The Pluta polarizing interference microscope is used to measure the refractive index profile and material dispersion of step index optical fibers. The refractive index profile of the fiber has been determined experimentally at different wavelengths using two-beam interference technique. Measuring these values at different wavelengths gives useful information about the structural behavior of highly oriented fibers. Also, the theoretical consideration for determining the refractive index is given. Some optical parameters which characterize the optical fiber such as the numerical aperture NA, normalized frequency ν, the acceptance angle θa and the number of modes MN propagating in the fiber with wavelength have been calculated. Also, the constants of the Cauchy’s dispersion formula were determined.Primijenili smo Plutinov polarizacijski interferometrijski mikroskop u mjerenjima profila indeksa loma i disperzije materijala optičkih vlakana sa skokovitim indeksima loma. Mjerili smo profil indeksa vlakna za više valnih duljina primjenom interferentne metode s dva snopa. Ta mjerenja na više valnih duljina dala su važne podatke o strukturnim svojstvima jako usmjerenih vlakana. Opisuju se također osnove teorije za određivanje indeksa loma u vlaknima. Izračunali smo niz optičkih parametara koji su značajke optičkih vlakana: brojnog otvora, normalizirane frekvencije, ν, kuta prihvaćanja, θa, i broja modova, MN , kojima se na nekoj frekvenciji šire valovi. Također smo odredili konstante Cauchyjeve disperzijske formule

Gerges, A. S.

Hassouba, M. A.

Mehanna, E. A.

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Printed ISSN 1330–0008Online ISSN 1333–9125CD ISSN 1333–8390CODEN FIZAE4CHARACTERIZATION OF STEP INDEX OPTICAL FIBERS USINGTWO-BEAM INTERFEROMETRIC METHODE. A. MEHANNAa, A. S. GERGESa and M. A. HASSOUBAbaMilitary Technical College, Cairo, EgyptbPhysics Department, Faculty of Science, Benha University, Benha, EgpytReceived 15 September 2004; Revised manuscript received 27 May 2006Accepted 30 August 2006 Online 22 December 2006The Pluta polarizing interference microscope is used to measure the refractive indexprofile and material dispersion of step index optical fibers. The refractive index pro-file of the fiber has been determined experimentally at different wavelengths usingtwo-beam interference technique. Measuring these values at different wavelengthsgives useful information about the structural behavior of highly oriented fibers.Also, the theoretical consideration for determining the refractive index is given.Some optical parameters which characterize the optical fiber such as the numericalaperture NA, normalized frequency ν, the acceptance angle θa and the number ofmodes MN propagating in the fiber with wavelength have been calculated. Also,the constants of the Cauchy’s dispersion formula were determined.PACS numbers: 42.79.-e, 42.81.Cn UDC 535.321, 535.326, 535.328Keywords: two-beam interference, step index optical fiber, refractive index profile, mate-rial dispersion1. IntroductionThe refractive index profile of the optical fiber core plays an important role incharacterizing the optical properties of the fiber. It allows determination of the fibernumerical aperture, the number of propagation modes within the fiber core and thedispersion of the fiber’s material. So, the detailed knowledge of the refractive indexprofile allows the prediction of the impulse response of the fiber and consequentlythe information carrying capacity of the fiber can be estimated [1]. The ideal mea-suring method should satisfy the following conditions: non destructive, applicableto any profile, high measurement accuracy, high resolution and easy measurementand data processing.FIZIKA A (Zagreb) 15 (2006) 2, 125–132 125mehanna et al.: characterization of step index optical fibers . . .Different methods were used to determine the fiber’s refractive index profilesuch as: near field method, X-ray microanalysis, scanning electron microscope andinterferometric methods [2].Many authors have applied interferometric techniques to determine the opticalproperties of fibers [3,4]. Pluta used his double refracting interference microscopewith variable amount and direction of wavefront shear to study the refractive indicesand birefringence of synthetic polymer fibers [5]. The idea of the Pluta polarizinginterfrence micoscope is based on the two-beam interference technique. The micro-scope gives a uniform field or fringe interference field with a continusly variableamount and direction of lateral image duplication [5].