Quasi-free-space optical coupling between diffraction grating couplers fabricated on independent substrates

Optical coupling between preferential-order volume diffraction grating couplers fabricated on independent substrates is demonstrated. The coupling efficiency between gratings is quantified as a function of both grating and waveguide fabrication technology and relative angular position of the two substrates. A maximum grating-to-grating coupling efficiency of 31% is reported for coupling between two nonoptimized, nonfocusing, unpatterned volume grating couplers.     

Fast and accurate modeling of waveguide grating couplers

A boundary variation method for the analysis of both infinite periodic and finite aperiodic waveguide grating couplers in two dimensions is introduced. Based on a previously introduced boundary variation method for the analysis of metallic and transmission gratings [J. Opt. Soc. Am. A 10, 2307, 2551 (1993)], a numerical algorithm suitable for waveguide grating couplers is derived. Examples of the analysis of purely periodic grating couplers are given that illustrate the convergence of the scheme. An analysis of the use of the proposed method for focusing waveguide grating couplers is given, and a comparison with a highly accurate spectral collocation method yields excellent agreement and illustrates the attractiveness of the proposed boundary variation method in terms of speed and achievable accuracy.     

Efficient coupling into polymer waveguides by gratings

Investigations of highly efficient grating couplers for polymer slab and strip waveguides fabricated by electron-beam lithography are reported. A maximum input efficiency of 67% is achieved. The electron-beam direct-writing technique allows one to replicate the original gratings into polymer substrates by embossing. An all-polymeric optical chip with efficient grating couplers is demonstrated. Waveguide grating couplers with blazed profile and variable grating depth are investigated. Thus, the intensity distribution of the outcoupled light is matched to a Gaussian-like profile. A focusing blazed grating that couples the light with an efficiency of 42% into a polymer strip waveguide is reported. A curvature correction of the grating lines allows one to improve the focusing properties.     

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.     

High-efficiency input coupling into optical waveguides using gratings with double-surface corrugation

Waveguide grating couplers that have surface corrugation on both boundaries of the waveguide were fabricated by the deposition of waveguide material at high-vacuum pressures onto a surface-relief grating etched into the substrate. A lateral shift between the two gratings along the direction of the common grating vector was created during the waveguide deposition when the substrate normal was tilted with respect to the direction of material deposition. A series of waveguide thicknesses having an identical angle of deposition were examined to observe the effect of the waveguide thickness, and corresponding lateral shift, on the branching ratio and input-coupling efficiency. Branching ratios of above 98% and input-coupling efficiencies near the theoretical limit for an incident Gaussian beam were obtained.     

Design, fabrication, and performance of preferential-order volume grating waveguide couplers

Both a nonfocusing and a focusing preferential-order volume grating waveguide coupler were designed, fabricated, and tested. These volume grating couplers are designed to outcouple a 633-nm wave guided in an adjacent polyimide waveguide film. The slanted-fringe volume gratings are recorded holographically by the interference of two 364-nm waves. The dynamics of the holographic photopolymer HRF600X001 are investigated in relation to the interaction with the guided wave. The fabricated couplers exhibited a preferential coupling of 98%, a spatial coupling rate of 3.6 mm(-1), and a coupling efficiency of 95%. The focusing grating coupler focused the outcoupled beam to a focal line with a full width at half-maximum of 10.49 mum located 25 mm above the grating.     

Does photosensitivity pave the way towards the fabrication of miniature coherent light sources in inorganic glass waveguides?

Photosensitivity designates the ability to permanently change the refractive index of a glass by optical processing. The phenomenon allows the fabrication of numerous phase structures, the simplest of which is the Bragg grating obtained by photoimprinting a periodic index modulation within the material. Bragg gratings have changed the way in which optical fibre (or planar waveguide) lasers are now used. Distributed Bragg Reflector (DBR) or Distributed Feed Back (DFB) lasers, when intracore Bragg gratings are used for linear cavity feedback, are commonly fabricated in rare earth doped optical silica-based fibres. On the other hand, photosensitivity can also result in effects which can prove to be detrimental to the fabrication of miniature coherent light sources. The paper will cover some of the advances that have been made in improving the photosensitivity of inorganic glasses, in searching new photosensitive materials and in characterizing Bragg grating properties relevant to laser applications.     

