Coupling of quantum dot light emission with threedimensional photonic crystal nanocavity

Size: px

Start display at page:

Download "Coupling of quantum dot light emission with threedimensional photonic crystal nanocavity"

Joan Fowler
5 years ago
Views:

1 S1 Coupling of quantum dot light emission with threedimensional photonic crystal nanocavity Kanna Aoki 1, Denis Guimard 1, Masao Nishioka 1, Masahiro Nomura 1, Satoshi Iwamoto 1,2, and Yasuhiko Arakawa 1,2 1 Institute of Industrial Science, the University of Tokyo, Komaba, Meguro, Tokyo , Japan 2 Research Center for Advanced Science and Technology, the University of Tokyo, Komaba, Meguro, Tokyo , Japan Correspondence should be addressed to K.A. ( kanna@iis.u-tokyo.ac.jp) and Y.A. (arakawa@iis.u-tokyo.ac.jp). Present address National Nanotechnology Laboratory, CNR/INFM, Università del Salento, 16 Via Arnesano, Lecce 73100, Italy Contents of Supplementary Information (1) Numerical data for resonant emission wavelengths in Figs. 2a and 2b (Table s1). (2) Dependence of emission peak intensities on PhC dimensions (Figs. s1). (3) Dependence of quality factors on crystal dimensions and clad materials (Fig. s2). (4) Numerically simulated far field patterns of resonant emissions from a point-defect cavity in 3D PhCs with various numbers of upper layers (Figs. s3). (5) References cited in Supplementary Information.

2 S2 (1) Numerical data for resonant emission wavelengths in Figs. 2a and 2b (Table s1) Table s1 shows the dependence of the emission peak wavelengths of the PhCs in Figs. 2a and 2b on the number of upper layers. As the total number of layers in a PhC increases, the wavelengths are slightly red-shifted due to an increase in the effective refractive index around the cavities. In all our measurements the two cavity peaks for the N l = 4 PhC appeared at shorter wavelengths than for the N l = 8 PhC. The peaks for the latter PhC shifted towards higher wavelength as the N u increased, before reaching constant values when the periodic structure surrounding the cavities had expanded sufficiently in all directions. Table s1 Experimental cavity mode wavelengths for PhCs containing four and eight lower layers, with in-plane periodicity a = 590 nm Eight lower layers Four lower layers Number of upper layers Peak#1 Peak#2 Peak#1 Peak#2 1 1, , , , , , , , , , , , , , , , , , , , , , Wavelengths are shown in units of nm.

3 S3 (2) Dependence of emission peak intensities on PhC dimensions (Figs. s1). The fluctuation of peak intensity in Fig. 2b according to the number of stacked layers can be attributed to a Fabry-Perot resonance between the bottom and top surface of a crystal. Normalized intensities of emission peaks observed from various 3D PhC point-defect cavities are plotted as a function of number of upper layers in Figs. s1. Most of them showed similar trend in fluctuation. This phenomenon was also observed in transmittance and reflectance spectra in our previous report 41. Fabry-Perot resonance occurs when following relation is fulfilled. N x!/2n e = L (1) Where N is an integer number,! is resonant wavelength in a free space, n e is effective refractive index of medium, and L is the length of a resonant medium. The rod width in one layer is fixed to 0.26a (a: in-plane period length) in this report. Thus, refractive index and volume fraction of gallium arsenide and air can be set to 3.2 (26 %) and 1 (74%), respectively: frame is not included in the calculation. As a result n e is calculated to be1.84. When we assumed the centre wavelength of Fabry-Perot resonance as 1.38!m (The resonant wavelength with the highest peak intensity among the series of measurements in Fig. 2b.), N became close to integer number at local maximum values of peak intensity, and intermediate-value of integers at local minimum values for most cases. This feature is very clear when the numbers of upper layers are 4, 5 and 6. Furthermore, estimated light extraction efficiency, calculated total Q-factors (Q total ) divided by partial Q-factors in stacking direction (Q v ) in Fig. 4a, showed similar trend to experimental data. These results confirm our estimation. Deviations from expected fluctuating trend observed in a couple of crystals would be attributed to weak peak intensities in entire PL measurements of those crystals.

