Abstract: According to one embodiment of the present invention, a semiconductor device includes a first layer of dielectric material disposed upon an upper surface of a substrate of a semiconductor device and a first non-conductive layer of metal disposed upon an upper surface of the dielectric material. The first layer of dielectric material and the first non-conductive layer of metal act as an optical trap for electromagnetic radiation received by the first non-conductive layer of metal. In particular embodiments, the semiconductor device may further comprise a second layer of dielectric material disposed upon an upper surface of the first non-conductive layer of metal and a second non-conductive layer of metal disposed upon an upper surface of the second layer of dielectric material.

Abstract: An optical modulation apparatus is provided which implements a stable amplifying function by reducing the effect of reflected light rays from end faces of a bidirectional optical amplifier by imposing a numerical limitation on the relationship between the gain of the bidirectional optical amplifier and the loss of the optical modulator, or by inserting a polarization rotation section in a reflection type optical modulator including the bidirectional optical amplifier or in a multi-wavelength collective optical modulation system combining the multiple optical modulators. An optical modulation apparatus is provided which implements a stable amplifying function and cost reduction by reducing the effect of reflected light rays by interposing optical isolators at every alternate SOAs in a transmission-type optical modulation apparatus including a plurality of semiconductor optical amplifiers (SOAs) connected in a multistage fashion.

Abstract: A wiring board includes a core composite layer having first and second core boards and an optical transmission portion; first electrodes disposed on one part of the core composite layer, being adapted to mount an optical semiconductor module on the core composite layer; upper and lower core board wirings disposed on another part of and beneath the core composite layer; and upper and lower build-up wirings stacked on the upper and lower core board wirings, being adapted to mount semiconductor modules.

Abstract: A method and system is disclosed for making time alignment for a data transmission system. A first reference clock signal is provided to a first multiplexer coupled to a data modulator through a data driver, and a second reference clock signal is provided to a second multiplexer coupled to a clock modulator through a clock driver. Phase adjustment of the reference clock signal are conducted before the first reference clock signal is provided to the first multiplexer, wherein the phase adjustment aligns a timing of data modulated by the data modulator with a periodically modulated light source generated by the clock modulator.

Abstract: A sensor and method for page-based optical data storage. The sensor includes a partially-reflective mirror, a reflective mirror disposed substantially collinear with and spaced apart from the partially-reflective mirror, and an active layer disposed substantially collinear with and between the partially-reflective mirror and the reflective mirror. The partially-reflective mirror has a first and second side and transmits a portion of light incident on the first side. The reflective mirror reflects light incident on the reflective mirror toward the partially-reflective mirror. The active layer absorbs at least a portion of the light oscillating at the resonant frequency.

Abstract: Undoped layers are introduced in the passive waveguide section of a butt-joined passive waveguide connected to an active structure. This reduces the parasitic capacitance of the structure.

Abstract: An optical spike is generated at an arbitrarily selected location within an arbitrary optical link. The optical spike is generated by deriving a spike signal having a plurality of components, and launching the spike signal into the a transmitter end of the optical link. An initial phase relationship between the components is selected such that the involved signal components will be phase aligned at the selected location. In order to achieve this operation, the initial phase relationship between the components may be selected to offset dispersion induced phase changes between the transmitter end of the link and the selected location. One or more optical spikes can be generated at respective arbitrarily selected locations within the link, and may be used for performance monitoring, system control, or other purposes.

Abstract: The present invention is a method and an apparatus for optical modulation, for example for use in optical communications links. In one embodiment, an apparatus for optical modulation includes a first silicon layer having one or more trenches formed therein, a dielectric layer lining the first silicon layer, and a second silicon layer disposed on the dielectric layer and filling the trenches.

Abstract: A light control device includes a substrate, a first reflective layer, a light modulating film in which the refractive index varies according to an applied electric field, a transparent electrode, and a second reflective layer having a reflection characteristic such that the reflection band and transmission band exhibit a steep switching pattern at a specified wavelength. The device is configured such that the specified wavelength and the resonant wavelength of a Fabry-Perot resonator defined by the first reflective layer, the light modulating film, the transparent electrode, and the second reflective layer are substantially the same. The reflection-type light control device has improved light utilization efficiency.

Abstract: A method and apparatus to accommodate differing output loads without sacrificing impedance matching in an optical modulator driver.

