Modeling and performance analysis of single fiber ring incorporated with fiber Bragg grating
TL;DR: In this article, a mathematical model of an optical ring resonator (RR) configuration using a single directional optical coupler (DOC) with a uniform fiber Bragg grating (FBG) incorporated and an RR configuration using two DOCs with an FBG incorporated is developed in the Z-domain.
Abstract: The mathematical model of an optical ring resonator (RR) configuration using a single directional optical coupler (DOC) with a uniform fiber Bragg grating (FBG) incorporated and an RR configuration using two DOCs with an FBG incorporated is developed in the Z-domain. The developed mathematical model is used for the evaluation of transmission response. Spectral characteristics in terms of peak transmittance, resonant frequency, and free spectral range are determined for a single fiber ring configuration using two DOCs with an FBG incorporated. The results are found to be in very close agreement with measured values. The transmission characteristic of the single waveguide structure comprising a ring of length 2 mm enclosing a Bragg grating is analyzed. By properly optimizing the grating reflectivity and power coupling ratios of the coupler, a narrow full width at half maximum of 4.72 GHz that is around 78 times sharper than the normal FBG resonance is obtained. Further narrowing of the spectral width is achieved by increasing the RR length. The grating lengths are chosen judiciously to minimize the side peaks. The group delay and dispersion characteristics are addressed.
Citations
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TL;DR: In this article, a ring resonator configuration with single and multiple phase-shifted fiber Bragg gratings (PSFBG) is modeled and analyzed using the delay line signal processing approach in Z domain and Mason's gain formula.
Abstract: The ring resonator (RR) configuration with single as well as multiple $\pi \!\!\!$ -phase-shifted fiber Bragg gratings(PSFBG) is mathematically modelled and analyzed using the delay line signal processing approach in Z domain and Mason’s gain formula. The integration of single $\pi \!\!$ -FBG in a ring results in much sharper linewidth at Bragg wavelength compared to the resonance linewidth of the $\pi \!\!$ -FBG alone. By proper optimization of grating length, ring length and coupling ratios of the couplers, the transmission spectrum depicts a much narrower spectral width of 62.6 MHz with virtually zero crosstalk. The dependence of the slope and bandwidth of the passband on the ratio of grating section length and grating coupling strength is also analyzed. For RR with double $\pi \!\!$ -phase-shifted FBG, RR with triple $\pi \!\!$ -phase-shifted FBG, RR with quadruple $\pi \!\!$ -phase-shifted FBG and RR with pentuple $\pi \!\!$ -phase-shifted FBG, the grating section lengths and the phase shift locations need to considered separately and incorporated in the Z domain model. With increasing number of phase-shifts, the resonant bandwidth of the composite structure decreases while the slope increases. The number of channels possible for the ring resonator with pentuple $\pi $ -phase-shifted FBG (RRPPSFBG) having a spectral width of 15.59 MHz is estimated around 11050. Moreover, theoretical analysis demonstrates that ultra-high resolution weak strain measurement of 44.23 f $\varepsilon ~\surd $ Hz is easily achievable using the interferometric interrogation of the proposed RRPPSFBG sensor.
1 citations
TL;DR: A review of the various methodologies is provided in this article , where the principles of fiber bragg gratings and the development of FBG-based sensors for temperature, pressure, liquid level, strain, and refractive index sensing in diverse applications are discussed.
Abstract: In-fiber Bragg grating filters continue to proliferate, and their applications expand with the rapid advancement of fiber optic component fabrication techniques. Mathematical models for the realisation, characterization, and simulation of fiber Bragg gratings (FBGs) are required to design gratings for various purposes. In this article, a review of the various methodologies is provided. The principles of FBG and the development of FBG-based sensors for temperature, pressure, liquid level, strain, and refractive index sensing in diverse applications have been discussed. The operating concept and performance of cavity structures based on FBG have been investigated. Different sensing architectures with high sensitivity and resolution are presented, including FBG encased in a ring configuration. The basic interrogation techniques are also discussed.
References
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TL;DR: In this paper, the spectral properties of fiber reflection and transmission gratings are described and examples are given to illustrate the wide variety of optical properties that are possible in fiber gratings.
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.
3,330 citations
Additional excerpts
...EQ-TARGET;temp:intralink-;e002;116;333 þ 0 k 1⁄4 Z1∕2Ek−1; E− 0 k 1⁄4 ZEk−1: (2)...
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Book•
15 Jun 1999
TL;DR: In this article, the authors present a unique, cutting-edge approach to optical filter design, focusing on filter characteristics and enabling readers to quickly calculate the filter response as well as tackle larger and more complex filters.
