impedance, and E; and Elm are the electric (Fig. 6.1-8). Rather than stating the angle 0 for an optical field amplitudes for the incoming light and for the light fiber, it is the convention to give sin A, which is called the propagating in mode LP, lm in the fiber, respectively. numerical aperture (NA). The NA is defined as Coherent light from a laser can often be approximated with a Gaussian beam; furthermore, if we restrict our- NA = n.sin A, (6.1.15) selves to a SM fiber, SO that the LP01 mode can also be approximated as a Gaussian field, it is possible to calcu- where n is the refractive index of the medium the light is late n analytically [7, 11]: coming from. In the case of coupling into an optical fiber, light is usually coming from air and subsequently n 11 1. A more useful formula for the NA can be obtained if we (6.1.21) use the dimensionless parameter A, where NA 11 n1V2A. (6.1.16) For an incoherent light source such as a light emitting A = (ks))2 diode (LED) one can show that the total power accepted by the fiber is given by [9] B = G2 + (D + 1) C = (D+1)F2 + : 2DFG sin 0 + D(G2+D+1)) sin2 0 (6.1.17) D=(2)2 where B is the LED's radiance (units for radiance is watts per area and steradian). NA III sin 0 cladding G = 2A7 where AZ is the separation distance between source and Fig. 6.1-8 Acceptance angle for an optical fiber. Reprinted from fiber, A is the lateral displacement, 0 is the angular dis- Ref. [1], p. 10, courtesy of Academic Press. placement, and S1 and S2 are the mode field radii or spot CHAPTER 6.1 Optical fiber, cable and connectors sizes of the source field and fiber field, respectively. The Emitter refractive index of the medium between source and fiber Optical Fiber is denoted no. Equation (6.1.21) takes into account four different coupling cases at once (Fig. 6.1-9). If only one of these different coupling cases is present at a time Eq. (6.1.21) can be simplified to: Case 1.1. Spot-size mismatch S1 # S2: Fig. 6.1-10 Lens for improving coupling efficiency. Reprinted from Ref. [1], p. 20,