Abstract: A semiconductor optical converter for use principally in an optical communications system or an optical information processing system. The semiconductor optical converter comprises an n-InP clad layer (12), an optical waveguide layer (13), an SI-InP clad layer (14), and an n-InP clad layer (15) formed sequentially on an SI-InP substrate (11), characterized in that a voltage is applied from an electrode (16) connected with the n-InP clad layer (15) and a ground electrode (17) connected with the n-InP clad layer (12). The semiconductor optical converter is especially applicable as a semiconductor phase modulator or a semiconductor Mach-Zehnder phase modulator operating at low voltages and having a low waveguide loss.

Abstract: In some embodiments, a dynamic optical tag communication system is provided which includes high and low index CCR, both having a modulator, such as TCFP-MQWs on a first side of the CCR configured to modulate in a first temperature range, and a modulator on a second side of the CCR to modulate in a second temperature range. In some embodiments another high index CCR having corresponding first and second temperature range modulators is provided. In some embodiments, a CCR may have three modulators, such as MQWs, one configured to modulate in a first temperature range, another to modulate in a second temperature range, and yet another to modulate in a third temperature range. In some embodiments, a dynamic optical tag communication system has CCRs which include a high index CCR having a DDG modulator and a low index CCR having a DDG modulator.

Abstract: Provided is a semiconductor optical modulator device in which a resistor for impedance matching is integrated in a device in order to improve performance and to reduce cost during the fabrication of an ultra high speed optical modulator module. A doped layer in an epitaxial layer of the optical modulator device is used as a resistor for impedance matching. According to this method, it is possible to more easily realize an optical device compared with optical device fabrication processes in which additional resistors are used in the outside and the inside of the device for impedance matching.

Abstract: The present invention relates to optical confinements, methods of preparing and methods of using them for analyzing molecules and/or monitoring chemical reactions. The apparatus and methods embodied in the present invention are particularly useful for high-throughput and low-cost single-molecular analysis.

Abstract: Described is a method for conforming electronics to arbitrary shapes. The method comprises acts of forming a device structure to have a growth substrate, an etch stop layer affixed with the growth substrate, and a micro-electronic array. The micro-electronic array comprises a plurality of components atop the etch stop layer. The micro-electronic array is thereafter embedded into a shrinkable layer. The shrinkable layer is then mounted onto a handle wafer that includes a layer of adhering film with the shrinkable layer being pressed into the layer of adhering film. The growth substrate and the etch stop layer are thereafter removed. The adhering film is then dissolved to demount the micro-electronic array and shrinkable layer. Finally, the shrinkable layer is shrunk to conform the micro-electronic array to a three-dimensional shape, with the growth orientation flipped such that metal interconnects may be made to both the top and bottom of the chip.

Abstract: Disclosed is a duobinary optical transmission apparatus using a semiconductor optical amplifier (SOA). The duobinary optical transmission apparatus includes a light source for generating a carrier wave; a duobinary precoder for encoding an input (non return to zero) electric signal; a semiconductor optical amplification unit to amplify the encoded signal from the duobinary precoder, wherein the amplification unit receives an optical amplification gain difference that varies with a bias current combined with the encoded signal; and an optical band pass filter for receiving a phase-modulated optical signal from the semiconductor optical amplification unit, filtering the received optical signal to a prescribed bandwidth, and thereby generates a duobinary optical signal.

Abstract: A light modulation apparatus including a Mach-Zehnder type light modulator, a driver for modulator outputting a control signal according to an input electric signal, a light branching circuit branching the output light signal, and a bias control circuit applying a bias voltage to the light modulator based on the branched light signal, the apparatus further comprises: a burst pause state detection circuit detecting a pause state of a burst signal included in the input electric signal; a photoelectric transducer converting an output light signal branched by the light branching circuit into an electric signal; a sampling circuit extracting the electric signal converted while the pause state is detected by the burst pause state; and a bias voltage adjustment circuit adjusting a bias voltage value of the bias voltage based on a voltage level of the extracted electric signal.

Abstract: An electro-optical modulator is disclosed that has a microwave input, chip with a thin film resistor or a lumped resistor located between an input RF connector and an RF electrode on a Lithium Niobate chip. The accessory connection chip has a broadband attenuator like a thin film resistor which is placed in a microstrip line for effecting the electrical transmission to Lithium Niobate chip. The insertion of the thin film resistor before the RF electrode lowers the electrical return loss value as a function of frequency, allowing a lower driving voltage design or a reduced chip length without degrading the performances.

