Temperature Effect on Dispersion in Single-Mode optical Fibers for Different Materials Al-Qadisiya Journal For Engineering Sciences Vol. 4 No. 3 Year 2011 ٣٨١ DISPERSION IN DIFFERENT SINGLE MODE OPTICAL FIBER MATERIALS AT DIFFERENT TEMPERATURES Aqeel Salim Raheem Technical College – Najaf ABSTRACT Optical fiber is a physical medium for optical communication system. It is offer high capacity, very wide band and high data rate. There are two main problems in this physical medium that are dispersion and power loss. The significant restriction in optical fiber system is the dispersion. The dispersion affects the performance of the system and bit error rate. There are two types of dispersion Intermodal and Intramodal. Intermodal occurs in multimode fiber only. Intramodal occur in all type of fiber. The total dispersion in single mode fiber is the sum of material and waveguide dispersion. In this paper the effect of temperature variations on fiber dispersion is investigated. The temperature variant is a vital factor which plays an effective role on activity of the communication system especially in environmental of Iraq and other Middle East country. The Sellemeier Coefficients equation is derived for fixed and discrete temperature values. A derivation for this equation to fit continues variation of temperature is done in this paper for optical fiber. Depend on formula of dispersion, Sellemeier Coefficients equation and relation of refractive index at any temperature derivation of propagation constant with normalized frequency for waveguide dispersion is done. The Temperature effect on total dispersion is modeled for most popular material used in fabrication optical fiber, silica (SiO2), aluminosilicate (Al2SiO5) and vycor glass (96.4%SiO2 ,3% B2O3, 0.5%Al2O3, 0.1% Miscellaneous Traces). Both single mode step index and graded index fibers are considered. The results investigated by using MATLAB and Maple programs. The refractive index temperature dependence for all three fiber types are fitted in to straight line. The material dispersion and zero material dispersion "λo" wavelengths have approximately linear temperature dependence for all three fiber types. For wide range of increasing temperature [-100◦C to 100◦C] SiO2 and vycor glass fiber has less effect than for Aluminosilicate. The temperature variation shows the step index fiber batter than graded index fiber. The SiO2 is the best one of three fiber types. عند درجات حرارة مختلفةالبصریة ذات النمط الواحدااللیافموادمختلففيالتشتت عقیل سالم رحیم النجف/ الكلیة التقنیة :الخالصة لتطور لمتطلبات انتیجةمع زیادة معدل نقل البیاناتو التي ،لالتصاالتالمستخدمةالمادیةاالوساطھي واحدة من الضوئیةأللیاف ا لقد تم أختیارو.ھذا العمل فيبعین االعتباراخذ و الذيشتت ،التشارة بسبب االتدھورتعاني من ،الحاصل في مجال االتصاالت http://en.wikipedia.org/wiki/Aluminium http://en.wikipedia.org/wiki/Silicon http://en.wikipedia.org/wiki/Oxygen Al-Qadisiya Journal For Engineering Sciences Vol. 4 No. 3 Year 2011 ٣٨٢ وما ، والضوئیةاأللیافعلىدراسة تأثیر تغیرات درجة الحرارة لموجي التشتت الماديعالقةالرئیسیة للتشتت واشتقاقعلى أساس الصیغةحیث ان حساباتنا اعتمدت، اللیف الضوئي ول ا الط مع .لدلیل الموجيلتشتت اتطبیعالار مع تردد كسنالاثابت عالقة واشتقاق دد ھذه المتغیرات عند اان القیم االساسیة لمتغیرات معامل االنكسار وعالقة ایج لكلي تشتتال.المعتمد في الدراسة موجودة في الملحق لماد شتتت الا درجة ختار تم ا .ويا درجات ان ر من بلدیكثوالبلدنایف الضوئي وذلك لئنلكعامل مؤثر على انتقال االشارة خالل ال الحرارة غرار وعلىاأللیاف الضوئیة كوسیلة المادیةخدامتاسباالتصاالتعالیة لفترة طویلة من السنة ، مما یعطي عامال ھاما في الحرارة استخدم افیھوالتحقیق ) المادي والدلیل الموجي(تأثیر درجة الحرارة على تشتت لزجاج ) 5SiO2Al(، ألومینوسیلیكات) 2SiO(السلیكامثل ، مجة ا نتائج ال.vycorوا بر استخدام من ال ب مواد نا.