Abstract: A laser spark plug is described for an internal combustion engine. According to the system, at least one volume Bragg grating element is situated in a beam path of the laser spark plug.

Abstract: One embodiment provides an apparatus for displaying an image comprising: a first optical substrate comprising at least one waveguide layer configured to propagate light in a first direction, wherein the at least one waveguide layer of the first optical substrate comprises at least one grating lamina configured to extract the light from the first substrate along the first direction; and a second optical substrate comprising at least one waveguide layer configured to propagate the light in a second direction, wherein the at least one waveguide layer of the second optical substrate comprises at least one grating lamina configured to extract light from the second substrate along the second direction; wherein the at least one grating lamina of at least one of the first and second optical substrates comprises an SBG in a passive mode.

Abstract: One embodiment provides an apparatus for displaying an image comprising: a first optical substrate comprising at least one waveguide layer configured to propagate light in a first direction, wherein the at least one waveguide layer of the first optical substrate comprises at least one grating lamina configured to extract the light from the first substrate along the first direction; and a second optical substrate comprising at least one waveguide layer configured to propagate the light in a second direction, wherein the at least one waveguide layer of the second optical substrate comprises at least one grating lamina configured to extract light from the second substrate along the second direction; wherein the at least one grating lamina of at least one of the first and second optical substrates comprises an SBG in a passive mode.

Abstract: A high quality factor optical resonator structure includes a substrate, a center disc formed on the substrate, and a plurality of concentric grating rings surrounding the center disc. The concentric rings are spaced apart from the center disc and from one another by regions of lower index of refraction material with respect thereto, and wherein spacing between the grating rings and the center disc is non-periodic such that a magnitude of a displacement distance of a given grating ring with respect to a ?/4 Bragg reflector geometry is largest for a first of the grating rings immediately adjacent the center disk and decreases in a radially outward direction.

Abstract: Methods and apparatus are disclosed for wirelessly communicating among integrated circuits and/or functional modules within the integrated circuits. A semiconductor device fabrication operation uses a predetermined sequence of photographic and/or chemical processing steps to form one or more functional modules onto a semiconductor substrate. The functional modules are coupled to an integrated waveguide that is formed onto the semiconductor substrate and/or attached thereto to form an integrated circuit. The functional modules communicate with each other as well as to other integrated circuits using a multiple access transmission scheme via the integrated waveguide. One or more integrated circuits may be coupled to an integrated circuit carrier to form Multichip Module. The Multichip Module may be coupled to a semiconductor package to form a packaged integrated circuit.

Abstract: An Electrically Switchable Bragg Grating (ESBG) despeckler device comprising at least one ESBG element recorded in a hPDLC sandwiched between transparent substrates to which transparent conductive coatings have been applied. At least one of said coatings is patterned to provide a two-dimensional array of independently switchable ESBG pixels. Each ESBG pixel has a first unique speckle state under said first applied voltage and a second unique speckle state under said second applied voltage.

Abstract: There is provided a wearable display comprising a light source emitting light of a first wavelength; a first SBG device having a front side and a rear side; first and second transparent plates sandwiching said SBG device; independently switchable transparent electrode elements applied to the opposing surfaces of said transparent plates, a means for spatio-temporally modulating light from the light source to provide image light and a means for coupling the image light into the light guide formed by the two transparent plates and the SBG device. The SBG device comprises a multiplicity of selectively switchable grating regions. The SBG device diffracts image into the pupil of an eye.

Abstract: An electric field detection device. In one embodiment, the electric field detection device includes an interferometer having a reference arm and an active arm. The reference arm comprises a first electro-optic waveguide. The active arm comprises a first electrically conductive plate, a second electrically conductive plate spaced apart from the first electrically conductive plate defining a first gap therebetween, a third electrically conductive plate disposed in the first gap and vertically extending from the first electrically conductive plate to define a T-shape structure and a second gap between the third electrically conductive plate and the second electrically conductive plate, where the second gap is substantially smaller than the first gap; and a second electro-optic waveguide disposed in the second gap and being in electrical communication with the second and third electrically conductive plates.

Abstract: An Electrically Switchable Bragg Grating (ESBG) despeckler device comprising at least one ESBG element recorded in a hPDLC sandwiched between transparent substrates to which transparent conductive coatings have been applied. At least one of said coatings is patterned to provide a two-dimensional array of independently switchable ESBG pixels. Each ESBG pixel has a first unique speckle state under said first applied voltage and a second unique speckle state under said second applied voltage.