Abstract: A spatial light modulator for use in projection display applications is provided. The spatial light modulator includes a substrate including a plurality of electrically active circuits and an electrode layer electrically coupled to at least one of the plurality of electrically active circuits. In one embodiment, the electrode layer includes a semi-continuous layer with at least one optical path. The spatial light modulator also includes a shielding layer electrically isolated from the electrode layer and disposed between the substrate and the plurality of electrically active circuits and an electrical connector coupling the shielding layer to a reference potential. In a specific embodiment, the shielding layer of the spatial light modulator converts incident light energy to electrical current and routes the current back to a source. In another specific embodiment, the shielding layer converts electrical field disturbance to electrical current and routes the current back to a source.

Abstract: A method for encoding information that is encoded in spatial variations of the intensity of light (24) of a first wave-length into light of a second wavelength, the method comprising: generating a first density distribution of electrons homologous with the spatial variations in intensity of the first wavelength light; generating a second additional electron density homologous with the first electron density distribution; trapping electrons from the first and second electron density distributions in a trapping region (34) to generate an electric field homologous with the density distributions in a material (36) that modulates a characteristic of light (22) that passes therethrough responsive to an electric field (46) therein; and transmitting the second wavelength light (22) through the modulating material (36) thereby modulating the second wavelength light in response to the electric field and encoding it with the information.

Abstract: A method for use in manufacturing a microelectromechanical system, such as a reflective stealth mirror includes the steps of: forming an I-shape mirror structure; forming a spacer layer over the I-shape mirror structure; and patterning the spacer layer to form at least one spacer along a side of the I-shape mirror structure.

Abstract: An electro-absorption light intensity modulator device is provided that comprises a first and a second layer disposed relative to the first layer so as to provide a light-absorbing optical confinement region. The first layer comprises a first insulator layer, and the light-absorbing optical confinement region comprises at least one quantum-confined structure. The at least one quantum-confined structure possesses dimensions such, that upon an application of an electric field in the at least one quantum-confined structure, light absorption is at least partially due to a transition of at least one carrier between a valence state and a conduction state of the at least one quantum-confined structure. A method is also provided for fabricating an electro-absorption light intensity modulator device.

Abstract: An optical modulator comprises a first waveguide layer and a barrier layer, and a quantum well layer sandwiched between the first waveguide layer and the barrier layer, where the quantum well layer has a graded composition that varies the bandgap energy of the quantum well layer between a minimum bandgap energy and the bandgap energy of at least one of the first waveguide layer and the barrier layer.

Abstract: A porous silicon filter for wavelength multiplexing and de-multiplexing. Preferred embodiments include rugate-type porous silicon filters with pores having continuously varying widths with pore depth an optical cross connect switch. In other preferred embodiments, the pores are filled with a material that changes index of refraction with changes in applied voltage, current or temperature. Important applications of these porous silicon filters are for multiplexing and de-multiplexing in fiber optic communication systems. For example, a preferred embodiment is an all optical fiber optic switch utilizing these filters.

Abstract: An optical transmitter-receiver is provided which is suitable for a high-speed optical communication system. A high-frequency electric line on a mounting substrate becomes a traveling-wave electrode of a semiconductor optical element equivalently by the following steps: separately manufacturing the mounting substrate having the high-frequency electric line, and the semiconductor optical element for which high-frequency design has been applied beforehand; and then bonding and mounting of drive electrodes of the mounting substrate and the semiconductor optical element through a soldering material. In addition, it is also possible to have a configuration in which not only junction down mounting of high-frequency semiconductor optical elements, but also that of an electronic element for electrically driving and controlling a light source such as a semiconductor laser and for electrically driving and controlling a high-frequency semiconductor optical element, is performed on the mounting substrate.

Abstract: A method is provided to provide a photodetector that can enhance the light receiving sensitivity with a relatively simple structure, and that can maintain a high speed responsiveness. A photodetector having a MSM (Metal-Semiconductor-Metal) structure, including a substrate, a multilayer film that is disposed over the substrate and includes a low refractive index layer and a high refractive index layer that are alternately laminated as a unit cycle. At least one of the low refractive index layer and the high refractive index layer is a photoabsorption layer composed of semiconductor, and a portion that is embedded in the multilayer film, the portion having at least one pair of opposing electrodes within the multilayer film.

