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Showing papers on "Step-index profile published in 2003"


Patent
19 Mar 2003
TL;DR: In this article, an optical fiber comprising a center core which forms a passageway for transmitting optical signals and a cladding which encloses the center core has a refractive index N 0.
Abstract: Disclosed is an optical fiber comprising a center core which forms a passageway for transmitting optical signals and has a refractive index N 1 , and a cladding which encloses the center core and has a refractive index N 0 . The optical fiber further comprises an upper core, which has a distribution of refractive indices increased starting from a refractive index N 2 (>N 0 ) at its outer circumference to the refractive index N 1 at its internal circumference, and a minutely depressed refractive index region, which is interposed between said upper core and cladding and has a refractive index N 3 . The refractive index N 3 is lower than the refractive index N 0 .

162 citations


Journal ArticleDOI
TL;DR: A significantly improved device that exhibits minimal edge effects, a larger NRI region permitting precise extraction of dispersion data, and a PRI region consisting of a microstrip grid, over which the fields may be observed are presented.
Abstract: We have previously shown that a new class of Negative Refractive Index (NRI) metamaterials can be constructed by periodically loading a host transmission line medium with inductors and capacitors in a dual (high-pass) configuration. A small planar NRI lens interfaced with a Positive Refractive Index (PRI) parallel-plate waveguide recently succeeded in demonstrating focusing of cylindrical waves. In this paper, we present theoretical and experimental data describing the focusing and dispersion characteristics of a significantly improved device that exhibits minimal edge effects, a larger NRI region permitting precise extraction of dispersion data, and a PRI region consisting of a microstrip grid, over which the fields may be observed. The experimentally obtained dispersion data exhibits excellent agreement with the theory predicted by periodic analysis, and depicts an extremely broadband region from 960MHz to 2.5GHz over which the refractive index remains negative. At the frequency at which the theory predicts a relative refractive index of -1, the measured field distribution shows a focal spot with a maximum beam width under one-half of a guide wavelength. These results are compared with field distributions obtained through mathematical simulations based on the plane-wave expansion technique, and exhibit a qualitative correspondence. The success of this experiment attests to the repeatability of the original experiment and affirms the viability of the transmission line approach to the design of NRI metamaterials.

123 citations


Journal ArticleDOI
TL;DR: A new method for measuring simultaneously the thickness and the refractive index of a transparent plate is proposed, based on a simple, variable lateral-shear, wavelength-scanning interferometer.
Abstract: A new method for measuring simultaneously the thickness and the refractive index of a transparent plate is proposed. The method is based on a simple, variable lateral-shear, wavelength-scanning interferometer. To achieve highly accurate measurements of both refractive index n and thickness d we use several means to determine these two quantities. We finely tune a distributed-feedback diode laser light source to introduce a phase shift into the detected signal, whereas we make the sample rotate to produce variable lateral shearing. Phase shifting permits precise determination of the optical thickness, nd, whereas refractive index n is obtained from the retrieved phase of the overall interference signal for all incidence angles.

98 citations


Patent
07 Aug 2003
TL;DR: In this article, the authors proposed an optical mode transformer (OMT) with a low index core, a high index core and a first tapered region for a waveguide.
Abstract: An optical mode transformer (100). The optical mode transformer (100) features a low index core (102), a high index core (104) having a first tapered region (110), with the high index core (104) embedded within the low index core (102) and with the low index core serving as a cladding for a waveguide defined by the high index core embedded in the low index core, and a cladding layer (106) surrounding the low index core, with the cladding layer including one or more materials with different refractive indices than those of the low index core and high index core.

70 citations


Journal ArticleDOI
TL;DR: Both the experimental measurements and the computational simulations turn out to be very useful to explain the behavior of refracting and tunneling rays along bent multimode waveguides and along finite-cladding fibers.
Abstract: Our main goal is to provide a comprehensive explanation of the existing differences in bending losses arising from having step-index multimode plastic optical fibers with different cladding thicknesses and under different types of conditions, namely, the variable bend radius R, the number of fiber turns, or the fiber diameter. For this purpose, both experimental and numerical results of bending losses are presented for different cladding thicknesses and conditions. For the measurements, two cladding thicknesses have been considered: one finite and another infinite. A fiber in air has a finite cladding thickness, and rays are reflected at the cladding-air interface, whereas a fiber covered by oil is equivalent to having an infinite cladding, since the very similar refractive index of oil prevents reflections from occurring at the cladding-oil interface. For the sake of comparison, numerical simulations based on ray tracing have been performed for finite-cladding step-index multimode waveguides. The numerical results reinforce the experimental data, and both the experimental measurements and the computational simulations turn out to be very useful to explain the behavior of refracting and tunneling rays along bent multimode waveguides and along finite-cladding fibers.

