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Fiber Grating Spectra
Abstract
In this paper, we describe the spectral characteristics that can
be achieved in fiber reflection (Bragg) and transmission gratings. Both
principles for understanding and tools for designing fiber gratings are
emphasized. Examples are given to illustrate the wide variety of optical
properties that are possible in fiber gratings. The types of gratings
considered include uniform, apodized, chirped, discrete phase-shifted,
and superstructure gratings; short-period and long-period gratings;
symmetric and tilted gratings; and cladding-mode and radiation-mode
coupling gratings
... (1) Figure 1(a) illustrates a conceptual diagram of an FBGA with different power metrics: P total input is the total injected power into the FBGA, P i ref is the reflected power from the i-th FBG, P i trans is the transmitted power over the i-th FBG, P total ref is the total reflected power from the whole FBGA, and P total trans is the total transmitted power over the whole FBGA. Figure 1(b) shows a typical reflected spectrum from a single FBG (simulated using the transfer matrix approach [30]), assuming a peak reflectivity of 90% for the FBG, where often only P ref (i.e., green curve) is used for sensing purpose while the P trans (i.e., cyan part) is usually wasted at the fiber's distal end. The delivered spectrum from the light source is supposed to be rectangular with uniform power distribution (i.e., flat PSD) across the range and sharp edges at λ min and λ max . ...
... The delivered spectrum from the light source is supposed to be rectangular with uniform power distribution (i.e., flat PSD) across the range and sharp edges at λ min and λ max . The reflected spectrum from a single FBG is typically narrow and centered at the Bragg wavelength, with a bandwidth of ∼0.3 nm, measured as the full-width half-maximum (FWHM) of the reflected spectrum [30]. Therefore, taking into account the cumulative effects of multiple similar FBGs (i.e., same peak reflectivity and bandwidth, but with different Bragg VOLUME 4, 2016 wavelengths) within a single FBGA (Figure 1(c)), the total reflected power P total ref and the total transmitted power P total trans from a number of N FBGs within the same FBGA can be calculated as: ...
... The reflected power from each FBG was computed using the transfer matrix approach, as illustrated in the insets of Figs. 3(b) and 3(c)) [30]. Following this, the transmitted power from FBGA1 was routed to EH unit 1 (EH 1 ), while the transmitted power from FBGA 2 was delivered to EH unit 2 (EH 2 ). ...
This work presents a new approach to energy harvesting (EH) from a quasi-distributed sensing network of fiber Bragg grating arrays (FBGAs). While maintaining accurate FBGA temperature sensing, our approach collects the typically unused transmitted power from the broadband light across an FBGA sensing network and converts and stores it as electrical energy to power up electronic-based sensors (EBSs). To demonstrate this concept, we reported on a quasi-distributed FBGA network topology consisting of two different FBGAs: one with 5 FBGs and the other with 10 FBGs. The system employs time-division multiplexing (TDM) via an optical switch to alternate the light between both FBGAs. Both FBGAs were calibrated for temperature sensing using their reflected spectra, showing typical sensitivity values of 11.72 pm/°C-12.43 pm/°C for FBGA1 and 12.86 pm/°C-14 pm/°C for FBGA2. The untapped power transmitted through both FBGAs was harvested using EH units based on supercapacitors. The EH process was investigated for different switching times (1 s, 100 s, 600 s, and 1000 s). The cumulative harvested power ranged from ∼6.56-7.06 mW, corresponding to the overall conversion efficiency of ∼25.8-27.8% for the entire system after leaving it for 60 min of temperature sensing. These results validate the potential of using quasi-distributed FBGA networks for simultaneous sensing and EH, providing a sustainable solution for autonomous multi-parameter hybrid sensing applications such as remote underwater or underground EBS.
... [11] The findings demonstrate an outstanding agreement with experimental investigations, and CMT has been effectively used to simulate a variety of fiber grating systems. The fabrication of FBG results in a perturbation on the effective refractive index neff of the guided modes which is given by [12]. ...
... The simplified coupled mode equations for a single-mode FBG are provided as [12]. ...
... With a uniform FBG, the grating chirp / =0, equations (11), (12), and (14) are constants, and is the mode propagation constant. Through the specification of suitable boundary conditions, the reflectivity's analytic expression can be found as follows [12,13] The parameters of the FBG utilized for the simulation are specified in Table 1. ...
Cancer cell detection is critical to early diagnosis and treatment, aiming to improve patient outcomes through timely interventions. One promising approach involves using Fiber Bragg Grating (FBG) sensors due to their high sensitivity, biocompatibility, and ability to operate in real time. Due to the blood's refractive index, the wavelength shift in an FBG sensor varies, leading to a change in the effective refractive index. This occurs because the interaction between the FBG sensor and the surrounding medium, like blood, alters the light propagation within the fiber. The shift in the reflected wavelength corresponds to changes in the effective refractive index, which can be used to detect cancer- related anomalies in the blood. However, the proposed grating structure provides a wavelength shift between 1.43184 and 1.47500 with an effective refractive Index between 1.360015 and 1.401017. Besides all wavelength shifts and effective refractive Index have been proposed for Blood, cervical, Adrenal, Breast, and Skin cancers. The wavelength vs effective refractive index relationship for various cancerous cells has been established.
... For the piecewise-uniform approach with transmission matrix, the grating is divided into a number of uniform pieces. The number of segments should not be made arbitrarily large and ~100 segments is sufficient, since the coupled-mode-theory approximations are not valid when a uniform grating section is only a few grating periods long [11]. When the Since the temperature and strain response of a DFB fiber laser is identical to that of a standard Bragg grating [2], the resonant wavelength shift of the DFB fiber laser due to the ambient temperature change can be attributed to the following four aspects: the thermaloptical effect of the fiber, the thermal expansion effect of the fiber, the elasto-optical effect caused by the thermal expansion of the fiber, and the waveguide effect caused by changes in the fiber core due to the thermal expansion. ...
... To calculating the transmission spectrum of a non-uniform grating, piecewise-uniform approach with transmission matrix is one of the most commonly used methods [11]. For the piecewise-uniform approach with transmission matrix, the grating is divided into a number of uniform pieces. ...
... For the piecewise-uniform approach with transmission matrix, the grating is divided into a number of uniform pieces. The number of segments should not be made arbitrarily large and 100 segments is sufficient, since the coupled-mode-theory approximations are not valid when a uniform grating section is only a few grating periods long [11]. When the pump light is injected into the fiber laser, due to the relatively low pump power, the temperature rise is on the order of dozens of K with a variation of less than 10 K along the fiber laser [3,5]. ...
The pump heating effect of DFB fiber laser is normally ignored due to the short length of the laser cavity. However, by fabricating a phase-shifted FBG on high concentration Er-Yb codoped fiber to obtain a 16 mm long DFB fiber laser, the gradient surface temperature distributions along the active grating with different pump powers were observed. The average surface temperature rose by 16.82 K with a variation of less than 1.11 K, and the position with the highest temperature moved towards the center of the grating by 5.5 mm, when the pump power was increased from 0 mW to 191.6 mW. The transmission spectrum of the active phase-shifted FBG at different pump powers were measured, and an additional drift of the transmission peak in the stopband was testified. It was identified as an equivalent phase shift up to −0.1 π, which was induced by the gradient longitudinal temperature distribution. Considering that the initial phase shift of the grating was about 1.15 π, the increasing chirp of the active grating due to the pump heating could compensate the phase shift deviation from π surprisingly. The experimental results coincided with the simulation results by using the transmission matrix method under the assumption of piecewise-uniform structure for the chirped phase-shifted grating. The modified model of the active phase-shifted FBG reveals the difference between the cool cavity and the hot cavity at different pump powers, which may be used as a self-optimization mechanism for DFB fiber laser operation.
