Phase Study of Optical Necklace States

Junying Huang and Luwei ZhouJunying Huang and Luwei ZhouPhys. Dept., Fudan Univ., Shanghai, People’s Republic of China

Localization will always occur in one dimension systems. But far away from the localized length, there still exist nonlocalized modes, which is so called necklace states. This has been observed in the periodic silicon layers. Here, we use the scattering matrix theory to study the phases between the localized and nonlocalized, which shows that the phases couple to a ring in localized states when randomized in nonlocalized states.

V. ConclusionsV. Conclusions Our calculation shows that the phases couple to a ring in localized states when randomized in nonlocalized states.

References:[1] Jacopo Bertolotti et.al, PRL. 94,113903[2] J. B. Pendry, J. Phys. C. 20, 733[3] M V Berry & S Klein, Eur.J.Phys.18,222

I. Scattering Matrix TransferI. Scattering Matrix Transfer

One surfaceOne surface

Several surfacesSeveral surfaces

in

id

1in 1in

s

…1n 2n 3n 2in 1in in

1d 2d 3d 2id 1id id

1

1

2exp( )

( )i i

i i ii i

n nt in kd

n n

1

1

( )exp(2 )

( )i i

i i ii i

n nr in kd

n n

1

1

i

i ii

i

i i

r

t tm

r

t t

2i iT t

2i iR r

12

12 121 2

12

12 12

1

1

L

L LL L

L

L L

r

t tM mm m

r

t t

2

12 LT t

II. Optical Necklace StatesII. Optical Necklace States

1n1n1n 2n2n2n 2n1n

…

1d 2d 1d 1d 1d2d 2d 2d

1 1 2 24 4n d n d

III. PhaseIII. Phase

Cos

2010-6-5