A new numerical method is developed for solution of the Gel'fand - Levitan - Marchenko inverse scattering integral equations. The method is based on the fast inversion procedure of a Toeplitz Hermitian matrix and special bordering technique. The method is highly competitive with the known discrete layer peeling method in speed and exceeds it noticeably in accuracy at high reflectance.
A novel approach for a delay line interferometer (DLI) based purely on forward Bragg scattering is proposed. We have numerically and experimentally demonstrated that a Bragg grating can deliver the functionality of a DLI in its transmission mode along a single common interfering optical path, instead of the conventional DLI implementation with two interfering optical paths. As a proof of concept, a fiber Bragg grating has been designed and fabricated, showing the desired functionality in the transmission mode of the Bragg grating. The proposed "Bragg-DLI" approach is applicable to any kind of …
A means to calculate the multimodal spectral response of Bragg gratings in general non-circular multimode waveguides is proposed. To illustrate the power of the technique, the spectra of two Bragg temperature sensors are numerically calculated in which coupling between 100 modes considered. It is shown how the Bragg wavelength in multimode Bragg grating waveguides is affected by the number of modes and energy distribution among them. Good matching of the simulated spectrum of a multimode Bragg grating on a planar inverted rib waveguide to the measured spectrum is seen.
We propose a new method to narrow the linewidth of entangled photons generated from spontaneous parametric down conversion (SPDC). An internal Bragg grating is incorporated onto a nonlinear optical crystal waveguide. We study theoretically the spectral characteristics of SPDC under two Bragg grating structures. We show that using the Bragg grating with a midway pi-phase shifter, it is a promising way to generate narrow-line entangled photons.
We have explored through numerical simulations the amplification of laser pulses in nonlinear fiber Bragg gratings with gain and normal dispersion. The distortion of the temporal intensity profile caused by the higher-order dispersion coefficients is examined. The stabilizing effect of fourth-order dispersion on pulse propagation is demonstrated. For some conditions, the amplified pulse shape evolves towards a Bragg similariton, a quasi-parabolic temporal profile with wave-breaking free temporal characteristics.
We propose the use of interleaved graphene sections on top of a silicon waveguide to implement tunable Bragg gratings. The filter central wavelength and bandwidth can be controlled changing the chemical potential of the graphene sections. Apodization techniques are also presented.
We present direct UV-written waveguides and Bragg gratings operating at 780 nm. By combining two gratings into a Fabry-Perot cavity we have devised and implemented a novel and practical method of measuring the group delay of Bragg gratings.
We report on the fabrication and characterization of photonic-based nanothermometers, a silicon photonic Bragg grating and photonic crystal cavity. When cladded with silicon dioxide layer the sensors have at least eight times better sensitivity compared to the sensitivity of conventional fiber Bragg grating sensors. We demonstrate that these photonic thermometers are a viable temperature sensing solution.
The inscription of Bragg gratings in chalcogenide (As2Se3) wires with sub-wavelength diameter is proposed and demonstrated. A modified transverse holographic method employing He Ne laser light at a wavelength of λw = 633 nm allows the writing of Bragg grating reflectors in the 1550 nm band. The gratings reach an extinction ratio of 40 dB in transmission and a negative photo-induced index change of δn~0.01. The inscription of Bragg gratings in chalcogenide microwires will enable the fabrication of new devices with applications in nonlinear optics, and sensing in the near-to-mid-infrared region …
We report on an optical imaging design based on common-path off-axis digital holography, using a multiplexed volume Bragg grating. In the reported method, a reference optical wave is made by deflection and spatial filtering through a volume Bragg grating. This design has several advantages including simplicity, stability and robustness against misalignment.
We report fabrication of THz fiber Bragg gratings (TFBG) using CO2 laser inscription on subwavelength step-index polymer fibers. A fiber Bragg grating with 48 periods features a ~4 GHz-wide stop band and ~15 dB transmission loss in the middle of a stop band. The potential of such gratings in design of resonant sensor for monitoring of paper quality is demonstrated. Experimental spectral sensitivity of the TFBG-based paper thickness sensor was found to be ~ -0.67 GHz / 10 um. A 3D electromagnetic model of a Bragg grating was used to explain experimental findings.
We report the first experimental observation of photosensitivity in As2Se3 glass at a wavelength of 1550 nm. We utilize this photosensitivity to induce the first Bragg gratings using a laser source at a wavelength of 1550 nm. We quantify the photosensitivity thresholds related to exposition intensity and exposition time. Finally, we demonstrate that As2Se3 Bragg gratings are widely tunable in wavelength as the microwire can withstand an applied longitudinal strain of 4 \times 104 με.