4 S4 Figure s1 Dependence of emission peak intensities on PhC dimensions. In-plane period length a is varied from 560 to 600 nm. Peak intensities in a to e are normalized by the highest intensity in each crystal. N l is fixed to 8 for all the crystals. Red number attached to marks indicates N in the formula (1). a, a = 560 nm; peak wavelength! = 1,404 nm, b, a = 570 nm; filled circle,! = 1,444 nm; open circle,! = 1,375 nm, c, a = 580 nm;! = 1,466 nm, d, a = 590 nm; filled circle,! = 1,442 nm; open circle,! = 1,381 nm, e, a = 600 nm; filled circle,! = 1,4392 nm; open circle,! = 1,394 nm, and f, Estimated light extraction efficiency in vertical direction for a crystal with a = 590 nm.

5 S5 (3) Dependence of quality factors on crystal dimensions and clad materials (Fig. s2). The crystals realized in this report form steric core-clad configuration with crystal itself as a core and air around the crystal as a clad. Thus, the 3D PhC point cavities in this report have achieved high Q-factors thanks to the combined effects of photonic bandgap and total internal reflection in spite of their much smaller crystal sizes compared to previous studies whose structures were surrounded by semiconductor wafers 33. To verify our assumption, we simulated Q-factors for crystals surrounded by dielectric materials with a refractive index equals to that of crystals fabricated in this report. As seen in Fig. s2, contribution of total internal reflection on Q-factors is obvious: Q-factors with air clads are greater than those with dielectric material clads in the majority of cases. Q-factors with dielectric material clads showed relatively high values when the direction of rods in the topmost layer is orthogonal to the polarization direction of a cavity mode, parallel to the longer side of a cavity, and low values with parallel positions. This feature agrees with reported numerical analysis s1. This trend is reversed for crystals with air clads. Magnitude relations of refractive index between a crystal and surroundings reverse depending on whether the clad is an air (crystal > clad) or a dielectric material (crystal < clad). Thus, change in clad material seems to switch reflecting manners of standing waves between free-end and fixed-end reflection. Balance of contributions from the two light confining effects should be controllable by arranging structural parameters of PhCs. These findings alter the established understanding, semi-infinite dimensions are prerequisite for light confinement by a 3D PhC, and provide us new guidelines in designing 3D PhC devices to achieve high controllability of light with less burdens of fabrication.

6 S6 Figure s2 Calculated Q-factor dependence on PhC dimensions and clad materials. N l is fixed to 8. Q- factors for crystals with dielectric material clad (refractive index = 3.2) and air clad (refractive index = 1) are indicated by red open circles and filled circles, respectively. Q-factors for crystals with air clad are identical to calculated Q-factors for crystal with N l = 8 in Fig. 4a (filled circles).

7 S7 (4) Numerically simulated far field patterns of resonant emissions from a pointdefect cavity in 3DPhCs with various numbers of upper layers (Fig. s3). Far field patterns (FFPs) of resonant emissions from a point defect cavity in a 3D PhC were simulated for structures with various N u. As seen in Figs. s3, FFPs revealed that spot shape and a full width at half maximum (FWHM, here width is expressed as an angle) are strongly affected by configuration of rods along the propagation path of emitted light. A kind of lens effect does not seem to be determined exclusively by a relative configuration between polarization direction of a cavity resonance and stripes in the topmost layer as Q-factors were in Fig. s2, since FFPs of and crystals, both of which have the identical rod pattern in the topmost layer, do not resemble each other. Håkansson suggested that an arranged dielectric rods function as a beam splitter 48 and a cloaking agent 50. In our case, it seems that upper layers of a crystal could function as a lens, a beam splitter or a spot size converter when their configuration falls under a proper condition. This result made us to realize that not only cavity design but also crystal design along a light path is one of the key issue in developing 3D PhC devices.

8 S8 Figure s3 Numerically simulated far field patterns of resonant emission from a point defect. First, second, and third column in each subsection are schematic sideview of a crystal, schematic correlation of a defect and rods in the top layer, and a simulated far field pattern, respectively. a, crystal, b, crystal, c, crystal, d, crystal, and e, crystal.

9 S9 (5) References cited in Supplementary Information. s1. Okano, M. & Noda, S. Analysis of multimode point-defect cavities in threedimensional photonic crystals using group theory in frequency and time domains. Phys. Rev. B 70, (2004).

Investigation on Mode Splitting and Degeneracy in the L3 Photonic Crystal Nanocavity via Unsymmetrical Displacement of Air-Holes

The International Journal Of Engineering And Science (Ijes) Volume 2 Issue 2 Pages 146-150 2013 Issn: 2319 1813 Isbn: 2319 1805 Investigation on Mode Splitting and Degeneracy in the L3 Photonic Crystal