Photonic Crystals and Their Various Applications

Transcription

1 Photonic Cystals and Thei Vaious Applications M Naci Inci Faculty of Engineeing & Natual Sciences Sabanci Univesity, Istanbul, Tukey

2 What is a Photonic Cystal? A peiodic stuctue of dielectic medium on a wavelength scale is called Photonic Cystal (PC)o Photonic Bangap Mateial (PBG) Light

3 Pefect Photonic Band Gap Mateials * Peiodic along one diection, and extends infinity along othe diections. * Peiodic along two axis, and extends infinity along the thid axis. * Peiodic along thee axes (x, y, z) and can be obtained by filling (eg. sphee, ba) a unit cell of any thee dimensional lattice and duplicating though space PERFECT INFINITY (not a slab with a finite height)

4 The idea of Photonic Cystals was fist intoduced by Yablonovitch 1 and John 2 1. E Yablonovitch, Phys Rev Lett (1987) 2. S John, Phys Rev Lett (1987)

5 The idea of a Photonic Cystal is based on dawing analogies between light and electons: Because both have a wave-like natue and can theefoe be diffacted!

6 Conside Electons and the Electonic Bandgap fist

7 The electonic bandgap of an insulato aises fom the diffactive inteaction of the electon wavefunction with the atomic lattice, esulting in destuctive intefeence at cetain wavelengths

8 What about Photons (ie, Light) and Oigin of the Photonic Bandgap?

9 Inteaction of l i g h t with m a t t e Mateial s efactive index (o dielectic constant ε) descibes the inteaction of light with matte!

10 Setting up a peiodic efactive index (like a peiodic potential of an atomic lattice) can esult in a simila `band theoy fo photons whee cetain fequencies cannot popagate In othe wods, the photonic equivalent of an insulato! Howeve,

11 Electons and photons ae not on the same wavelength scale Wavelength of Visible Light: Wavelength of Electon: 400 nm-700 nm 0.1 nm

12 To see the diffactive effects, we must make lage atificial `atoms on the same scale as the wavelength

13 Compute models fo doing the calculations fo semiconductos cannot be used fo photons! Schodinge s equation govens electons, but Maxwell s equations descibe the behavio of light. With photons, one cannot safely neglect polaization the way one can with electons

14

15 The electomagnetic popeties of the photonic cystals ae completely detemined by the solutions of the macoscopic Maxwell s equations 0 ) ( H ω (Tansvesality condition) ) ( ) ( ) ( 1 2 H c H ω ω ω ε = (Bloch-Floquet theoem) ) ( ) (, H e H k k i ω ω = Peiodicity of ε() is descibed by the Bavias lattice associated with the cystal ( ) ε is the spatially peiodic dielectic function that descibes the cystal

16 H ω ( ) = e ik H ( ), ω k k : Bloch vecto (cystal momentum) M Γ X

17 ) (, H k ω denotes the lattice peiodic pat of the Bloch function, i.e., ) ( ) (,, H R H k k ω ω = + ) ( ) (, H e H k k i ω ω = fo all lattice vectos R

18 Resticting the Bloch vecto to the fist BZ, coesponds to a back-folding of the dispesion elation in the infinitely extended k-space into the 1 st BZ by means of tanslations though ecipocal lattice vectos This intoduces a discete band index n N such that the band stuctue is descibed by the set [ ] ω k ), H n { }, k 1 st BZ, n N n ( ω, k associated with ε 1 ( ) H ω ( ) = ω c 2 H ω ( )

19 ig BZ G k G G k k e u e H st = + = 1 2 1, ) (,,, ) ( ω 1,2 0,, = = q e q ) (, k G u (tansvese unit vectos) (expansion coefficients - to be detemined...) ) ( ) (, H e H k k i ω ω = ) ( ) ( ) ( 1 2 H c H ω ω ω ε =

20 One Dimensional Photonic Cystals unit cell a z x (lattice constant) y Fo the sake of simplicity, if we assume the stuctue itself the same with its ecipocal lattice (a 2π/a), we would descibe the ieducible Billouin zone with the half of the unit cell [0, π/a] shown in the figue.

21 (ωa/2πc) fequency (wa/2πc) One Dimensional Photonic Cystal PHOTONIC BAND GAP GaAs/Ai Multilaye Film altenating layes of width 0.5a dielectic band wavevecto (ka/2π) wave (ka/2π) vecto ai band (0.5,0.25) (0.5,0.15)

22 /4n H Light /4n L

23 nh=1.52 nl=1.38

24 (squae lattice of dielectic ods, ε = 8.9 = 0.2a) a

25 Two Dimensional Photonic Cystal (ωa/2πc) (squae lattice of dielectic ods, ε = = 0.2a) TE modes TM modes TE PHOTONIC BAND GAP TM PHOTONIC BAND GAP (ka/2π) Γ X Μ Γ M Γ M X

26 2D Hexagonal lattice stuctue (ε = 13, = 0.48a )

27 2D Hexagonal (ωa/2πc) ε = 13, = 0.48a COMPLETE PHOTONIC BAND GAP 0.3 M K 0.2 TE modes TM modes Γ (ka/2π) Γ M K Γ

28 (Joannoupoulos s goup / MIT)

29 (Joannoupoulos s goup / MIT)

30 f=w/d=0.28 c/d=1.414 Face centeed tetagonal lattice symmety Complete bandgap (0.46c/a c/a) S Y Lin et al Natue (1998)

31 O Toade and S John, Science (2001)

32 What we did...

33 Woking Pinciple * A 2D PBG Stuctue fo Suface Tempeatue Mapping * Based on BB Radiation Chaacteistics of the Taget

34 Intensity I(l i,t) I(l j,t) I(l k,t) I(l,T) = [2phc 2 ]/[l 5 (e hc/lkt -1)] O(l i,t) O(l j,t) O(l k,t) I(,Τ) Ο(,Τ) = SγΙ(,Τ) l i l j l k wavelength

35 Poposed PBG Stuctue: Design Paametes * 2D Photonic Csytal Slab * Tiangula aay (ie, 2D Hexagonal)of ai holes * GaAs: Lossless aound 1.55-µm * /a = 0.3 (a = µm) * ε = 11.4 * Complete TE band-gap: (c/a) * Defect adii: 0.51a, 0.54a, 0.57a.