Žurek and Zakrzewski [6] determined the refractive indices and birefringence ofcotton fibers using the Pluta microscope. Hamza et al. [7] used Pluta polarizinginterference microscope to study the refractive index profiles of cylindrical fibershaving core-cladding structure.Hamza et al. [8] determined the core cladding refractive index difference and theindex gradient profile parameter of the graded inex (GR-IN) optical fibre. Multiple-beam Fizeau fringes and Pluta polarizing microscope are used for this study. A newmethod, based on a derived mathematical expression is used to estimate the fringeshift inside GR-IN of the fibre core. The estimated and experimental values of thefringe shift, along the core radius, are used to obtain the refactive index profile ofthe optical fibre.Kovacević et al. [9] studied the modelling of the loss and mode coupling due toan irregular core-cladding interface in step index plastic optical fibers. They modelsuch loss and mode coupling by ray tracing. The results show mode coupling andrelative loss per unit fiber length caused by the core cladding interface irreguarities.The loss is high close to the input fiber end where mode coupling is intense.Material dispersion dn/dλ plays an important role in fiber optics performance,where n is the refractive index and λ is the wavelength of the light [10,11]. Thisquantity is described by the well-known Cauchy’s formula.The aim of the present work is to use Pluta polarizing interference microscopeto measure the refractive index profile of optical fibers. Experimental results ofrefractive index profile for a step index multi-mode fiber at different wavelengthshave been obtained and consequently, the material dispersion of the fiber was de-termined. The relationship between some optical properties which measured anddispersion properties are also illustrated throughout the spectral dispersion curveand some dispersion parameters for this fibre.2. Theoretical considerations2.1. Determination of refractive-index profiles of fibersA Pluta two-beam interference microscope with a modified method is used todetermine the refractive indices of a core-cladding structure fiber [7]. This methodis applied to fibers with regular and irregular cross-sections. In this study, the126 FIZIKA A (Zagreb) 15 (2006) 2, 125–132mehanna et al.: characterization of step index optical fibers . . .irregularity in the fiber cross-section is dealt with by considering the area enclosedunder the fringe shift produced in the microinterferogram. This area represents theoptical path difference integrated across the fiber [12].When a beam of plane-polarized monochromatic light is incident on a homoge-neous fiber, the incident wave front will be distorted [10]. Consider a fiber havinga core-cladding structure with circular cross-section of radius R and cylindricalcore surrounded by a cylindrical cladding of thickness e. Let nL, ncl and nC bethe refractive indices of the immersion liquid, the cladding and the core, respec-tively. Using the Pluta interference microscope with light of the wavelength λ, theinterference fringes suffer shifts Z(x) as they cross the fiber at distance x from itscentre.The relation between the interference fringe shift Z(x), nL, ncl and nC is givenby [7]Z(x)λh= 2ncl{[R2 −(nLdncl)2]1/2−[(R − e)2 −(nLdncl)2]1/2}(1)+2nC[(R − e)2 −(nLdnC)2]1/2− nL[(R2 − d)1/2 + (R2 − x2)1/2],for R > d ≥ 0, where d is the distance between the incident beam and the fibercentre. For a homogeneous fiber with a constant refractive index (ncl = nC), e = 0,Eq. (1) takes the formZ(x)λh= 2ncl[R2 −(nLdnC)2]1/2− nL[(R2 − d2)1/2 + (R2 − x2)1/2], (2)for R > d ≥ 0. Using Eqs. (1) and (2), one can determine the refractive indexprofile of the optical fiber from the data taken from the interferograms.2.2. Material dispersionIn Ref. [12], mathematical formulae have been derived for the shape of two-beam interference fringes crossing a cylindrical multi-layer fiber, immersed in aliquid of refractive index nL and having m layers. The refractive indices of