We investigate the performance of waveguide Bragg gratings as a function of imperfections introduced in the fabrication process. Effects of stitching errors introduced in the electron-beam and UV-lithography are discussed in details.
An all optical soliton diode (AOSD) is proposed based on a sandwich nonlinear Bragg-grating structure: a linearly chirped Bragg-grating linked to a uniform Bragg-grating and again to a chirped Bragg-grating. The nonreciprocity is achieved by introducing two spatially asymmetric chirped Bragg-gratings with optical nonlinearity. High transmission ratio up to 150 is obtained when launching a picosecond Gaussian pulse into the setting. We find that such pulses in a form of solitons propagate at a rather small velocity ($<0.03c$) when pulse wavelength is selected in the vicinity of photonic bandgap…
We study nanofibers with Bragg gratings from equidistant holes. We calculate analytically and numerically the reflection and transmission coefficients for a single grating and also for a cavity formed by two gratings. We show that the reflection and transmission coefficients of the gratings substantially depend on the number of holes, the hole length, the hole depth, the grating period, and the light wavelength. We find that the reflection and transmission coefficients of the gratings depend on the orientation of the polarization vector of light with respect to the holes. Such a dependence is …
We demonstrate apodized fiber Bragg gratings inscribed with a point-by-point technique. We tailor the grating phase and coupling amplitude through precise control over the longitudinal and transverse position of each laser-inscribed modification. This method of apodization is facilitated by the highly-localized, high-contrast modifications generated by focussed IR femtosecond laser inscription. Our technique provides a simple method for the design and implementation of point-by-point fiber Bragg gratings with complex apodization profiles.
We present here the inscription of single-mode waveguides with Bragg gratings in sapphire. The waveguide Bragg gratings have a novel multi-layer depressed cladding design in the 1550 nm telecommunications waveband. The Bragg gratings have a narrow bandwidth (<0.5 nm) and have survived annealing at 1000°C. The structures are inscribed with femtosecond laser direct writing, using adaptive beam shaping with a non-immersion objective. A single-mode sapphire fiber Bragg grating is created by writing a waveguide with a Bragg grating within a 425 μm diameter sapphire optical fiber, providing signific…
The ring interferometer with zero optical path difference known as Sagnac one is offered with a diffraction splitting of the entering light beam. As the beamsplitter, a transmission holographic Bragg grating is used. Conditions of normal operation of this interferometer achieve under the equal intensity of beam copies and the adjustable phase shift between them in its two interferometer shoulders. These conditions are met with the holographic grating, which provides the phase shift 180^0 on the central Bragg wavelength. Experimental approbation of the modified interferometer validates the expe…
Measurement and analysis of diffraction parameters of thick transmission holographic phase gratings recorded on PHC-488 photopolymer are presented. Precision determination of the spatial grating period is executed by Bragg angle measurement for two precisely known wavelengths in the first diffraction order and also by Bragg angle measurement on one wavelength in the first and second diffraction orders. Determination of actual grating thickness and depths of spatial modulation of a holographic recording, which are responsible for their main optical characteristics, is carried out with the appli…
A photonic analogue of Klein tunneling (KT), i.e. of the exotic property of relativistic electrons to pass a large repulsive and sharp potential step, is proposed for pulse propagation in a nonuniform fiber Bragg grating with an embedded chirped region. KT can be simply observed as the opening of a transmission window inside the grating stop band, provided that the impressed chirp is realized over a length of the order of the analogue of the Compton wavelength.
We report on the impact of realistic gain and loss models on the bistable operation of nonlinear parity-time Bragg gratings. In our model we include both dispersive and saturable gain and show that levels of gain/loss saturation can have significant impact on the bistable operation of a nonlinear PT Bragg grating based on GaAs material. The hysteresis of the nonlinear PT Bragg grating is analyzed for different levels of gain and loss and different saturation levels. We show that high saturation levels can improve the nonlinear operation by reducing the intensity at which the bistability occurs…
We propose a novel kind of the low-loss THz Waveguide Bragg Grating (TWBG) fabricated using plasmonic two-wire waveguide and a micromachined paper grating for potential applications in THz communications. Two TWBGs were fabricated with different periods and lengths. Transmission spectra of these TWBGs show 17 dB loss and 14 dB loss in the middle of their respective stop bands at 0.637 THz and 0.369 THz. Insertion loss of 1-4 dB in the whole 0.1-0.7 THz region was also measured. Finally, TWBG modal dispersion relation, modal loss and field distributions were studied numerically, and low-loss, h…
It is widely accepted that Bragg reflection from linearly chirped Bragg gratings (LCBGs) can compensate for a chromatic dispersion by reflecting different wavelengths at different location along the axis of the gratings for ultra-short pulses. In this paper, we studied the possibility of making use of such a dispersion-compensating property to construct a white light cavity (WLC). A pair of LCBGs is suggested as the reflectors of the cavity. The analytical and numerical analysis shows that the reflection by a LCBG does not solely occur at the position where Bragg condition is reached. The accu…
We derive the rogue wave solution of the classical massive Thirring model, that describes nonlinear optical pulse propagation in Bragg gratings. Combining electromagnetically induced transparency with Bragg scattering four-wave mixing, may lead to extreme waves at extremely low powers.