المابلماتالب والبرامج البرنامج تقظھر"oλ"الطول الموجي الصفريتشتت المادي وال،خط مستقیمنطبق على شكلا ضوئیة الوصنوعة من األلیاف الظھر أن]مئویة١٠٠الى ١٠٠-[تغیر درجة الحرارةمن لمدى واسعحیث. األلیاف الثالثةأنواع )2SiO وVycor (أللومینوسیلیكاتاااللیاف المصنعة منأقل منت بشكل تأثر)5SiO2Al( .ال ]2SiO[أنو.، فضل من اللیف ذو مؤشر المتدرجاللیف ذو مؤشر الخطوة أدرجة الحرارة .ثالثةالمن أنواع األلیاف KEYWORDS Temperature effect on dispersion, total dispersion, zero dispersion wavelengths, chromatic dispersion, optical fiber, Sellmeier coefficients, intermodal dispersion, interamodal dispersion, Sellemeier Coefficients, refractive index. INTRODUCION Optical fiber is more preferred medium for high capacity communication systems.[ Michael 2002] Due to the fast grow up of communication system. Due to low insertion loss, high flexibility in spectral design and high data rate transmission many intensive studies done for applications in optical communications. Dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or when the group velocity depends on the frequency. Dispersion of the transmitted optical signal causes distortion (broadening) of transmitted signal (pulses) along optical fibers. There are two types of dispersion intermodal and interamodal. The intermodal dispersion results from the propagation delay differences between modes within a multimode optical fiber. Intramodal or chromatic dispersion occur in all fiber types and results from the finite spectral line width of the optical source. Chromatic dispersion it is wavelength-dependent nature. Single mode fiber has only intramodal mechanisms. The propagation delay differences between the different spectral components of the transmitted signal may be caused by:  The dispersive properties of the fiber material (material dispersion; Dm)  The guidance effects within the fiber structure (waveguide dispersion Dw). .[Rostami 2007][ Jeong2009][ Michael2002] Generally two sources of Intramodal (or chromatic) dispersion: material dispersion and waveguide dispersion.  Material dispersion comes from a frequency dependent on waveguide material. Waveguide dispersion comes from a frequency dependent on waveguide geometric. It is independent on materials from which it is constructed. .[Rostami 2007][ Jeong2009][ Tzong1995] In 1982, most applications started converting from multimode to step index single-mode fibers operating at 1300 nm. Today, a few applications are being planned for use with multimode fibers and the systems operating wavelength has to move to 1550 nm. [DeBell1989] Much research deal with dispersion, experimentally measured the refractive index and dependent on temperature for calcium telluride by using liquid helium as a coolant. [DeBell1989] Al-Qadisiya Journal For Engineering Sciences Vol. 4 No. 3 Year 2011 ٣٨٣ modeled the chromatic dispersion in single mode fiber by using material dielectric function for material dispersion and dependence of both propagation constant and normalized frequency on wavelength. [Moustafa1991] proposed a novel numerical approach for calculation of dispersion coefficients of dual mode elliptical core fiber with arbitrary refractive index profile. [Kato2000] measured refractive indices of several fused silica and calcium fluoride. [Gupta1998] experimentally study the change of chromatic dispersion of optical fiber with temperature by demonstrated the empirical model of last reaches. [Hamp2002]. investigates imperially the impact of dispersion and dispersion slop on transmission performance including the effect of temperature variation of fiber optic.