thelayers are n1, n2, . . . nm, where n1 is the refractive index of the outer layer and nmis that of the inner layers (core).The following equation represents a relation between the fringe shift Z(x) andthe refractive index at a point x along the fibre radius [7](λ2h)Z =M∑Q=1(nQ − nQ−1)(r2Q − x2)1/2, Q = 1, 2, . . . ,m , (3)FIZIKA A (Zagreb) 15 (2006) 2, 125–132 127mehanna et al.: characterization of step index optical fibers . . .where λ is the wavelength of the used monochromatic light, h is the interferingspacing and rQ are the radii of layers, which are given by [12]rQ =(y2 − x2)1/2. (4)To calculate the fiber cladding and core refractive indices ncl and nc, the fiber isimmersed in a liquid of refractive index nL. When x = rC and x = 0, respectively,Eq. (3) takes the following form [12](λ2h)Zcl =(ncl − nL)rclc, (5)(λ2h)Z0 =(ncl − nL)rcl +(nC − ncl)rC , (6)where rclc = (r2cl−r2C)1/2 and rcl, rC are the radii of cladding and core, respectively.Zcl is the fringe shift in the cladding region, Z0 is the fringe shift in core region [7].The variation of the refractive index of the fiber material with the wavelength canbe written using the known Cauchy’s dispersion formula for the fiber [13]n(λ) = a +bλ2, (7)where n(λ) is the refractive index at a given wavelength λ, and a and b are theCauchy’s constants which depend on the fiber material and characterize its disper-sion activity. The dispersive power of the fiber material is given by the followingequation [13]dndλ= −2bλ3. (8)Equations (7) and (8) can be used for light vibrating parallel and perpendicular tothe fiber axis.3. Results and discussionA multimode step index optical fiber [Ge-B doped SiO2], having a core radius(rc = 10.8 µm) and total diameter 24 µm, is used to show the effect of refractionof the incident beam by the fiber when differences between the fiber cladding andcore refractive indices are detectable. The fiber is placed on a microscope slide withfixed ends and is immersed in a matching liquid. The objective prism of the Plutapolarizing interference microscope is rotated to obtain maximum duplication of thetwo images of the fiber. Then the slit diaphragm is rotated to make a suitable anglewith the fiber axis to obtain the sharpest fringes. Microinterferograms have beenregistered by a CCD camera fixed to the microscope to show the effect of variationof refractive index of the fiber with wavelength [13]. These microinterferograms,which consist of dark and bright fringes of equal width, are shown in Figs. 1a to1d, which were obtained using wavelengths of 546 nm, 550 nm, 577 nm and 590nm, respectively. Special computer software [7] is used to determine the refractiveindex profile of the optical fiber using the data taken from the interferogram.128 FIZIKA A (Zagreb) 15 (2006) 2, 125–132mehanna et al.: characterization of step index optical fibers . . .Fig. 1. Interferograms of step index optical fiber at wavelengths: λ = 546 nm andλ = 550 nm (upper left and right), and λ = 577 nm and λ = 590 nm (lower leftand right).Fig. 2. The refractive index profiles for the wavelengths, a) λ = 546 nm, b) λ = 550nm, c) λ = 577 nm and d) λ = 590 nm.The calculated refractive index profiles are shown in Figs. 2a – 2d with an accu-racy of about 0.001 µ. These figures show the refractive index profiles at differentFIZIKA A (Zagreb) 15 (2006) 2, 125–132 129mehanna et al.: characterization of step index optical fibers . . .wavelengths.One can notice from Fig. 2 that the refractive index of the core is nearly constantfor the same wavelength. Using Eqs. (5), (6) and figures in the microinterferograms,ncl and nc may be calculated, hence, the dispersive power of the fibers is obtained.The variation of refractive index n at the fiber centre (r = 0) with wavelengths aregiven in Table 1. Figure 3 shows the spectral dispersion curve of step index opticalfiber core. Plot of the relation between the refractive index and the reciprocal ofthe square of the wavelength of the incident light is shown in Fig. 4. This figureshow that the dispersion is well described by the Cauchy dispersion formula.Fig. 3. The spectral dispersion curve of step index optical fiber core.TABLE 1. Variation of refractive index n at the fiber center with wavelength λ.Wavelength [nm] n(λ)546 1.6377 ± 0.001550 1.6362 ± 0.001577 