In recent years there has been considerable interest in utilizing embedded fiber optic based sensors for fabricating smart materials. One of the primary motivations is to provide real-time information on the structural integrity of the material so as to enable proactive actions that prevent catastrophic failure. In this preliminary study we have examined the impact of embedding on the temperature-dependent response of fiber Bragg gratings.
Femtosecond laser writing is applied to form Bragg grating waveguides in the diamond bulk. Type II waveguides are integrated with a single pulse point-by-point periodic laser modification positioned towards the edge of the waveguide core. These photonic devices, operating in the telecommunications band, allow for simultaneous optical waveguiding and narrowband reflection from a 4th order grating. This fabrication technology opens the way towards advanced 3D photonic networks in diamond for a range of applications.
In wavelength division multiplexed (WDM) optical networks, intraband and/or interband crosstalk plays a major role in limiting practical implementation of an OXC subsystem. Again FIBER BRAGG GRATINGS (FBGs), due to their properties, are emerging as very important elements for both the optical fiber communication and sensing fields. The crosstalk sources are related to the different individual components of the OXC's. In this paper, an analytical model is established to evaluate the performance of an FBG-OC-based optical cross connect and proposed a novel scheme of transmission Fiber Bragg Grat…
We realize a fiber Bragg grating InGaN based laser diode emitting at 400 nm and demonstrate its high coherency. Thanks to the fabrication of a narrow band fiber Bragg grating in the near-UV, we can reach single-mode and single-frequency regimes for the self-injection locked diode. The device exhibits 44 dB side-mode-suppression-ratio and mW output power. Detailed frequency noise analysis reveals sub-MHz integrated linewidth and 16 kHz intrinsic linewidth. Such a narrow linewidth laser diode in the near-UV domain with a compact and low-cost design could find applications whenever coherency and …
We introduce a new optical component - a rotated chirped volume Bragg grating (r-CBG) - that spatially resolves the spectrum of a normally incident light beam in a compact footprint and without the need for subsequent free-space propagation or collimation. Unlike conventional chirped Bragg volume gratings in which both the length and width of the device must be increased to increase the bandwidth, by rotating the Bragg structure we sever the link between the length and width of an r-CBG, leading to a significantly reduced device footprint for the same bandwidth. We fabricate and characterize s…
The integration of photonic sensors into microfluidic devices provides opportunities for dynamic measurement of chemical and physical properties of fluids in very small volumes. We previously reported on the use of commercially available Fiber Bragg Gratings (FBGs) and on-chip silicon waveguides for temperature sensing. In this report, we demonstrate the integration of FBGs into easy-to-fabricate microfluidic devices and report on their sensitivity for temperature and pressure measurement in microliter volumes. These sensors present new routes to measurement in microfluidic applications such a…
Scenarios for controllable creation, trapping and holding of single and multiple solitons in a specially designed nonlinear Bragg grating (BG) are proposed. The setting includes a chirped BG segment, which is linked via a local defect to a uniform BG with a built-in array of defects. A parabolic relation between the trapping position of the incident soliton and its power is obtained. Simultaneous trapping of two and three solitons at different locations is demonstrated too.