... Fiber Bragg gratings (FBGs) are extensively used for distributed measurement of physical parameters such as temperature [1] or strain [2] and as a result have been extensively studied in both the single-mode and multi-mode regimes. Kogelnik [3] used coupled mode theory (CMT) to derive the spectral response of an electric field interacting with a refractive index perturbation; Erdogan [4] extended this approach and presented coupled first order differential equations describing the interaction of multiple modes in circular waveguides. Uniform and non-uniform gratings can be modeled using the transfer matrix method [5] (TMM). ...
... δn e f f λ [4] for single mode FBGs for light with wavelength λ. In RBGs, κ has multiple values for every possible mode combination and thus must be numerically computed. ...
... Based on Erdogan's description [4] of multimode waveguides, the magnitude of modes A j and B j evolve along z as ...
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.
... The simplest configuration is represented by the uniform FBG, in which the modulation of n eff has a constant grating period (Λ) along the fiber length. 41 This structure works as a narrowband optical filter. When a broadband light signal passes through the fiber, the FBG reflects only a narrow range of wavelengths centered around the so-called Bragg wavelength (λB), whereas the residual ones are transmitted undisturbed along the fiber. ...
... When a broadband light signal passes through the fiber, the FBG reflects only a narrow range of wavelengths centered around the so-called Bragg wavelength (λB), whereas the residual ones are transmitted undisturbed along the fiber. 41 The reflectivity values typically range from 10% to 90%. λB depends on n eff of the fiber core and Λ, according to ...
Healthcare has rapidly evolved in the last decades, driven by the demand for personalized therapies and advancements in enabling technologies. Among many solutions, fiber Bragg grating (FBG) sensors have gained significant acceptance in the medical field, due to their good static and dynamic performance, small dimensions, biocompatibility and immunity to electromagnetic interferences. The integration of artificial intelligence (AI) with FBGs is emerging as a breakthrough approach, enabling the design of smart systems for medical applications, like minimally invasive surgery, physiological monitoring, biomechanics, and medical biosensing. These systems harness the potential of FBGs and the advanced data processing capabilities of AI to improve diagnostics and therapeutic procedures. This perspective provides an overview of the sensing systems that combine FBG and AI technologies in medicine, focusing on their working principle, potentials, and challenges. It also explores the open research directions for encouraging further investigations in this field.
... These gratings are formed by means of periodic modulation of a refractive index in the fiber core along the longitudinal coordinate. FBGs in SM fibers have been well studied and its main characteristics are well known [1,2]. ...
... For the mathematical description of the reflection of laser radiation from FBGs the theory of coupled modes is generally used: transverse optical radiation modes propagating in opposite directions are "coupled" with each other if the phase matching condition is fulfilled. There is an analytical solution of the equations of the coupled mode theory for SM waveguides in the approximation of a large overlap of the fundamental (Gaussian) mode and the fiber core [1]. ...
A novel approach for the reconstruction of the mode composition of optical radiation in multimode fiber is presented. It is based on the analysis of the reflection spectrum from the multimode fiber Bragg grating. The mode composition of radiation in the multimode fiber with 40 µm core diameter, sustaining 17 transverse LP modes, was experimentally studied. The experimentally obtained spectral reflection peaks from the multimode fiber Bragg grating coincide very well with the theoretically calculated ones. At the same time, additional spectral peaks corresponding to the cross-reflection of some modes into others were discovered. The introduced method also made it possible to determine the parameters of the studied multimode fiber Bragg grating. Furthermore, the presented method allows the determination of the bending losses for different transverse modes of radiation. The obtained results can help to characterize the operation of few-mode or multimode laser systems.
... In the case of a photorefractive waveguide core, (13) needs to be modified for the mode index n = n eff + Γ∆n sin(Kx ′ + ∆φ). (16) ∆n is weighed by the mode confinement factor Γ to approximate the sensed grating amplitude [26]. More generally, Γ is given by the projection of the scattered pump beam core field on the output mode profile, which is not the confinement factor for cross-polarization coupling due to the electric field profile mismatch between TM and TE modes. ...
... 7) Time-dependence: In general, the grating formation follows an overdamped oscillatory behavior [22], [23]. In our experiments, the simplified exponential saturation expression is adequate, yielding a synaptic scattering coefficient (weight) (26) w(t) = −ms max e i∆φ (1 − e −t/τ ) + w 0 e −t/τ (32) with w 0 the boundary condition for t = 0, and s max = |s D |/m (26) the maximum scattering coefficient amplitude. ...
The computational cost of AI could be alleviated by accelerating the synaptic transfer calculations in artificial neural networks with an analog crossbar array processor. In this work, we present the core building blocks of an all-optical integrated photorefractive crossbar array for artificial neural network training by demonstrating photorefractive synapses in an integrated 2-D beam interaction network. We show that the photorefractive quality of the circuits resembles that of the bulk GaAs crystal that they were fabricated from. Then, this work experimentally validates the integrated photorefractive crossbar array design and constitutes a framework for engineering photorefractive integrated photonics.
... Due to that the laser relaxation period is changed in a small range by adjusting current or feedback strength, this method is only suitable for short feedback cavity comparable to the relaxation period. Thereafter, other different approaches were proposed [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. These approaches can be classified into two types. ...
... Therefore, based on convolution theorem, the dispersive feedback term is numerically calculated by inverse Fourier transform of H(ω)•FT{E(t−τ)}, where FT{} denotes Fourier transform and H(ω) is the complex reflection spectrum of the chirped grating. The chirped grating spectrum is obtained by the piecewise-uniform approach [30], which is outlined as follows. The chirped grating is equally divided into M small pieces and each piece is considered as a uniform grating. ...
Time delay signature (TDS) of a semiconductor laser subject to dispersive optical feedback from a chirped fiber Bragg grating (CFBG) is investigated experimentally and numerically. Different from mirror, CFBG provides additional frequency-dependent delay caused by dispersion, and thus induces external-cavity modes with irregular mode separation rather than a fixed separation induced by mirror feedback. Compared with mirror feedback, the CFBG feedback can greatly depress and even eliminate the TDS, although it leads to a similar quasi-period route to chaos with increases of feedback. In experiments, by using a CFBG with dispersion of 2000ps/nm, the TDS is decreased by 90% to about 0.04 compared with mirror feedback. Furthermore, both numerical and experimental results show that the TDS evolution is quite different: the TDS decreases more quickly down to a lower plateau (even background noise level of autocorrelation function) and never rises again. This evolution tendency is also different from that of FBG feedback, of which the TDS first decreases to a minimal value and then increases again as feedback strength increases. In addition, the CFBG feedback has no filtering effects and does not require amplification for feedback light.
... The behaviour of light within Bragg gratings is usually described by means of coupled mode theory (see [6] for a comprehensive review). Analytical solutions to the coupled mode equations exist in the case of uniform, sinusoidal gratings, while for more complex structures the equations can easily be integrated numerically, requiring only the knowledge of the envelope of the index profile along the grating. ...
