All-dielectric reflection gratings: a study of the physical mechanism for achieving high efficiency

The physical mechanism for the all-dielectric reflection gratings to achieve high efficiency in the -1st-order Littrow mounting is studied. The all-dielectric gratings consist of two parts, a surface-relief grating and a highly reflecting dielectric stack. The surface-relief grating sits on top of the reflecting stack. A simple analytical expression for diffraction efficiency is obtained in terms of the S-matrix elements of the two parts. By analyzing the expression we show that the diffraction can be interpreted as the interference of a symmetric wave and an antisymmetric wave. The conditions for achieving high diffraction efficiency are also identified. The analytical results are illustrated by numerical computations.     

Wavelength response of waveguide volume grating couplers for optical interconnects

The wavelength response of a waveguide volume grating coupler (WVGC) is analyzed for coupling light from a slab waveguide into the superstrate. A leaky-mode approach is used in conjunction with rigorous coupled-wave analysis. A quantitative theoretical study of the effect of index modulation, waveguide index, and grating thickness on the wavelength bandpass of a WVGC is also presented. The FWHM wavelength bandpasses found for high-efficiency couplers range from 173 to 525 nm. The various Bragg conditions that can be used in designing a WVGC are also presented and compared. The use of the propagation constant of the mode being outcoupled as the incident wave vector in the Bragg condition is shown to produce the highest coupling efficiency.     

Effective grating theory for resonance domain surface-relief diffraction gratings

An effective grating model, which generalizes effective-medium theory to the case of resonance domain surface-relief gratings, is presented. In addition to the zero order, it takes into account the first diffraction order, which obeys the Bragg condition. Modeling the surface-relief grating as an effective grating with two diffraction orders provides closed-form analytical relationships between efficiency and grating parameters. The aspect ratio, the grating period, and the required incidence angle that would lead to high diffraction efficiencies are predicted for TE and TM polarization and verified by rigorous numerical calculations.     

Infrared quarter-wave reflection retarders designed with high-spatial-frequency dielectric surface-relief gratings on a gold substrate at oblique incidence

One- and two-dimensional high-spatial-frequency dielectric surface-relief gratings on a Au substrate are used to design a high-reflectance quarter-wave retarder at 70° angle of incidence and 10.6-μm light wavelength. The equivalent homogeneous anisotropic layer model is used. It is shown that equal and high reflectances (>98.5%) for the p and the spolarizations and quarter-wave retardation can be achieved with two-dimensional ZnS surface-relief gratings. Sensitivities to changes of incidence angle, light wavelength, grating filling factor, and grating layer thickness are considered.     

反射型阶梯光栅的特性分析

衍射效率是评价二元光学器件质量性能的重要指标之一.针对反射性阶梯光栅,利用几何方法计算出斜入射情况下光束在台阶边缘的光程差的分布情况,根据多缝夫琅和费衍射推导出反射型阶梯光栅的衍射光强表达式.并在此基础上,讨论了台阶数N取2和N趋向于无穷两种极限情况下阶梯光栅光强公式的变化情况,得到区别于一般文献所表达的衍射效率公式.初步试验表明,反射型阶梯光栅的衍射效率与台阶数、蚀刻深度与入射波长的比值均有密切相关.     

Finite-number-of-periods holographic gratings with finite-width incident beams: analysis using the finite-difference frequency-domain method

The effects of finite number of periods (FNP) and finite incident beams on the diffraction efficiencies of holographic gratings are investigated by the finite-difference frequency-domain (FDFD) method. Gratings comprising 20, 15, 10, 5, and 3 periods illuminated by TE and TM incident light with various beam sizes are analyzed with the FDFD method and compared with the rigorous coupled-wave analysis (RCWA). Both unslanted and slanted gratings are treated in transmission as well as in reflection configurations. In general, the effect of the FNP is a decrease in the diffraction efficiency with a decrease in the number of periods of the grating. Similarly, a decrease in incident-beam width causes a decrease in the diffraction efficiency. Exceptions appear in off-Bragg incidence in which a smaller beam width could result in higher diffraction efficiency. For beam widths greater than 10 grating periods and for gratings with more than 20 periods in width, the diffraction efficiencies slowly converge to the values predicted by the RCWA (infinite incident beam and infinite-number-of-periods grating) for both TE and TM polarizations. Furthermore, the effects of FNP holographic gratings on their diffraction performance are found to be comparable to their counterparts of FNP surface-relief gratings.     

Efficiency-enhanced third-order grating coupler

A third-order grating coupler with a grating period 3 times that of a first-order grating is discussed in terms of efficiency enhancement. A reflection film is integrated between the optical buffer layer and the substrate beneath the grating-guiding core. The power-distribution ratio for each diffracted wave depends on the optical buffer layer's thickness because of interference effects. The thickness is determined to suppress first- and second-order diffraction and to enhance the power distribution to the output air-radiation wave generated by third-order diffraction. A demonstrator was designed and examined at a wavelength of 0.82 mum. The measured output coupling efficiency was 40%, whereas the theoretical prediction was 60%.     