Abstract: Even for a driving impedance of 25 ?, high transmission waveform quality of an optical transmission module is maintained using an optical modulator element designed for a driving impedance of 50 ?. The above can be achieved by adopting an optical module 100 that includes an input electrode for electrical signals, an optical modulator element for modulating laser light using the electrical signals, a termination resistance element, a first bonding wire for connecting the input electrode and the optical modulator element, a second bonding wire for connecting the optical modulator element and the termination resistance element, and a third bonding wire for connecting the input electrode and the termination resistance element.

Abstract: An apparatus and method for high speed phase modulation of optical beam with reduced optical loss. In one embodiment, an apparatus includes a first region of an optical waveguide disposed in semiconductor material. The first region has a first conductivity type. The apparatus also includes a second region of the optical waveguide disposed in the semiconductor material. The second region has a second conductivity type opposite to the first conductivity type. A first contact is included in the apparatus and is coupled to the optical waveguide at a first location in the first region outside an optical path of an optical beam to be directed through the optical waveguide. The apparatus also includes a first higher doped region included in the first region and coupled to the first contact at the first location to improve an electrical coupling between the first contact and the optical waveguide. The first higher doped region has a higher doping concentration than a doping concentration within the optical path.

Abstract: An apparatus and method for modulating a phase of optical beam independent of polarization. In one embodiment, an apparatus according to embodiments of the present invention includes a first region of an optical waveguide disposed in semiconductor material, the first region having a first conductivity type, and a second region of the optical waveguide disposed in the semiconductor material, the second region having a second conductivity type opposite to the first conductivity type. The apparatus also includes a substantially V shaped insulating region disposed between the first and second regions of the optical waveguide, wherein a vertex of the substantially V shaped insulating region forms an intersecting line that is substantially parallel to an optical path of an optical beam to be directed through the optical waveguide.

Abstract: An electro-optic (EO) device having a high-resistivity semiconducting crystal and a method of operating such a device. The local shielding of the externally applied field lowers the EO effect, which can be partially or completely inhibited particularly in the low-frequency regime, i.e., less than about 105 Hz. By holding a high-resistivity semiconducting crystal at a suitable temperature, EO response and efficiency are improved, in particular for light signals that are non-modulated or modulated at low frequencies. Preferably, the temperature at which the semiconducting crystal is held during functioning is between 50 and 150° C. Enhancement of the EO effect has been demonstrated also for EO devices operating at relatively large optical powers, i.e., larger than about 0.1 mW.

Abstract: An electroabsorption modulator (10) includes at least one quantum well (26) in a conduction band and a corresponding quantum well (26) in a valence band. A barrier made from InGaAlAs or InGaAsP is formed within each of the quantum wells in the conduction and valence bands.

Abstract: An optical amplifier having a uniform gain profile uses a photonic crystal to tune the density-of-states of a gain medium so as to modify the light emission rate between atomic states. The density-of-states of the gain medium is tuned by selecting the size, shape, dielectric constant, and spacing of a plurality of microcavity defects in the photonic crystal. The optical amplifier is particularly useful for the regeneration of DWDM signals in long optical fibers.

Abstract: A radiation-sensitive semiconductor body which has at least one radiation-absorbent active area (2) between at least two contact layers (6, 7) and which receives electromagnetic radiation in a wavelength range between ?1 and ?2 where ?2>?1. A filter layer (5) is arranged between the active area (2) and a radiation input surface (9). The active area (2) detects electromagnetic radiation at a wavelength below ?2. The filter layer (5) absorbs electromagnetic radiation at a wavelength below ?1, and passes electromagnetic radiation at a wavelength above ?1.

Abstract: An optical system includes an InGaAsP photodiode having a bandgap and configured to operate in Gieger mode, a first light source configured to emit an optical signal of a first wavelength less than the bandgap at a first intensity, a second light source configured to emit light of a second wavelength greater than the bandgap at a second intensity, a beam combiner configured to combine the first and second wavelengths to simultaneously irradiate the photodiode with the first and second wavelengths, an electric field applied across the photodiode greater than a breakdown voltage thereof and configured to result in avalanching of electrons in the photodiode when the optical signal from the first light source is incident thereon and resulting in a photorefractive response within the photodiode, and an image capture device in optical communication with and configured to capture modulated light of the second wavelength reflected from the photodiode.