... Taking the refractive index of the guide as 1.46, the physical cavity length becomes L eff = 5.40 mm. This is longer than the distance L = 4 mm between the innermost planes of the two gratings because the light penetrates inside the gratings; the penetration length L g = (L eff − L)/2 [7] is directly linked to the grating group delay τ g = dφ /dω [6] by τ g = 2L g n/c. Indeed, the group delay calculated in this way (6.84 ± 0.04 ps) matches exactly the coupled mode theory calculation of Fig. 3(a). ...
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.
... Channel waveguides with one-dimensional (1D) periodic modulations in refractive index, such as twodimensional (2D) photonic crystal (PhC) slab defect waveguides [1,2], optical fiber gratings [3], and distributed Bragg reflector (DBR) pillars [4] are very important as a platform of slow light [5], waveguide quantum electrodynamics [6], chiral quantum optics [7], and multiharmonic generation [8]. They are characterized by welldefined dispersion relations of light outside the light cone, having band gaps at the boundary of the Brillouin zone. ...
... Here, we have the rotational symmetry about the cylindrical axis, so that the t-matrix is diagonal with respect to angular momentum index l. Such a t-matrix is also obtained in optical fiber gratings [3] and structured optical fibers with a periodic array of holes inside [22]. ...
A hybrid computational method of plane-wave and cylindrical-wave expansions for distributed Bragg-reflector (DBR) pillars is proposed. The plane-wave expansion is employed to represent the one-dimensional periodic structure of the DBR. The cylindrical-wave expansion is employed to describe the scattering by circular pillars with the DBR structure inside. This formalism enables us to calculate the radiation fields, t-matrices, scattering cross sections, photonic band structures, and quality factors of the DBR pillars. Furthermore, optical properties of arrayed DBR pillars are also investigated with the aid of the multiple-scattering method. Using this formalism, we demonstrate explicitly that high Q photonic band modes including the so-called bound states in continuum are obtained both in isolated and arrayed DBR pillars. We also present a novel formation of gapless Dirac-cone surface states in a three-dimensional photonic crystal composed of a two-dimensional periodic arrangement of core-shell DBR pillars.
... As shown in Fig. 4(b), the insertion loss of the cladding Bragg grating increases with the laser pulse energy. However, as the laser energy increases, the local refractive index modulation in the fiber material becomes more pronounced, resulting in enhanced coupling efficiency within the FBG [30], which subsequently leads to an increase in the reflection intensity, as illustrated in Fig. 4(c). According to the experimental results, it was observed that a laser energy of 50 nJ could ensure a balance between insertion loss and backscattering signal strength. ...
Optical fibers are commonly employed in telecommunications for transmitting data. However, it is difficult to distinguish optical conduits from one another when servicing data transmission cables due to the large number of optical fibers and optical cables. Conventional methods of physically marking fibers are cumbersome, and the label information is accessible to any potential user. In this work, we propose and demonstrate an encrypted optical fiber tag based on an ultra-low-loss encoded cladding-type fiber Bragg grating (cladding-FBG) array. Using the femtosecond laser point-by-point (PBP) technique, binary data sequences are successfully embedded into the different positions of the optical fiber cladding in the form of Bragg gratings. The cladding-FBGs redistribute light within the cladding, enabling information retrieval via backscattered signals while having minimal impact on the core light transmission. Consequently, the insertion loss of a single encoded cladding grating is suppressed to an exceptionally low level of just 0.00155 dB, which is favorable for optical communication. The data capacity and security of the tag can be enhanced by optimizing the parameters of cladding-FBGs, such as grating periods and spatial distributions. Therefore, the proposed low-loss optical fiber tag presents significant potential for integration into network systems for optical network link identification and data storage.
... where C r is the normalization constant [26] with an expression ...
We present the detailed mathematical derivation and systematically analyze the mode coupling characteristics of refractive index-modulated tilted waveguide gratings (RI-TWGs). In this paper, we have simulated the mode coupling between a guided mode and a cladding mode/radiation mode of RI-TWGs. Compared with tilted fiber Bragg gratings (TFBGs), the noncircular symmetric structure of RI-TWG made it separate into two transverse dimensions, which greatly simplified the analyzing process of the tilted grating vector. Unlike TFBGs, the RI-TWG only excited the . The simulation results have shown that the mode coupling coefficient between the guided mode and the cladding mode has a Sinc-like relationship, and the profile of the mode coupling behavior could be tuned by changing the tilt angle of grating, which as increasing of tilt angle, the maximum coupling of the cladding mode is moving to the higher cladding mode order. For radiation mode coupling, the RI-TWG has a similar transmission spectrum, which has a wide bandwidth and polarization-dependent attenuation. The results in this work give theoretical guidance and prediction for using the extra dimension of grating tilt to expand the functions and applications of RI-TWGs.
... Optical fiber-based gratings comprise of a periodic alteration of amplitude index modulation of refraction through the core section of an optical fiber. There are two major species of fiber-based gratings such as the short period grating as well as the long period grating (LPG) [3]. The gratings with short period, too indicated as Fiber Bragg Grating (FBG), having periodicity on the range of half a micrometer (µm), whereas the LPGs have periods of a few hundred-thousand micrometer (µm) [4,5]. ...
An apodized Long Period Grating (LPG) is presented to compute and depict the temperature sensitivity for different resonant wavelengths in the transmission spectrum. The spectrum often gets distorted due to overlapping of multiple modes and appearance of large quantity side lobes as a result of the impacts of higher order period. Therefore, the introduction of apodization profile is necessary to obtain the proper shape of the spectrum by preventing any distortions. It has been noted that the higher order mode (LP07) shows greater temperature sensitivity with 0.043 nm/o C as compared with the lower order modes (i.e., LP04, LP05, LP06) for 100–600° C. Different Machine Learning models are implemented for the predictive analysis of resonant wavelength changes in accordance with the temperature effects for enhancing the effectiveness of the sensor response. This approach is highly desirable in various applications by ensuring the safety, efficiency and reliability of the LPG-based sensing outcomes.
... These reflections interfere constructively, forming a maximum that can be detected at the fiber's output end [27]. Strain or temperature changes alter both the grating spacing (Λ) and the effective refractive index, leading to a measurable shift in the reflected wavelength peak along the spectrum (Fig. 4b) [28,29]. Various sources indicate that FBGs are a valid method for determining residual stresses [30,31]. ...
Combining different materials in a thermally activated manufacturing process into a hybrid composite can lead to residual stresses if there is a difference between the adhesion temperature TAD and the application temperature TAP. If such hybrid composites are subjected to high cyclic loads, residual stresses may influence their durability. While residual stress analysis has been extensively studied in the context of metal-plastic hybrids, the residual stress condition is unknown for thermoset-thermoplastic hybrids produced by injection molding. Therefore, we firstly apply a calculational model to estimate the residual stress for the investigated material combination of glass fiber-filled polyamide (PA6.6 GF30) and a unidirectional glass fiber-reinforced plastic (UD-GFRP) with a polyurethane acrylate matrix. Secondly, these results are compared to a corresponding computational simulation model. Integrating Fiber-Bragg-Grating (FBG) sensors in the UD-GFRP allows for the determination of residual strain in the thermoset component at different temperatures and thereby both the calculational and computational simulation methods could be validated against experimental results. The results show that process-related residual stresses occur in the hybrid composite and are not negligible. Normal stresses of − 39.6 MPa have been observed in thermoset material. Furthermore, the calculational determined normal stresses are in accordance with the experimentally determined values.
