Design of phased-array wavelength division multiplexers using multimode interference couplers

Novel designs for phased-array wavelength-division multiplexers based on self-imaging properties of multimode interference (MMI) couplers are presented. These devices, which operate on N equally spaced wavelength channels, consist of two MMI couplers connected by an array of N monomode waveguides. The MMI couplers function as power splitters/combiners, and the waveguide array is the dispersive element. The excellent characteristics of MMI couplers offer the possibility of designing small-size devices with low loss and with high uniformity among different channels. A general theoretical formulation for an N-channel multiplexer is presented, and a simple procedure for finding an optimum set of lengths for the array guides is given. We show that these multiplexers can function as N x N wavelength-selective interconnecting components. The simulated performance of three variations of a five-channel device, designed in a rib waveguide system, is given. It is demonstrated that sidelobes in the multiplexer spectral response can be suppressed by weighting the power samples in the array waveguides through appropriate design of a nonuniform MMI power splitter.     

Design of an ultrashort Si-nanowaveguide-based multimode interference coupler of arbitrary shape

A design procedure for an arbitrarily tapered multimode interference (MMI) coupler based on Si nanowaveguides is presented. First a series of the effective indices of the zeroth and first eigenmodes in multimode waveguides are obtained as the core width increases by using a full-vectorial finite-difference method. Two polynomial functions are used to fit the two relations between the effective indices and the core width. The phase difference Delta phi between the zeroth and first eigenmodes can then be easily calculated when the light goes through any given arbitrarily tapered MMI section. By making the phase difference Delta phi equal to a certain value Delta phi 0 required for an N-fold self-imaging, the length of a MMI coupler is determined. With the present design procedure, an ultrashort 2 x 2 parabolic MMI coupler is designed as an example. The size of the designed ultrashort MMI section is only approximately 1.4 microm x 4.7 microm.     

Electro-optic up-conversion mixer amenable to photonic integration

A novel electro-optical up-conversion mixer architecture comprising four electro-optical phase modulators situated in the arms between an interconnected 1 × 4 distribution tree and a complementary 4 × 2 combination tree is proposed. The distribution and combination trees are based on multi-mode interference couplers (MMI). The novelty lies in the use of the intrinsic phase relations between the MMI ports to realize a broadband and free of drift design requiring no static phase shift elements. A transfer-matrix approach is followed to represent the main building blocks in the proposed design, and hence to describe the operation of the entire optical up-conversion mixer. The concept is demonstrated by computer simulations. A single side-band modulation with carrier suppression is obtained at the output of the proposed architecture, which is in agreement with the analytical development. Scenarios considering both ideal and imperfect power balances and phase relations in the MMIs, as well as imperfect phase relations of the electrical drives to the phase modulators are analyzed.     

A 2×2 multimode interference coupler with exponentially tapered waveguide

An exponentially tapered structure is introduced into multimode interference (MMI) devices. Compared with a parabolically tapered structure, which has been successfully used in MMI devices, this structure can further reduce the length of these devices. The performances of the 2×2 MMI coupler with exponentially tapered structure, such as the optical transmission, the splitting ratio, the wavelength response and the fabrication tolerance, are investigated by the 2D finite difference beam propagation method. Results show that the exponentially tapered MMI coupler exhibits a similar property to that with a parabolically tapered structure except for the splitting ratio. The exponentially tapered structure can offer a possible application in MMI couplers with a free choice of the splitting ratio.     

Enhancement of the precision of fiber-optic interferometers by using couplers with high spectral power or antisymmetric supermode cutoff

It is shown that in 2×2 single-mode optical-fiber directional couplers operating with cutoff of the antisymmetric normal mode of a composite waveguide, the additional stray phase shift of the waves in the forward and cross channels (found in normal couplers) vanishes. Thus, by using these couplers (instead of the usual ones) in various interferometers, the precision can be enhanced substantially. It has also been shown that the precision of interferometers with wide-band radiation sources (such as white-light interferometers and fiber-optic gyroscopes) can be improved by replacing the usual couplers with couplers of high spectral power whose splitting ratio can execute a large number of oscillations within the radiation line width, efficiently eliminating the afore-mentioned stray phase shift. Pis’ma Zh. Tekh. Fiz. 23, 76–80 (July 26, 1997)     