Abstract: A method and system for providing an optical grating are described. The optical grating is configured for light of a wavelength and includes a first optically transparent layer, a stop layer on the first optically transparent layer, and a second optically transparent layer on the stop layer. The first optically transparent layer is continuous and includes a material. The second optically transparent layer also includes the material. The second optically transparent layer also includes a plurality of discrete ridges spaced apart by a pitch. The stop layer is configured to be invisible to the light.

Abstract: A wavelength tunable filter and a wavelength tunable laser module are a codirectional coupler type whose characteristics do not vary significantly with a process error. They are structured so as to include a semiconductor substrate which has a first optical waveguide and a second optical waveguide. The first and the second optical waveguides are extended from a first side of the semiconductor substrate to an opposing second side thereof. The first optical waveguide includes a first core layer, which has a planar layout having periodic convexes and concaves, and a pair of electrodes, which vertically sandwich the first core layer. The second optical waveguide includes a second core layer, which has a lower refractive index than the first core layer. Further, a layer having the same composition and film thickness as the second core layer is placed under the first core layer.

Abstract: An optical switch includes: an input-output port with three or more ports arranged along a direction; a modulator that includes an incident layer, a reflective layer, and a modulation layer disposed between these layers, spatially modulates light entering the incident layer from any port of the input-output port, and outputs the light spatially-modulated toward any of other ports of the input-output port; and a condensing lens that optically couples the input-output port and the modulator, wherein x2?2x1+x0 holds where: a coordinate axis is along the direction of the input-output port and an optical axis of the lens is set as an origin of the coordinate axis; x0, x1, and x2 respectively are coordinates of a first port to/from which light is input/output, and a second port and a third port from/to which light input to or output from the first port is output/input; and x1,x2>0.

Abstract: Provided is a semiconductor integrated circuit. The semiconductor integrated circuit includes a semiconductor pattern disposed on a substrate and including an optical waveguide part and a pair of recessed portions. The optical waveguide part has a thickness ranging from about 0.05 ?m to about 0.5 ?m. The recessed portions are disposed on both sides of the optical waveguide part and have a thinner thickness than the optical waveguide part. A first doped region and a second doped region are disposed in the recessed portions, respectively. The first and second doped regions are doped with a first conductive type dopant and a second conductive type dopant, respectively. An intrinsic region is formed in at least the optical waveguide part to contact the first and second doped regions.

Abstract: A wavelength division multiplexing and optical modulation apparatus includes at least two modulation region-added grating-assisted cross-state directional coupler units and a modulation region-added cross-state directional coupler. The modulation region-added grating-assisted cross-state directional coupler units and the modulation region-added cross-state directional coupler unit are connected to one another in serial. Each of the modulation region-added grating-assisted cross-state directional coupler units each includes a modulation region-added cross-state directional coupler, a grating and a modulation region. The modulation region-added cross-state directional coupler unit includes an output waveguide, an input waveguide and a modulation region.

Abstract: A conductive polymer and a semiconducting carbon nanotube material are combined to form a highly conductive composite. The composite can be used for EMI shielding, optical sensing, optical switching, and other uses.

Abstract: An electromagnetically responsive element includes sets of arrangements of self-resonant bodies, such as atoms or quantum dots that form an effective dielectric constant, typically at or near a resonance.

Abstract: An electromagnetically responsive element includes sets of arrangements of self-resonant bodies, such as atoms or quantum dots that form an effective dielectric constant, typically at or near a resonance.

Abstract: Apparatus and methods for providing an optically based planar scanner for generating an image are provided. In one embodiment, the apparatus includes a switchable Bragg grating. An area of the switchable Bragg grating is configured to be activated to direct light to a platen. The platen is configured to reflect the light to a waveguide or to refract the light. The light reflected to the waveguide is guided to a light detector. By activating a number of the areas of the switchable Bragg grating and measuring the intensity of the light with a light detector, an image of an object contacting the platen may be formed.

Abstract: An optical selector includes: an optical waveguide which includes a first light guide section having a first refractive index, a second light guide section having a second refractive index provided to the side of and along the entire circumference of the first light guide section, and a reflector provided at opposing positions on both surfaces of each of the first and second light guide sections while exposing the outer circumferential surface of the second light guide section; a single or plurality of LDs that are placed on the outer circumference of the optical waveguide, and emit light toward the first light guide section; and a single or plurality of photodetectors that are placed on the outer circumference of the optical waveguide, and receive light emitted from the outer circumference of the optical waveguide.