[Vorbeck 2003] determine numerically the dispersion in optical fiber modeled investigated by Vorbeck.[Chich-Chenge Chou 2003] derive chromatic dispersion slop variation with temperature as a function of zero dispersion wavelength and chromatic dispersion slop at zero dispersion wavelength.[Andre 2004] experimentally demonstrated a novel chromatic dispersion monitoring techniques using frequency modulated and amplitude modulated pilot tones.[Pual2006] use analytical method to compensated the chromatic dispersion in optical fiber by management of optimum group velocity dispersion.[Rostami 2007] presents a modification of interferometric method for measurement of optical fiber chromatic dispersion using Michelson interferometer.[Peterka 2008] modeled a new method to control free spectral range of long period fiber grating.[Jeong2009] experimentally measure the temperature and pressure verses wavelength in different elliptical core fiber.[Urbanczyk 2010] Mathematical Model In the following, the equations of Sellmeier coefficients for the core refractive index are described for three kinds of fiber glasses: SiO2, aluminosilicate (Al2SiO5), and vycor glasses. The temperature dependence of these coefficients is determined. Material and waveguide dispersion parameters are studied leading to the zero dispersion wavelengths, λo, of the total dispersion parameter. The temperature effect on λo is investigated. The result obtained for λo under different temperature environments.  Sellemeier Coefficients The core refractive index, n, as a function of the operating wavelength, λ, is defined through the Sellmeier equation which has the form: [.Li1989], [Paul 2006][ Gupta1989] E D C B An     2 2 2 2 2     (1) Where: A, B, C, D and E: are Sellmeier coefficients  : is the wavelength of optical signal (nm) n: is the refractive index of optical fiber core The first and second terms represent, respectively, the contribution to refractive index due to higher energy and lower energy gaps of electronic absorption, while the last term accounts for the decrease in refractive index due to lattice absorption. The values of the Sellmeier coefficients are listed (table (1)) in appendix and the relation of finding these coefficients at any temperature are given by: .[ Matsuoka1989] )()( dT dn RTnn RT  (2) Where: http://en.wikipedia.org/wiki/Aluminium http://en.wikipedia.org/wiki/Silicon http://en.wikipedia.org/wiki/Oxygen Al-Qadisiya Journal For Engineering Sciences Vol. 4 No. 3 Year 2011 ٣٨٤ T: is the temperature in degree centigrade, R: is the room temperature, nT and nR are the refractive indexes at T and room temperature, respectively  Material Dispersion Total dispersion of a fiber is conventionally expressed as temporal broadening per unit length of the fiber, per unit width of the light source used. This total dispersion caused by material and structural properties of the fiber is in fact totally coupled. However, the total dispersion parameter, DT, is expressed As[ Chou2003][ Jeong2009][ . Bass 2002] DT = MD + WD (3) Where: MD: material dispersion (ps / nm.km) WD: waveguide dispersion (ps / nm.km) Material dispersion manifests through the wavelength dependence of the refractive index, n(λ), by the following relation: [ Chou2003][ Jeong2009][ Hamp 2002][ Paul and Park2006] 2 2 *)(    d nd c M D  (4) Where: DM : is the material dispersion (ps / nm.km)  : is the wavelength of optical signal (nm) c: is the free space speed of light.  