Chiral germanium micro-gears for tuning orbital angular momentum

Abstract

Group IV light sources with vertical emission and non-zero orbital-angular momentum (OAM) promise to unlock many novel applications. In this report, we demonstrate cylindrically symmetrical germanium micro-gear cavities, fabricated by etching a grating around the circumference of standard micro-disks, with periods ranging from 14 to 22. Photoluminescence (PL) measurements were done to identify the confined whispering-gallery modes (WGM). Finite-difference time-domain (FDTD) simulations were conducted to map the resonant modes to their modal profiles and characteristics. Vertical emission of WGMs with non-zero OAM was demonstrated, with a clear dependence of the OAM order ($$\ell$$ ℓ ) on the WGM azimuthal order and the number of micro-gear grating periods. As the chirality, or the direction of rotation, is not controlled in a symmetrical cavity, we propose introducing staircase or triangular-shaped gear periods resulting in an asymmetry. By choosing the diameter, number of periods, and the asymmetrical direction of the gear-teeth, it is possible to generate OAM signals with certain wavelength, OAM order and chirality.

Quantum commutation relationship for photonic orbital angular momentum

“…Then, we have applied the ladder operation to the input, as l+ Ψ 0 0 (r, ϕ, z), and we have calculated the amplitude and the phase of the output, as shown in Figures 1C, D. We confirmed the typical doughnut shape in the intensity [5,6,[8][9][10][11][12][13], while the left vortex is confirmed for increasing the phase along the counter-clock-wise direction. The phase singularity is found at the centre of the mode, where the intensity vanishes.…”

“…We also realise that the mode is degenerate with another mode with the opposite chirality of the right vortexed state, |R, m〉 |Ψ −m 0 〉. Then, according to the quantum mechanical superposition principle, we consider the superposition state between orthogonal states of |L, m〉 and R, m〉, which forms the SU(2) states [2,3,9,9,10,13,[36][37][38][79][80][81][82][83][84][85][86][87][88]. The generators of rotation in su(2) Lie algebra [89][90][91][92]…”

“…However, this elegant theoretical framework of angular momentum is less trivial in applying to a photon [5][6][7][8][9][10][11][12][13], since a photon is usually uni-directionally propagating (say, along z). Therefore, the apparent spherical rotational symmetry is absent for a photon, such that the situation is rather different from that of an electron confined in a spherically symmetric 3D space.…”

“…Therefore, the apparent spherical rotational symmetry is absent for a photon, such that the situation is rather different from that of an electron confined in a spherically symmetric 3D space. The propagation direction of a photon sets a natural quantisation axis; along the propagation direction, the angular momentum operator, Lz , is successfully obtained by the classical analogue using the Poynting vector [5][6][7][8][11][12][13][14]. However, angular momentum operators along the directions perpendicular to the propagation direction (x-y plane) are not defined uniquely in a gauge-invariant way [6][7][8].…”

Проявление анизотропии интерфейсов в квантовых ямах CdTe/CdZnTe

“…Несмотря на ширину запрещенной зоны, близкую к оптимальной, наибольшая на сегодняшний день эффективность преобразования энергии в солнечном элементе CdTe, достигнутая с использованием поликристаллического CdTe, составля-ет 21% (это намного меньше предела Шокли-Квиссера ∼ 32% для однопереходной ячейки). Исследования показывают, что включение барьера Cd 1−x Mg x Te в структуру солнечного элемента может улучшить напряжение холостого хода [4] и, в конечном счете, эффективность элемента.…”