Abstract: A method and system for providing an optical grating are described. The optical grating is configured for light of a wavelength. The optical grating includes a top cladding, a core, and bottom cladding. The core resides between the bottom cladding and the top cladding. The core includes a plurality of discrete ridges spaced apart by a nonlinear pitch. The light traverses the top cladding before the core and has a plurality of angles of incidence with the core. The nonlinear pitch of the core is larger for a larger angle of incidence of the plurality of angles of incidence.

Abstract: An electro-optic device is provided. The electro-optic device includes a junction layer disposed between a first conductivity type semiconductor layer and a second conductivity type semiconductor layer to which a reverse vias voltage is applied. The first conductivity type semiconductor layer and the second conductivity type semiconductor layer have an about 2 to 4-time doping concentration difference therebetween, thus making it possible to provide the electro-optic device optimized for high speed, low power consumption and high integration.

Abstract: An Electrically Switchable Bragg Grating (ESBG) despeckler device comprising at least one ESBG element recorded in a hPDLC sandwiched between transparent substrates to which transparent conductive coatings have been applied. At least one of said coatings is patterned to provide a two-dimensional array of independently switchable ESBG pixels. Each ESBG pixel has a first unique speckle state under said first applied voltage and a second unique speckle state under said second applied voltage.

Abstract: The waveguide-type polarizer includes: a Z-cut lithium niobate substrate; an optical waveguide having a ridge structure and formed on the substrate; a low refractive index film formed with a thickness satisfying 0?n·t/??0.3742 (where n is a refractive index, t (?m) is the thickness of the film, and ? (?m) is the wavelength of a light wave) on the side of the ridge structure; and a high refractive index film formed with a thickness satisfying 0.089?n·/? on the low refractive index film. The width of the ridge structure is a ridge width where the distribution of ordinary light of the light waves propagated through the optical waveguide changes and the distribution of extraordinary light of the light waves does not change, the angle of the ridge structure is less than 90°, and the waveguide-type polarizer has a function of transmitting extraordinary light.

Abstract: A first exemplary aspect of the present invention is a wavelength-tunable optical transmitter including: a semiconductor substrate (101); a wavelength-tunable light source that is formed on the semiconductor substrate (101) and includes at least a first reflector (102) of a wavelength-tunable type and a gain region (104); a semiconductor optical modulator formed on the semiconductor substrate (101); a first semiconductor optical waveguide (105c) that is formed on the semiconductor substrate (101) and smoothly connected to the wavelength-tunable light source; a second semiconductor optical waveguide (105d) that is formed on the semiconductor substrate and smoothly connected to the semiconductor optical modulator; a waveguide coupling region (108) in which the first and second semiconductor optical waveguides are collinearly coupled with a length LC that is not equal to m/2 (m: integer) times a complete coupling length LC0; and a second reflector (113) formed at an end of the waveguide coupling region (108).

Abstract: There is provided a planar optical waveguide element comprises a core of an optical waveguide; and first Bragg grating pattern and second Bragg grating pattern that are provided on the core, wherein the first Bragg grating pattern and the second Bragg grating pattern are mutually parallel along a propagation direction of guided light.

Abstract: There is provided an optical waveguide element comprises: a core of an optical waveguide; and a Bragg grating pattern that is provided on the core, wherein a pitch of the Bragg grating pattern takes a value from among three or more predetermined discrete values; the pitches that take the respective discrete values are present in a plurality of locations over an entire length of the optical waveguide respectively; and if a value from among all of the discrete values which has the highest distribution frequency is taken as M, and if the closest value to the M which is larger than the M is taken as A, and if the closest value to the M which is smaller than the M is taken as B, then a difference expressed as A?M is equal to a difference expressed as M?B.

Abstract: Fibre substrates act as a conduit for light along which response signals are transmitted to a controller in the form of an electronic device associated with a component. The processed signals are stored in a local memory to provide a component history and a prediction of future performance and life. Service and repair history may be added to the component device memory to enable a complete history to be stored with the component. A controller may transmit data to an external controller or display through typically a wireless connection. Power to the component electronics may be provided by an induction loop or transformer.