Waveguide Dispersion The waveguide dispersion in optical fibers is given by: [Jeong2009][Hamp 2002][Paul and Park2006] 2 22 2 dV d c V W D    (5) Where: WD: Waveguide dispersion (ps / nm.km) V: is the normalized frequency β: is the propagation constant. c: is the free space speed of light. Now the normalized frequency “V “given by: [12] 2 1 22 )(.. 2 bn nnaV    (6) Where: nn: core refractive index, nb: cladding refractive index, Al-Qadisiya Journal For Engineering Sciences Vol. 4 No. 3 Year 2011 ٣٨٥ a: is the core radius (µ m)  : is the wavelength of optical signal (nm) For step-index fibers, the propagation constant, β, is given by: [ .Rostami2007][ Paul and Park2006] 5.0 2 2 2 2 2          aa V   (7) Where: β:is the propagation constant a: is the core radius (µ m), Δ: is the relative refractive index difference between core and cladding Δ= nn - nb V: is the normalized frequency While, for graded-index fibers, β is given by: [Rostami2007][Paul and Park2006] 5.0 22 2 6 2          a V a V  (8) Results and Discussion The temperature dependent of refractive index (using equation (1)) simulated for the SiO2, aluminosilicate (Al2SiO5), and vycor glasses which are used in fabrication of optical fiber, the results shown in Figure (1). The refractive indices are calculated at 850nm wavelength and at temperature ranged from 20 oC to 100 oC , the Sellmeier coefficients that used in simulation listed in appendix and relation of founding Sellmeier coefficients at any temperature written in appendix. The refractive index results are found to fit nicely into straight lines for the three material simulated. Material dispersion is calculated for the three optical fiber glass types (SiO2, aluminosilicate (Al2SiO5), and vycor glasses) at 26 ◦C using the temperature dependence of Sellmeier coefficients, as shown in Figure (2). The zero material dispersion wavelengths are 1.2734, 1.3929 and 1.2682 μm for SiO2, aluminosilicate (Al2SiO5) and vycor glass, respectively, and the dispersion characteristics are approximately linear for the whole spectral region. For a wide range of temperature (-100◦C to 100◦C), the material dispersion and the zero material dispersion wavelength, λo, has been calculated for the three optical fiber glass types. The obtained results are shown in Figure (3), Figure (5) and Figure (6) for the SiO2, aluminosilicate and vycor glass, respectively. The material dispersion linearly related to temperature, and increases with increase the wavelength for all three tested optical fiber material. The zero material dispersion wavelength (λo) as a function of temperature (T ◦C) is displayed in Figure (4) for SiO2. Interestingly, the temperature dependence is linear and dλo/dT=0.0242 nm/oC for SiO2. This value has a fair agreement with the published experimental values 0.029±0.004 nm/oC and 0.031± 0.004nm/oC for two dispersion shifted fibers within the experimental accuracy. The values of dλo/dT are found to be 0.0223 nm/oC for vycor glasses. While the corresponding values of dλo/dT are found to be 0.03 nm/oC for aluminosilicate (Al2SiO5). Using the temperature dependent Sellmeier coefficients and the corresponding values of the V- number, Waveguide Dispersion and Total Dispersion for Single mode step index fiber calculated at http://en.wikipedia.org/wiki/Aluminium http://en.wikipedia.org/wiki/Silicon http://en.wikipedia.org/wiki/Oxygen http://en.wikipedia.org/wiki/Aluminium http://en.wikipedia.org/wiki/Silicon http://en.wikipedia.org/wiki/Oxygen http://en.wikipedia.org/wiki/Aluminium http://en.wikipedia.org/wiki/Silicon