Abstract: A modulator, including: an active modulator layer including a plurality of step quantum wells, wherein at least one of the plurality of step quantum wells is configured to have a leaky electron energy state; and at least one inactive layer bounding the active modulator layer.

Abstract: An electrooptical device is provided comprising at least one substrate, at least one pair of electrodes and at least one layer of an electrooptical material. The electrooptical material represents an optically anisotropic thin crystal film and contains molecules having aromatic rings and possessing a lattice with an interplanar spacing (Bragg's reflection) of 3.4±0.2 ? along one of optical axes. The electrooptical material has anisotropic refractive indices and/or anisotropic absorption coefficients that are depended on an electric field strength.

Abstract: A substrate for an electrooptic device comprising a light-transmissive base member, a reflection layer formed on the base member so as to include each reflection portion and a corresponding transmission portion having a transmission factor higher than that of the reflection portion, a light transmission layer formed over the base member so as to coincide with the reflection layer and to include each hollow at a position that coincides with the transmission portion in plane, and an orientation film formed over the base member so as to coincide with the light transmission layer and to define a concavity while entering the corresponding hollow. The thickness “b” of a liquid crystal layer corresponding to the concavity is greater than the thickness “a” of the liquid crystal layer at the other positions thereof.

Abstract: The device includes an oscillator (1) to generate an electrical signal of a predetermined frequency and a signal divider (2) to split the electrical signal into first and second signals. The frequency of the second signal is tripled by tripler (3) and the tripled second signal is recombined with the first signal at signal adder (9) to produce a combined electrical signal. This combined electrical signal drives a Mach-Zehnder modulator (10).

Abstract: A voltage storage cell circuit includes an access transistor and a storage capacitor, wherein the source of said access transistor is connected to a bitline, the gate of said access transistor is connected to a wordline, and wherein the drain of said access transistor is connected to a first plate of said storage capacitor forming a storage node, and wherein the second plate of said storage capacitor is connected to a pump signal. This arrangement allows for a novel pixel circuit design with area requirements comparable to that of a 1T1C DRAM-like pixel cell, but with the advantage of an output voltage swing of the full range allowed by the breakdown voltage of the pass transistor. A spatial light modulator such as a micromirror array can comprise such a voltage storage cell.

Abstract: A method and apparatus for a tunable optical spectrum analyzer that can measure the optical spectrum of a demultiplexed DWDM signal are presented. The signal level and Optical Signal to Noise Ratio (OSNR) of an individual channel of the DWDM signal can be obtained from the measured optical spectrum. The device employs a rapid tuning and detection technique to obtain the optical spectrum of the incoming signal. In a preferred embodiment the apparatus is fabricated on a single chip resulting in a compact measurement device. Using the device of the preferred embodiment, single channel OSNR can be determined in as small a time interval as approximately 225 microseconds. Using an array of these devices an entire DWDM mixed signal can be monitored as to OP and OSNR in the same time interval.

Abstract: A transmittance overcoat with effectively planar top surface and specified optical and materials properties is applied above a microlens layer to extend the focal length and enhance the performance of long focal length microlenses for semiconductor array color imaging devices. The geometrical optics design factors and microelectric fabrication sequence to achieve optimized long focal length microlens performance are disclosed. The principal advantages of the adaptive process taught in the present invention is shown to enable real-time compensation adjustments for process and material variations. The overcoat process enables simplified single-layer integrated microlens optics for low-cost, high volume manufacturing of CMOS and CCD color video cameras.

Abstract: A differential drive semiconductor optical modulator includes: a differential driver circuit having output pads which can output a pair of differential signals; a transmission-line substrate having transmission lines connected to the output pads and ground lines; and semiconductor modulators mounted on the transmission-line substrate, arranged in series along a common optical axis; terminal resistors connected to terminal ends of the transmission lines and inductances interposed between the semiconductor modulators and the terminal resistors, on the transmission-line substrate, producing an appropriate optical modulation waveform with a high extinction ratio and enhanced modulation bandwidth.