69 citations


Journal ArticleDOI
TL;DR: In this article, the environmental sensing behavior of long period gratings written in three fibers with different refractive index profiles: step, W and a progressive three layered fiber was compared and significant differences in the behaviour of the three fiber types were found.

56 citations


Patent
20 Jun 2003
TL;DR: In this paper, the authors provided a planar waveguide structure with a first core layer, a second core layer and a cladding layer, where the cladding layers are disposed between the first and second core layers to form an inter-core claddings.
Abstract: There is provided a planar waveguide structure (700) having a first core layer (708), a second core layer (704) and a cladding layer (706), wherein the cladding layer (706) is disposed between the first core layer (708) and the second core layer (704) to form an inter-core cladding layer (706). The inter-core cladding layer (706) comprises a first region (722) having a first refractive index and an array of sub-regions (724) formed therein having a second refractive index. The subregions (724) do not extend into either the first or the second core layer, and they give rise to a photonic band structure region, which is effective to perturb an evanescent field of an optical signal propagating through the core layers.

53 citations


Journal ArticleDOI
TL;DR: In this paper, an anisotropic metamaterial based on a transmission line (TL) approach is presented, characterized and demonstrated in terms of analytic dispersion diagrams, equivalent refractive indexes, and circuit-simulated voltage/current/power distributions.
Abstract: An anisotropic metamaterial, based on a transmission line (TL) approach, that exhibits positive refractive index (PRI) in one direction and negative refractive index (NRI) in another (orthogonal) direction is presented, characterized and demonstrated in terms of analytic dispersion diagrams, equivalent refractive indexes, and circuit-simulated voltage/current/power distributions. This anisotropic structure may also be implemented in distributed architectures and lead to novel antenna and reflector applications.

48 citations


Journal Article
TL;DR: In this paper, the authors examined the refractive index changes near the absorption edge in semiparabolic quantum wells as a function of the incident optical intensity, and an analytic formula for the changes in the this paper was obtained by using the compact-density matrix approach and an iterative method.

45 citations


Journal ArticleDOI
TL;DR: In this article, changes in axial stress and refractive index have been measured as a function of the total UV-irradiation fluence during the formation of Bragg gratings in B/Ge and Sn/Ge-codoped core fibers.

44 citations


Patent
14 Jan 2003
TL;DR: In this article, the authors proposed a segmented core profile for optical transmission fiber with a high effective area, low nonlinearity coefficient, nonzero dispersion, and relatively flat dispersion slope.
Abstract: An optical transmission fiber has a refractive index profile with an area of increased index of refraction at the inner core of the fiber, an annular region positioned radially outward from the inner core with an index of refraction exceeding the index of the inner core, and at least a low dopant content region in a cross-sectional region between the inner core and the annular region. A low loss cladding layer surrounds the core region. The optical transmission fiber with this segmented core profile provides a high effective area, low non-linearity coefficient, nonzero dispersion, and relatively flat dispersion slope.

Journal ArticleDOI
TL;DR: In this paper, a Monte Carlo curved ray-tracing method is used to analyze the radiative heat transfer in one-dimensional absorbing-emitting-scattering semitransparent slab with variable spatial refractive index.

Patent
28 Aug 2003
TL;DR: In this article, a graded effective refractive index is provided by varying the relative thicknesses of the two materials in the local region of the optical medium, where the thickness of the layers of at least one of the materials is substantially less than the effective light wavelength of interest.
Abstract: An optical medium has a graded effective refractive index with a high maximum refractive index change. The medium is formed using alternating layers of two or more materials having significantly different refractive indices. The thickness of the layers of at least one of the materials is substantially less than the effective light wavelength of interest. The effective index of refraction in a local region within the medium depends on the ratio of the average volumes of the two materials in the local region. A graded index of refraction is provided by varying the relative thicknesses of the two materials.