... 24,25 Compared with ordinary fiber waveguides, the optical field in the grating region is coupled in various modes due to different phase-matching conditions, so the optical field near the grating region can be modulated by optical wavelength, grating period, optical power, incident directions, and tilt angle. 26,27 Fiber Bragg gratings (FBGs) with uniform grating period have irregularity of the overall envelope by scanning the evanescent field resonant line along the fiber grating. 28 When the grating period of chirped fiber Bragg gratings (CFBGs) varies gradually along the axial length, the evanescent field of CFBG appears varies axially with the incident wavelength. ...
Microfluidic switches are important operating units in microfluidics that enable controlled fluid flow on the chip, providing more functionality of platform. Most fiber based photofluidic devices mainly modulate temperature gradient and microflow by varying optical power. However, only power regulation limits the diversity of the optical field, which makes it difficult to achieve microfluidic control at different localized regions. Here, optical field of a tilted fiber Bragg grating (TFBG) can be theoretically modulated by the incident light wavelength and direction based on the finite element method. A photothermal vortices based microfluidic switch is built by TFBG with multiple linear heat sources. In the simulation, when the incident light is coupled in the forward or reverse direction of TFBG, the reflected position of the optical field is positively moved along the grating region as the wavelength increases. In the experiment, the opening of the microfluidic at different positions and directions can be clearly observed when the wavelength-matched laser is incident at the TFBG in the forward or reverse direction. It is believed that the microfluidic switch provides ideas for more flexible operation and functional integration for photothermal microfluidic devices in the future.
... M R (M TA ) corresponds to the multiplication of the complex reflection (transmission) coefficient r (t) by a 2 × 2 unitary diagonal matrix. r and t can be defined as [25]: ...
In this paper, the detrimental polarization effects in direct detection fiber Bragg grating (FBG)-assisted phase-OTDR sensing systems are investigated. The detrimental effects result from a mismatch between the states of polarization reflected by two successive FBGs. A numerical analysis is first performed to quantify the polarization dependence of the sensor response. It is shown that the use of standard single-mode and polarization-maintaining fibers could present a non-negligible polarization dependence. The mitigation of the polarization effect when using spun fibers is also quantified. Second, an experimental setup allowing the measurement of the polarization dependence of the sensor response is proposed, and results obtained for standard single-mode, polarization maintaining, and spun fibers are presented. The results showed a good agreement with the numerical data.
... To significantly increase the reflectivity of Pl-by-Pl gratings, it is desirable to maximize the ratio κ/α [32]. Further to investigate the mechanism of the RIM induced by fs-writing FBG, the index modulation amplitudes ∆n eff and grating-induced effective indices n eff has been evaluated [33]. The n eff of the grating can be expressed by λ B = 2n eff Λ, where λ B is the Bragg resonance wavelength. ...
The fiber Bragg grating (FBG) is fabricated by the femtosecond laser writing technique with a plane-by-plane (Pl-by-Pl) method in the double-cladding fiber (DCF). The refractive index modified (RIM) region formed by this method is 12 μm × 8 μm in size. Due to the Pl-by-Pl method, high-order Bragg resonances with reflectance greater than 99% can be achieved. The fabricated high-quality FBG features a narrow full width at 3 dB bandwidth of approximately 0.45 nm, a high reflectivity above 99%, and almost no side-mode peaks. To investigate the application of fabricated FBGs, we have built a thulium-doped all-fiber oscillator with purely forward-pumped structures. A thulium-doped fiber laser (TDFL) at a central wavelength of 1953.79 nm was constructed by using the prepared fiber grating. The signal-to-noise ratio (SNR) is above 56 dB. When the pump power is 19 W, the total output power of the continuous wave is 4 W, and the output efficiency is 25.6%. In addition, the numerical calculation has been carried out to further optimize the output power. This work provides a possible approach for designing and implementing a continuous Tm-doped fiber laser with enhanced output efficiency.
... This assists in generating dual-wavelength pulses by reflecting different wavelengths. A fiber Bragg grating operates as a wavelength-selective mirror, carefully structured with distinct grating periods that align with the targeted wavelengths at which they reflect light [223,224]. The fiber Bragg grating's design parameters, such as the period and amplitude of the refractive index variation, determine the specific wavelength that the grating reflects. ...
The fiber laser combines the fiber gain medium's function as a fiber amplifier, transforming it into laser output through integration within a cavity configuration. Meanwhile, a pulsed fiber laser is capable of generating short bursts of laser emission characterized by high peak power levels. This concept is known as Q-switching. A saturable absorber material is essential for passive Q-switching, as it is integrated into the laser cavity to produce an instantaneously Q-switched pulse fiber laser. While these materials have been effective in generating pulsed lasers, they often come with unresolved issues, such as long-term exposure to two-dimensional materials can pose health risks. To address this gap, researchers have shifted their interest toward natural or organic materials in the quest for new saturable absorbers. This mini-review provides a comprehensive overview of the saturable absorber mechanism, including essential theoretical equations and key measurement parameters. The next section continues by exploring the fundamentals and early development of saturable absorbers, followed by an in-depth explanation of the Q-switched pulse generation process using erbium-doped fiber as the gain medium and saturable absorber. Critical parameters influencing the performance of Q-switched pulse fiber lasers are discussed, with special attention given to recent advancements in organic-based saturable absorbers for Q-switching. The potential of spider silk as an innovative saturable absorber in Q-switched pulse fiber laser applications is highlighted. Finally, the review delves into the wide-ranging applications of these lasers, including tunable and switchable dual-wavelength fiber lasers with sensor for temperature measurement and to detect adulteration in pure kelulut honey and sucrose solution.
... To suppress these parasitic pairs we imagine introducing a dual stop-band, or moiré, grating [30], opening stop-bands centered at both ω Bx = 2πc/ (1560 nm) and ω By = 2πc/ (1540 nm) though reducing κ by a factor of two. Assuming a grating index contrast of ∆n = 2.1 × 10 −3 and the grating to have the same effect on both polarizations, we calculate that 94,000 periods of length 536 nm (L = 50 mm) can achieve a grating strength of κL ∼ 137 with photonic stop-bands of width ∆λ ≈ (1550 nm) 2 κ/ [πn SiO2 (1550 nm)] ≈ 1.4 nm centered at both ω Bx and ω By [31]. We note that SFWM has been observed in even shorter pieces of glass [32,33]. ...
We calculate that an appropriate modification of the field associated with only one of the photons of a photon pair can suppress generation of the pair entirely. From this general result, we develop a method for suppressing the generation of undesired photon pairs utilizing photonic stop bands. For a third-order nonlinear optical source of frequency-degenerate photons we calculate the modified frequency spectrum (joint spectral intensity) and show a significant increase in a standard metric, the coincidence to accidental ratio. These results open a new avenue for photon-pair frequency correlation engineering.
... Moreover, let us recall that analytical modeling of apodized Bragg filters or chirped Bragg reflectors, even after introducing the lowamplitude approximation, requires the implementation of a special function, namely the hypergeometric function [39,60]. On the other side, another well-known technique, the coupled-mode method, is less demanding; yet, it is a perturbation-type theory that introduces various approximations; in particular, it is limited to low index modulation [30,61]. A third method requires computing an infinitely nested set of integrals involving the logarithmic derivative of the admittance profile; again, for a practical implementation, only the first orders can be taken into account [31]. ...