Embossed Bragg Gratings Based on Organically Modified Silane Waveguides in InP

Considering the large variety of applications for optical glass waveguide gratings, the effective production method of embossing for micropatterning, and the unique advantages of InP-based materials, we expect that hybridization of embossed optical glass waveguide gratings and InP substrates will inevitably lead to new applications in integrated optics. We present our preliminary results of research toward the development of solgel-derived glass waveguide gratings made by embossing on InP. Theoretically, the dependence of the stop-band FWHM and transmission contrast of the grating filter on the grating length, and the relationship between the Bragg grating's reflective wavelength and the dopant concentration in the solgel waveguide, are obtained. Experimentally, using organically modified silane, we solve the problem of mismatching of SiO(2) and InP, and successfully fabricate an embossed glass grating with a second-order Bragg reflection wavelength of 1580 nm and a FWHM of 0.7 nm fabricated upon a solgel waveguide on an InP substrate.     

单光纤光栅实现窄带全光纤反射器的分析

提出了一种由单个光纤光栅和一个光纤方向耦合器组成的新型全光纤反射器,推导出了当光栅为均匀 Bragg 光栅、器件任意端口输入时,任何一端口的输出解析式。分析表明器件具有法布里-珀罗腔干涉仪的特点,耦合器的耦合比系数类似于法布里-珀罗腔的反射率, 耦合比系数越大,输出光谱半高全宽度(FWHM)越窄, 消光比越好。当耦合比系数大于 0.8 时,FWHM 可以窄到0.02nm,消光比大于 0.9。如果光栅是“强”耦合,器件具有均匀分布的多通道梳状输出特性;光栅为“弱”耦合时,则能实现 FWHM 小于 0.02nm 的单频输出。器件只需单个光栅,克服了制作两个完全相同光栅的困难。     

Narrowband, polarization-independent free-space wave notch filter

A two-dimensional-corrugated-slab-waveguide add/drop filter providing 100% resonant reflection at 1.55 microm wavelength for both TE and TM polarizations with identical FWHM is designed. The fabricated device exhibits a reflectivity spectrum of more than 95% peak reflection for both polarizations at 1.537 microm. The coupling scheme involves the TE0 guided mode only; it is made relatively tolerant by means of a double-sided crossed grating.     

Diffraction efficiency of a grating coupler for an array illuminator

The diffraction efficiency of a grating coupler having a surface-relief grating is calculated by the use of coupled-wave theory. The grating couplers are fabricated to examine the validity of the calculated result. The dependence of the measured diffraction efficiency on the groove depth of the grating coupler agrees well with the calculated results. The array illuminator, which emits 10 and 20 beams with equal intensity, is designed and fabricated through the use of these numerical results. The uniformity error of the output beam caused by the error of the diffraction efficiency is also discussed.     

Preferential-order waveguide grating couplers: a comparative rigorous analysis using the finite-difference time-domain method

We rigorously analyze and compare preferential-order waveguide grating output couplers using the finite-difference time-domain method in the total-field/scattered-field formulation for TE and TM polarizations. Four kinds of preferential-order grating couplers are studied: volume holographic grating couplers, slanted parallelogrammic surface-relief grating couplers, double-corrugated surface-relief grating couplers, and reflecting-stack surface-relief grating couplers. The outcoupling efficiencies and branching ratios of the couplers, revealing their preferentiality, are calculated and compared with the rigorous coupled-wave analysis leaky-mode method. In addition, their performance is examined in terms of the main design parameters and the excitation wavelength.     

Design and fabrication of binary slanted surface-relief gratings for a planar optical interconnection

We propose the use of binary slanted surface-relief gratings with parallel-groove walls as input and output couplers in a planar optical interconnect. Parametric optimization of cascaded output couplers is employed to design an interconnect consisting of N output couplers producing a uniform intensity distribution with a high efficiency that may be realized in one lithographic etching step. The sensitivity of a N = 4 interconnect to various fabrication errors is analyzed. We demonstrate the operation of a slanted surface-relief grating manufactured with electron-beam lithography and reactive-ion etching for an operating wavelength of lambda = 0.633 mum.     

Binary blazed reflection gratings

A reflection grating with a binary surface profile is presented that has high diffraction efficiency. The measured intensity for the + 1st diffracted order was 77%. The binary grating is composed of a minilattice with feature sizes comparable with the wavelength of the incident light. The overall structure is designed in such a way that it imitates a conventional blazed grating. The grating also has interesting polarization properties. The main part of the TE-polarized light is diffracted into the 1st diffracted order, and most of the TM-polarized light remains in the 0th diffracted order. The measurements of the grating are compared with rigorous diffraction theory and found to be in reasonable agreement.     

