Experimental demonstration of second-order processes in photonic crystal microcavities at submilliwatt excitation powers

Murray W. McCutcheon, Jeff F. Young, Georg W. Rieger, Dan Dalacu, Simon Frédérick, Philip J. Poole, and Robin L. Williams

Phys. Rev. B 76, 245104 – Published 5 December 2007

Abstract

The far-field second-order radiation pattern from a wavelength-scale, InP-based photonic crystal microcavity that confines light in three dimensions is measured when excited on resonance by $300 μ W$ of continuous-wave power from a laser diode. The measurements are accurately simulated using the finite-difference time-domain method, showing that both absorption and scattering play significant roles in determining the pattern of the radiation. The results show that the bulk second-order nonlinear susceptibility mediates the nonlinear process. In a separate set of experiments, a short-pulse laser is used to simultaneously populate two distinct modes of a similar microcavity. The detected second-order spectra show features due to the second harmonic generated by each mode, as well as the sum-frequency generation due to nonlinear intermode mixing. The key phenomena that determine the second-order response of these fundamentally small optical cavities are identified.

Received 14 September 2007

DOI:https://doi.org/10.1103/PhysRevB.76.245104

Authors & Affiliations

Murray W. McCutcheon, Jeff F. Young, and Georg W. Rieger

Department of Physics and Astronomy, University of British Columbia, Vancouver, Canada V6T 1Z1

Dan Dalacu, Simon Frédérick^*, Philip J. Poole, and Robin L. Williams^*

Institute for Microstructural Sciences, National Research Council, Ottawa, Canada K1A OR6

^*Also at Department of Physics, University of Ottawa, Ottawa, Canada K1N 6N5.

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 76, Iss. 24 — 15 December 2007

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(Color online) Second-order spectroscopy setup. The experiment is performed in transmission, allowing independent excitation and collection lens focal lengths. The second-order radiation can be spectrally resolved with a grating spectrometer, or imaged directly onto the CCD array. The resonant scattering spectrum is monitored in reflection with a Fourier transform (FT) spectrometer.Reuse & Permissions
Figure 2
(Color online) Photoluminescence (PL) spectrum from the InAs quantum dots distributed at a density of $1 - 2 μ m^{- 2}$ throughout the wetting layer in the middle of an L3 cavity (shown in the inset). There are three $y$ -polarized and two $x$ -polarized modes near the lower edge of the band gap, which extends from $188 to 260 THz$ , and one QL mode near the top of the dielectric band (DB). The relative orientation of the photonic axes $(x, y)$ and InP crystal axes is shown. The circled modes are studied in different samples in this paper. The freestanding InP photonic crystals in this work are characterized by a lattice constant $a = 510 nm$ and a slab thickness $d = 223 nm$ . This PL spectrum is obtained from a sample with an air-hole radius $r = 183 nm$ and an outward side-hole shift $s = 60 nm$ (holes marked $s$ ) (Ref. 22).Reuse & Permissions
Figure 3
cw resonant scattering spectrum of the fundamental mode $(y_{1})$ of an L3 microcavity.Reuse & Permissions
Figure 4
(Color online) (a) CCD image of the second-order radiation pattern collected from the $y_{1}$ mode in Fig. 3 during a $2 h$ integration. The scale bar shows the total counts. The concentric rings show the solid angle of collection up to 40°, the limit of the $NA = 0.65$ collection objective. The InP crystal axes are rotated by 45° with respect to the photonic axes $(x, y)$ . PhC parameters: hole radius $r = 189 nm$ , pitch $a = 510 nm$ , and shift of nearest neighbors $s = 30 nm$ . (b) Electric field intensity distribution of the $y_{1}$ mode in the middle plane of the slab as simulated by FDTD (dimensions are $μ m$ ). (c) Second-order radiation pattern collected during a $15 \min$ integration from a quasilocalized mode, which has the simulated ${∣ E ∣}^{2}$ distribution shown in (d). The scale bar in (c) shows the total counts. The InP crystal axes for the sample studied in (c) are rotated by 15° with respect to the cavity frame. PhC parameters: $r = 192 nm$ , $a = 510 nm$ , and $s = 15 nm$ . The intensity scales in (b) and (d) are arbitrary.Reuse & Permissions
Figure 5
(Color online) (a) $z$ -oriented second-order polarization distribution for the $y_{1}$ mode simulated using FDTD (intensity scale is arbitrary). Far-field images of ${∣ E ∣}^{2}$ generated when the $P_{z}$ distribution in (a) is modeled by a sum of discrete dipoles in an InP slab (b) with and (c) without absorption. The image in (b) well reproduces the experimental data of Fig. 4a. The numeric values of the scale bars in (b) and (c) refer to the same absolute scale.Reuse & Permissions
Figure 6
(Color online) Second-order radiation spectrum acquired when a train of $130 fs$ laser pulses is used to excite the $x$ -dipole modes (Ref. 27) in a PhC microcavity with $r = 165 nm$ and $s = 60 nm$ . The insets show ${∣ E ∣}^{2}$ in the middle plane of the slab for each mode.Reuse & Permissions

Physical Review B

covering condensed matter and materials physics