Design of integrated 1×2, 1×4 low driving voltage polymer electro-optic switches based on Y-fed directional couplers

Two integrated 1 × 2 and 1 × 4 polymer electro-optic switches based on Y-fed directional couplers are designed and optimized in terms of the coupled mode theory, electro-optic modulation theory, conformal transforming method and image method. The principle of the 1 × 2 electro-optic switch is described. Parameters including the core size, buffer layer thickness, electrode thickness, electrode width and electrode gap are optimized. Simulation results show that the length of the designed 1 × 2 switch is about 3.126 mm, the driving voltages of the two branches are as low as 0.891 and ?0.891 V, respectively, the crosstalk and insertion loss are less than ?30 and 1.42 dB, respectively, within the operation wavelength from 1527 to 1574 nm. Under the same driving voltages, the 1 × 4 optical switch with a total length of less than 7 mm can be switched by altering the voltages applied on the electrodes of the three Y-fed directional couplers. Simulation results from the beam propagation method (BPM) indicate that the two designed devices exhibit favorable switching functions.     

Design and modeling of ultrashort MMI-based couplers

In this work, based on the Gaussian-modes theory, modeling and analysis of ultrashort (<10 µm) MMI couplers is performed. Using the introduced model, temporal behaviors and also other features such as insensitivity to input polarization, insensitivity to operating wavelength and manufacturing tolerances of these devices are studied. In addition, the optimal refractive-index structures with no sensitivity to the polarization are obtained. A comparison is made between this model and the semi-sinusoidal model and it is shown that the Gaussian model is necessary to handle these ultrashort devices. In addition, accuracy of the model is justified using a comparison with results of direct simulations obtained using the FEMLAB environment and FDTD method.     

Compact silicon-on-insulator-based multimode interference coupler with bilevel taper structure

A novel compact silicon-on-insulator- (SOI-)based multimode interference (MMI) coupler with bilevel taper structures was designed. The MMI section and the S-bend sections of the input-output waveguides are deeply etched. The input-output waveguides connecting to single-mode fibers or other photonic light circuits are etched shallowly to yield single-mode operation. A bilevel taper is introduced in the transition region between the shallowly and deeply etched regions. It is predicted theoretically that this design will not only improve the quality of the self-imaging in the MMI section but will also make the structure compact. Both the excess loss and the nonuniformity of the MMI coupler are reduced. By use of a three-dimensional beam propagation method, the performance of a 1 x 4 MMI coupler based on a SOI is simulated as a numerical example of the novel design. The simulated nonuniformity and the excess loss are approximately 0.0285 and 0.2 dB, respectively.     

Towards incorporating the influence of cover cracking on steel corrosion in RC design codes: the concept of performance-based crack width limits

This paper advocates for the adoption of performance-based limiting crack widths with respect to steel corrosion in reinforced concrete structures. The authors argue that, from both durability and sustainability viewpoints, the practice of adopting a universal limiting crack width for a wide range of in-service exposure conditions and concrete cover conditions and quality is not valid. As new performance-based concrete design codes are being developed and/or improved, the influence of cover cracking on steel corrosion needs to be incorporated in these codes. An experimental set-up was designed to investigate the influence of cover cracking, cover depth and concrete quality on chloride-induced corrosion. Beam specimens (120?×?130?×?375?mm) were cast using five concretes made using two w/b ratios (0.40 and 0.55) and three binders (100?% CEM I 42.5?N (PC), 50/50 PC/GGBS and 70/30 PC/FA). Other variables in the experiments included cover depth (20 and 40?mm), crack width (0, 0.4 and 0.7?mm). A total of 105 beam specimens were cast and exposed to cyclic 3-days wetting (with 5?% NaCl solution) and 4-days air-drying in the laboratory (23?°C, 50?% relative humidity). Corrosion rate was monitored bi-weekly in the specimens. The results relevant to this paper are presented and discussed. For a given concrete quality and cover depth, corrosion rate increased with increasing crack width. If crack width and cover depth are kept constant, corrosion rate increases with decreasing concrete quality, and vice versa. A model framework that can be used to objectively select cover depth, concrete quality and crack width is proposed. Such a model can be improved into, for example, a nomograph and used in the design process for RC structures prone to corrosion. Performance-based crack width limits should be adopted in the design of RC structures prone to steel corrosion. These crack width limits should be dependent on a complex interaction of, inter alia, concrete quality, cover depth, crack characteristics and prevailing exposure conditions. This study showed the inter-relationship between crack width, cover depth and concrete quality in affecting chloride-induced corrosion rate. Accurate corrosion rate prediction models incorporating the influence of cover cracking on corrosion are a pre-requisite to implementing the influence of cover cracking in future concrete design codes.     