A class of four-parameter solvable profiles of the electromagnetic admittance has recently been discovered by applying the newly developed Property & Field Darboux Transformation method (PROFIDT). These profiles are highly flexible. In addition, the related electromagnetic-field solutions are exact, in closed-form and involve only elementary functions. In this paper, we focus on those who are S-shaped and we provide all the tools needed for easy implementation. These analytical bricks can be used for high-level modeling of lightwave propagation in photonic devices presenting a piecewise-sigmoidal refractive-index profile such as, for example, antireflection layers, rugate filters, chirped filters and photonic crystals. For small amplitude of the index modulation, these elementary profiles are very close to a cosine profile. They can therefore be considered as valuable surrogates for computing the scattering properties of components like Bragg filters and reflectors as well. In this paper we present an application for antireflection layers and another for 1D quasicrystals (QC). The proposed S-shaped profiles can be easily manipulated for exploring the optical properties of smooth QC, a class of photonic devices that adds to the classical binary-level QC.
... FBGs convert the mentioned strain into an optical signal combining high metrological properties (e.g., high sensitivity, resolution, accuracy and fast response time) with biocompatibility, electric safety, small size, lightweight, and multi-point measurements [16], [17], [18]. The output signal of a Fiber Bragg Grating (FBG) is a light with a narrow spectrum centered around a specific wavelength, known as the Bragg wavelength (lB), which can be expressed as follows [19]: ...
This paper reviews wearable solutions for cardiorespiratory monitoring that leverage chest wall motion as the primary sensing mechanism. The most popular sensing technologies are categorized into two main groups based on the underlying measurement principles: systems that rely on changes in physical dimensions (i.e., strain and quantities that cause strain) and those based on inertial measurements (i.e., accelerometers and gyroscopes). For each available solution, the paper provides an in-depth analysis of the working principle, design and fabrication of the sensing part, integration onto the wearable systems, key application scenarios, along with performance evaluations of these systems in each context. Additionally, this review outlines the state-of-the-art algorithms and signal processing techniques used to estimate cardio-respiratory parameters, such as respiratory and heart rate, and other cardiorespiratory variables from sensors' output. Current limitations and future trends and challenges are also discussed, aiming to guide further innovations and improve the practical usability of these wearable monitoring systems.
... its difference between illuminated zones and non-illuminated zones. These two parameters play a role in defining the grating reflectivity coefficient ( ) and its full width (FWHM) [17]: where is a parameter related to the mode interacting with the RI modulation. The effective index and the grating period Λ evolve with temperature through the thermo-optic and thermal expansion effects [18], [19] and with strain applied to the fiber due to its elasto-optic properties [20]. ...
This review focuses on silica-based optical fibers, guiding light through the total internal reflection mechanism, that are currently used in telecommunications and sensor networks. Section I briefly introduces the fiber and fiber sensor technologies. Section II presents their various applications in radiation environments. In section III, the radiation effects on optical fibers are explained, first at a microscopic scale, with the description of point defects generated by irradiation. Then, the macroscopic consequences of the appearance of these point defects are discussed, in particular the phenomena of radiation-induced attenuation (RIA), radiation-induced emission (RIE) and radiation-induced refractive index change (RIRIC). RIA impacts nearly all applications under irradiation. We then detail the various parameters, intrinsic or extrinsic to the optical fibers that influence their amplitudes and kinetics. This improved knowledge paved the way for the radiation hardening of optical fibers through various approaches, either at material, component or system levels, that are described in section IV. Recent advances are presented for passive and for active rare-earth doped optical fibers and systems. Then, the use of fiber optic sensors is introduced, starting in section V with the latest advances in radiation-hardened point or distributed sensors. Then, the potential of this technology for radiation detection, beam instrumentation and dosimetry applications is assessed in section VI. Finally, the future prospects and the main challenges to be met in order to accelerate the implementation of this technology in the harshest environments are discussed.
In this study, we conduct a quantitative analysis of the interferometric-based phase-sensitive interrogation principle for πFBG sensors using numerical simulations. The path imbalance of the interferometer arms and the line-shape function of the light signal from the πFBG sensor are critical factors influencing the sensitivity and dynamic range characteristics of the interferometric interrogation principle. Our analysis reveals several unique response characteristics that will be valuable for designing and optimizing interferometric interrogation principle using πFBGs as sensing elements. The simulation results are validated through experimental studies on πFBG sensors with in-house fabricated fiber-based Mach–Zehnder interferometers, which have path length differences of 10 mm, 19.40 mm, 28.90 mm, and 37.10 mm, respectively.
Thanks to the highly localized fiber Bragg grating obtained by a femtosecond laser and point-by-point inscription method, a cladding mode spectral range of over 80 nm is achieved in polymer optical fibers. After grating inscription, refractometric measurement is conducted within a range from 1.38 to 1.54 to measure the surrounding refractive index, and the evolution of the cladding mode resonances is analyzed accordingly. By monitoring the cutoff mode, the refractive index sensitivity is found to be 527 nm/RIU (refractive index unit). The originality of our work lies in the production of highly localized FBGs for the first time with a large spectral range of cladding mode resonances in polymer optical fibers, capable of measuring refractive indices in a wide range in aqueous solutions and (bio)chemical media.
We accomplish a compact 150-MHz figure-9 Er:fiber laser through the use of a hybrid device of wavelength division multiplexer and phase shifter. By combining the time-independent rate equation and nonlinear Schrödinger equation, evolution of the intracavity field towards stable mode locking state is presented. We further quantify the output characteristics of the 150-MHz figure-9 laser. Explicitly, 5.8-mW average power, center wavelength of 1561.2 nm and 3-dB spectral bandwidth of 29.2 nm are obtained. More importantly, an integrated root-mean-square relative intensity noise of 0.0016% [1 Hz, 1 MHz] and 75.8 fs timing jitter [100 Hz, 1 MHz] are measured at the fundamental repetition rate. Moreover, by referencing to a stable radio frequency, the fundamental repetition rate is locked with an in-loop relative instability of 2.78 × 10
−12
at 1-s gate time.
Optical spectrum analyzers are instruments useful across many areas of science and industry. However, these devices are still expensive, and that hinders its possible applications in certain fields. One such field is the optical instrumentation, where most of the cost of systems lies in the interrogation process. To lower the cost, device-specific interrogation techniques are usually employed. This paper proposes a technique for general-purpose spectrometry based on the spectral sweeping with a modulated LPFG and the Richardson-Lucy deconvolution algorithm. By using a sensor device it could also allow for easier construction of custom interrogation systems by those who already have the knowledge and infrastructure to build the sensors. The method was validated with simulations that included noise and the effect of variable coupling between the core and the cladding of the LPFG kernel. The results were promising, consistently reaching similarities, defined as the Pearson correlation coefficients, between the original spectrum and the rebuilt one of about 0.987 for scenarios with 40 dB SNR. The areas with a visible mismatch all had valleys narrower than that of the kernel LPFG, and most of those valleys were recognized and had the rebuilt positions close to the original ones, with the mismatch happening at the power values. As such, the method could be useful for the construction of interrogation systems for other LPFGs and as a general spectrometer for inputs without narrow sections.