Journal ArticleDOI
TL;DR: In this paper, an automated chemical process for tapering highly multimoded plastic optical fiber tapers was developed, in order to obtain repeatable, optically clear and mechanically robust tapers in a minimum time period.
Abstract: An automated chemical process for tapering highly multimoded plastic optical fibre tapers was developed. On-line monitoring was performed whilst varying the solvent composition to optimize taper formation, in order to obtain repeatable, optically clear and mechanically robust tapers in a minimum time period. A model of the process is presented in terms of fibre core radius and core/cladding refractive index. A relationship between core radius, cladding refractive index and numerical aperture was derived that had application for dynamic prediction and compensation of optical parameters. When characterized with a range of refractive indices, the tapered POF sensor exhibited two distinct regions: the water/alcohol region below 1.4 refractive index units, and the oil region above 1.4 suggesting the sensor's use as an oil-in-water, or water-in-oil sensor. From 95% confidence limits, the accuracy of the POF was ±0.006 refractive index units (to 2 standard deviations) or 0.4% above 1.4. Tapered POF is sensitive to refractive index providing a cheap, easy-to-handle and rugged throwaway sensor for water and beverage process and quality monitoring.

Journal ArticleDOI
TL;DR: In this paper, the nonlinear refractive index n 2 of silica fiber (24 m) and erbium-doped fiber (10 m) is measured to within an accuracy of 5% by use of time-delayed photorefractive beam coupling of intense 53-ps, 1.064-μm pulses that experience self-phase modulation in the fibers.
Abstract: The nonlinear refractive index n 2 of silica fiber (24 m) and erbium-doped fiber (10 m) is measured to within an accuracy of 5% by use of time-delayed photorefractive beam coupling of intense 53-ps, 1.064-μm pulses that experience self-phase modulation in the fibers. The resultant induced grating autocorrelation response yields a value of n 2 /A eff and a calibration standard for the fiber. A phase shift of the order of 0.19π can be detected and is limited only by laser amplitude fluctuations. A unique advantage of this technique is its ability to measure n 2 accurately in short lengths (z≤25 m) of fiber, whereas other approaches typically use much longer lengths of fiber (z≥100 m) .

Journal ArticleDOI
TL;DR: In this paper, a low-loss and high-bandwidth graded-index plastic optical fiber (GI-POF) was obtained by a thermal drawing of the preform fabricated by the centrifugal deposition method.
Abstract: Low-loss and high-bandwidth graded-index plastic optical fiber (GI-POF) was obtained by a thermal drawing of the preform fabricated by the centrifugal deposition method. In the method, a mixture of methyl methacrylate and benzyl methacrylate is fed into a rapidly rotating tube. The mixture forms a thin layer on the tube wall due to the centrifugal force and polymerizes simultaneously by thermal reaction. The feeding rate and the composition of the mixture were changed to form a desired refractive index profile. The refractive index profile of the fiber was the same as the preform. The GI-POF has the optical loss of 120 dB/km and the bandwidth of 3.45 Gbit/s 100 m at the wavelength of 650 nm.

Patent
29 Dec 2003
TL;DR: In this paper, a method for fabricating an optical tapered waveguide is presented, where the refractive index n1 of the tapered core of the coupling waveguide (4) is selected so that the first and second effective refractive indices differ from each other in absolute value less than 30% of the difference (n2 − n2 - n2eff) between the core this paper.
Abstract: An optical mode converter comprises a coupling waveguide (4) and a receiving waveguide (3). The coupling waveguide has at an input end a first effective refractive index n1eff and includes a tapered core (41) of a substantially constant refractive index n1 with a substantially square cross section at the input end (5), having a size that tapers down moving away from the input end. The coupling waveguide has also a cladding (42) at least partially surrounding the tapered core. The receiving waveguide has a second effective refractive index n2eff at an output end and comprises a core (31) of a substantially constant refractive index n2, greater than the refractive index n1 of the tapered core (41) of the coupling waveguide, and a cladding (32) at least partially surrounding the core. A side surface (43) of the tapered core of the coupling waveguide (4) is optically in contact, in a coupling portion, with the receiving waveguide (3) so as to allow optical coupling between the coupling waveguide (4) and the receiving waveguide (3). The refractive index n1 of the tapered core of the coupling waveguide (4) is selected so that the first effective refractive index n1eff and the second effective refractive index n2eff differ from each other in absolute value less than 30% of the difference (n2 - n2eff) between the core refractive index and the effective refractive index of the receiving waveguide (3). A method for fabricating an optical tapered waveguide is also disclosed.