http://en.wikipedia.org/wiki/Oxygen http://en.wikipedia.org/wiki/Aluminium http://en.wikipedia.org/wiki/Silicon http://en.wikipedia.org/wiki/Oxygen Al-Qadisiya Journal For Engineering Sciences Vol. 4 No. 3 Year 2011 ٣٨٦ a core radius, a = 2 μm , relative refractive index difference between core and cladding ∆ = 0.005, and temperature 26 oC. The waveguide dispersion results of optical fiber (SiO2 material) are shown in Figure (7) and material, waveguide and total dispersion shown in Figure (8). The waveguide dispersion results of optical fiber (aluminosilicate (Al2SiO5)) are shown in Figure (9) and material, waveguide and total dispersion shown in Figure (10). The waveguide dispersion results of optical fiber (vycor glass) are shown in Figure (11) and material, waveguide and total dispersion shown in Figure (12). The waveguide dispersion results have line curved and shift of total dispersion from material dispersion. For SiO2 fiber material dispersion has (λo = 1.2723 µ m) and total dispersion has (λo = 1.28 µ m), aluminosilicate fiber, material dispersion has (λo = 1.3925 µ m) and total dispersion (λo = 1.397 µ m), vycor glass fiber, material dispersion has (λo =1.2675 µ m) and total dispersion has (λo = 1.275 µ m). The waveguide dispersion results has line curved and slight shift of total dispersion from material dispersion, since the value of waveguide dispersion be smaller than the material dispersion the aluminosilicate (Al2SiO5) fiber give little different results from that given by SiO2 fiber and vycor glass fiber. Waveguide Dispersion and Total Dispersion for Single mode graded index fiber calculated at a core radius, a = 2 μm, relative refractive index difference between core and cladding ∆ = 0.0085, and temperature 26 oC. The waveguide dispersion results of optical fiber (SiO2 material) are shown in Figure (13) and material, waveguide and total dispersion shown in Figure (14). The waveguide dispersion results of optical fiber (aluminosilicate (Al2SiO5)) are shown in Figure (15) and material, waveguide and total dispersion shown in Figure (16). The waveguide dispersion results of optical fiber (vycor glass) are shown in Figure (17) and material, waveguide and total dispersion shown in Figure (18). The waveguide dispersion results have line curved and shift of total dispersion from material dispersion. For SiO2 fiber material dispersion has (λo = 1.2723 µ m) and total dispersion has (λo = 1.285 µ m), aluminosilicate fiber, material dispersion has (λo = 1.3925 µ m) and total dispersion (λo = 1.405 µ m), vycor glass fiber, material dispersion has (λo =1.2675 µ m) and total dispersion has (λo = 1.28 µ m) The first and second derivative of refractive index is as follow: 5.0 2 2 2 2 2 3 22 3 )( 2 )( 2 5.0                      E D C B A E D C B d dn          5.0 2 2 2 2 22 2 32 4 22 2 32 4 5.1 2 2 2 2 2 2 3 22 3 2 2 )( 8 )( 8 )( 2 )( 8 5.0 )( 2 )( 2 25.0                                               E D C B A E D E D C B C B E D C B A E D C B d nd                      The first and second derivative of step index propagation constant equation done is as follow: http://en.wikipedia.org/wiki/Aluminium http://en.wikipedia.org/wiki/Silicon http://en.wikipedia.org/wiki/Oxygen http://en.wikipedia.org/wiki/Aluminium http://en.wikipedia.org/wiki/Silicon http://en.wikipedia.org/wiki/Oxygen http://en.wikipedia.org/wiki/Aluminium http://en.wikipedia.org/wiki/Silicon http://en.wikipedia.org/wiki/Oxygen Al-Qadisiya Journal For Engineering Sciences Vol. 4 No. 3 Year 2011 ٣٨٧ The first and second derivative of graded index propagation