Photonic-crystal waveguides with disorder: measurement of a band-edge tail in the density of states

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Photonic-crystal waveguides with disorder:

measurement of a band-edge tail in the density of states

1 1

S.R. Huisman , G. Ctistis ,

1 1,3 2 1 1

J.L. Herek , A. Lagendijk , P. Lodahl , W.L. Vos , P.W.H. Pinkse

2 1

S. Stobbe , A.P. Mosk ,

1 +

MESA Institute for Nanotechnology, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands

2

Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100, Copenhagen, Denmark

3

Center for Nanophotonics, FOM Institute for Atomic and Molecular Physics (AMOLF), Science Park 113, 1098 XG Amsterdam, The Netherlands

Lifshitz tail B A D Van Hove singularity Localized modes C Ideal-system_DOS Reconstructed DOS 1 0 10 -1 10 -2 10 -3 10 C A PC modes B LL

SFT Amplitude

Experimentally reconstructed band structure . We collected near-field patterns over a wide spatial range for many laser frequencies and obtai-ned their spatial Fourier transform. The color represents the amplitude of the spatial Fourier coefficients. The black lines are fitted modes (tri-angles: TM-like, circles: TE-like, squares: light line).

left: Localized modes smear out the band edge. right: Experimentally

reconstructed DOS (black) compared with a fitted DOS (red) for an ideal periodic waveguide. The DOS is approximated by counting the

[3]

number of Dk-bins at a given frequency, and agrees well with theory . The dashed line (blue) is a guide to the eye for the Lifshitz tail.

4. Bandstructure

5. Density of states

Nanophotonic structures are excellent model systems to investigate the effects of disorder on band-edge phenomena, like Anderson localization

[1-3]

and band-edge tails . We perform phase-sensitive near-field

[4,5]

microscopy on photonic-crystal waveguides . Such a waveguide approximates a 1D system, in which the Van Hove singularity is a divergence in the density of states (DOS). We experimentally reconstruct the band structure and investigate wave propagation near the band edge. We reconstruct the DOS, demonstrating the absence of

[6]

the Van Hove singularity and a first direct observation of a Lifshitz tail .

1. Introduction

Near-field tip

GaAs

photonic-crystal

waveguide

Continous-wave

incident light

a

x

y

z

2. Experiment

Localized modes (1, 2) appear as perturbations on top of a periodic background. These only occur at the band edge of the TE-like guided

[1-3, 6]

mode , and are excited by TM-like modes (periodic background).

1

2

Amplitude

0

1

948.7 nm

948.5 nm

948.6 nm

948.6 nm

(a)

(c)

(b)

(d)

3. Localized modes

6. Outlook

Ensemble averaging gives the possibility to study the shape of the Lifshitz tail. The Lifshitz tail should also appear when the DOS is probed by emission of embedded quantum dots.