04 Ibn Al-Haitham Jour. for Pure & Appl. Sci. 33 (1) 2020 Aqeel R. Salih Abstract In this work, a step-index fiber with core index and cladding index has been designed. Single-mode operation can be obtained by using a fiber with core diameters 4–13 µm operating at a wavelength of 1.31 µm and by 4–15 µm at 1.55 µm. The fundamental fiber mode properties such as phase constant, effective refractive index, mode radius, effective mode area and the power in the core were calculated. Distributions of the intensity and the amplitude were shown. Key words: Single mode fiber, Step-index fiber, Optical communications. 1. Introduction Fiber optics plays a key role in communications [1]. A step-index fiber (SIF) consists of a core of refractive index surrounded by a cladding of slightly lower refractive index , as shown in Figure 1 [2]. This difference enables the fiber to guide the light by total internal reflection [3]. These indices are close to 1.5 for silica glass fibers [4]. Figure 1. Refractive index profile of a SIF [2]. A single-mode fiber (SMF) is designed to propagate only a single guided mode (fundamental mode), where LP stands for linearly polarized [5]. In 1966, Kao and Hockham discussed the theory and potential use of optical fiber for communications [6]. In 1970, a SMF with attenuation below 20 dB/km was developed [7]. This is recognized as the start of fiber optic communications [8]. In 1979, SMFs with a loss of only 0.2 dB/km at 1.55 µm were fabricated [9]. The SMFs have continued to evolve. Kao (1933–2018) was awarded the 2009 Nobel prize in physics for his theoretical work on the SMF [10] which is extensively used in optical communication systems [11]. draqeelrsalih@gmail.com Article history: Received 3 December 2019, Accepted 5 January 2020, Publish January 2020. Design of Single Mode Fiber for Optical Communications Doi: 10.30526/33.1.2373 Ibn Al Haitham Journal for Pure and Applied Science Journal homepage: http://jih.uobaghdad.edu.iq/index.php/j/index Department of Physics, College of Education for Pure Science Ibn Al- Haitham / University of Baghdad, Baghdad, Iraq. file:///C:/Users/المجلة/Downloads/draqeelrsalih@gmail.com file:///C:/Users/المجلة/Downloads/draqeelrsalih@gmail.com 04 Ibn Al-Haitham Jour. for Pure & Appl. Sci. 33 (1) 2020 2. Important Parameters and Basic Equations In designing a SMF, several parameters that affect its performance must be considered. 1. Numerical Aperture (NA) The fiber NA is given by [12] √ It describes the light-gathering capacity of the fiber [13]. 2. V Number The V number is defined as [14] where ⁄ is the vacuum wavenumber, is the vacuum wavelength of operation and is the core radius. Two low loss operating wavelengths used in optical communication systems are 1.31 µm and 1.55 µm [9, 15]. The V number determines the number of guided modes. If the fiber will be SM [16]. 3. Phase Constant ( ) The phase change per of propagation along the fiber. The phase constant is [14] The effective refractive index ( ) lies between and . 4. Effective Mode Area The effective mode area is defined as [17] It determines how tightly light is confined to the core. For a SI SMF, the mode radius can be calculated either from Marcuse's formula [18]. ( √ ) or from a modified formula [19] ( √ ) which becomes ( √ ) 5. P in core The fraction of power propagating within the fiber core is [17] ⁄ For SMFs, that fraction is low for low values and reaches near 04 Ibn Al-Haitham Jour. for Pure & Appl. Sci. 33 (1) 2020 3. Results and Discussion In this work, a SIF with and , giving has been designed. Design variables are the core radius and the wavelength. The fundamental mode properties can be calculated from RP Fiber Calculator software. It is evident from Tables 1, 3. that the phase constant β lies between and . This means that the effective refractive index lies within the range of and .The effective mode area decreases when V<2 and then increases when V >2. The V number, the phase constant (and thus and P in core increase with increasing fiber core radius . With increasing V number, the fraction of the power propagating within the core increases more and more.When V >2, more than 74% of the power is carried in the core and less than 26% in the cladding. Table 1. V number and mode parameters at λ= 1.31 µm. from RP Fiber Calculator from Eq. 2 r mµ P in core % m) 2 µ) β mµ/ V 1.4 6788.4 1.443003 6.92111 0.7290 2 9.7 738.2 1.443037 6.92127 0.9113 2.5 23.9 281.4 1.443126 6.92170 1.0936 3 38.5 181.8 1.443256 6.92233 1.2758 3.5 51.0 149.5 1.443404 6.92303 1.4581 4 60.8 138.7 1.443551 6.92374 1.6403 4.5 68.4 137.2 1.443689 6.92440 1.8226 5 74.3 140.7 1.443814 6.92500 2.0049 5.5 78.8 147.3 1.443926 6.92554 2.1871 6 82.4 156.1 1.444025 6.92601 2.3694 6.5 Values for are listed in Tables 2, 4. The mode radius is larger than the core radius. Values of calculated from Eq. 6 and values of P calculated from Eq. 7 are in good agreement with those in Tables 1, 3. Table 2. Mode radius, effective mode area and P in core for V >1.2 at λ= 1.31 µm. r mµ from Eq. 5 from Eq. 6 from Eq. 7 ω mµ m) 2 µ) ω mµ m) 2 µ) P in core % 3.5 8.544 229.3 7.495 176.5 35.3 4 7.476 175.6 6.967 152.5 48.3 4.5 7.058 156.5 6.766 143.8 58.7 5 6.933 151.0 6.736 142.5 66.8 5.5 6.955 152.0 6.802 145.3 73.0 6 7.061 156.6 6.926 150.7 77.7 6.5 7.216 163.6 7.088 157.8 81.4 04 Ibn Al-Haitham Jour. for Pure & Appl. Sci. 33 (1) 2020 Table 3. V number and mode parameters at λ= 1.55 µm. from RP Fiber Calculator from Eq. 2 r mµ P in core % m) 2 µ) β mµ/ V 0.1 151755.6 1.443000 5.84944 0.6162 2 2.5 4815.5 1.443007 5.84947 0.7702 2.5 10.5 937.9 1.443041 5.84961 0.9242 3 22.6 416.0 1.443116 5.84991 1.0783 3.5 35.2 274.4 1.443223 5.85035 1.2323 4 46.4 221.8 1.443345 5.85084 1.3864 4.5 55.7 200.2 1.443471 5.85135 1.5404 5 63.3 192.6 1.443593 5.85185 1.6944 5.5 69.3 192.5 1.443708 5.85231 1.8485 6 74.2 196.9 1.443813 5.85274 2.0025 6.5 78.1 204.5 1.443908 5.85313 2.1566 7 81.3 214.3 1.443995 5.85348 2.3106 7.5 Table 4. Mode radius, effective mode area and P in core for V >1.2 at λ= 1.55 µm. from Eq. 7 from Eq. 6 from Eq. 5 r mµ P in core % m) 2 µ) ω mµ m) 2 µ) ω mµ 32.0 260.8 9.112 354.5 10.62 4 43.5 223.1 8.427 266.6 9.212 4.5 53.3 206.2 8.102 230.3 8.562 5 61.3 200.0 7.979 215.5 8.281 5.5 67.8 199.8 7.975 211.1 8.198 6 72.9 203.4 8.046 212.7 8.229 6.5 77.0 209.5 8.166 217.9 8.329 7 80.3 217.5 8.321 225.6 8.474 7.5 From the above tables, it can be seen that, as the wavelength increases: 1. The V number decreases. 2. The phase constant (and thus decreases. 3. The mode radius (and thus increases, and P in core decreases accordingly. Figures 2, 3. show 2D profiles and plots of the radial dependence. Both can be based either on intensities or amplitudes. The amplitude is proportional to the square root of the intensity. The fundamental mode corresponds to a circular spot. In the radial profiles, the gray vertical line shows the position of the core-cladding interface. The intensity drops quickly with increasing radial position. For large values of , the mode has an approximate Gaussian profile. 00 Ibn Al-Haitham Jour. for Pure & Appl. Sci. 33 (1) 2020 r (µm) Type of plot 4 3.5 3 2.5 2 2D profile intensity 2D profile amplitude radial intensity radial amplitude r (µm) Type of plot 6.5 6 5.5 5 4.5 2D profile intensity 2D profile amplitude 04 Ibn Al-Haitham Jour. for Pure & Appl. Sci. 33 (1) 2020 radial intensity radial amplitude Figure 2. mode profiles of the fiber at λ= 1.31 µm. r (µm) 4.5 4 3.5 3 2.5 2 04 Ibn Al-Haitham Jour. for Pure & Appl. Sci. 33 (1) 2020 r (µm) 7.5 7 6.5 6 5.5 5 Figure 3. mode profiles of the fiber at λ= 1.55 µm. 4. Conclusions In this work, several parameters have been considered. It is shown that to obtain SMF, the diameter of the core must be less than or equal to 13 µm at a wavelength of 1.31 µm and 15 µm or less at 1.55 µm. It is desirable to have most of the power in the core. 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