Question

The V number or normalized frequency for an optical fiber is given by 210 21 V= a NA= anore nzladding 2 2 a) Consider a long dielectric rod of radius of 0.3um. The rod has a refractive index of v2. Illuminate the end of the rod with light of wavelength 2.. Describe what you see at the output of the rod as you decrease 2 from 1um to 400nm. b) How would you optimize getting light into the rod? Be specific and as detailed as possible. c) Consider a 3mm long dielectric rod made from the same material as in a) but of radius 3cm. Describe what you see at the output of the rod as you decrease 2 from lum to 400nm. d) If you coat the input and output surfaces of this rod with a noble metal, and repeat the experiment, what if anything will change?

Answer 1

Solutions ne V-number or normalived frequency of an optical fibey is given by V=24 a Incore - neadding n cladding1 지 ncore=1.414 , giren that a=0.3um. V 2x3.142.0-3 X10-6 |(1-41432 -11) 2x3.1480-3 X o ggg lot v = 1188 3 x 10-6 지 * får VE -cicy da 400 nm warelength range decrease from lum to 400nm för talum. 1.883 x 10-6 1.883. 1 x loro V=2.405 is cut off normalized free V<7.405, so lingle nolle probogatim dos posible at output neem.bes of guided modes Mzu? * ford Mx (1.88372 Ma 1.77 Va 11803 X 60-6 le. 1 mode single mode AX lo< x [0-9 at output 110883 x 6 number of guided moder at outful v a 4.70 을 11 mode at output [V> 2.405 abore eutoff frequency no single mode 4 MT v2 ~ 2 11.045

since the core has a od the TIR will meet. are que modes (6) than the cladding higher refractive inden light will be confined to. core of if the angular condition of there are two broad classification of modes - radiation modes ie. carry energy out of the core guided confined to the core, and propogate along the fiber the lowest order guided modes es designated as Lol for warelength d= lum there is v<2:45 for warelength t = hoonm there is u>2.405 (0 radius ne: 1 Vzda (1,2-1,3382 Ve 283.14 X3 X 10-2 = 3cm = a=3cm n = 1.414 x oiggg V- 18.82116 x 10-2 for t= 1 um V= 18.82116 X lo' 1 x 10-6 V= 18.02x104 V is large Ma number of mode uz 354.21 X108 2 M 177.1 x 10 O moden. for de yoonm, V = 18.82116 X10-2 400 x lo-g v=4.705x lor

number of modes M X v2 2 Ma 11.06% lo lo mody