1. AR Coating for the case n2 > n3> n1 In Lecture 4A, we asked the question if we could make AR coating (targeting ), of 900 nm) using an layer n2 between n1 and n3 where n2 > n3> n1. (a) use the kinematic argument to decide the thickness /2 for AR coating layer. (b) Plot reflectance spectrum from A = 400 to 1400nm for your choice of /2 in part (a). Use n1=1 (air), n2=3 and n3=2 in your plot. n, =air n2 n3Application: Quarter-Wavelength AR coating: how to choose I & n2 to reduce R=Irl . Case 1 : n3 > n 2 > n, = 1 ( an ) n. (ani ) n z n3 r = Z ri all passes 1 Streff. riz 123 Uncoated glasses lens (top) 2 "d reff . tiarastyle v 28 versus lens with antireflective coating. Note the tinted reflection 2Tn. 0 of = K2l = no from the coated lens. good : To reduce reflection 1Kinematic t = 2n. Consideration : to reducer , so between 1 it pan & 2nd paws must be TI ( 180 ' ) or ( 2* +1 ) 75 hithz $ 1 = X riz = TC ( riz n, ; riz = ni+nz = $tiz + * tz1+ $ 123 -20 = 0 for destructive interference , $ ( Ist pan ) - F ( 2nd pan ) = ( 2*+1 ) To T - ( 71- 20 ) = (2K+1 ) TC 20 = (2* + 1 ) 17 shortent I corresponds to zo = It, on d = = ( a quarter of a cyde 2TT ) wavelength in layer 2 .. I would ourresponds to a quarter of 2 ( 2 quarter wave ) $ = K2d = 2In l n. is free space wavelength set ( = = =) = ( 2. : wavelength in free space 1 2 : wavelength in a media l = An 4 with refractive index nDynamic Condition : To find R, we have from F-B etalon, and minimize Irl n2 + n , 50 r= here R = 1 21- 1 23 I n2-13 0 at $ = 3 r = r12 - r23 It R Can r = 0 ? set (12- 123 = 0 nz-n3 & solve for n3 nithz n2 ( nyms ) - n2 thing = n2( n x-3 ) th2- ning 2 n 2 = 2nin3 n2 = ning For n,= 1 ( air ) , n3= 3 , zero reflection when 12 = 13 = 1. 732 Case 2 n2>n3 zn, : leave as a HW question. n2 7 3=3 To see how R varies with o and n2, we plot R vs o and n2 using a 3D plot (left) and a color-coded contour plot (right)2nv 5 d = - - Mal or = and n3 = 3 n2 4 3 2 nz> ng 3 JT 1 0.600 1516 1.432 R 1.348 2 3 .264 1.180 1.096 2 1.732 0.012 0 13 2 n 3 TT Contours of Reflectance vs o and n2 2 2 TT If we design a 2/4 AR coating for 550nm using n2 = 1.732, then /2 = = 550 nm 1 = 79.4 nm. The 4n12 reflection spectrum for this AR-coated material is shown below