Abstract: A wavelength division multiplexing and optical modulation apparatus includes at least two modulation region-added grating-assisted cross-state directional coupler units and a modulation region-added cross-state directional coupler. The modulation region-added grating-assisted cross-state directional coupler units and the modulation region-added cross-state directional coupler unit are connected to one another in serial. Each of the modulation region-added grating-assisted cross-state directional coupler units each includes a modulation region-added cross-state directional coupler, a grating and a modulation region. The modulation region-added cross-state directional coupler unit includes an output waveguide, an input waveguide and a modulation region.

Abstract: An Electrically Switchable Bragg Grating (ESBG) despeckler device comprising at least one ESBG element recorded in a hPDLC sandwiched between transparent substrates to which transparent conductive coatings have been applied. At least one of said coatings is patterned to provide a two-dimensional array of independently switchable ESBG pixels. Each ESBG pixel has a first unique speckle state under said first applied voltage and a second unique speckle state under said second applied voltage.

Abstract: A wavelength converter includes a supporting substrate and a ferroelectric substrate, the ferroelectric substrate includes at least one waveguide facing the supporting substrate and at least one wavelength-filtering pattern positioned between the waveguide and the supporting substrate, the waveguide includes a plurality of inverted domains and non-inverted domains configured to convert an infrared light into a green light, and the infrared light emitted from the semiconductor laser enters the waveguide of the wavelength converter. For example, the wavelength-filtering pattern includes a Bragg grating.

Abstract: In a conventional optical signal processing device, a confocal optical system is configured in which a focusing lens is positioned at a substantially-intermediate point of a free space optical path. Thus, the free space optical system had a long length. It has been difficult to reduce the size of the entire device. The optical signal processing device of the present invention uses a lens layout configuration different from the confocal optical system to thereby significantly reduce the length of the system. The optical signal processing device consists of the first focusing lens positioned in the close vicinity of a signal processing device, and the second focusing lens positioned in the vicinity of a dispersing element. A distance between the dispersing element and the signal processing device is approximately a focal length of the first focusing lens. Compared with the conventional technique, the length of the optical path can be halved.

Abstract: Methods and devices for optical beam steering are disclosed including coupling a laser light into an apparatus comprising a first substrate; an array of air core photonic crystal waveguides; columnar members etched around each air core waveguide; a pair of metal electrodes around the columnar members; a trench around the pair of metal electrodes surrounding each air core photonic crystal waveguide; a second substrate coupled to the first substrate comprising electrical interconnection lines; and a holographic fanout array comprising a third substrate; a photopolymer film coated on the third substrate; a hologram written in the photopolymer film configured to couple the laser light into the third substrate; and an array of holograms recorded in the photopolymer film configured to couple a portion of the laser light into the waveguides; and passing a current through the electrodes to induce a refractive index change in the first substrate to control the phase of the portion of the laser light that passes throug

Abstract: A wavelength tunable filter and a wavelength tunable laser module are a codirectional coupler type whose characteristics do not vary significantly with a process error. They are structured so as to include a semiconductor substrate which has a first optical waveguide and a second optical waveguide. The first and the second optical waveguides are extended from a first side of the semiconductor substrate to an opposing second side thereof. The first optical waveguide includes a first core layer, which has a planar layout having periodic convexes and concaves, and a pair of electrodes, which vertically sandwich the first core layer. The second optical waveguide includes a second core layer, which has a lower refractive index than the first core layer. Further, a layer having the same composition and film thickness as the second core layer is placed under the first core layer.

Abstract: An electric field detection device. In one embodiment, the electric field detection device includes an interferometer having a reference arm and an active arm. The reference arm comprises a first electro-optic waveguide. The active arm comprises a first electrically conductive plate, a second electrically conductive plate spaced apart from the first electrically conductive plate defining a first gap therebetween, a third electrically conductive plate disposed in the first gap and vertically extending from the first electrically conductive plate to define a T-shape structure and a second gap between the third electrically conductive plate and the second electrically conductive plate, where the second gap is substantially smaller than the first gap; and a second electro-optic waveguide disposed in the second gap and being in electrical communication with the second and third electrically conductive plates.