constant equation is as follow: Conclusion: The refractive index temperature dependence for all three fiber types are fitted in to straight line. The material dispersion and zero material dispersion " λo" wavelengths has approximately linear temperature dependence for all three fiber types, SiO2 and vycor fibers give nearly similar results while Aluminosilicate give little difference one. For wide range of increasing temperature [-100◦C to 100◦C] SiO2 and vycor glass fiber has less effect than for Aluminosilicate, since the zero material dispersion shifted by 0.01 for SiO2 and vycor fiber while 0.025 for Aluminosilicate fiber. The linearly shift the total dispersion zero wavelength. For large variation of temperature range step index fiber batter than graded index fiber since for step index "λo" affected by fiber core radius and little affected by the relative refractive index difference between core and cladding " Δ" while for graded index fiber "λo" affected by fiber core radius and relative refractive index difference between core and cladding " Δ". The SiO2 is the best one of three fiber types. The aluminosilicate (Al2SiO5) fiber give different results from that given by SiO2 fiber and vycor glass fiber. 5.0 2 2 2 2 2 5.1 2 2 2 2 22 2 2 2 5.0 2 2 2 2 2 5.0 5.0 5.0 2 5.0 5.0 5.0                         aaM V a aaM V a V dV d aaM V a V dV d     5.0 22 2 2 5.1 22 2 2 22 2 2 5.0 22 2 22 65.0 5.0 65.0 6 25.0 65.0 6 5.0                                             a V a V a a V a V aa V aV d a V a V aa V aV d   http://en.wikipedia.org/wiki/Aluminium http://en.wikipedia.org/wiki/Silicon http://en.wikipedia.org/wiki/Oxygen Al-Qadisiya Journal For Engineering Sciences Vol. 4 No. 3 Year 2011 ٣٨٨ Reference: [1] A.G.DeBell, E.L.Dereniak, J.Harvey, J.Nissley, J.Palmer, A.Selvarajan and W.L.Wolfe," Cryogenic refractive indices and temperature coefficients of cadmium telluride form 6µm to 22µm", Applied Optics, Vol.18, No.18, 15 September 1989. [2] A.Rostami," A Principle investigation of the group velocity dispersion profile for optimum dispersion compensation in optical fiber", Progress In Electromagnetics Research, PIER 75, 209–224, 2007. [3] Chich-Chenge Chou," Numerical Analysis of Dispersion in optical Fibers", IEEE, Vol.1, P.107, 19 Dec 2003. [4] H.H.Li, "Refractive index of ZnS, ZnSe and ZnTe and its Wavelength and Temperature Derivatives", Journal of Physics and Chemistry Reference Data, Vol.13, No.1, 1989. [5] H.Jeong, "Theoretical Analysis of Cladding-Mode Waveguide Dispersion and Its Effects on the Spectra of Long-Period Fiber Grating" Journal of Light wave Technology, Vol. 21, NO. 8, August 2009. [6] J. Y. Huh, "Effect of Temperature Variation on Performance of Optical Phase Conjugation", Optical Fiber communication Conference (OFC) Anaheim, California, 6 March 2005. [7] J. Matsuoka, N. Kitamura, S. Fujinaga, T. Kitaoka, and H. Yamashita, “Temperature dependence of refractive index of Si02 Glass,” Journal of Non-Crystal Solution, vol. 135, pp. 86-89, 1991. [8] Michael Bass, "FIBER OPTICS HANDBOOK", 2nd Edition, McGRAW-HILL, 2002. [9] Michael J. Hamp," Investigation into the Temperature Dependence of Chromatic Dispersion in Optical Fiber", IEEE Photonics Technalogy Letters, Vol. 14, NO. 11, November 2002. [10] Moustafa H.ALY," Chromatic Dispersion in Graded-Index Single-Mode Optical Fibers", IEEE Pacific Rim Conference on Communications, Computers and Signal Processing, NO.18, May 9-10, 1991. [11] N. SHIBATA, "Refractive Index Dispersion of Lightguid Glass at High Temperature" Electronics Letters Vol.17 No. 8, 16th April 