Abstract: An apparatus and method for modulating a phase of optical beam independent of polarization. In one embodiment, an apparatus according to embodiments of the present invention includes a first region of an optical waveguide disposed in semiconductor material, the first region having a first conductivity type, and a second region of the optical waveguide disposed in the semiconductor material, the second region having a second conductivity type opposite to the first conductivity type. The apparatus also includes a substantially V shaped insulating region disposed between the first and second regions of the optical waveguide, wherein a vertex of the substantially V shaped insulating region forms an intersecting line that is substantially parallel to an optical path of an optical beam to be directed through the optical waveguide.

Abstract: The invention provides “engineered” nonlinear nanocomposite materials with an extremely large ?(3) and fast temporal response along with optical properties that can be precisely tuned to satisfy the requirements of a particular application (e.g., optical, thermal, mechanical, etc.). In particular, the magnitude of the linear and nonlinear index of refraction can be adjusted substantially independently of the absorption spectrum of the material. In addition, the optical characteristics can be engineered substantially independently from the mechanical and chemical characteristics, providing exceptional performance and flexibility in terms of device-incorporation and process-stability.

Abstract: Provided is an optical modulator for modulating light comprising: a superlattice structure having a plurality of interleaved narrow and wide bandgap semiconductor layers, wherein wave functions of energy states of electrons and holes in different narrow bandgap layers are coupled; and a power supply that applies voltage to the superlattice structure between a first non-zero voltage and a second non-zero voltage to modulate the light.

Abstract: Optoelectronic devices and methods for their fabrication having enhanced and controllable rates of the radiative relaxation of triplet light emitters are provided exemplified by organic light emitting devices based on phosphorescent materials with enhanced emission properties. Acceleration of the radiative processes is achieved by the interaction of the light emitting species with surface plasmon resonances in the vicinity of metal surfaces. Non-radiative Förster-type processes are efficiently suppressed by introducing a transparent dielectric or molecular layer between the metal surface and the chromophore. For materials with low emission oscillator strengths (such as triplet emitters), the optimal separation distance from the metal surface is determined, thus suppressing energy transfer and achieving a significant acceleration of the emission rate.

Abstract: Disclosed is an electro-absorption optical modulator using a semiconductor device. The optical modulator makes use of a change in light absorption caused by displacement of an absorption curve depending on a bias voltage applied to the device. Here, a level of the light absorption depending on the bias voltage is expressed as a transfer function of output light to the applied bias, and the transfer function has a non-linear profile due to a characteristic of a material. Unlike signal modulation of a digital optical communication system, an analog optical transmission system can be subjected to deterioration in performance, because the non-linear characteristic of the transfer function for the optical modulator generates signal distortion when an electrical signal is converted into an optical signal. The typical optical modulator has an absorption layer constituted of quantum wells having the same width.

Abstract: A grating coupled surface plasmon resonance optical modulator is disclosed. A electro-optic polymer dielectric is deposited on the metallic surface of a diffraction grating to provide a metal/dielectric interface. A surface plasmon will propagate at the metal/dielectric interface in a resonant condition, e.g., when the metal surface is illuminated by transverse magnetic (TM) polarized light of the appropriate wavelength, angle of incidence and phase velocity. In the present invention, phase velocity is controlled by the diffraction grating. A transparent electrode deposited on the electro-optic layer allows an electrical potential to be applied across the electro-optic polymer. The applied electrical potential (voltage) changes the index of refraction of the electro-optic polymer, thereby disrupting the resonant condition to produce an optically detectable change in reflectance of incident light from the metal layer.

Abstract: Disclosed is a high speed optical signal processor which includes a saturable absorber area including a substrate, an active layer, a clad layer and a first upper electrode which are sequentially formed on one face of the substrate, and a first lower electrode formed on the other face of the substrate; and a gain-clamped optical amplifier area including a substrate having a diffraction grating for generating a laser beam, an active layer, a clad layer and a second upper electrode which are sequentially formed on one face of the substrate, and a second lower electrode formed on the other face of the substrate, the second upper electrode being isolated from the first upper electrode of the saturable absorber area.

Abstract: The present invention is directed to an electrically switchable laminate construction for applications including smart windows, and other uses and applications in which light management is desired. The electro-optical laminate construction has scattering and transparent modes of operation for dynamically controlling electromagnetic radiation flow.