1 Photonic Crystals its all about the mirrors

1 Photonic Crystals – it’s all about the mirrors Maksim Skorobogatiy Canada Research Chair in Photonic Band Gap materials and devices I would like to thank Prof. Yoel Fink fiber research group at MIT, and Prof. Steven Johnson at MIT for their contributions.

2 Periodic electromagnetic media Low index of refraction High index of refraction 3 D photonic crystal

3 Plane-waves in a uniform dielectric l/n n

4 Scattering regimes a>>l incoherent scattering a a~l coherent scattering a a<<l averaging a Photonic crystals

Photonic Crystals 5 Periodic electromagnetic media 1887 1987 2 -D 3 -D 1977 p eriodic in one directio n periodic in two directions periodic in three direction s quazi-1 D quazi-2 D Bragg fibers microstructured fibers

6 Photonic Crystals Components periodic electromagnetic media with defects can trap light in cavities and waveguides (“wires”)

7 1 D Photonic Crystal 1 -D

8 Uniform dielectric (transverse wavevector) kt (preferred direction) b n (propagation constant) w Our first band diagram light cone light propagation light line: w=cb/n no light propagation, kt is IMAGINARY b

9 Two uniform dielectrics (intuitive picture) k 1 t < q 2 n 1 b n 2 k 2 t w light cone 1, 2 iel tp h g i l light line 1: w = c b / n 1 ic ectr tio ga opa r on gati opa pr ght li d n in tr in ec diel nly o ic 2 light line 2: w = c b / n 2 no light propagation in dielectrics 1, 2 b

A quest for a perfect mirror 10 Reflectance 1 As index contrast increase Dielectric mirror, low loss, but strong angular and polarization dependence TE TM As index contrast increase 0 tan-1(n 2/n 1) 90 o Reflectance is getting more uniform for all polarizations and wider region of angles as index contrast increases q 1 Metallic mirror, low angular and polarization dependence, but very high loss for optical frequencies

11 Projected Bands of a 1 d Crystal (a. k. a. a Bragg mirror) Quaterwave stack condition d 1 n 1=d 2 n 2=l/4 n 1 d 1 n 2 d 2 b conserved Light in the multilayer 1 d band gap w TM TE modes in crystal propagation perpendicular to the layers b

12 Omnidirectional Reflection [ J. N. Winn et al, Opt. Lett. 23, 1573 (1998) ] w Air b conserved f o e in these w ranges, there is no overlap between modes of air & crystal all incident light li rw i a in l t h g = cb TM TE modes in crystal (any angle, polarization) is reflected from flat surface b needs: sufficient index contrast & nhi > nlo > 1

13 Omnidirectional Mirrors in Practice [ Y. Fink et al, Science 282, 1679 (1998) ] Te / polystyrene contours of omnidirectional gap size 3 50% 2. 8 2. 4 Reflectance (%) 40% 2. 6 30% 2. 2 20% 2 10% 1. 8 0% 1. 6 Dl/lmid 1. 4 1. 2 1 1 1. 2 1. 3 1. 4 1. 5 1. 6 1. 7 1. 8 1. 9 Smaller index, n 1 2