1989. [12] Paul K. J. Park," A Novel Chromatic Dispersion Monitoring Technique Using Frequency-Modulated and Amplitude-Modulated Pilot Tones", Optical Fiber Communication Conference 5-10 May 2006. [13] P. Peterka, "Measurement of chromatic dispersion of microstructure optical fibers using interferometric method", Optica Applicata, Vol. 38, No. 2, 2008. [14] P. S. Andre, "Effect of Temperature on the Single Mode Fibers Chromatic Dispersion", Journal of Microwave and Optoelectronics, Vol.3, No.5, July 2004. [15] R. Gupta, "Absolute Refractive Indices and Thermal Coefficients of Fused Silica and Calcium Fluoride near 193 nm", Journal of Applied Optics Vol.37, No.25, 1 September 1998. [16] R. Tripathi, "Reduction of Crosstalk in Wavelength Division Multiplexed Fiber Optics Communication System", Progress In Electromagnetics Research, PIER 77, 367–378, 2007. [17] S. P. Singh," Nonlinear Scattering Effects in Optical Fibers", Progress Electromagnetics Research, PIER 74, 379–405, 2007. [18] S. Vorbeck, "Dispersion and Dispersion Slope Tolerance of 160-Gb/s Systems, Considering the Temperature Dependence of Chromatic Dispersion", IEEE Photonics Technology Letters, Vol. 15, No. 10, October 2003. Al-Qadisiya Journal For Engineering Sciences Vol. 4 No. 3 Year 2011 ٣٨٩ [19] T. Kato," Temperature Dependence of Chromatic Dispersion in Various Types of Optical Fibers", Optical Fiber Communication Conference, Baltimore, Maryland,7 March 2000. [20] U.Schlarb, "A Generalized Sellemeier Equation for the Refractive Indices of Lithium Niobate", Ferroelectronics, Vol.156, pp.99-104, 1994. [21] Tzong-Lin Wu," An Efficient Numerical Approach for Determining the Dispersion Characteristics of Dual-Mode Elliptical-Core Optical Fibers", Journal of Lightwave Technology, Vol. 13, No. 9, September 1995. [22] W. Urbanczyk, "Dispersion Effects in Elliptical-Core Highly Birefringent Fibers", Journal of Applied Optics Vol. 40, No. 12, pp: 1911–1920, Apr. 20, 2001. Table (1) Sellmeier coefficients Material Temp. (◦C) A B C D E SiO2 20 1.310723 0.7935797 1.0959659*10 -2 0.9237144 100 26 1.3121622 0.7925205 1.0996732*10-2 0.9116877 100 45.2 1.3066410 0.7994875 1.091946*10-2 0.9598566 100 471 1.3148367 0.8034391 1.1248041*10-2 0.9119589 100 Alumino-silicate 28 1.4136733 0.8503994 1.3249011*10-2 0.9044591 100 526 1.5205253 0.8556256 1.520523*10-2 0.9092824 100 Vycor glass 28 1.2754213 0.8271916 1.0653107*10-2 0.9384236 100 526 1.3488048 0.7695233 1.1884981*10-2 0.946169 100 Al-Qadisiya Journal For Engineering Sciences Vol. 4 No. 3 Year 2011 ٣٩٠ 20 40 60 80 100 1 2 3 4 5 6 7 Temperature R ef ra ct iv e In de x Alumino-silicate Vycor glass Fused Silica 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 Wavelength D is pe rs io n, p s/ nm .k m Material dispersion at 26 C for different material Vycor SiO2 Aluminosilicate Figure (1) Refractive index for three types of fiber material µm Figure (2) Material dispersion at 26ºC for different material -100 -50 0 50 100 1.268 1.269 1.27 1.271 1.272 1.273 1.274 1.275 1.276 Temperature oC Variation of zero material dispersion wavelengths with temperature for SiO2 glass. λ◦ λ ◦ Figure (3) Material dispersion of SiO2glasss at different temperature Figure (4) Variation of zero material dispersion wavelengths with temperature for SiO glass µm 1.26 1.265 1.27 1.275 1.28 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 Wavelength, µm Material dispersion of SiO2 glass at different temperatures -100 C -60 C 0 C 60 C 100 C M a te ri a l D is p e rs io n , p s /n m .k m 1.38 1.385 1.39 1.395 1.4 1.405 1.41 1.415 1.42 