Abstract: From the Publisher:
A Unique, Cutting-Edge Approach to Optical Filter Design With more and more information being transmitted over fiber-optic lines, optical filtering has become crucial to the advanced functionality of todays communications networks. Helping researchers and engineers keep pace with this rapidly evolving technology, this book presents digital processing techniques for optical filter design. This higher-level approach focuses on filter characteristics and enables readers to quickly calculate the filter response as well as tackle larger and more complex filters. The authors incorporate numerous theoretical and experimental results from the literature and discuss applications to a variety of systemsincluding the new wavelength division multiplexing (WDM) technology, which is fast becoming the preferred method for system upgrade and expansion. Special features of this book include:
*The theory underlying various architectures that can approximate any filter function
*Filter design techniques applicable to a broad range of materials systemsfrom silica to fiber to microelectromechanical (MEM) systems
*Design examples relevant to filters for WDM systems and planar waveguide devices
*250 figures as well as problem sets for use in graduate-level studies
621 citations
Additional excerpts
...EQ-TARGET;temp:intralink-;e010;116;443 fðzÞ 1⁄4 P1Δ1 Δ 1⁄4 − ffiffiffiffiffiffiffiffi κ1κ2 p HðzÞZ−2M1 1 − C1C2HðzÞZ−ð2M1þM2Þ : (10)...
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01 Jul 1984
TL;DR: In this paper, the authors discuss the implementation of fiber-optic lattice structures incorporating singlemode fibers and directional couplers, and show that the pole of the system transfer function with the largest magnitude is simple and positive-valued (in the Z-plane), and that the magnitude of the frequency response can nowhere exceed its value at the origin.
Abstract: We discuss the implementation of fiber-optic lattice structures incorporating single-mode fibers and directional couplers. These fiber structures can be used to perform various high-speed time-domain and frequency-domain functions such as matrix operations and frequency filtering. In this paper we mainly consider systems in which the signals (optical intensities) and coupling coefficients are nonnegative quantities; these systems fit well in the theory of positive systems. We use this theory to conclude, for example, that for such systems the pole of the system transfer function with the largest magnitude is simple and positive-valued (in the Z-plane), and that the magnitude of the frequency response can nowhere exceed its value at the origin. We also discuss the effects of various noise phenomena on the performance of fiber-optic signal processors, particularly considering the effects of laser source phase fluctuations. Experimental results are presented showing that the dynamic range of the fiber systems, discussed in this paper, is limited, not by the laser source intensity noise or shot noise, but by the laser phase-induced intensity noise. Mathematical analyses of lattice structures as well as additional applications are also presented.
362 citations
Additional excerpts
...EQ-TARGET;temp:intralink-;e014;116;617 0 fðzÞ 1⁄4 P 2 n1⁄41 P 0 nΔ 0 n Δ 0 1⁄4 P1 0Δ1 0 þ P2 0Δ2 0 Δ 0 1⁄4 C −HðzÞδZ −2M1 0 1 − CHðzÞδZ−2M1 0 : (14)...
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TL;DR: In this paper, an experimental investigation of the transfer characteristics of a fiber ring resonator for various values of the resonator finesse was carried out to measure the spectral dependence of the intensity transmission and the induced phase shift in the undercoupled, critically coupled, and overcoupled regimes.
Abstract: We present the results of an experimental investigation of the transfer characteristics of a fiber ring resonator for various values of the resonator finesse. In particular, we measure the spectral dependence of the intensity transmission and the induced phase shift in the undercoupled, critically coupled, and overcoupled regimes. We also demonstrate tunable optical (true time) group delay via a fiber ring resonator and show that a high finesse is unnecessary. Our laboratory results are in excellent agreement with theoretical predictions.
238 citations
Additional excerpts
...EQ-TARGET;temp:intralink-;e004;116;723 kðzÞ 1⁄4 ξkðzÞEðk−1ÞðzÞ; (4)...
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TL;DR: In this paper, the authors describe means of producing and operating fiber Bragg grating (FBG) sensors that support structural slow light with a group index that can be in principle as high as several thousand.
Abstract: On the edge of the bandgap in a fiber Bragg grating (FBG) narrow peaks of high transmission exist at frequencies where light interferes constructively in the forward direction. In the vicinity of these transmission peaks, light reflects back and forth numerous times across the periodic structure and experiences a large group delay. Since the sensitivity of a phase sensor to most external perturbations is proportional to the reciprocal of group velocity, in these slow-light regions the sensitivity of an FBG is expected to be significantly enhanced over traditional FBG sensors operated around the Bragg wavelength. In this paper, we describe means of producing and operating FBGs that support structural slow light with a group index that can be in principle as high as several thousand. We present simulations elucidating how to select the FBG parameters, in particular index modulation, length, and apodization, to generate such low group velocities, and quantify the very large improvement in strain and temperature sensitivities resulting from these new slow-light configurations. As a proof of concept, we report an FBG with a group index of 127, or a group velocity of ~2,360 km/s. This is by far the lowest group velocity reported to date in an FBG. Used as a strain sensor, this slow-light FBG is shown to be able to detect a strain as small as 880 fe/ √Hz , the lowest value reported for a passive FBG sensor.
80 citations
"Modeling and performance analysis o..." refers background in this paper
...(3) gives the TF of the unit cell as follows:...
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...EQ-TARGET;temp:intralink-;e003;116;264 þ k 1⁄4 1 τ2 ðEþ 0 k þ Γ2E 0 k Þ and Ek 1⁄4 1 τ2 ðΓ2Eþ 0 k þ E− 0 k Þ; (3)...
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