Synthesis of Hadamard transformers by use of multimode interference optical waveguides

We propose a synthesis method of optical Hadamard transformer using multimode interference (MMI) couplers. By using the signal transfer matrix of 2 x 2, 4 x 4, and 8 x 8 MMI couplers, we show that sum and difference units of input signals can be synthesized. An interchange unit of two signals can also be synthesized. One synthesis method of Hadamard transformers is a combination of only 2 x 2 units, and the other is a combination of N x N(N > or = 4) units as well as 2 x 2 units. The design examples of operation units are shown, and the size and the output power of Hadamard transformers are estimated.     

Investigation and Simulation of a Two-Channel Drop Filter with Tunable Double Optical Resonators

In this paper, a photonic crystal (PhC) two-channel drop filter based on two 2×2 & 2×3 ring resonators is proposed. This structure is made of Germanium rods in an air background at a two-dimensional (2D) square lattice. Refractive index is chosen in a way in which that device can be easily fabricated. The photonic crystal two-channel drop filter is composed using a horizontal waveguide and two ring resonators, which are placed symmetrically about the horizontal axis. These ring resonators operate as energy coupling and capture the electromagnetic energy propagated in bus waveguide at their resonance frequencies. The filter characteristics are calculated using 2D finite-difference time-domain (FDTD) and plane wave expansion (PWE) methods. We show a two-channel drop filter with two resonators, based on studied basic structures and achieving optimal modes for channel drop filters with one resonator. We have done this through choosing the proper radii for all rods of lattice, setting radii of coupling rods, lattice constant, and studying basic structures having different refractive indexes. Finally, we show 84 % and 100 % dropping efficiencies can be achieved at D and C ports in the communication window and 100 % in direct port. The size of this device is 14.56 μm (length)×11.96 μm (width). This small size makes it possible to use the device in multiplexer applications in future communication systems and in all-optical integrated circuits.     

Fabrication of ridge waveguide on the ion-implanted TGG crystal by femtosecond laser ablation

The ridge waveguide on the TGG crystal has been fabricated through the combination of the ion implantation and the femtosecond laser ablation. Firstly, optical planar waveguide was formed on the top surface of TGG crystal by ion implantation. To investigate the damage induced by the 6.0?MeV Si ion implantation at a dose of 2.0 × 10¹⁵ ions/cm², the vacancy distribution was obtained by the SRIM simulation programme. Subsequently, the ridge waveguide with a width of 20?µm was produced by femtosecond laser ablation. The optical guiding properties of the ridge TGG waveguide were measured at the near-infrared wavelength (976?nm) by the end-face coupling technique. The work demonstrated that the manufactured waveguide structure possesses the ability to confine the light into guided mode, making it potentially valuable in integrated devices.     

Controlling the polarization dependence of dual-channel directional couplers formed by silicon-on-insulator slot waveguides

The polarization dependence of directional couplers (DC) formed by silicon-on-insulator (SOI) slot waveguides was studied, and its applications as highly efficient polarization beam splitters (PBSs) and polarization-independent directional couplers (PIDCs) were investigated. The coupling lengths for the quasi-TE and quasi-TM modes may vary with the waveguide geometry due to structural birefringence; thus numerical simulations of the coupling effects in the directional couplers with different aspect ratios and waveguide spacing were conducted to obtain the optimal design parameters for high efficiency as well as compact device size. The lengths of the coupling regions of the designed PBS and PIDC are 47.61 and 23.13 μm, respectively, and they delivered good performance, with an extinction ratio greater than 20 and 1 dB bandwidth larger than 100 nm. The tolerance of fabrication error in the practical device is also discussed.     