36 Radiation Guiding EM Modes though the waveguide Obtaining the Scaled Intensities Tapping by the coesponding point defects Obtaining tempeatue using BBRC and PC tansmission esponse

37 Relation between measued optical powe and esonant wavelengths (output adiation and BBR ae linked) d d dp d d dp T P i i i i i i v v i vi ), ( + = 2 / 2 / ), ( ), ( i i i i d T I S T P i i vi γ = γ γ d T I d T I T P T P j i j vj i vi ), ( ), ( ), ( ), ( Ratio of optical powes fo any two defects i and j [ ] [ ] j m l jl i n k ik j i m l jl jl vjl n k ik ik vik T hc T hc P P δ δ γ γ δ δ δ δ δ δ = 1) / exp( 1/ 1) / exp( / 1 Discete fomulisation fo numeical analysis } { }

38 ) ik i i / 2 + ( k 1/ 2 δi ) ( n jl j j / 2 + ( l 1/ 2 δ j 1) δ i = i } Notation { Analytical Solution n k m l δp δp vik vjl γ γ i j k l [ 1/ exp( hc / kt 1) ] [ 1/ exp( hc / T 1) ] l δ δ j i f ( T ) } lim ' f ( T) = 0 { Constant scaling factos T T Obtain tempeatue, T S = XΘ R

39 Ou Photonic Cystal Stuctue (ωa/2πc) (ε = 11.4, = 0.3a) TE Photonic Band Gap TE TE modes modes M K TM modes Γ 0 (ka/2π) Γ Μ Κ Γ

40 (A line defect is intoduced in the peiodic aay)

41 Line defect is intoduced in the peiodic aay... (ωa/2πc) (ε = 11.4, = 0.3a) TE Photonic Band Gap waveguide modes 0.10 TE modes (ka/2π)

42

43 and point defects ae intoduced (ωa/2πc) 0.25 waveguide modes TE modes (ka/2π)

44 Radiation Guiding EM Modes though the waveguide Obtaining the Scaled Intensities Tapping by the coesponding point defects Obtaining tempeatue using BBRC and PC tansmission esponse

45 Defect Size: = 0.51a waveguide egion point-defect egion localisation Suface plot fo the intensity of H y component of EM field fo the defect adius of 0.51a, coesponding to the esonant wavelength of 1.73 µm. Amplitude of the H y component of the field in a.u. fo the defect, 0.51a. The each coloed line indicates one slice passing though the isolated point defect.

46 Defect Size: = 0.54a waveguide egion point-defect egion localisation Suface plot fo the intensity of H y component of EM field fo the defect adius of 0.54a, coesponding to the esonant wavelength of µm. Amplitude of the H y component of the field in a.u. fo the defect, 0.54a. The each coloed line indicates one slice passing though the isolated point defect.

47 Defect size: = 57a waveguide egion point-defect egion localisation Suface plot fo the intensity of H y component of EM field fo the defect adius of 0.57a, coesponding to the esonant wavelength of µm. Amplitude of the H y component of the field in a.u. fo the defecct, 0.57a. The each coloed line indicates one slice passing though the isolated point defect.

48 (µm) (a) Coup. (Γ) Inp. Rad. (W/cm 2.µm) Out. Rad. (W/cm 2.µm).S Calculated input and output adiations and coupling atios, coesponding to the esonant wavelengths in the fist column, ae illustated. Second column gives the coesponding defect adii, while the thid column indicates the elative powe coupling fo these defects, which is calculated by the FDTD method, in tems of a constant Γ. In the fouth and fifth columns ae given the input adiation in BB adiation fom and output adiation, which is emitted fom the cystal stuctue, espectively. Note that the output adiation has a constant scaling facto S, which ou method fo tempeatue eading makes use of. Blue colou (last ow) indicates the fouth defect, which has a diffeent pofile than the othes.

49 SOME OTHER PC APPLICATIONS

50 Ulta-small optical integated cicuits by 3D Photonic Cystals ulta-small multiwavelength light souce ulta-small wavelength DEMUX cicuit (S Noda, Kyoto Univesity, Japan)

51 Photonic Bandgap Lases on InP Substates Ring defect PBG Lase * A small defect (ing with no holes) is intoduced in patten. * Light is tapped in the ing defect and geneates lase oscillations. * Wold s smallest lase. (Yokohama National Univesity/Baba Reseach Lab)

52 2D PBG Lase H Pak et al, APL (2001)

53 Photonic Cystal Waveguide (A Mekis,et al Phys. Rev Lett. 77 (1996)

54 High Density Multi-laye PBG Inteconnects (Univesity of Delawae)

55 Cosstalk Reduction Using Photonic Cystal Resonatos (Johnson et al, Optics Lettes, Dec 1998)

56 Tapped Delay Line Filte RF Signal Modulated on Optical Caie (MIT Lincoln Laboatoy)

57 New Ways to Guide Light J C Knight and P St Russell, Science (2002)