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Journal ArticleDOI

Prediction of propagation characteristics of photonic crystal fibers by a simpler, more complete and versatile formulation of their effective cladding indices

01 May 2014-Optical Engineering (International Society for Optics and Photonics)-Vol. 53, Iss: 5, pp 056111-056111
TL;DR: In this article, a more complete and versatile formulation for the effective cladding index of a solid core photonic crystal fiber (PCF) with a triangular lattice of air holes in the cladding region is presented.
Abstract: We present a simpler, more complete and versatile formulation for the effective cladding index of a solid-core photonic crystal fiber (PCF) with a triangular lattice of air holes in the cladding region. This index depends on two fundamental geometrical parameters: the air hole diameters and their separation in the endlessly single mode region of the PCF corresponding to a prescribed upper limit of relative air hole size as well as the wavelength of the light used. Our earlier available formulation for the normalized propagation constants of the infinite cladding region of the same PCF and hence its effective cladding index takes care only of the dependence on the relative air hole size and wavelength at a particular hole pitch. Now, the hole pitch dependence is also taken into account to make the formulation complete in all senses. The proposed new formulation is shown to be accurate on the basis of a comparison of our results with those obtained by available techniques. Further, to check its validity in different problems of practical interest, we apply our new formulation to evaluate various propagation characteristics of the PCF. On comparison with the previously available results, our results are seen to agree excellently with them. The formulation should find wide use for simple verification by system designers and users.
Citations
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Journal ArticleDOI
TL;DR: In this paper, a simple and accurate theoretical investigation is presented, based on a novel, effective, and straight-forward ABCD matrix technique, in relation to estimation of optimum coupling efficiency between the laser diode and the photonic crystal fiber (PCF) with a hyperbolic microlens (HML) on its tip.
Abstract: A simple and accurate theoretical investigation is presented, based on a novel, effective, and straight- forward ABCD matrix technique, in relation to estimation of optimum coupling efficiency between the laser diode and the photonic crystal fiber (PCF) with a hyperbolic microlens (HML) on its tip. By tailoring different parameters, such as the air-filling factor and lattice constant of the PCF, the criteria for achieving maximum coupling are predicted and reported for two different light wavelengths of practical interest. It is observed that such fiber parameters play a crucial role in predicting the optimum focal length of HML for a particular wavelength. The formulation should find application in the design of HML, for achieving a long working distance between the laser source facet and the fiber tip. © 2015 Society of Photo-Optical Instrumentation Engineers (SPIE) (DOI: 10.1117/1.OE.54.8 .086102)

11 citations


Additional excerpts

  • ...EQ-TARGET;temp:intralink-;e017;326;271 1⁄4 1þ dLð1 − μÞ μ b 2 a ; (17)...

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Journal ArticleDOI
TL;DR: In this article, a theoretical investigation of coupling optics involving a laser diode and a series of photonic crystal fibers with different air filling ratio and hole pitch via a parabolic microlens of three different focal parameters on the fiber tip in absence and presence of possible transverse and angular misalignments is presented.
Abstract: We present, for the first time, a theoretical investigation of coupling optics involving a laser diode and a series of photonic crystal fibers with different air filling ratio and hole pitch via a parabolic microlens of three different focal parameters on the fiber tip in absence and presence of possible transverse and angular misalignments. By employing Gaussian field distributions for both the source and the fiber and also already derived ABCD matrix for parabolic microlens under paraxial approximation, we formulate analytical expressions for the concerned coupling efficiencies for two different light-emitting wavelengths of 1.3 and 1.5 µm, respectively. Further, it is observed that, for a fit focal parameter of 8.0 µm of parabolic microlens, photonic crystal fiber with air filling ratio of 0.35 and hole pitch of 5.0 µm comes out to be the most suitable one to couple laser diode for both wavelengths of practical interest. Moreover, the coupling efficiency can reach to 97.13% for excitement by a laser diode emitting specially light of wavelength λ = 1.3 µm. The analysis should find use in ongoing investigations for optimum launch optics for the design of parabolic microlens on the single mode photonic crystal fiber tip to achieve long working distance.