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 wavelength M at er ia l D is pe rs io n, p s/ nm .k m Material dispersion of aluminosilicate glass at different temperatures -100 C -60 C 100 C 0 C 60 C 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.3 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 Wavelength M at er ia l D is pe rs io n, p s/ nm .k m Material dispersion for vycor glass at diffrent temperature -100 C -60 C 0 C 100 C 60 C Figure (5) Material dispersion of aluminosilicate glass at different temperature Figure (6) Material dispersion for vycor glass at different temperature µm µm Al-Qadisiya Journal For Engineering Sciences Vol. 4 No. 3 Year 2011 ٣٩١ Figure (7) Waveguide dispersion for SiO2 at T= 26 ºC Figure (8) Total dispersion parameter for SiO2 at T=26 ºC Figure (9) Waveguide dispersion for Aluminosilicate at T=26ºC Figure (10) Total dispersion parameter for Aluminosilicate glass at T=26ºC 1 1.2 1.4 1.6 1.8 2 -1.1 -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 Wavelength D is pe rs io n, p s/ nm .k m Waveguide dispersion for SiO2 at T=26 C 1 1.2 1.4 1.6 1.8 2 -1.2 -1.1 -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 Wavelength D is pe rs io n, p s/ nm .k m Waveguide dispersion for Aluminosilicate at T=25 C 1 1.2 1.4 1.6 1.8 2 -1.1 -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 Wavelength D is pe rs io n, p s/ nm .k m Waveguide dispersion for Vycor glass at T=26 C 1 1.1 1.2 1.3 1.4 1.5 1.6 -50 -40 -30 -20 -10 0 10 20 30 40 Wavelength D is pe rs io n, p s/ nm .k m Total dispersion parameter for SiO2 at 26 C M T 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 Wavelength D is pe rs io n, p s/ nm .k m Total dispersion parameter for aluminosilicate glass at T=26 C 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 -50 -40 -30 -20 -10 0 10 20 30 Wavelength D is pe rs io n, p s/ nm .k m Total dispersion parameter for Vycor at 26 C Figure (11) Waveguide dispersion for Vycor glass at T=26ºC Figure (12) Total dispersion parameter for Vycor glass at T=26ºC w T MW T M W µm µm µm µm µm µm Al-Qadisiya Journal For Engineering Sciences Vol. 4 No. 3 Year 2011 ٣٩٢ Figure (13) Waveguide dispersion for SiO2 (graded index) Figure (14) Dispersion behavior for SiO2 (graded index) Figure (15) Waveguide dispersion for aluminosilicate at T=26ºC (graded index) 1 1.1 1.2 1.3 1.4 1.5 1.6 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 Wavelength D is pe rs io n, p s/ nm .k m Waveguid dispersion for SiO2 (Graded Index) 1 1.1 1.2 1.3 1.4 1.5 1.6 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 Wavelength D is pe rs io n, p s/ nm .k m Waveguid dispersion for aluminosilicate at 26oC(Graded Index) 1 1.1 1.2 1.3 1.4 1.5 1.6 -50 -40 -30 -20 -10 0 10 20 30 40 Wavelength D is pe rs io n, p s/ nm .k m Dispersion behavior for SiO2 at 26oC(Graded Index) 1.1 1.2 1.3 1.4 1.5 1.6 -70 -60 -50 -40 -30 -20 -10 0 10 20 30 Wavelength D is pe rs io n, p s/ nm .k m Dispersion behavior for aluminosilicate glass at 26oC(Graded Index) 1 1.1 1.2 1.3 1.4 1.5 1.6 -50 -40 -30 -20 -10 0 10 20 30 40 Wavelength D is pe rs io n, p s/ nm .k m Dispersion behavior for Vycor glass at 26 C(Graded Index) 1 1.1 1.2 1.3 1.4 1.5 1.6 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 Wavelength D is pe rs io n, p s/ nm .k m Waveguid dispersion for Vycor glass at 26 C(Graded Index) Figure (16) Dispersion behavior for aluminosilicate at T=26ºC (graded index) Figure (17) Waveguide dispersion for Vycor at T=26ºC (graded index) Figure (18) Dispersion behavior for vycor glass at T=26ºC (graded index) T M W T M W T M W µm µm µm µm µmµm