1.6353 ± 0.001590 1.6345 ± 0.001From the slope and intersect, the constants a and b of the Cauchy’s formulaare obtained. Figure 4 expresses the fact that the refractive index decreased as thewavelength increased. Thus, the fiber materials have normal dispersion behaviourin this region of the spectrum.The Cauchy’s constants were calculated and found to be a = 1.618 and b = 5935nm2, whenever the dispersive power is equal to 3.65 × 10−5 nm−1.The cladding – core refractive index difference governs some optical fibre pa-rameters such as the numerical aperture, the acceptance angle, the normalizedfrequency and the number of modes. These parameters are determined using theexperimental data and shown in Table 2.130 FIZIKA A (Zagreb) 15 (2006) 2, 125–132mehanna et al.: characterization of step index optical fibers . . .Fig. 4. Variation of refractive index n with 1/λ2.TABLE 2. Variation of numerical aperture NA, normalized frequency ν and thenumber of modes MN with wavelength.λ [µm] NA ν MN θa [deg]0.546 0.2804 35.089 308 16.280.550 0.3023 37.2785 347 17.580.577 0.3373 39.6484 393 19.700.590 0.3390 38.97 380 19.804. ConclusionTwo-beam interference Pluta microscope is used to study the optical propertiesof step index optical fiber sample in the case where difference between the fibrecladding and core refractive indices is detectable. The refractive index profiles weremeasured experimentally using this technique. This technique is based on Plutapolarizing interference microscope with a CCD video camera to determine the re-fractive index profile of the core-cladding fiber. The dispersion curve of the fibermaterial is obtained using plane polarized monochromatic light vibrating paralleland perpendicular to the fiber axis and hence the dispersion of the fiber materialhas been investigated. It is concluded that the refractive index of the core is nearlyconstant for the same wavelength.Cauchy’s dispersion constants and dispersive power of the fiber material, whichwell describe the interaction of the light ray with the fiber material on the molecularlevel, have been determined.FIZIKA A (Zagreb) 15 (2006) 2, 125–132 131mehanna et al.: characterization of step index optical fibers . . .References[1] J. Gowar, Optical Communication Systems, Prentice-Hall of India, New Delhi (1987).[2] M. John Senior, Optical Fiber Communication (Principles and Practice), Prentice-HallInternational, London (1986) p. 202.[3] N. Barakat and A. A. Hamza, Interferometry of Fibrous Materials, Adam Hilger (1990)p. 114..[4] A. A. Podviaznyi and D. V. Svistunov, Optics Comm. 201 (2002) 325.[5] M. Pluta, Microscopy J. 96 (1972) 309.[6] W. Žurek and S. Zakkrzewski, J. Appl. Polym. Sci. 28 (1983) 1277.[7] A. A. Hamza, A. M. Ghander, T. Z. N. Sokkar, M. A. Mabrouk and W. A. Ramadan,Pure and Appl. Optics 3 (1994) 943.[8] A. A. Hamza, M. A. Mabrouk, W. A. Ramadan and M.A. Shams-Eldin, Optics Comm.200 (2001) 131.[9] D. Kovacevic, D. Nikezic and A. Djordjevich, Appl. Opt. 44 (2005) 3898.[10] B. E. A. Saleh and M. C. Teich, Fundamental of Photonics, John Wiley and Sons(1991).[11] J. H. Chae and Y. T. Lee, Optics Comm. 206 (2002) 1.[12] A. A. Hamza, T. Z. N. Sokkar and M. M. Shahin, J. Appl. Phys. 10 (1991) 69.[13] M. Pluta, Advanced Light Microscopy, Vol. 1, Warszawa, PWN (1988).PROUČAVANJE OPTIČKIH VLAKANA SA SKOKOVITIM INDEKSIMALOMA INTERFEROMETRIJSKOM METODOM S DVA SNOPAPrimijenili smo Plutinov polarizacijski interferometrijski mikroskop u mjerenjimaprofila indeksa loma i disperzije materijala optičkih vlakana sa skokovitim indek-sima loma. Mjerili smo profil indeksa vlakna za vǐse valnih duljina primjenom inter-ferentne metode s dva snopa. Ta mjerenja na vǐse valnih duljina dala su važne po-datke o strukturnim svojstvima jako usmjerenih vlakana. Opisuju se takod–er osnoveteorije za odred–ivanje indeksa loma u vlaknima. Izračunali smo niz optičkih parame-tara koji su značajke optičkih vlakana: brojnog otvora, normalizirane frekvencije,ν, kuta prihvaćanja, θa, i broja modova, MN , kojima se na nekoj frekvenciji širevalovi. Takod–er smo odredili konstante Cauchyjeve disperzijske formule.132 FIZIKA A (Zagreb) 15 (2006) 2, 125–132

Proučavanje optičkih vlakana sa skokovitim indeksima loma interferometrijskom metodom s dva snopa

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