Patent
Gerhard Reichinger1, Georg Kodl1
10 Feb 2003
TL;DR: In this paper, a pressure sensor for an anti-pinch device in the motor vehicle industry is described, where the fiber guide is pressed against the optical fiber such that the condition for the total reflection required for the normal optical waveguidance in the optical waveguide is no longer fulfilled, and attenuation takes place.
Abstract: A pressure sensor includes an optical waveguide having an optical fiber with a refractive index n1, located in a fiber guide with a refractive index n3, forming an intermediate region. A medium with a refractive index n2 is located in the intermediate region. The refractive indices correspond to the relation n3 > n1 > n2. When subjected to a pressure, the fiber guide is pressed against the optical fiber such that the condition for the total reflection required for the normal optical waveguidance in the optical waveguide is no longer fulfilled, and attenuation takes place. The attenuation is evaluated in a corresponding control unit. The pressure sensor is especially provided for an anti-pinch device in the motor vehicle industry.

Proceedings ArticleDOI
01 Dec 2003
TL;DR: A new and accurate refractive index profile synthesis method for optical waveguides is demonstrated using the transmitted near electric field data and results of numerical reconstruction of step index, parabolic, and segmented optical fibreRefractive index profiles are demonstrated.
Abstract: A new and accurate refractive index profile synthesis method for optical waveguides is demonstrated using the transmitted near electric field data. This method is based on an inverse transmission line technique. From Maxwell's equations, we derive a transmission line equivalent circuit for the refractive index profile of a cylindrical dielectric waveguide. We demonstrate how to use this model and carry out the inverse problem and synthesize the exact refractive index profile numerically from near field data. Based on knowledge of the electric field, we demonstrate results of numerical reconstruction of step index, parabolic, and segmented optical fibre refractive index profiles. The accuracy of the reconstructed waveguides is examined numerically.

Journal ArticleDOI
TL;DR: In this article, a double refracting polarizing interference microscope is used with a suggested method to determine the refractive index profile and birefringence profile of partially and highly oriented fibers.
Abstract: Double refracting polarizing interference microscope designed by Pluta is used with a suggested method to determine the refractive index profile and birefringence profile of partially and highly oriented fibers. The application of this method depends on using Pluta polarizing interference microscope in two positions (crossed position for the duplicated images and subtractive position for the nonduplicated image of the fiber). The mathematical representation of the suggested method is given. The refraction of the light beam inside the fibers is taken into consideration while measuring the fringe shift profile. The refractive index profiles of polypropylene fiber with draw ratio 3.5 are determined using the conventional method. The results are compared with those obtained with the suggested method and found to be in good agreement. The suggested method is applied to determine the refractive index profile of poly(aryl ether ether ketone) partially oriented fiber and poly(ethylene terephthalate) highly oriented fiber. The diffraction of He–Ne laser beam is used to determine the average diameters of these fibers. Microinterferograms are given for illustration. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 87: 2341–2347, 2003

Journal ArticleDOI
TL;DR: In this article, the authors present the results of a theoretical analysis of transmission characteristics of a fiber optic refractometric transducer with a hemispherical glass detection element, where the internal reflection of light from the element's spherical surface depends on the refractive index of the surrounding medium.
Abstract: We present the results of a theoretical numerical analysis of transmission characteristics of a fiber optic refractometric transducer with a hemispherical glass detection element. In this transducer, the internal reflection of light from the element's spherical surface depends on the refractive index of the surrounding medium. We examine the effects of the transducer's geometrical and optical parameters and its refractive index on the transmission function, its nonlinearity, and the transducer's sensitivity to the refractive index of the surrounding medium. We show that through a proper choice of the transducer's material and geometrical parameters, it is possible to obtain a transmission function of any necessary span over a wide interval of the refractive index of the surrounding medium (from n = 1.0 to 1.7), and to modify the form of the transmission function from a linear one to a steplike one in virtually the same device. This permits us to use the proposed transducer for two contrasting applications: assessing the refractive index, and discriminating between two liquids or between air and a liquid, as in the detection of liquids, level measurement, etc. In addition, it is possible to adjust the transducer input range to the refractive index of a particular fluid (or fluids) of interest.