Agriculture has gone through tremendous change due to the application of IoT technologies which has enabled the creation of smart plant monitoring systems. These types of systems deploy a number of IoT based sensors and systems to measure in real time the most relevant of the variables affecting the health of plants including the soil moisture content, temperature and humidity as well as the light received by the plants. By incorporating IoT systems with data analytics as well as cloud computing, such systems are effective in providing real insights on farming activities which optimizes resource use while improving the productivity of crops. This paper analyzes the concepts and techniques, operationalization and case studies of IoT based smart plant monitoring systems with the emphasis on remote control functions such as active disease monitoring and self irrigation systems. These system, however, have disadvantages as well towards the overall effectiveness of such systems on the reduction of cost and time to perform target operations due to deployment costs, data security measures and constraints in areas remote from cities or towns. This review outlines the present status, advantages and constraints of the plant monitoring systems enabled by IoT technology and outlines guidelines for further examination and engineering in green farming.
Structural health monitoring (SHM) has become increasingly common in assessing built structures and the ongoing monitoring of older ones, whether for preventive maintenance applications or for assuring the integrity of deteriorating structures. Several sensing technologies have been developed and utilized for these applications. Over the past two decades, optical fiber sensors (OFS) have been utilized in various civil engineering projects due to their inherent advantages. This includes properties such as lightweight, size, immunity to electromagnetic interference (EMI), corrosion resistance, and embedding capability. Several monitoring systems based on OFS have been developed to measure and assess real-time data of various civil infrastructures continuously. Since its inception, Fiber Bragg grating (FBG) has been an ideal candidate for OFS technology; currently, most OFS systems use FBG. Due to its inherent characteristics and potential applications, considerable efforts and advancements have been made in the FBG-based sensing field. One of the most developed FBG sensors is strain OFS. Not just because of their benefits compared to the traditional strain gauge but also because of their high sensitivity and low cost. FBG strain sensors acquire an essential share of the SHM market. This review paper aims to give a general understanding of the basic principles of FBG sensors, advances in sensing and data processing techniques, developments of novel optical fiber sensors, temperature compensation techniques, and practical applications of FBG sensing technology in SHM. Moreover, this paper aims to contribute to the existing knowledge by highlighting the evolving landscape of FBG sensors and suggesting potential research areas in the context of SHM.
A novel fiber Bragg grating (FBG) sensing system with a core laser source comprising a high-density integrated distributed feedback (DFB) laser array based on the reconstruction-equivalent-chirp (REC) technique is presented and demonstrated. This study proposes a fast and wideband wavelength-swept laser (WSL) based on a DFB laser array. 24 lasers are monolithically integrated with an 8×3 matrix structure with a wavelength spacing of 2.1 nm. The REC technique is used to simplify the grating fabrication and enhance the precise control of the wavelength spacing. Furthermore, a high-speed FBG sensing system using field-programmable gate arrays (FPGA) is proposed and demonstrated, achieving stable high-speed sweeping with a wavelength coverage of 50.4 nm and a sweeping frequency of up to 5.85 kHz without mode hopping. The FBG sensing system has a solid-state design without moving parts, allowing real-time, high-speed, and stable monitoring of temperature, pressure, strain, and displacement. It maintains superior stability even under challenging vibration and shock environments. Additionally, the system is cost-effective and is anticipated to have diverse industrial applications.
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.
Respiratory rate (RR) and heart rate (HR) are essential vital signs for monitoring patients in both emergency and routine medical settings. In this work, we developed a lightweight, adhesive, and reusable sensor using a polymer optical fiber Bragg grating (POFBG) embedded in a polydimethylsiloxane (PDMS) film for RR and HR measurements. The performance of the POFBG-embedded sensor was compared to its silica optical fiber Bragg grating (SOFBG) counterpart, demonstrating superior results. Both SOFBG and POFBG were inscribed using the femtosecond laser point-by-point writing technique. The POFBG was embedded in the PDMS film, with adjustable stickiness provided by ethoxylated polyethylenimine (PEIE), enabling easy attachment to the skin over the brachial artery at the forearm fossa. This film probe was used to measure the RR and HR in normal physiological condition and post-exercise condition. In addition, the reusability of film probe was characterized by a series of peeling-and-reattaching trials. Though after repeated usages of 50 times, the sensor probe lost its adhesiveness due to the skin-sebum contamination, its functionality could be recovered to around 30% after an ethanol cleansing process. After the reusability tests, experiments of the same probe were performed on four different volunteers, and the results indicated that RR and HR signals could be accurately investigated with a maximum error of 2 bpm and 2.18 bpm for RR and HR, respectively. The results presented here offer a convenient, fast, and effective solution to reduce the workload of medical professionals and enhance the efficiency of patient monitoring.
A detailed theoretical treatment is presented of bound-mode to bound-mode Bragg reflection and bound-mode to radiation-mode coupling loss in a tilted optical-fiber phase grating. Numerical predictions of the effects of grating tilt on the spectral characteristics of such a grating are calculated. These predictions are compared with experimentally measured spectra of strong gratings written by ultraviolet irradiation of deuterium-sensitized fiber with grating tilt angles ranging from 0° to 15°. Good agreement is obtained between the theoretical predictions and the experimental results.
This paper describes the adaptation of Rouard’s method, a familiar computational technique used in thin-film coating design, to the analysis of waveguide diffraction gratings. The approach can be used to generate the spectral and the angular characteristics of arbitrary straight-line gratings (periodic or nonperiodic), is easy to implement on a computer, and provides an intuitively appealing picture of the operation of such gratings. The application of the thin-film method is extended to periodic gratings as well as to gratings having either a linear or a quadratic chirp in period. Specific examples are used to compare the results of the thin-film computational method with those predicted by previous authors.
The transmission of a mode guided by the core of an optical fiber through an ultraviolet-induced fiber grating when substantial coupling to cladding modes occurs is analyzed both experimentally and theoretically. A straightforward theory is presented that is based on the calculation of the modes of a three-layer step-index fiber geometry and on multimode coupled-mode theory that accurately models the measured transmission in gratings that support both counterpropagating (short-period) and co-propagating (long-period) interactions. These cladding-mode resonance filters promise unique applications for spectral filtering and sensing.
We describe hybrid lasers combining a semiconductor gain section and fiber cavity with integrated chirped Bragg reflector. These devices have produced output powers of 27.5 mW in a narrow linewidth (400 KHz) stable single longitudinal mode. The use of a chirped reflector to stabilize the single mode output, and correct grating orientation are described. The laser output has a side‐mode suppression ratio of over 55 dB at 27.5 mW output, and relative intensity noise (RIN) below 160 dB/Hz.
We consider linear propagation through shallow, nonuniform gratings, such as those written in the core of photosensitive optical fibers. Though, of course, the coupled-mode equations for such gratings are well known, they are often derived heuristically. Here we present a rigorous derivation and include effects that are second order in the grating parameters. While the resulting coupled-mode equations can easily be solved numerically, such a calculation often does not give direct insight into the qualitative nature of the response. Here we present a new way of looking at nonuniform gratings that immediately does yield such insight and, as well, provides a convenient starting point for approximate treatments such as WKB analysis. Our approach, which is completely within the context of coupled-mode theory, makes use of an effective-medium description, in which one replaces the (in general, nonuniform) grating by a medium with a frequency-dependent refractive index distribution but without a grating.