Optical fibers typically confine light through total internal reflection or through photonic bandgaps. Here we show that light can be perfectly guided in optical fibers through a different mechanism based on bound states in the continuum (BICs). In fibers with periodic Bragg gratings, we predict bona fide BICs in pure-polarization modes, as well as quasi-BICs in hybrid-polarization modes. These guided modes exist robustly without the need for fine structural tuning, and they persist even with the very small grating index contrasts that are available in conventional fiber Bragg gratings. The su…
In this paper we propose a new optical ring resonator with a very high Q-factor, to be used as a basic element in a wide range of physics and engineering applications. We theoretically demonstrate that in large size conventional ring resonators, a value of the Q-factor higher than 109 is achievable by exploiting the band-edge resonances in a waveguiding long period Bragg grating closed loop, excited through a bus waveguide. The dispersion introduced by the Bragg grating is responsible for a reduction in the band edge resonance linewidth, which is inversely proportional to the square of the num…
We find exact solutions describing bidirectional pulses propagating in fiber Bragg gratings. They are derived by solving the coupled-mode theory equations and are expressed in terms of products of modified Bessel functions with algebraic functions. Depending on the values of the two free parameters the general bidirectional X-wave solution can also take the form of a unidirectional pulse. We analyze the symmetries and the asymptotic properties of the solutions and also discuss about additional waveforms that are obtained by interference of more than one solutions. Depending on their parameters…
The supersymmetric (SUSY) structure of coupled-mode equations that describe scattering of optical waves in one-dimensional Bragg gratings is highlighted. This property can find applications to the synthesis of special Bragg filters and distributed-feedback (DFB) optical cavities. In particular, multiple SUSY (Darboux-Crum) transformations can be used to synthesize DFB filters with any desired number of resonances at target frequencies. As an example, we describe the design of a DFB structure with a set of equally-spaced resonances, i.e. a frequency comb transmission filter.
We propose an efficient method to determine the effective refractive index of step-index optical fibers from the visible to the mid-IR and thus allowing to infer their dispersive properties over a broad spectral range. The validity of the method, based on the writing of an array of fiber Bragg gratings (FBGs) with known periods using the fs scanning phase mask technique, is first confirmed with a standard silica fiber, then applied to various fluoride glass fibers to determine their effective refractive index and dispersion over more than three octaves, i.e. from 550 to 4800 nm.
The thermal drift of the characteristic wavelength of fiber Bragg gratings (FBGs) photowritten in the core of microstructured fibers (MOFs) is significantly reduced by inserting a liquid of suitable refractive index into their holes. For instance, the spectral range of variations is divided by a factor of 4 over a temperature range larger than 20\degree C in a six-hole MOF, and the maximum sensitivity is reduced. Such passive FBG temperature compensation technique is of great interest for applications involving accurate sensing free of thermal effects.
Resistance thermometry is a time-tested method for taking temperature measurements. In recent years fundamental limits to resistance-based approaches spurred considerable interest in developing photonic temperature sensors as a viable alternative. In this study we demonstrate that our photonic thermometer, which consists of a silicon waveguide integrated with a Bragg grating, can be used to measure temperature changes over the range from 5 C to 160 C with a combined expanded uncertainty [k = 2 ; 95% confidence level] of 1.25 degree C. The computational modeling of the sensor predicts the reson…
It is shown that the optical-electronic system consisted of the transmission Bragg grating, a laser and the intermediate sensitive to the vibrations mirror can detect the vibrations, when touched by them laser beam scan will exceed the angular divergence of the beam. The mathematical model of the sensor of the vibrations presented in the form of Taylor series describes the system response taking into account the operating point, in particular, describes the effect of the doubling of the modulation frequency response relative to the frequency of acting vibrations.
In recent years there has been considerable interest in developing photonic temperature sensors such as the Fiber Bragg gratings (FBG) as an alternative to resistance thermometry. In this study we examine the thermal response of FBGs over the temperature range of 233 K to 393 K. We demonstrate, in a hermetically sealed dry Argon environment, that FBG devices show a quadratic dependence on temperature with expanded uncertainties (k = 2) of ~500 mK. Our measurements indicate that the combined measurement uncertainty is dominated by uncertainty in determining the peak center fitting and by therma…
We performed light optical diffraction experiments on a nanoparticle-polymer volume holographic grating in an angular range including also far off-Bragg replay. A comparison of three diffraction theories - on the same level of complexity - with our experimental results shows that the dynamical theory of diffraction and the first-order two-wave coupling theory using the beta-value method fit the data very well. In contrast, the prevalent two-wave coupling theory using the K-vector closure method yields a poor fit with an order of magnitude worse mean squared error. These findings must be consid…
Strong retardation of ultrashort optical pulses, including their deceleration and stoppage in the form of Bragg solitons in a cascaded Bragg-grating (BG) structure, is proposed. The manipulations of the pulses are carried out, using nonlinear effects, in a chirped BG segment which is linked, via a defect, to a uniform grating. The storage of the ultrashort pulses is shown to be very robust with respect to variations of the input field intensity, suggesting the feasibility of storing ultrafast optical pulses in such a structure. Physical estimates are produced for the BGs written in silicon.
