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Topological photonic crystal nanocavity laser

Ota, Yasutomo, Katsumi, Ryota, Watanabe, Katsuyuki, Iwamoto, Satoshi, Arakawa, Yasuhiko·2018·Communications Physics
DOI 10.1038/s42005-018-0083-7
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Abstract

Topological edge states exist at the interfaces between two topologically distinct materials. The presence and number of such modes are deterministically predicted from the bulk band topologies, known as the bulk-edge correspondence. This principle is highly useful for predictably controlling optical modes in resonators made of photonic crystals (PhCs), leading to the recent demonstrations of microscale topological lasers. Meanwhile, zero-dimensional topological trapped states in the nanoscale remained unexplored, despite its importance for enhancing light–matter interactions and for wide applications including single-mode nanolasers. Here, we report a topological PhC nanocavity with a near-diffraction-limited mode volume and its application to single-mode lasing. The topological origin of the nanocavity, formed at the interface between two topologically distinct PhCs, guarantees the existence of only one mode within its photonic bandgap. The observed lasing accompanies a high spontaneous emission coupling factor stemming from the nanoscale confinement. These results encompass a way to greatly downscale topological photonics.

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Figure 1 Topological nanocavity design concept. (a) Schematic of the nanocavity formed by interfacing two PhCs with a common bandgap and distinct Zak phases. The Zak phases denoted in the bracket are respectively for the lowest (left) and the second lowest (right) band. (b) Detailed description of the design. The two PhCs are in essence the same but differ in the way to define the unit cells. Blue unit cell arranges the small air hole with a width of d 1 at the center, while red unit cell has the large air hole with d 2 at the center. The centers of the two holes respectively correspond to the inversion centers of the double periodic PhC. The sum of d 1 and d 2 equals to 0.5 a . (c) Band structures and wavefunctions at the band edges calculated for the PhC with the blue (left) and red (right) unit cell. The color of the band curve expresses its Zak phase (blue = π , red =0). A band inversion occurs when swapping the unit cells. The center panel shows the case for d 1 = d 2 = 0.25 a , exhibiting a Dirac point at the band edge.
Figure 1 Topological nanocavity design concept. (a) Schematic of the nanocavity formed by interfacing two PhCs with a common bandgap and distinct Zak phases. The Zak phases denoted in the bracket are respectively for the lowest (left) and the second lowest (right) band. (b) Detailed description of the design. The two PhCs are in essence the same but differ in the way to define the unit cells. Blue unit cell arranges the small air hole with a width of d 1 at the center, while red unit cell has the large air hole with d 2 at the center. The centers of the two holes respectively correspond to the inversion centers of the double periodic PhC. The sum of d 1 and d 2 equals to 0.5 a . (c) Band structures and wavefunctions at the band edges calculated for the PhC with the blue (left) and red (right) unit cell. The color of the band curve expresses its Zak phase (blue = π , red =0). A band inversion occurs when swapping the unit cells. The center panel shows the case for d 1 = d 2 = 0.25 a , exhibiting a Dirac point at the band edge.CC-BY · From the PDF
Figure 2 Numerical simulation results. (a) Calculated electric ( Ey ) field profiles for the nanocavities with different d 1s. A large modification in the mode extents as d 1 increases can be clearly seen. f denotes the normalized frequency of the confined mode. (b) Simulated normalized frequencies (red) and mode volumes (black) plotted as a function of d 1. The resonant frequencies are bound closely to the Dirac point, while the mode volumes vary largely as the PhC bandgap narrows by increasing d 1. (c) Computed Q factors, showing a peak value of ~ 60,000 at d 1=0.19 a . The quick decay of Q factor for d 1 > 0.19 a originates from the photon leakage from the finite-size simulation region, while the reduction for d 1 < 0.19 a is due to the light leakage into free space due to the tighter optical confinement.
Figure 2 Numerical simulation results. (a) Calculated electric ( Ey ) field profiles for the nanocavities with different d 1s. A large modification in the mode extents as d 1 increases can be clearly seen. f denotes the normalized frequency of the confined mode. (b) Simulated normalized frequencies (red) and mode volumes (black) plotted as a function of d 1. The resonant frequencies are bound closely to the Dirac point, while the mode volumes vary largely as the PhC bandgap narrows by increasing d 1. (c) Computed Q factors, showing a peak value of ~ 60,000 at d 1=0.19 a . The quick decay of Q factor for d 1 > 0.19 a originates from the photon leakage from the finite-size simulation region, while the reduction for d 1 < 0.19 a is due to the light leakage into free space due to the tighter optical confinement.CC-BY · From the PDF
Figure 3 Basic experimental characterization of the topological nanocavities. (a) Scanning electron microscope image of a fabricated nanocavity with d 1 = 0.19 a . (b) Measured PL spectra for the fabricated PhC nanobeams with different d 1 s. The colored curves are of topologically-nontrivial interfaces, while the black curves are of regular PhCs. Arrows indicate the spectral peak positions of the topological 0D edge modes (colored) and of the band edges (gray). The right panels show the close up spectra of the topological edge states. The black curves overlaid on the graphs are fitting. (c) Summary of the measured peak positions plotted as a function of d 1. The magenta data points are of the 0D confined modes, while the brown (dark green) data points are of the higher (lower) energy band edges. The error bar for each point expresses the standard deviation deduced from the measurement on ten samples with the same design. The solid lines show simulated peak positions by the three dimensional plane wave expansion method. The simulated curves are plotted with a constant offset for better comparison with the experimental results. (d) Position dependent PL intensities measured for the topological nanocavities with different d 1s. Tighter mode localization for smaller d 1, as expected from the numerical modeling, is demonstrated.