Characterization of a compact silicon-based slot-to-strip waveguide crossing

A compact crossing scheme for a silicon-based slot-to-strip (or vice versa) waveguide is proposed and analyzed by using a finite-difference time-domain method, where a strip–multimode waveguide (SMW) crossing is used at the center and two logarithmically tapered slot-to-strip mode converters are incorporated into the ports with slot waveguides. For the input ports with slot waveguides and output ports with strip waveguides, the guided modes are efficiently transformed through the mode converter, and then enter into the SMW, where the fields converge at the center of the intersection due to the self-imaging effect. Hence, the size of the input beam is much smaller than the width of the SMW at the crossing center, leading to significant reductions of both crosstalk and radiation loss. The numerical results show that a slot-to-strip waveguide crossing operating at a wavelength of 1.55?μm can be achieved with insertion loss, crosstalk, and reflection of 0.134/0.182, ?36.18/?38.6, and ?35.8/?42.02?dB for input ports with slot/strip waveguides, respectively.     

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.     

Modelling,design and optimization of compact taper and gratings for mode coupling to SOI waveguides at C-band

In this work, the design and optimization of compact taper is presented to enable coupling of infrared light in the C-band with the nano-photonic silicon-on-insulator (SOI) integrated optical waveguide. The proposed compact taper results in ～96% transmission efficiency for the taper length of ～5?µm and ～99.5% transmission efficiency for the taper length of 10?µm. The use of the proposed compact taper significantly reduces the foot print of optical coupler (grating and proposed compact taper) to (10?×?5)?µm² with ～96% transmittance and (10?×?10)?µm² with ～99.5% transmittance. The end-to-end coupling loss is less than 0.01?dB in the C-band. The compact taper along with grating presented in this work can be used as an efficient optical coupler for mode coupling from fibre to SOI single-mode optical waveguide in high density optical integrated circuits operating at 1550?nm.     

Waveguide confinement of cerenkov second-harmonic generation through a graded-index grating coupler: Electromagnetic optimization

Abstract

The feasibility of making a frequency doubler for integrated optics is studied with the electromagnetic theory of gratings and graded-index waveguides as a tool. The device consists of a first waveguide filled with a sol-gel nonlinear material doped or grafted with a nonlinear chromophore whose thickness is chosen to generate a second-harmonic Cerenkov radiation in a dispersive glass substrate. The Cerenkov radiation is coupled into a second waveguide through a graded-index layer produced by ion exchange into glass, lying on top of an ion-etched grating coupler. The aim of the study is to optimize the optogeometrical parameters of the device in order to obtain a resonance line of the second waveguide modes that has an angular width large enough to match the experimental constraints, and which leads to a good enough coupling coefficient. The electromagnetic theory of grating couplers is developed into an S-matrix propagation algorithm form in order to be combined with the electromagnetic analysis of the thick graded-index waveguide with a view to analysing the device.     

The Finite-conjugate Self-imaging and the Generalized Lau Effect Due to Complex Gratings

Abstract

Laser induced gratings in nonlinear optical media, which are complex or phase gratings, are the key structures in many applications involving laser beam-nonlinear material interactions. The concept of coded imaging of self-imaging structures, developed elsewhere, has been utilized to make a comprehensive study of the self-imaging properties, at finite conjugates, of model complex or phase gratings. The same approach has been used to extend our previous work on the generalized Lau effect. An interesting application of the self-imaging process has been made to visualize, at a certain primary magnification, laser induced thin photorefractive grating in a BSO crystal. Possible applications of this technique include visualization of dynamic or developed laser induced gratings in thin nonlinear optical materials.     

Input waveguide grating couplers designed for a desired wavelength and polarization response

Input grating couplers are used to couple light from free space into a waveguide and can provide additional functions such as focusing and beam splitting of the light into arbitrary desired positions in the waveguide. We show that it is possible to design the couplers so that they perform different desired functions depending on the polarization or wavelength of the incident light. We demonstrate experimentally a number of couplers that may be of interest, e.g., in optical fiber communications. Examples are polarization-independent couplers, designed to have the same response for two orthogonal polarizations of the incident light, and couplers for demultiplexing in wavelength division multiplexing applications, designed to separate and focus different input wavelengths to different positions in the waveguide.     

70-nm-bandwidth achromatic waveguide coupler

We report a general approach to the design of broadband waveguide couplers. A double-parallel grating assembly is used to cancel the first chromatic order, and a proper choice of prism glass and base angle is made to compensate for the second chromatic order. The technique was applied to a Corning glass 7059 waveguide, and a spectral bandwidth of 70 nm was measured by the use of two complementary procedures.