By Joseph T. Verdeyen

Most sensible vendor for introductory classes in Laser Electronics and Quantum Electronics. this can be a sensible method of introductory laser electronics that emphasizes real-world functions and problem-solving talents over thought, delivering a transparent realizing of either optical and microwave frequencies

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20a) (r > a2 ). 20b) (r > a2 ). where βt1 = n 21 k02 − β 2 , βt2 = |n 22 k02 − β 2 |, and βt3 = |n 23 k02 − β 2 |. By usual notations, Jν and Nν are the νth-order Bessel functions of the ﬁrst and second kinds; Iν and K ν are the modiﬁed Bessel functions of the ﬁrst and second kinds. The third region is usually the air with n 3 = 1. When the incident angle at the boundary between the cladding and the surrounding medium is less than the critical angle, the optical beam is radiation mode with β < n 3 k0 and R(r ) = C Hν (βt3r ), where Hν is the Hankel function.

20a) (r > a2 ). 20b) (r > a2 ). where βt1 = n 21 k02 − β 2 , βt2 = |n 22 k02 − β 2 |, and βt3 = |n 23 k02 − β 2 |. By usual notations, Jν and Nν are the νth-order Bessel functions of the ﬁrst and second kinds; Iν and K ν are the modiﬁed Bessel functions of the ﬁrst and second kinds. The third region is usually the air with n 3 = 1. When the incident angle at the boundary between the cladding and the surrounding medium is less than the critical angle, the optical beam is radiation mode with β < n 3 k0 and R(r ) = C Hν (βt3r ), where Hν is the Hankel function.

16 shows a ray propagating in a medium with index n = n(x), which is modeled as a multilayer medium with homogeneous index in each layer. The ray is refracted at each interface according to Snell’s law: n i cos ϕi = n i+1 cos ϕi+1 . In the limitation of δx → 0, the ray should obey an equation of n(x) cos ϕ(x) = n(0) cos ϕ0 = Const. 1, the GRIN ﬁber was invented at an early stage, and is still used widely. Its characteristics have been investigated in detail [3,9,32]. 81b) where = [n 2 (0) − n 2 (a)]/2n 2 (0) ≈ [n(0) − n(a)]/n(0) = (n 1 − n 2 )/n 1 .