Figure 3 Basic experimental characterization of the topological nanocavities. (a) Scanning electron microscope image of a fabricated nanocavity with d 1 = 0.19 a . (b) Measured PL spectra for the fabricated PhC nanobeams with different d 1 s. The colored curves are of topologically-nontrivial interfaces, while the black curves are of regular PhCs. Arrows indicate the spectral peak positions of the topological 0D edge modes (colored) and of the band edges (gray). The right panels show the close up spectra of the topological edge states. The black curves overlaid on the graphs are fitting. (c) Summary of the measured peak positions plotted as a function of d 1. The magenta data points are of the 0D confined modes, while the brown (dark green) data points are of the higher (lower) energy band edges. The error bar for each point expresses the standard deviation deduced from the measurement on ten samples with the same design. The solid lines show simulated peak positions by the three dimensional plane wave expansion method. The simulated curves are plotted with a constant offset for better comparison with the experimental results. (d) Position dependent PL intensities measured for the topological nanocavities with different d 1s. Tighter mode localization for smaller d 1, as expected from the numerical modeling, is demonstrated.CC-BY · From the PDF
Figure 4 Laser oscillation from the topological nanocavity designed with d 1 = 0.19 a . (a) PL spectra measured with two different peak pump powers. For the low pumping power of 5 μ W, broad background emission from the QDs, spanning from ~ 900 nm to 1200 nm, dominates the spectrum. For the higher pumping power, the background is suppressed and the cavity emission peak in turn prevails. (b) Light-in-light-out plot for the emission peak of the 0D edge state. The black solid line is the fitting to the data points. Laser transition with a threshold peak pump power of 46 μ W is seen. (c) Logarithmic plots of the LL curve (red) and of the evolution of the intensities of the background emission (light green). The LL curve exhibits a mild S-shaped curve, which is typical for highβ lasers. The vertical dashed line indicates the threshold pump power. The background emission clamps above the laser threshold. The diagonal dashed line is an eye guide with a linear increase. The scattered data points above the threshold originate from the noisy PL spectra for the QD emission, due to strong cavity emission and the limited dynamic range of our detector. (d) Measured evolution of cavity linewidths as a function of peak pump power. The linewidths were extracted by fitting to the high resolution spectra with Lorentzian peak functions convolved with a Gaussian function representing the spectrometer response (~40 μ eV). Linewidths shows a significant narrowing of nearly an order of magnitude. The increase of the linewidth above the lasing threshold is likely due to heating in the nanocavity.
Figure 4 Laser oscillation from the topological nanocavity designed with d 1 = 0.19 a . (a) PL spectra measured with two different peak pump powers. For the low pumping power of 5 μ W, broad background emission from the QDs, spanning from ~ 900 nm to 1200 nm, dominates the spectrum. For the higher pumping power, the background is suppressed and the cavity emission peak in turn prevails. (b) Light-in-light-out plot for the emission peak of the 0D edge state. The black solid line is the fitting to the data points. Laser transition with a threshold peak pump power of 46 μ W is seen. (c) Logarithmic plots of the LL curve (red) and of the evolution of the intensities of the background emission (light green). The LL curve exhibits a mild S-shaped curve, which is typical for highβ lasers. The vertical dashed line indicates the threshold pump power. The background emission clamps above the laser threshold. The diagonal dashed line is an eye guide with a linear increase. The scattered data points above the threshold originate from the noisy PL spectra for the QD emission, due to strong cavity emission and the limited dynamic range of our detector. (d) Measured evolution of cavity linewidths as a function of peak pump power. The linewidths were extracted by fitting to the high resolution spectra with Lorentzian peak functions convolved with a Gaussian function representing the spectrometer response (~40 μ eV). Linewidths shows a significant narrowing of nearly an order of magnitude. The increase of the linewidth above the lasing threshold is likely due to heating in the nanocavity.CC-BY · From the PDF
Figure S1 Unit cells under consideration
Figure S1 Unit cells under considerationCC-BY · From the PDF
Figure S2 Existence and absence of topological interface states at the interfaces between several different combinations of 1D PhC nanobeams
Figure S2 Existence and absence of topological interface states at the interfaces between several different combinations of 1D PhC nanobeamsCC-BY · From the PDF

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Metadata

Authors
Ota, Y., Katsumi, R., Watanabe, K., Iwamoto, S., & Arakawa, Y.
Venue
Communications Physics
Publisher
Springer Science and Business Media LLC
Published
2018-11-22
Volume
1
Issue
1
ISSN
2399-3650
DOI
10.1038/s42005-018-0083-7
Cited by
239
References
4
Language
en
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Ota, Y., Katsumi, R., Watanabe, K., Iwamoto, S., & Arakawa, Y. (2018). Topological photonic crystal nanocavity laser. Communications Physics. https://doi.org/10.1038/s42005-018-0083-7