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Chapter 2 Optical fibers Chapter 2 Optical fibers Optical fiber losses have been reduced from about 1000 dB/km before 1970, to around 20 dB/km in 1970, and 0.2 dB/km at 1.55-µm region in 1979. • • • • Most optical fiber consist of a cylindrical piece of glass surrounded by an acrylic (made from a thermoplastic resin) jacket. The glass consists of a core, of refractive index n1, and a surrounding cladding, of refractive index n2, with n1 > n2. The index of the jacket is such that any light reaching the cladding-jacket index is dissipated (or stripped) out of the cladding. Light propagates down the fiber through the core at the speed, v ≅ 2 × 108 m/s, so that it takes approximately 5 µs to travel down a length of 1 km of fiber. The outside diameter (OD) of standard communications fiber is 125 micron (µm) while the core diameter is 9 µm for single-mode fiber and 50 or 62.5 µm for multimode fiber. The OD of the jacketed fiber is 250 µm. The refractive index of the core is higher than that of the cladding, but by less than 1%. What are the physical principles that describe light propagation in a fiber? • Light is bound to the core by total internal reflection. The Geometrical Optics description is valid when the core radius, a is much greater than the wavelength λ, i.e., a >> λ. • Wave-propagation theory (Maxwell’s Equations) must be used when a is of the same order as λ. What are some of the degradations affecting light propagation in an optical fiber? • There are several mechanisms that affect the rate of attenuation of the optical signal. These include Rayleigh scattering, micro-bending and macro-bending, modal attenuation and several absorption mechanisms. • Modal dispersion is a source of signal degradation that results in pulse broadening. • Chromatic dispersion is another source of optical-signal degradation. 1 Jianping Yao Chapter 2 Optical fibers • There are more that will be discussed when encountered. Types of optical fibers: Step-index fibers • • Graded-index fibers Single-mode fibers Multi-mode fibers 2 Jianping Yao Chapter 2 Optical fibers Geometrical-Optics Description Law of Refraction (Snell's Law): When a ray of light is refracted at an interface dividing two uniform media, the transmitted ray remains within the plane of incidence and the sine of the angle of refraction is directly proportional to the sine of the angle of incidence. φ1 = φ '1 n1 sin φ1 = n2 sin φ2 Reflected and refracted rays for the light incident at the interface of two media Critical Angle and Total Internal Reflection: When light passes from a medium of larger refractive index index n1 into one of smaller refractive n2 , the refracted ray is bent away from the normal. If the incident ray is at the critical angle θ c , the angle of refraction is 900. The critical angle is determined from Snell's Law and is given by sinθ c = n2 / n1 . 3 Jianping Yao Chapter 2 Optical fibers When the angle of incidence exceeds the critical angle, all the incident light is reflected back into the medium from which it came. This is known as total internal reflection. Example 1: (a) Apply Snell’s law, we have n1 sin( 90 0 − θ 1 ) = n2 sin( 90 0 − θ 2 ) The critical angle: φ c = sin −1 ( n 1 ) = sin −1 ( ) = 40.50 n2 1.54 Step-index fibers Based on the Snell’s Law of Refraction, we have the following relation at the fiber-air interface n0 sin θ i = n1 sin θ r where n0 and nr are refractive indices of the air and the fiber core. 4 Jianping Yao Chapter 2 Optical fibers The refracted ray hit the core-cladding interface and is refracted again. To confine the light within the fiber, the angle of incidence φ should be greater than the critical angle φ c , which is given sin φ c = n2 / n1 n2 is the cladding index. Since such reflections occur throughout the fiber length, all rays with φ > φ c remain confined to the fiber core. This is the basic mechanism behind light where confinement in optical fiber. Numerical Aperture: The maximum angle that the incident ray should make with the fiber axis to remain confined inside the core: n0 sin θ i = n1 cosφ c = (n12 − n22 )1 / 2 n0 sin θ i is known as numerical aperture (NA), which represents the light-gathering capacity of an optical fiber. For n1 ≈ n2 NA = (n − n ) 2 1 2 1 /2 2 = n1 (2 ∆ ) [ = (n1 + n 2 )(n1 − n 2 ) ] 1/ 2 n − n2 ≈ 2n12 ( 1 ) n1 1/ 2 1/ 2 5 Jianping Yao Chapter 2 Optical fibers ∆ should be made as large as possible in order to couple maximum light into the fiber. However, this type of fiber is not useful for high bit rate communications because of multipath dispersion or modal dispersion. Multipath dispersion: different rays travel along paths of different lengths, which leads to rays disperse in time. A short pulse would broaden considerably as a result of different path lengths. The estimation of pulse broadening: ∆T = L n12 n1 L = ∆ c sinφc − L c n2 It is the delay between the two rays taking the shortest and longest paths. To be able to retrieve the information in case of dispersion, the broadening than the allocated bit slot TB = 1 / B , that is, ∆T < TB , or ∆T ⋅ B < 1 . ∆T should be less So we have ∆T ⋅ B = n1 L L n12 n2 c B = ∆B ⇒ BL < 2 c sin φc − L c n2 n2 ∆ For example, an unclad fiber with n1 = 1.5 , n2 = 1 , then the BL < 0.4 (Mbps)-km. A cladded fiber with ∆ = 2 ×10 −3 , BL < 100 (Mbps)-km. Such fiber can communicate data at 10 Mbps over distance over 10 km, which may be suitable for Local Area Networks (LAN). Example 2: 6 Jianping Yao Chapter 2 Optical fibers Graded-Index Fibers The refractive index of the core in graded-index fibers decreases gradually from its maximum value n1 to its minimum value n2 at the core-cladding interface. Most graded-index fibers can be modeled as [ ] n 1 − ∆( ρ / a )α ; n( ρ ) = 1 n1 [1 − ∆]; ρ<a ρ ≥a where a is the fiber core radius. α determines the index profile. A step index profile is approached with a large α . A parabolic-index profile corresponds to α = 2 . The multipath dispersion or intermodal dispersion is reduced with graded-index fibers. The reason is that the path is longer for more oblique rays, but the ray velocity changes along the path because of variations in the refractive index. Geometrical optics can be used to show that a parabolic-index profile leads to nondispersive pulse propagation within the paraxial approximation. The trajectory of a paraxial ray is obtained by solving ∂ 2 ρ 1 dn = dz 2 n dρ where ρ is the distance of the ray from the axis. It can be proved that a parabolic-index fiber does not exhibit intermodal dispersion. The BL product of graded index fibers is improved by nearly three orders of magnitude over the step-index fibers. 7 Jianping Yao Chapter 2 Optical fibers Example 3: 8 Jianping Yao