The emergence of optical micro/nano-fiber (MNF) with a subwavelength diameter, which has ultra-light mass and an intense light field, brings an opportunity for develop fiber based optomechanical systems. In this study, we theoretically show an optomechanical effect in silica MNF Bragg gratings (MNFBGs). The light-induced mechanical effect results in continuously distributed strain along the grating. It is shown that the power-related strain introduces an optically reconfigurable chirp in the grating period. We develop new optomechanical coupled-mode equations and theoretically analyze the infl…
The first demonstration of narrowband spectral filtering of multimode light on a 3D integrated photonic chip using photonic lanterns and waveguide Bragg gratings is reported. The photonic lanterns with multi-notch waveguide Bragg gratings were fabricated using the femtosecond direct-write technique in boro-aluminosilicate glass (Corning, Eagle 2000). Transmission dips of up to 5 dB were measured in both photonic lanterns and reference single-mode waveguides with 10.4-mm-long gratings. The result demonstrates efficient and symmetrical performance of each of the gratings in the photonic lantern.…
A fiber Bragg grating (FBG) with an inverse-Gaussian apodization function is proposed and fabricated. It is shown that such a FBG possesses easily controllable dual-wavelength narrow transmission peaks. Incorporating such a FBG filter in a fiber laser with a linear cavity, stable dual-wavelength emission with 0.146 nm wavelength spacing is obtained. It provides a simple and low cost approach of achieving the dual-wavelength fiber laser operation.
We report a novel design of a compact wavelength add-drop multiplexer utilizing dielectric-loaded surface plasmon-polariton waveguides (DLSPPWs). The DLSPPW-based configuration exploits routing properties of directional couplers and filtering abilities of Bragg gratings. We present practical realization of a 20-$μ$m-long device operating at telecom wavelengths that can reroute optical signals separated by approximately 70 nm in the wavelength band. We characterize the performance of the fabricated structures using scanning near-field optical microscopy as well as leakage-radiation microscopy a…
State-of-the-art fiber Bragg grating interrogators utilize mature concepts and technologies like tunable lasers, optical spectrum analyzers and a combination of time, wavelength, or spatial division demultiplexing approaches. Here, we propose the use of computational compressed sensing (CS) techniques for interrogation of fiber Bragg gratings, reducing interrogator complexity by using a broadband ASE light source and single-pixel detection. We demonstrate temperature sensing using a pre-calibration approach to achieve reconstruction accuracy comparable to uncompressed measurements. We extend t…
We report a new gateway to enhance the sponatnesous emission rate of single quantum emitters by introducing a cavity in tilted nanofiber Bragg grating (TNFBG). We found that light emitter's coupling efficiency into the tilted grating structure's guided mode is 65%, with 70 grating periods. This novel tilted structure has a high Q factor ~ 1408.71 and low mode volume ~ 0.66 microm3- an important requirement. Further, the Purcell factor of a quantum light emitter inside the nanofiber is nine times more than that of an emitter on the cavity's surface. The further optimized system with enhanced pe…
A polymer/liquid crystal-based fiber Bragg grating (PLC-FBG) is fabricated with visible two-beam holography by photo-induced modulation of a pre-polymer/LC solution infiltrated into the hollow channels of a solid core photonic crystal fiber (PCF). The fabrication process and effects related to the photonic bandgap guidance into the infiltrated PCF, and characterization of the PLC-FBG are discussed. Experimental data here presented, demonstrate that the liquid crystal inclusions of the PLC-FBG lead to high thermal and bending sensitivities. The microscopic behavior of the polymer/liquid crystal…
The time-dependent Bragg diffraction by multilayer gratings working by reflection or by transmission is investigated. The study is performed by generalizing the time-dependent coupled-wave theory previously developed for one-dimensional photonic crystal [Andr{é} J-M and Jonnard P, J. Opt. 17, 085609 (2015)] and also by extending the Takagi-Taupin approach of the dynamical theory of diffraction. The indicial response is calculated. It presents a time-delay with a transient time that is a function of the extinction length for reflection geometry and of the extinction length combined with the thi…
Supercontinuum generation is an extensively studied and arguably the most important and all-encompassing nonlinear phenomenon. Yet, we do not have a good control over all the signals generated in this process. Usually a large part of an octave spanning spectrum has orders of magnitude too much weaker signal than the peak to be useful for any application. In this work we show strong signal generation within a supercontinuum using a silicon Bragg grating waveguide. We show up to 23 dB of signal enhancement over a 10 nm full-width-at-half-maximum bandwidth at the Bragg resonance in the telecom wi…