A unified approach to obtain the characteristics of almost-periodic grating slab waveguides including gain in the waveguide is reported. In this approach the waveguides are divided into short segments, and in each segment the gratings are assumed to be periodic, that is, parameters such as coupling coefficient, grating phase, deviations from the Bragg frequency, and gain in the waveguide are independent of a propagation direction z. Then characteristics of almost-periodic grating slab waveguides can be obtained by multiplying each F matrix of a short segment with the proper grating phase conditions at the interface between two adjacent segments. The appropriateness of this approach is shown for typical aperiodic grating waveguides such as tapered, chirped, and phase-shifted gratings. The results obtained by this method are compared with others and prove to be in good agreement with the results obtained by other methods. In addition to these characteristics, it is shown that the F matrix can be used to obtain the threshold conditions for distributed feedback laser oscillations including reflections from cleaved edges.
Aperiodic distributed-parameter waveguides are considered for use as reflectors and filters in integrated optics. Coupled-mode theory is used to predict the effects on modal propagation of aperiodic perturbations induced in a slab waveguide. In particular, it is shown that aperiodic perturbations can couple forward-traveling bound modes to backward-traveling bound modes; and that the frequency dependence of such a coupling process can be controlled through the aperiodicity. It is suggested that aperiodic coupling may be used to realize optical-waveguide reflectors and filters having predetermined spectral-response characteristics. As examples, the spectral-response characteristics of a narrow band-stop filter, a broadband-stop filter, and a narrow band-pass filter are calculated and presented.
Chirped fiber Bragg gratings control the pulse width and energy in Kerr mode-locked erbium fiber soliton lasers. We create high-energy pulses by providing large amounts of excessive negative dispersion, which increases the pulse width while keeping the nonlinearity of the cavity constant. With a chirped fiber grating of 3.4-ps² dispersion, 3-ps pulses with an energy content higher than 1 nJ are generated at a repetition rate of 27 MHz. By controlling the polarization state in the cavity, we obtain a tuning range from 1.550 to 1.562 μm.
To obtain the coupling constant for core-mode–cladding-mode coupling, it is necessary to calculate the total power carried by the cladding mode, and the related formulas are given by T. Erdogan [J. Opt. Soc. Am. A 14, 1773 (1997)] and [ J. Opt. Soc. Am. A 17, 2113 (2000) ]. I found that my formulas for P 1 and P 3 are the same as Eqs. (B2) and (B16) in the 1997 paper, but Eqs. (B3)–(B15) for P 2 are worth commenting on, and this comment gives our derivations.
The use of a linearly chirped Bragg grating filter for dispersion cancellation in an optical-fiber link is discussed. Numerical and theoretical calculations are made, which show that, with the proper taper function, the filter can have a high reflectivity and a quasi-constant nonzero dispersion, proportional to the inverse of the chirp. The filter can compress dispersion-broadened pulses by factors of 2–5 or more, if many filters are cascaded. Its compactness and efficiency would make it suitable for on-line implementation.
We present a new class of long-period fiber gratings that can be
used as in-fiber, low-loss, band-rejection filters. Photoinduced
periodic structures written in the core of standard communication-grade
fibers couple light from the fundamental guided mode to forward
propagating cladding modes and act as spectrally selective loss elements
with insertion losses act as backreflections <-80 dB,
polarization-mode-dispersions <0.01 ps and
polarization-dependent-losses <0.02 dB
The properties of optically written gratings in photosensitive germanosilicate fibres are reviewed. Externally written and self-organized grating formation techniques and theories of the self-organization of Bragg reflectors are discussed. The material properties of germanium doped fibres are described along with the various mechanisms proposed to explain the photosensitivity of optical fibre. Lastly, numerous applications of optically induced gratings are considered with particular emphasis placed on their future use in telecommunications.
Optical waveguides, also known as “dielectric” waveguides, are the structures that are used to confine and guide the light in the guided-wave devices and circuits of integrated optics. This chapter is devoted to the theory of these waveguides. Other chapters of this book discuss their fabrication by such techniques as sputtering, diffusion, ion implantation or epitaxial growth. A well-known optical waveguide is, of course, the optical fiber which usually has a circular cross-section. In contrast, the guides of interest to integrated optics are usually planar structures such as planar films or strips. Our discussion will focus on these planar guides even though most of the fundamentals are applicable to all optical waveguide types.
The filter response of nonuniform, almost-periodic structures, such as corrugated optical waveguides, is investigated theoretically. The filter process, leading to reflection of a band of frequencies near the Bragg frequency, is treated as a contradirectional coupled-wave interaction and shown to obey a Riccati differential equation. The nonuniformity of the structure is represented by a tapering in the coupling strength (e.g., the depth of the corrugation) and by a chirp in the period of the structure. For small reflectivities, the filter response is a Fourier transform of the taper function. For large reflectivities, the Riccati equation was evaluated numerically and plots are given for the response of filters with linear and quadratic tapers and with linear and quadratic chirps.
Citation
WILLIAM W. MOREY, GARY A. BALL, and GERALD MELTZ, "Photoinduced Bragg Gratings in Optical Fibers," Optics & Photonics News 5(2), 8-14 (1994)
http://www.opticsinfobase.org/opn/abstract.cfm?URI=opn-5-2-8
We discuss two aspects of nonlinear propagation of fiber gratings. The first of these is grating solitons, which were recently observed experimentally. Grating solitons exist because of the balancing of nonlinearity and grating dispersion. The second is the nonlinear interaction occuring when a strong pump pulse and a weak signal pulse copropagate through a grating. This is predicted to lead to pulse compression and enhanced parametric amplification of the signal pulse. Although these latter effects have not yet been observed experimentally, the required parameters are comparable to those for observing grating solitons.
Photoinduced Bragg grating in an optical fiber was made by Hill years ago, it wasn't until relatively recently that the field received intensive research interest. In 1989 Meltz et al. reported the formation of a grating using a holographic side-writing technique and the realization that this technique could be used to write well controlled structures into the fiber resulted in a resurgence of interest in the photosensitivity of optical fibers
Principles of Optics is one of the classic science books of the
twentieth century, and probably the most influential book in optics
published in the past forty years. This edition has been thoroughly
revised and updated, with new material covering the CAT scan,
interference with broad-band light and the so-called Rayleigh-Sommerfeld
diffraction theory. This edition also details scattering from
inhomogeneous media and presents an account of the principles of
diffraction tomography to which Emil Wolf has made a basic contribution.
Several new appendices are also included. This new edition will be
invaluable to advanced undergraduates, graduate students and researchers
working in most areas of optics.
The techniques for fabrication and the properties of periodic and aperiodic fibre Bragg gratings produced by UV exposure in photosensitive optical fibres are reviwwed with an emphasis on applications.