Journal ArticleDOI
TL;DR: In this paper, a planar optical waveguide was implanted by 3.0 MeV B 3+ ions at room temperature, forming planar waveguides at a dose of 4 × 10 14 ions/cm 2, and the prism-coupling method was used to take dark mode measurements.
Abstract: Optically polished LiNbO 3 was implanted by 3.0 MeV B 3+ ions at room temperature, forming planar optical waveguides at a dose of 4 × 10 14 ions/cm 2 . The prism-coupling method was used to take dark mode measurements. Four waveguide modes were observed for both ordinary and extraordinary light. Contrary to high-dose ion-implanted waveguides, the extraordinary refractive index was found to increase in the guide region for low-dose implantations. The reflectivity calculation method was used to reconstruct the refractive index profile in the waveguide. TRIM’98 was also used to simulate the damage distribution in the LiNbO 3 .

Patent
21 Aug 2003
TL;DR: In this article, an optical fiber having a clad diameter of 125 µm is made by adding Ge to a core (41) having a core diameter of 8 µm and a relative index difference of 0.3% and two refractive index grating parts having a slant angle of 2~ are formed in series in the optical fiber.
Abstract: An optical fiber (4) having a clad diameter of 125 µm is made by adding Ge to a core (41) having a core diameter of 8 µm and a relative index difference of 0.3% and two refractive index grating parts (41a, 41b) having a slant angle of 2~ are formed in series in the optical fiber (4) by a phase mask method using KrF excimer laser (.lambda.=248 nm). The central period (2.LAMBDA.) of the phase mask of a chirped grating is 1140 nm, the chirp rate (C) of the period is 1.2 nm/mm, the length (G) of the first and second index grating parts (41a, 41b) is 8 mm, the effective refractive index of the first and second index grating parts (41a, 41b) is 1.447, the refractive index modulation is 3×10-3, and the gap between the first and second index grating parts (41a, 41b) is 1 mm.

Journal ArticleDOI
TL;DR: In this article, the specific heat and the refractive index change formed by laser spot heating on tellurite glass surfaces were investigated, and a good linear correlation between the reciprocal of the heat index and the specific index change was found in cases where the specific temperature change was less than 0.1.
Abstract: Correlation between the specific heat and the refractive index change formed by laser spot heating on tellurite glass surfaces has been investigated. The ternary tellurite glasses of TeO 2 –Na 2 O–Al 2 O 3 , TeO 2 –Na 2 O–GeO 2 and TeO 2 –Na 2 O–TiO 2 doped with 2 mol% of CoO were irradiated by a green light beam spot (532 nm) from a second harmonic generator of a Q switch pulse YAG laser. The refractive index map of the glass surface was measured with a He–Ne laser beam using a scanning ellipsometric technique, showing the formation of the refractive index dot patterns lower than the matrix by 0.05–0.22. The specific heat of the glasses was measured by CO 2 laser flashing method. The glasses containing Al 2 O 3 possessed the lowest specific heat among the three glass systems, giving the largest refractive index change on the glass surfaces. A good linear correlation between the reciprocal of the specific heat and the refractive index change was found in cases where the refractive index change was less than 0.1, suggesting that the refractive index change derived from the change of the fictive temperature of the glasses.

Patent
24 Dec 2003
TL;DR: In this article, a low loss micro-ring resonator device (10, 100, 10') is described, which comprises a closed-loop resonator waveguide (2) having a first refractive index (nr), and an upper cladding (20) covering the inner region (16), and a lateral cladding(21) in contact with the outer curved edge (15) and extending in the outer region (17).
Abstract: It is disclosed a low loss micro-ring resonator device (10; 100; 10') which comprises a closed-loop resonator waveguide (2) having a first refractive index (nr), the resonator waveguide (2) defining an inner (16) and an outer region (17) by an outer curved edge (15) of the waveguide (2). The resonator waveguide is arranged on a substrate (6; 6') having a second refractive index (nb), the refractive index difference (Δn1) between the first refractive index (nr) and the second refractive index (nb) is greater than 0.3. The device (10) also comprises an upper cladding (20) covering the inner region (16) of the resonator waveguide (2) having a third refractive index (nuc); and a lateral cladding (21) in contact with the outer curved edge (15) and extending in the outer region (17), said lateral cladding (21) having a fourth refractive index (nlc), the fourth refractive index (nlc) being lower than said third refractive index (nuc). A method for reducing propagation losses of a resonator device (10; 100;10') is also described.