4 citations

Journal ArticleDOI
01 Nov 2017-Optik
TL;DR: In this article, an optical coupling scheme of such a single mode photonic crystal fiber with a laser diode through easily fabricable hemispherical microlens using ABCD matrix formulation is presented.

4 citations

14 Nov 2017
TL;DR: In this paper, the authors investigated theoretically the coupling optics involving a laser diode and a series of circular core photonic crystal fibers with different air filling ratio and hole-pitch via hemispherical microlens of allowable aperture on the tip of such fiber in absence and presence of possible transverse and angular misalignments.
Abstract: We investigate theoretically the coupling optics involving a laser diode and a series of circular core photonic crystal fibers with different air filling ratio and hole-pitch via hemispherical microlens of allowable aperture on the tip of such fiber in absence and presence of possible transverse and angular misalignments. By employing Gaussian field distributions for both the source and the fiber and also the already derived ABCD matrix for hemispherical microlens, we formulate analytical expressions for the concerned coupling efficiencies for practically interesting two different light emitting wavelengths of 1.3 μm and 1.5 μm , respectively. Further, it is observed that, for a fit radius of curvature of 6.0 µm of hemispherical microlens, photonic crystal fiber with air filling ratio of 0.45 and hole-pitch of 4.5 µm comes out to be the most suitable one to couple laser diode emitting light of wavelength . Moreover, the coupling efficiency can reach to 86.88% with simultaneous optimization of radius of curvature and working distance of specific lensed fiber. Such analysis which as per our knowledge is the first theoretical investigation, will be extremely important in ongoing investigations for the design of optimum launch optics involving hemispherical microlens on the tip of photonic crystal fiber. Moreover, the results are extremely useful for assessing deeply the sensitivity of such coupler with reference to above kinds of misalignments.

3 citations


Cites background or methods from "Prediction of propagation character..."

  • ...0 μm ) [29] are then calculated [29, 30] and shown in Table 4 where we also present the relevant working distances (u) with corresponding maximum coupling efficiencies and transmittivity factors for m μ λ 3 ....

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  • ...The procedure for obtaining the value of FSM n for given parameters of the CCPCF at operating wavelength of light is detailed in Appendix A [29, 30]....

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  • ...Since the core-index COn is greater than that of the effective cladding index FSMn , the fiber can guide light by the mechanism of MTIR as in case of a conventional step index fiber (CSF) [29, 30]....

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  • ...In CSFs, the single-mode optical bandwidth is typically limited by macro-bend loss at long wavelengths and a higher-order mode cutoff at short wavelengths [40]....

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  • ...The upper and lower limits of the propagation constants β of the guided modes through the core of the CCPCF satisfy [8, 30] k FSM CO n β β > > (2)...

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Journal ArticleDOI
TL;DR: For a range of fiber parameters and wavelengths, the splice losses between photonic crystal fiber and a single mode fiber are calculated using a simplified and effective model of photonic fiber following a recently developed elaborate method.
Abstract: Abstract For a range of fiber parameters and wavelengths, the splice losses between photonic crystal fiber and a single mode fiber are calculated using our simplified and effective model of photonic crystal fiber following a recently developed elaborate method. Again, since the transverse offset and angular mismatch are the serious factors which contribute crucially to splice losses between two optical fibers, these losses between the same couple of fibers are also studied, using our formulation. The concerned results are seen to match fairly excellently with rigorous ones and consistently in comparison with earlier empirical results. Moreover, our formulation can be developed from theoretical framework over entire optogeometrical parameters of photonic crystal fiber within single mode region instead of using deeply involved full vectorial methods. This user-friendly simple approach of computing splice loss should find wide use by experimentalists and system users.

2 citations


Cites background or methods or result from "Prediction of propagation character..."

  • ...The procedure to obtain the value of nFSM for given fiber parameters and wavelength of light using [8] is elucidated in the Appendix section....

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  • ...Such modification in the fitting is advantageous in the manner that, it will help us to reduce computation time, since only 9 coefficients are required to compute instead of 27 coefficients [8]....

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  • ...(12) with nFSM and this has enabled us to propose a modified simpler formulation of [8] as follows:...