Design and Fabrication of a Hybrid Diffractive Optical Device for Multiple-Line Generation over a Wide Angle

A new hybrid optical device that is capable of splitting a monochromatic laser beam into an arbitrary number of lines over a wide angle is presented. It consists of a binary surface-relief computer-generated phase hologram and a continuous parabolic surface-relief grating. In this device the phase hologram serves to generate three small, parallel lines while the continuous parabolic surface-relief phase grating acts as an array of diverging parabolic lenses to widen these lines. The binary surface-relief was generated into one side of a quartz substrate through a plasma-etching process, and the parabolic profile was generated into a thick photoresist deposited on the other side of the quartz substrate. Calculations showed that a diverging parabolic lens with a f-number of 0.5 would deliver the desired optical pattern of multiple beams distributed over 90 degrees . A surface-relief depth of 6.0 mum was calculated with consideration of the phase distributions of such lens. The parabolic profiles were fabricated in a 10-mum-thick photoresist, by use of a contact exposure through a mask with a space pattern of repetitive 4- and 6-mum lines. He-Ne laser light was passed through a device that generated three parallel lines over a 90 degrees angle. The resulting diffraction patterns were characterized, and a satisfying result was obtained. The resulting multiple-line pattern can be used in robot vision and other applications.     

Rectangular surface-relief transmission gratings with a very large first-order diffraction efficiency (~95%) for unpolarized light

Computer optimization shows that the first-order diffraction efficiency of a lossless-transmission surface-relief grating with a rectangular surface profile can be made very large (~95%) simultaneously for light of TE and TM polarizations incident near the Bragg angle by the proper choice of the fill factor. The case for visible light incident close to the Bragg angle on unslanted gratings with periodicities corresponding to Bragg angles of 30 degrees , 37.5 degrees , and 45 degrees is presented. The refractive index of the grating material was chosen in the range between 1.2 and 2.     

Interferometric fabrication of modulated submicrometer gratings in photoresist

Interferometric recording is applied to the fabrication of modulated submicrometer gratings in photoresist.High diffraction efficiency requires optimized recording conditions, which are obtained by the use of an on-axis continuous surface-relief grating for the generation of the object beam. The optimized phase function is copied into the resist layer by means of a self-aligned two-step recording process with an intermediate copy in a volume photopolymer hologram. As a result, we demonstrate high carrier frequency surface-relief off-axis fan-out gratings for illumination in transmission with visible light.     

On-axis beam extinction through diffraction design and analysis

To optimize the functions of the surface-relief diffractive optical elements for optical limiters and other applications, we present a systematic design and analysis with numerical illustrations of the transmission properties of different surface-relief phase gratings and Fabry-Perot elements. The spectral response and the tolerance of fabrication errors have been included. An analysis shows that the blazed grating and the echelon grating, a multilevel element as a substitute of the blazed grating, can make the on-axis transmittance very low (less than 1% with one grating) over the broad visible band with a large tolerance of fabrication errors. The results are highly significant for the design of optical-limiting devices.     

Effects of process errors on the diffraction characteristics of binary dielectric gratings

The effects of fabrication errors on the predicted performance of surface-relief phase gratings are analyzed with a rigorous vector diffraction technique. For binary elements, errors in the dimensions of the profile [depth, linewidth (fill factor), and grating period], as well as errors in the shape of the profile, are investigated. It is shown that the dimension errors do not have a significant effect on grating performance when the grating is designed for either maximum or minimum diffraction efficiency. A trapezoid is used to model the shape error of the profile. For the first time, design rules that significantly reduce the effects of any shape error are presented.     

Design of a high-efficiency volume grating coupler for line focusing

A volume grating for outcoupling and line focusing of waveguided infrared light is designed and optimized. A local grating vector approach is used in combination with the rigorous coupled-wave analysis. By design, this volume grating coupler is holographically constructed on top of a waveguide by the interference of two coherent 364-nm ultraviolet waves formed with two aberration-optimized cylindrical lenses. This focusing coupler exhibits preferential-order coupling (92.9%) into the cover as well as very low focal intensity side lobes. This is accomplished through a chirped, slanted-fringe volume grating with a designed spatial variation in the attenuation coefficient (describing the outcoupling of the guided mode) along the length of the grating. This is achieved by a specific variation in the grating slant angle along the grating length. By design, the 1000-mum-length coupler focuses an 850-nm infrared guided wave to a line with an intensity FWHM of 3.32 mum and a 90% power width of 5.53 mum at a focal distance of 4 mm directly above the grating. Its performance is compared with that of a corresponding electron-beam-written surface-relief coupler design.