Proceedings ArticleDOI
14 Apr 2003
TL;DR: In this paper, a class of low-loss single-mode optical fibers with ring refractive index profile is considered for long distance signal transmission as well as photonic signal processing.
Abstract: This work analyzes theoretically, technologically and practically a class of low-loss single-mode optical fibers with ring refractive index profile. The fibers are considered for long distance signal transmission as well as photonic signal processing. Trunk transmission, ring index fibers have shifted and flattened dispersion characteristics and much larger effective area as compared with standard step-index single-mode. Signal processing, device oriented, ring-index fibers have a unique capability of transmitting either quasi planar modes for large ring diameters or the second order mode in a quasi single-mode regime at lossy discrimination of the fundamental mode, for small ring diameters. Ring-index fibers can maintain singlemode transmission for considerable values of normalized frequency for particular cases of the refractive index profile. Theoretically predicted features of single-mode ring index fibers were confirmed experimentally on samples manufactured by the author is cooperation with TU of Bialystok. Parts of the work were published in Optica Applicata and reprinted with permission. Part of the work was realized within the KBN grant 4-T08D-001-22 submitted to Technical University of Bialystok.


Patent
25 Apr 2003
TL;DR: In this paper, a system and method for inspection of a substrate having a first refractive index was proposed, the method including the steps of: (i) defining an apodization scheme in response to a characteristic of the layer, (ii) applying an apoderizer to apodize a beam of radiation in response, and (iii) directing the apodized beam to impinge on the substrate, whereby a plurality of rays are reflected from the substrate.
Abstract: A system and method for inspection of a substrate having a first refractive index, the method including the steps of: (i) defining an apodization scheme in response to a characteristic of the layer; (ii) applying an apodizer to apodize a beam of radiation in response to the apodization scheme; (iii) directing the apodized beam of radiation to impinge on the substrate, whereby a plurality of rays are reflected from the substrate; whereas the apodized beam of radiation propagates through an at least partially transparent medium having a third refractive index and an at least partially transparent layer having a second refractive index and is subsequently reflected from the substrate; whereas the second refractive index differs from the first refractive index and from the third refractive index; and (iv) detecting at least some of the plurality of reflected rays.

Journal ArticleDOI
TL;DR: In this article, the authors describe the transmission of electromagnetic waves through a four-layer structure, where the two end layers are semi-infinite dielectrics with the same refractive index (n1 = n4 > 1), the 2nd layer is a vacuum gap (n2 = 1) of width d2, and the 3rd layer is made of a material with a negative (n3 < 0) for the wavelength of interest.
Abstract: Materials with a negative refractive index have some unique properties and may be used to enhance photon tunneling through a distance comparable to the wavelength. This study describes the transmission of electromagnetic waves through a four-layer structure, where the two end layers are semi-infinite dielectrics with the same refractive index (n1 = n4 > 1), the 2nd layer is a vacuum gap (n2 = 1) of width d2, and the 3rd layer is made of a material whose refractive index is negative (n3 < 0) for the wavelength of interest. The effects of layer widths and the value of n3 on the tunneling transmittance are investigated. The calculation results show that the insert of a negative-refraction layer can increase the hemispherical transmittance, suggesting that materials with negative refractive indexes may be used to construct microscale energy conversion devices.

Patent
19 Feb 2003
TL;DR: Optical fibers with high nonlinearity and low dispersion suitable for the Raman amplification are offered in as mentioned in this paper, where the structural and characteristic specifics are as follows: first core 1 with a profile surrounded with second core 2, further second core surrounded with cladding 5 ; setting first core 2 for no less than 1.8% of relative refractive index difference from cladding 6, setting second core 6 for no more than −0.4% of as mentioned in this paper.
Abstract: Optical fibers with high non-linearity and low dispersion suitable for the Raman amplification are offered. Their structural and characteristic specifics are as follows: first core 1 with a profile surrounded with second core 2, further second core surrounded with cladding 5 ; setting first core 1 for no less than 1.8% of relative refractive index difference from cladding 5; setting second core 2 for no more than −0.4% of relative refractive index difference from cladding 5 , setting α for 1.5 or larger, making second core 2 at least 2.2 times as large as first core 1 in diameter; and an effective area of no more than 15 μm 2 , a dispersion slope of 0.05 ps/nm 2 /km or lower in absolute value, a dispersion of no less than 5 ps/nm/km and no more than 20 ps/nm/km, in absolute value, a cutoff wavelength of 1350 nm or shorter, and a bending loss of 5.0 dB or lower in a bending diameter of 20 mm, each at a wavelength of 1.55 μm.