Negligible birefringence in dual-mode ion-exchanged glass waveguide gratings

Polarization dependence of UV-written Bragg gratings in buried ion-exchanged glass waveguides is investigated. A polarization-dependent shift in Bragg wavelength of less than 0.02 nm is measured, both for the even and the odd modes of a laterally dual-mode waveguide. The measured wavelength shift corresponds to a waveguide birefringence of the order of 10(-5), which is negligible for most applications in optical communications. It is observed that the UV-induced birefringence is small, within the limits of the measurement accuracy. The thermal stability of the fabricated gratings is also very good. The results are of particular importance for devices considered here since they require a polarization-independent mode-converting waveguide Bragg grating. Polarization-independent performance of these gratings enables the fabrication of a new class of integrated optical devices for telecommunication applications.     

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.     

Use of grating theories in integrated optics.

Recently [Opt. Lett. 25, 1092 (2000)], two of the present authors proposed extending the domain of applicability of grating theories to aperiodic structures, especially the diffraction structures that are encountered in integrated optics. This extension was achieved by introduction of virtual periodicity and incorporation of artificial absorbers at the boundaries of the elementary cells of periodic structures. Refinements and extensions of that previous research are presented. Included is a thorough discussion of the effect of the absorber quality on the accuracy of the computational results, with highly accurate computational results being achieved with perfectly matched layer absorbers. The extensions are concerned with the diversity of diffraction waveguide problems to which the method is applied. These problems include two-dimensional classical problems such as those involving Bragg mirrors and grating couplers that may be difficult to model because of the length of the components and three-dimensional problems such as those involving integrated diffraction gratings, photonic crystal waveguides, and waveguide airbridge microcavities. Rigorous coupled-wave analysis (also called the Fourier modal method) is used to support the analysis, but we believe that the approach is applicable to other grating theories. The method is tested both against available numerical data obtained with finite-difference techniques and against experimental data. Excellent agreement is obtained. A comparison in terms of convergence speed with the finite-difference modal method that is widely used in waveguide theory confirms the relevancy of the approach. Consequently, a simple, efficient, and stable method that may also be applied to waveguide and grating diffraction problems is proposed.     

Theoretical performance of Bragg gratings based on long-range surface plasmon-polariton waveguides

A plasmon-polariton Bragg grating (PPBG) concept, based on the propagation of the long-range ss0b mode in structures comprising a thin metal film of finite width embedded in a homogeneous background dielectric, is discussed theoretically. The PPBGs are operated in an end-fire arrangement with access plasmon-polariton waveguides or optical fibers being directly butt-coupled to their input and output ports. A model for the PPBGs, which was recently proposed and validated experimentally for third order structures, is used to generate theoretical results describing their expected performance for various architectures. First order uniform periodic, interleaved, and apodized grating structures are considered and compared. Third order uniform periodic designs are also considered. The gratings investigated are based on a 20 nm thick Au film embedded in SiO2 and have a Bragg wavelength near 1550 nm. First order uniform periodic gratings provide the strongest reflection, with a maximum reflectance of about 97% being achievable over a length of a few millimeters and over a full width at half-maximum bandwidth of about 0.8 nm. The off-resonance insertion loss of the gratings can be as low as a few decibels. Specific Bragg wavelengths can easily be attained using interleaving without requiring extraordinary resolution from the fabrication process. Apodized designs providing low sidelobe levels are also investigated.     

Optimization of the parallelogrammic grating diffraction efficiency for normally incident waves

The diffraction directivity of parallelogrammic gratings with second-order pitch is examined for a plane wave normally incident upon a corrugated waveguide structure. The three diffracted components are assumed to be in the form of guided waves, which permits a self-consistent calculation. The efficiencies of diffraction into the horizontal components are obtained. Also, the dependence of efficiency on grating thickness, waveguide thickness, grating pitch, and angle of inclination is determined. The approach provides a useful simulation tool for optimizing the design parameters for waveguide couplers with an orthogonal source.     

Narrow-band Resonant Grating Waveguide Filters Constructed with Azobenzene Polymers.

Resonant grating waveguide structures were used to fabricate narrow-bandwidth optical filters. Azopolymer films were deposited on top of slab waveguides, and surface relief gratings were optically inscribed on them to be used as couplers. This technique is a simple one-step process and produces efficient gratings with high accuracy. Sharp resonant peaks are observed in the transmission and the reflection spectra of these structures. The thickness and the index of refraction of the waveguide can be accurately determined from these resonances by use of modal theory. These parameters are then used in the design of an optical filter. Bandwidths of less than 1 nm and a decrease in transmitted signal of 60% are reported. Measurement of these values was limited by the divergence of the probe beam.     

Hybrid silica–polymer structure for integrated optical waveguides with new potentialities

We report some features of a new waveguide structure in integrated optic providing new potentialities. We propose to use specific polymers as overlayer of ridge silica waveguides. This method can be used to finely tune the superstrate refractive index in order to adjust performances of components. In this paper, we give as examples, the auto-stabilization of integrated Bragg gratings and also, first experiments to realize thermo-optic directional couplers which can be achieved by combining these two materials in the waveguide structure.     

