Optical Fiber Sensors for Biomedical Applications

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666 L.C.L. Chin et al.17.3 Fiber Fundamentals17.3.1 Light TransmissionA typical optical fiber consists of (1) a central core of refractive index n 1 ;(2)acladding that encases the core with index of refraction n 2 (with n 2 < n 1 ); and (3)a buffer coating – also known as a “jacket.” The role of the buffer is to improvethe mechanical robustness of the fiber and minimize structural compromise frombending. A step-index fiber is shown in Fig. 17.3 which is characterized by a discretestep in the index of refraction at the boundary of the core (n 1 ) and cladding. Anothercommon design, the graded-index fiber, where the index of refraction decreasesgradually from the center of the core to the cladding, and will be discussed later.When a light ray is directed at the entrance of a fiber with core index of refractionn 1 , a portion of the incoming beam is reflected back into the surrounding medium(index of refraction n 0 ), while a portion of the beam is transmitted into the fiberaccording to Snell’s law:sin(α 1 )sin(α 0 ) = n 0n 1(17.2)where α 0 is the incidence angle and α 1 is the transmission angle into the fiber.Light transport inside optical fibers is based on the concept of total internal reflection,which requires that n 2 < n 1 and that the incidence angle at the core/claddingboundary is greater than a critical value, θ c according to:sin (θ c ) = n 2n 1(17.3)Light rays incident at angles less than θ c such as at point B in Fig. 17.3 (i.e., more“normal” to the interface) are refracted from the core into the cladding and, hence,do not propagate along the fiber. Now, it is clear from Fig. 17.3 that α c = 90 ◦ − θ c .Hence, in order to propagate light along an optical fiber, it is necessary to direct lightFig. 17.3 Optical fiber design. n 0 , n 1 and n 2 are the refractive indices of the surrounding medium,fiber core and fiber cladding, respectively. Light rays incident at point A with angles greater than θ c(Eq.(17.3)) undergo total internal reflection and constitute the propagating light modes; those lightrays incident at angles smaller than θ c (point B) are refracted from the core into the cladding anddo not propagate down the fiber. A step-index fiber is shown for illustration (sharp n 1 /n 2 boundary)
17 Optical Fiber Sensors for Biomedical Applications 667into the fiber such that it refracts at or below the critical propagation angle, α c .Themaximum angle of incidence that a light ray can enter a fiber and be transportedalong the fiber (propagate at or below α c ) is known as the acceptance angle, θ a .For fiber characterization, the acceptance angle is typically reported in terms of anumerical aperture, NA:NA = n 0 sin (θ a ) =√n 2 1 − n2 2(17.4)Hence, for a given acceptance angle, light enters (or leaves) the fiber within anacceptance cone of 2θ a .From Eq. (17.4), it follows that the NA can be expressed in terms of the refractiveindices of the fiber material (core n 1 , and cladding n 2 ), but is also dependent on therefractive index of the surrounding environment n 0 . As such, compared to an airenvironment (n 0 =1), the acceptance angle will be correspondingly smaller in water(n 0 =1.33). The NA of an optical fiber characterizes not only its ability to collectlight from a source, but also preserve the light inside the fiber.The choice of wavelength range plays an important role in the selection of appropriatecore and cladding materials that allow for suitable transmission of light.Conventional glass and plastic core fibers, highly transparent to wavelengths in thevisible spectrum, have absorption losses on the order of 0.1% per meter or less.However, optical transmission in the ultraviolet (UV) or infrared (IR) wavelengthranges requires the use of high-grade fused silica cores. In these wavelength ranges,the presence of hydroxyl (OH) radicals in the silica core strongly affects the absorptionand transmission characteristics of the fiber. For wavelengths in the UV region(200 nm < λ < 360 nm), high-OH fibers are preferred, whereas in the near infrared(NIR) and up to ∼2400 nm, low-OH concentration fibers provide the most favorabletransmission. In the infrared region beyond ∼2400 nm, absorption by silica beginsto dominate. In this regime, sapphire fibers provide superior transmission but cansuffer additional signal decreases due to high reflection losses at the fiber interface(because of sapphire’s high refractive index).17.3.2 Fiber ClassificationsFibers fall into two broad categories, single mode or multi-mode. A mode is definedas a set of similar paths that light rays travel along the fiber. The term single mode isused to describe a fiber that supports one transmission mode, whereas multi-modedescribes a fiber that can support more than one transmission mode. Multi-modefibers are commonly employed in biomedical applications and come in two basicconfigurations: step-index and gradient index.The step-index multi-mode fiber is the simplest design, and operates in the fundamentalmanner described in Section 17.3.1. Its name comes from the sharp changein refractive index in the fiber material at the core-cladding boundary. In contrast,with gradient-index fibers, the refractive index decreases gradually from the centerof the core to the cladding.
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Optical Fiber Sensors for Biomedical Applications

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