Abstract: A semiconductor laser includes: a first portion, made from a silicon-containing material, including an optical waveguide, a first diffraction grating including a phase shift, and a second diffraction grating; a second portion including a light-emitting layer made from a material different from that of the first portion; a laser region including the first diffraction grating, and the optical waveguide and the light-emitting layer provided in a position corresponding to the first diffraction grating; and a mirror region including the second diffraction grating, and the optical waveguide and the light-emitting layer provided in a position corresponding to the second diffraction grating.

Abstract: The present invention provides an apparatus for pressure sensing. The apparatus comprises a light guide, a Bragg grating incorporated into the light guide and a moveable wall portion. The moveable wall portion has opposite first and second sides and is being positioned so that a change in pressure at one of the sides relative to a pressure at the other side will move the moveable wall portion. The moveable wall portion is coupled to the Bragg grating so that the movement of the moveable wall portion causes a force on a side of the Bragg grating. The force has a component that is transversal to the Bragg grating and effects a change in strain of the Bragg grating and thereby a change in an optical period of the Bragg grating.

Abstract: An improved optic system for measuring and/or controlling displacement, force, pressure, position, or chemistry is disclosed. This apparatus allows for more accurate, robust, and economical communication between the transducer (or control input element) and the reader device (or control output), allows the use of a single optic fiber and/or or a gap for the communication link, and produces substantial insensitivity to attenuation due to mechanical, chemical, thermal, and radiation effects acting on the optic fiber or open space in which the signal propagates. It is also significantly immune to interference from electromagnetic radiation, since the link can be easily produced as a non-conductor which will not propagate unwanted electrical energy or lightning, and is intrinsically safe from igniting fires or explosions. It also facilitates use on rotating machinery and remote location of the transducer by the ability to transmit the signal across a large gap or air space.

Abstract: A frequency-conversion method that uses a nonlinear optical process to transfer energy between a surface-plasmon (SP) wave that is guided along an electrically conducting strip and a light beam that is guided along an optical waveguide whose core is adjacent to the electrically conducting strip. A periodic structure spatially modulates the nonlinear susceptibility of the waveguide core with a spatial period that is related to a momentum mismatch in the nonlinear optical process. The spatial modulation provides quasi-phase matching for the SP wave and the light beam and enables efficient energy transfer between them.

Abstract: The invention relates to a method for producing a slotted guide, in which: a) a layer of a material having a refractive index less than that of silicon, for example Material having a refractive index less than that of silicon (26), is formed on an etching barrier layer (22), b) two parallel trenches are etched into said material having a refractive index less than that of silicon, with the etching barrier on said etching barrier layer, these two trenches being separated by a wall of said material having a refractive index less than that of silicon (36), c) the trenches thus made are filled with silicon (42, 44).

Abstract: The invention relates to micromechanical elements deflectable in an oscillating manner and to a method for the operation of such elements. In this respect, it is the object of the invention to be able to operate the micromechanical elements in a stable and simple manner on the oscillating deflection while taking account of the respective mechanical resonant frequency. A least one spring element is present on elements in accordance with the invention with which it is held. It is deflected between two reversal points using an electrical AC voltage. The one or more spring element(s) has/have non-linear spring characteristics so that a changed mechanical resonant frequency results in dependence on the respective deflection.

Abstract: An optical frequency converter that uses a nonlinear optical process to transfer energy between a surface-plasmon (SP) wave that is guided along an electrically conducting strip and a light beam that is guided along an optical waveguide whose core is adjacent to the electrically conducting strip. The optical frequency converter has a periodic structure that spatially modulates the nonlinear susceptibility of the waveguide core with a spatial period that is related to a momentum mismatch in the nonlinear optical process. The spatial modulation provides quasi-phase matching for the SP wave and the light beam and enables efficient energy transfer between them.

Abstract: The configurations of an electro-optic Bragg deflector and the methods of using it as a laser Q-switch in a Q-switched laser and in a Q-switched wavelength-conversion laser are provided. As a first embodiment, the electro-optic Bragg deflector comprises an electrode-coated electro-optic material with one of a 1D and a 2D spatially modulated electro-optic coefficient. When a voltage is supplied to the electrodes, the electro-optic material behaves like a Bragg grating due to the electro-optically induced spatial modulation of the refractive index. The second embodiment relates to an actively Q-switched laser, wherein the electro-optic Bragg deflector functions as a laser Q-switch. The third embodiment of the present invention combines the Q-switched laser and a laser-wavelength converter to form a Q-switched wavelength-conversion laser, wherein the EO Bragg deflector can be monolithically integrated with a quasi-phase-matching wavelength converter in a fabrication process.