Optimization of nonbinary slanted surface-relief gratings as high-efficiency broadband couplers for light guides

We propose and investigate the use of slanted surface-relief gratings with nonbinary profiles as high-efficiency broadband couplers for light guides. First, a Chandezon-method-based rigorous numerical formulation is presented for modeling the slanted gratings with overhanging profiles. Then, two typical types of slanted grating couplers--a sinusoidal one and a trapezoidal one--are studied and optimized numerically, both exhibiting a high coupling efficiency of over 50% over the full band of white LED under the normal illumination of unpolarized light. Reasonable structural parameters with nice tolerance have been obtained for the optimized designs. It is found that the performance of the couplers depends little on the grating profile shape, but primarily on the grating period and the slant angle of the ridge. The underlying mechanism is analyzed by the equivalence rules of gratings, which provide useful guidelines for the design and fabrication of the couplers. Preliminary investigation has been performed on the fabrication and replication of the slanted overhanging grating couplers, which shows the feasibility of fabrication with mature microfabrication techniques and the perspective for mass production.     

Optical add-drop multiplexers based on the antisymmetric waveguide Bragg grating

A novel optical add-drop multiplexer (OADM) based on a null coupler with an antisymmetric grating was designed and experimentally demonstrated. The antisymmetric grating exclusively produces a reflection with mode conversion in a two-mode waveguide. This improves the performance compared with previous demonstrations that used tilted Bragg gratings. Our design minimizes noise and cross talk produced by reflection without mode conversion. In addition, operational bandwidth and, versatility are improved while the compactness and simplicity of the null coupler OADM are maintained.     

Effect of fabrication errors in channel waveguide Bragg gratings

The spectral performances of nonideal rectangular Bragg gratings, integrated in a rib waveguide, are analyzed by a multilayer approach based on the effective-index method. The effects of errors on the photolithographic definition of the grating, that is, period and shape, and of errors on the control of etching depth are investigated. Also the influence of the stitching error, which is unavoidable when the grating is realized by means of electron-beam photolithography, is addressed. A novel analytical approach that extends coupled-mode theory to the analysis of real gratings is also presented.     

Optical demultiplexer using a silicon concave diffraction grating

A demultiplexer composed of a concave diffraction grating and a multimode slab waveguide is attractive since it has many advantageous features. However, this type of demultiplexer has had high demultiplexing losses until now, because the concave diffraction gratings used had poor diffraction efficiency. A silicon concave diffraction grating has been developed to overcome this problem, manufactured by cylindrically bending a thin silicon plane diffraction grating. The diffraction efficiency of this grating was 82% at a blaze wavelength. The five-channel demultiplexer was assembled with this grating as well as with a multimode slab waveguide and a fiber array. Its branching loss was in the 1.4-1.8-dB range.     

Fabrication and comprehensive modeling of ion-exchanged Bragg optical add-drop multiplexers

Optical add-drop multiplexers (OADMs) based on asymmetric Y branches and tilted gratings offer excellent-performance in wavelength-division multiplexed systems. To simplify waveguide fabrication, ion-exchange techniques appear to be an important option in photosensitive glasses. Optimum OADM performance depends on how accurately the waveguide fabrication process and tilted Bragg grating operation are understood and modeled. Results from fabrication and comprehensive modeling are compared for ion-exchange processes that use different angles of the tilted grating. The transmission and reflection spectra for the fabricated and simulated OADMs show excellent agreement. The OADM's performance is evaluated in terms of the measured characteristics of the Y branches and tilted gratings.     

Analysis of fiber bragg gratings by a side-diffraction interference technique

A new nondestructive, noncontact, and sensitive technique for fiber Bragg grating geometry and index-fault location measurements is presented. Two plane-wave probe laser beams are incident upon the grating from the side at angles that satisfy the Bragg-reflection condition. An interference pattern is formed behind the fiber between the first-order diffracted beam (from one probe beam) and the zero-order transmitted beam (from the second probe beam). The axial grating index modulation and the grating period are functions of the fringe visibility and the fringe period, respectively. The method is sensitive and is applicable even in the case of relatively weak gratings. Unchirped and chirped Bragg gratings have been studied with the proposed technique. We demonstrate accuracies of 1 x 10(-4) for measurement of the index modulation and 0.01 nm for measurement of the period. As well as for the analysis of most already-fabricated gratings, this technique is useful for in situ analysis of a long fiber Bragg grating as such a grating is translated along its axis during the fabrication process.