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  • ...In fact, very recently, a simple, complete, and versatile method has been proposed to predict the effective cladding index of a PCF [8]....

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  • ...Our EIM [8] formulations are, extensively and elaborately, developed on the basis of scalar framework [1, 2]....

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References
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Journal ArticleDOI
17 Jan 2003-Science
TL;DR: In this article, a periodic array of microscopic air holes that run along the entire fiber length are used to guide light by corralling it within a periodic arrays of microscopic holes.
Abstract: Photonic crystal fibers guide light by corralling it within a periodic array of microscopic air holes that run along the entire fiber length Largely through their ability to overcome the limitations of conventional fiber optics—for example, by permitting low-loss guidance of light in a hollow core—these fibers are proving to have a multitude of important technological and scientific applications spanning many disciplines The result has been a renaissance of interest in optical fibers and their uses

3,918 citations


"Prediction of propagation character..." refers background in this paper

  • ...Now, the propagation constants β of the guided modes through the core of the PCF are given by the relation3 knCO > β > βFSM; (1) where k ¼ 2π∕λ, λ being the operating wavelength, nCO is the index of the core material or silica, and βFSM is the propagation constant of the FSM, which is the fundamental mode in the infinite photonic crystal cladding without any core or defect....

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  • ...knCO > β > βFSM; (1) where k 1⁄4 2π∕λ, λ being the operating wavelength, nCO is the index of the core material or silica, and βFSM is the propagation constant of the FSM, which is the fundamental mode in the infinite photonic crystal cladding without any core or defect....

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Journal ArticleDOI
TL;DR: An effective-index model confirms that an all-silica optical fiber made by embedding a central core in a two-dimensional photonic crystal with a micrometer-spaced hexagonal array of air holes can be single mode for any wavelength.
Abstract: We made an all-silica optical fiber by embedding a central core in a two-dimensional photonic crystal with a micrometer-spaced hexagonal array of air holes. An effective-index model confirms that such a fiber can be single mode for any wavelength. Its useful single-mode range within the transparency window of silica, although wide, is ultimately bounded by a bend-loss edge at short wavelengths as well as at long wavelengths.

2,905 citations


"Prediction of propagation character..." refers background in this paper

  • ...(3) for fixed λ and Λ values, the value of the concerned u is determined from the following equation:(1)...

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Journal ArticleDOI
TL;DR: The history, fabrication, theory, numerical modeling, optical properties, guidance mechanisms, and applications of photonic-crystal fibers are reviewed.
Abstract: The history, fabrication, theory, numerical modeling, optical properties, guidance mechanisms, and applications of photonic-crystal fibers are reviewed

1,488 citations

Book
01 Dec 2007
TL;DR: In this article, the authors present a detailed analysis of planar optical waveguide and a step-index fiber model for optical fiber communication and demonstrate the properties of a step index fiber.
Abstract: 1. Introduction 2. Basic optics 3. The optical fiber 4. Ray analysis of planar optical waveguide 5. Graded index optical fibers 6. Material dispersion 7. Planar waveguides 8. Characteristics of a step-index fiber 9. Graded Index fibers 10. Waveguide dispersion and design considerations 11. Sources for optical fiber communication 12. Detectors for optical fiber and communication 13. Fiber optic communication system design 14. Optical fiber Amplifiers 15. Dispersion compensation and chirping phenomenon 16. Optical solitons 17. Single-mode fiber optic components 18. Single mode optical fiber sensors 19. Measurement methods in optical fiber: I 20. Measurement methods in optical fibers: II 21. Periodic interactions in waveguides 22. Ray equation in Cartesian coordinates 23. Ray paths 24. Leaky modes.

843 citations

Journal ArticleDOI
TL;DR: In this paper, the authors proposed an accurate vector analysis of the lowest electromagnetic modes of photonic crystal fibers, and the likeness of their propagation characteristics to those of step index fibers was emphasized.

317 citations


"Prediction of propagation character..." refers background in this paper

  • ...53(5) Optical Engineering 53(5), 056111 (May 2014)...

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  • ...53(5) Kundu and Sarkar: Prediction of propagation characteristics of photonic crystal fibers....

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