Abstract: A Bragg grating has a local reflection strength which varies with position along the length of the grating so as to generate a non-uniform wavelength reflection spectrum, enabling compensation for a non-uniform gain profile of the gain section of a tunable laser. In another aspect, a Bragg comb grating is modulated by an envelope function which can also compensate for a non-uniform gain profile. The comb grating may be a phase change grating, with the envelope function shape being controlled by the length between phase changes and/or size of the phase changes.

Abstract: A reflective metrological scale has a metal tape substrate and a scale pattern of elongated side-by-side marks surrounded by reflective surface areas of the substrate. Each mark has a furrowed cross section and may have a depth in the range of 0.5 to 2 microns. The central region of each mark may be rippled and darkened to provide an enhanced optical reflection ratio with respect to surrounding surface areas. A manufacturing method includes the repeated steps of (1) creating a scale mark by irradiating the substrate surface at a mark location with overlapped pulses from a laser, each pulse having an energy density of less than about 1 joule per cm2, and (2) changing the relative position of the laser and the substrate by a displacement amount defining a next mark location on the substrate at which a next mark of the scale is to be created.

Abstract: An optical fiber 200 with a high thermal resistance fiber Bragg grating (FBG) 130. Compared to existing FBG's, the invention provides greatly enhanced thermal stability, being stable up to 1200° C. The grating reflectivity and resonant wavelength are maintained for extended duration at high temperatures. The FBG is thus suitable in high temperature sensors. The high thermal resistance of the FBG is obtained in a method of pre-annealing the optical fiber 105 at high temperature prior to inscribing the FBG. The high thermal resistance is optionally enhanced in a post-FBG creation step of heat treating the optical fiber 105 and FBG.

Abstract: Light emitting and waveguide devices with single-sided photonic bandgaps are provided. The light emitting device is formed from a heavily doped silicon (Si) bottom electrode, and a Si-containing dielectric layer embedded Si nanoparticles overlying the bottom electrode. A transparent indium tin oxide (ITO) top electrode overlies the Si-containing dielectric layer, and a photonic bandgap (PBG) Bragg reflector underlies the Si bottom electrode. The PBG Bragg reflector includes at least one periodic bi-layer of films with different refractive indexes. The single-sided photonic bandgap planar waveguide interface is formed from a planar waveguide and a PBG Bragg reflector underlying the planar waveguide.

Abstract: Narrow surface corrugated gratings for integrated optical components and their method of manufacture. An embodiment includes a grating having a width narrower than a width of the waveguide on which the grating is formed. In accordance with certain embodiments of the present invention, masked photolithography is employed to form narrowed gratings having a desired grating strength. In an embodiment, an optical cavity of a laser is formed with a reflector grating having a width narrower than a width of the waveguide. In another embodiment an integrated optical communication system includes one or more narrow surface corrugated gratings.

Abstract: The present invention relates generally to electro-optically active waveguide segments, and more particularly to the use of a selective voltage input to control the phase, frequency and/or amplitude of a propagating wave in the waveguide. Particular device structures and methods of manufacturing are described herein.

Abstract: This invention provides a novel wavelength-separating-routing (WSR) apparatus that uses a diffraction grating to separate a multi-wavelength optical signal by wavelength into multiple spectral channels, which are then focused onto an array of corresponding channel micromirrors. The channel micromirrors are individually controllable and continuously pivotable to reflect the spectral channels into selected output ports. As such, the inventive WSR apparatus is capable of routing the spectral channels on a channel-by-channel basis and coupling any spectral channel into any one of the output ports. The WSR apparatus of the present invention may be further equipped with servo-control and spectral power-management capabilities, thereby maintaining the coupling efficiencies of the spectral channels into the output ports at desired values.

Abstract: An optical apparatus comprises a planar optical waveguide having at least one set of diffractive elements and confining in at least one transverse spatial dimension optical signals propagating therein. Each diffractive element set routes, between corresponding input and output optical ports, a corresponding diffracted portion of an input optical signal propagating in the waveguide that is successively incident on the diffractive elements and is diffracted by the diffractive element set. The optical signals propagate in the waveguide in corresponding diffractive-region optical transverse modes in regions where the diffractive elements are present, and in corresponding non-diffractive-region optical transverse modes in regions where the diffractive elements are absent.