High-spatial-resolution near-field photoluminescence and imaging of whispering-gallery modes in semiconductor microdisks with embedded quantum dots

A. M. Mintairov, Y. Chu, Y. He, S. Blokhin, A. Nadtochy, M. Maximov, V. Tokranov, S. Oktyabrsky, and J. L. Merz

Phys. Rev. B 77, 195322 – Published 23 May 2008

Abstract

Near-field photoluminescence (NPL) spectroscopy with a spatial resolution below the light diffraction limit was used to study the optical fields of whispering-gallery modes (WGMs) in GaAs and AlGaAs microdisks (radii $R = 1 - 3 μ m$ and quality factors $Q \sim 5 \times 10^{3}$ ) containing InAs quantum dots (QDs). WGMs with azimuthal mode numbers $m = 10 - 36$ and radial mode numbers $l = 1 - 3$ , together with low- $Q$ Fabry-Pérot modes and other non-WGMs, have been resolved in NPL spectra in the range of $1.1 - 1.3 μ m$ . We found that spectrally resolved NPL intensity images of the WGMs reveal $m$ azimuthal maxima around the disk circumference, which correspond to the period of the field amplitude. Using finite-difference-time-domain (FDTD) calculations, we show that the amplitude imaging arises from the interference between the WGMs and a background field formed by low- $Q$ modes. We show further that such interference reflects the inhomogeneity of the radiation decay of the QD ensemble in the MD. We demonstrate a direct measurement of WGM quantum numbers in microdisks by using NPL imaging, which shows good agreement with FDTD calculations.

Received 15 April 2008

DOI:https://doi.org/10.1103/PhysRevB.77.195322

Authors & Affiliations

A. M. Mintairov¹, Y. Chu¹, Y. He¹, S. Blokhin², A. Nadtochy², M. Maximov², V. Tokranov³, S. Oktyabrsky³, and J. L. Merz¹

¹University of Notre Dame, Notre Dame, Indiana 46556, USA
²Ioffe Physico-Technical Institute, St. Petersburg, Russia
³Institute for Materials, SUNY Albany, Albany, New York 12203, USA

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Issue

Vol. 77, Iss. 19 — 15 May 2008

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Images

Figure 1
(Color online) $μ -PL$ spectra (solid curves) of InAs QDs embedded in GaAs $(λ \sim 1.3 μ m)$ and AlGaAs $(λ \sim 1.2 μ m)$ MDs having $R$ : (a) $3 μ m$ and (b) 1 and $2 μ m$ . The lower spectra (thin solid curves) are $μ -PL$ spectra of unprocessed wafers. The dotted curves are Fabry-Pérot etalon transmission for thickness of $2 R$ . The insets are the SEM images of MDs (upper) and $0.24 \times 0.32 μ m^{2}$ TEM images of InAs QDs (lower).Reuse & Permissions
Figure 2
(Color online) Near-field spectra of $R = 1 μ m$ MD calculated by FDTD for (a) edge and (b) center TE excitations $(τ_{1} = 20 fs)$ . The center insets are the calculated patterns of the radial electric field at $t = 0.4 ps$ . The right insets are the calculated time decays of the (a) ${TE}_{12, 1}$ and (b) ${HE}_{1, 3}$ modes $(τ_{2} = 2 ps)$ . The left insets show the source position (dot) and light passes (arrows) in the MD. Spectra and decays were calculated at field maxima nearest to the excitation source.Reuse & Permissions
Figure 3
(Color online) Near-field spectra of the $R = 2 μ m$ MD taken at positions 4 $(x / y = 2.5 / 1.2 μ m)$ and 8 $(x / y = 2.5 / 2.4 μ m)$ , which are marked by large dots in the disk topographic image in the upper right inset. The upper left inset shows a three-dimensional contour plot of spatially resolved NPL spectra taken by using a linear scan along the disk diameter (see topography for tip positions). The lower right inset shows the ${TE}_{26, 1}$ mode line in the NPL spectra at four tip positions.Reuse & Permissions
Figure 4
(Color online) NPL spectra and images of 15 WGM spectral lines of MDs having $R (μ m)$ : (a) 3, (b) 2, and (c) 1, together with [(d)–(f)] the enlarged images of nine selected WGMs and (g) comparison of simulated field and NPL intensity distributions to experiment for the ${TE}_{12, 1}$ mode. The topography of each MD is shown in the leftmost inset in (a)–(c). Scan sizes for images and topography in (a), (b), and (c) are $8 \times 8$ , $5 \times 5$ , and $2.5 \times 2.5 μ m^{2}$ , respectively. The center inset in (c) is the NPL intensity profile of the ${TE}_{11, 1}$ mode taken along a 5–11 o’clock line of the image. The NPL images in (d) and (e) are for ${TE}_{35, 1}$ , ${TE}_{32, 2}$ , and ${TE}_{24, 3}$ $(R = 3 μ m)$ and ${TM}_{21, 1}$ , ${TE}_{24, 1}$ , and ${TE}_{21, 2}$ $(R = 2 μ m)$ , respectively. The images in (f) are $1 \times 1 μ m^{2}$ regions of ${TM}_{22, 1}$ , ${TE}_{25, 1}$ $(R = 2 μ m)$ , ${TE}_{35, 1}$ $(R = 3 μ m)$ , and ${TE}_{10, 1}$ $(R = 1 μ m)$ mode images from (a)–(c) (see the small arrows marking the positions of these mode excerpts). In (g), images 1 and 2 are plots of $I = E_{x}^{2} + E_{y}^{2}$ for multiple source excitation calculated at $t = τ_{2}$ and $τ_{2} / 5$ $(τ_{2} = 2 ps)$ , respectively; image 3 is $I = {(E_{x} + E_{0})}^{2} + {(E_{y} + E_{0})}^{2}$ of plot 2 (where $E_{0} = | E_{x}^{max} | / 2$ ); images 4 and 6 are “probe-diffused” plots of 1 and 3, respectively; and image 5 is the experiment.Reuse & Permissions
Figure 5
(Color online) Calculated (small symbols) and measured (large symbols) spectral dependence of azimuthal numbers for ${TE}_{m, 1}$ (circles), ${TE}_{m, 2}$ (squares), ${TE}_{m, 3}$ (triangles), ${TM}_{m, 1}$ (stars), and ${TM}_{m, 2}$ (pentagons) for MDs having $R$ $(μ m)$ : (a) 2 and (b) 3 and 1—inset in (a). The horizontal and vertical bars show the calculation and experimental uncertainties, respectively.Reuse & Permissions

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