the TIR gratings. With the criterion of high diffraction efficiency, low electric field enhancement and sufficient manufacturing latitude, TIR compression gratings with optimized constructive parameters are obtained for TE- and TM-polarized incident light, respectively. The grating for TE-polarized light exhibits diffraction efficiencies higher than 0.95 within 23 nm bandwidth and relatively low square of electric field enhancement ratio of 5.7. Regardless of the internal electric field enhancement, the grating for TM-polarized light provides diffraction efficiencies higher than 0.95 within 42 nm bandwidth. With compact structure, such TIR compression gratings made solely of fused silica should be of great interest for application to chirped pulse amplification (CPA) systems.     

Beam splitting, combining, and cross coupling through multiple superimposed volume-index gratings

We investigate the diffraction properties of multiple-superimposed index gratings from a vector synthetic viewpoint using coupled wave analysis with Bragg and non-Bragg readout. The vector synthetic gratings consist of two volume-index gratings with different grating wave vectors, which can be obtained in photorefractive materials, in optical fibers or in Bragg cells with two driving acoustic waves. This structure can realize beam splitting, beam combining, and beam cross coupling, etc. Analytic expressions for the diffraction efficiency as well as the amplitude of the waves involved are obtained. The results are presented and discussed.