In future fiber communications systems, efficient mode conversion
has the potential to enable improved devices for dispersion compensation
and wavelength routing. Previous reports of symmetric-asymmetric mode
conversion in circular, multimode optical fibers have shown nonideal
spectral characteristics due to polarization dependence and/or mode
splitting of nearly degenerate components of the higher order LP<sub>11
</sub> mode. This work avoids these problems through use of nominally
polarization-independent UV-induced phase gratings while exploiting a
reflective phase-matching condition that is much less sensitive to the
mode splitting of the LP11 mode than prior work
Standardization for absolute laser frequency assignment in
projected dense wavelength-division multiplexing (DWDM) networks has
become a very important issue. Recently, we have proposed a referencing
scale of standard optical frequencies that are exact multiples of 100
GHz. Such a scale is independent of the atomic or molecular reference
used to set the absolute value and is uniformly applicable to all
spectral ranges. Here, we propose the use of sampled Bragg gratings to
realize the optical resonator. This resonator is adaptable, robust,
potentially cost efficient and readily compatible with the fiber network
The asymmetric slab waveguide is examined, giving attention to
geometrical optics, the guided modes of the waveguide, radiation modes,
leaky waves, hollow dielectric waveguides, and rectangular dielectric
waveguides. Weakly guiding optical fibers are discussed along with
coupled mode theory and coupled power theory. Applications of the
coupled mode theory are also considered, taking into account a slab
waveguide with sinusoidal deformation, fibers with sinusoidal diameter
changes, change of polarization, fibers with more general interface
deformations, and Rayleigh scattering.
The authors report the experimental realisation of a 10cm long 1.55µm Er3+-doped DFB fibre laser, with a permanent phase shift incorporated into the fibre grating during writing. Output powers of 1mW and an optical linewidth of 13kHz are observed.
Chirped fibre gratings are compact and potentially cheap and have become an attractive alternative to technologies such as dispersion compensating fibres for the upgrade of the installed non-dispersion shifted fibre (NDSF) base. In particular the recent demonstrations of 10 Gbit/s transmission over 700 km of NDSF and 40 cm broadband (4 nm) linearly chirped gratings for much-increased source wavelength and operating condition tolerance confirm this potential. These long gratings have essentially flat reflectivity over their usable bandwidth with raised cosine apodisation at both ends of the spectrum. The delay characteristic can be controlled to be linear with less than 2% error with a dispersion slope as high as ~1700 ps/nm (enough for 100 km of standard fibre). At the same time, the broad bandwidth available from the long linearly chirped gratings makes it possible for the first time to achieve dispersion compensation over a significant length of NDSF at several tens of Gbit/s data rates. To date 40 Gbit/s transmission over a significant length of NDSF at 1.55µm has only been demonstrated using dispersion compensating fibres. The best result to our knowledge is an error-free transmission over 150 km of standard fibre. Without any means of dispersion management, the maximum transmission distance is ~4 km for this bit-rate.
In this paper we report the first demonstration of 40 Gbit/s transmission over 109 km of NDSF at 1.55µm by employing two continuously-chirped 40 cm long, 4 nm-bandwidth gratings. In addition, a continuously-chirped 5.2 nm bandwidth 1 metre grating is demonstrated
The authors propose a 1.3 m long super-step-chirped fibre grating
with a continuous delay of 13.5 ns and bandwidth of 10 nm for broadband
dispersion compensation. Gratings of 0.2, 0.5 and 0.7 m in length are
also reported for the first time
The author report the experimental realisation of a 10 cm long
1.55 μm Er3+-doped DFB fibre grating during writing.
Output powers of 1 mW and a optical linewidth of 13 kHz are observed
An apodised in-fibre Bragg grating reflector is fabricated using
the phase mask photoimprinting technique. The reflector has a centre
wavelength of 1550 nm, a bandwidth of 0.22 nm and a peak reflectivity of
90%. At 0.4 nm (50 GHz) from centre wavelength the reflectivity is 40 dB
lower than peak reflectivity; this is an improvement of more than 20 dB
over an unapodised Bragg grating reflector with similar bandwidth and
peak reflectivity
A 40 mm long optical fibre grating superstructure is written by
translating an ultraviolet writing beam along a fibre and phase-mask
assembly while its intensity is periodically varied. The grating
reflects at multiple wavelengths, equally spaced by 0.13 nm, over a
range of more than 1.0 nm. This grating structure has applications in
signal processing and tunable fibre lasers
High pressure 'hydrogen loading' has been used to sensitise standard singlemode fibres, resulting in the largest reported UV induced index changes for low GeO2 fibres. Grating bandwidths of 4 nm and peak nu ns of 5.9*10-3 have been reproducibly achieved. Substantial index changes have also been achieved by rapidly heating H2 loaded fibres of various compositions.
An erbium fibre amplifier with a highly flattened gain spectrum is demonstrated for the first time using an all fibre photosensitive Bragg grating. An ASE spectrum flattened to within +or-0.5 dB over a bandwidth of 35 nm in the 1550 nm window is achieved with a 3 mm long radiation coupling Bragg fibre grating.
A novel approach to grating writing in optical fibres is described. This method involves writing the grating point by point through the side of the fibre using a UV laser source. Efficient mode conversion between forward propagating modes is demonstrated. The wavelength at which conversion occurs is determined by the periodicity of the grating. The grating can be designed to couple light at any wavelength of interest.
The authors report a mode-locked pulse source with extremely wide operating frequency range and very stable operation, through the use of a long, linearly chirped Bragg reflector as the output coupler integrated in a fiber external cavity. A 1.55 mu m strained MQW laser diode is used, with one facet high reflectivity (HR) coated for improved cavity Q, and the other antireflection (AR) coated to allow coupling to the external cavity and suppress Fabry-Perot modes. Near-transform-limited pulses are obtained over a frequency range of 700 MHz around a system operating frequency of 2.488 GHz, with pulsewidths of 50 ps, as required for a practical soliton transmission system.< >
The authors measure and calculate the optical properties of strong
(δn/n~10-3) in-core optical fiber phase gratings
written by the UV laser sidewriting technique. A pronounced fine
structure on the main reflection peak is observed and explained, along
with a short wavelength loss associated with radiation mode coupling,
modulated by cladding effects
The problem of propagation and interaction of optical radiation in dielectric waveguides is cast in the coupled-mode formalism. This approach is useful for treating problems involving energy exchange between modes. A derivation of the general theory is followed by application to the specific cases of electrooptic modulation, photoelastic and magnetooptic modulation, and optical filtering. Also treated are nonlinear optical applications such as second-harmonic generation in thin films and phase matching.
In a distributed feedback (DFB) laser with spatial index modulation, an antisymmetric taper of the feedback parameter, k , removes the threshold degeneracy, which is characteristic of uniform structures, and leads to one mode of particularly low threshold. Exact solutions are presented for the special case of an antisymmetric step of k . An approximate perturbation method is developed which gives simple expressions for the threshold gains, and external Q 's of some tapered distributed feedback structures. The method is tested against two exact solutions, the uniform, and the stepped- k DFB laser. It is shown that the threshold of the stepped- k DFB laser is the lowest of any structure with an antisymmetric taper and a prescribed maximum value of |k| .
Theory of optical waveguides, " in Guided-Wave Opto-electronics, T. Tamir, Ed
- H Kogelnik
H. Kogelnik, " Theory of optical waveguides, " in Guided-Wave Opto-electronics, T. Tamir, Ed. New York: Springer-Verlag, 1990.
55 m transmission over 109 km of nondispersion shifted fiber with long continuously chirped fiber gratings
- Gbit
Gbit/s 1.55 m transmission over 109 km of nondispersion shifted fiber with long continuously chirped fiber gratings, " in Optic. Fiber Commun. Conf., Dallas, TX, Feb. 16–21, 1997, paper PD6.
Theory of optical waveguides
- T Tamir