Photonic Quantum Ring

Abstract

We report a quantum ring-like toroidal cavity naturally formed in a vertical-cavity-like active microdisk plane due to Rayleigh's band of whispering gallery modes. The √ T -dependent redshift and a square-law property of microampere-range threshold currents down to 2 µA are consistent with a photonic quantum wire view, due to whispering gallery mode-induced dimensional reduction.PACS number: 42.55. Sa, 42.60.Da For the last several years, there have been intensive developments of microdisk semiconductor lasers of whispering gallery(WG) modes for low-power and high-density photonic array applications. These efforts of earlier photo-pumped thumbtack-type WG lasers [1] have been evolving to photonic-wire lasers [2] and electro-pumped thumbtack-type WG lasers [3,4] of submilliampere threshold currents.In this letter, we demonstrate a cylindrical vertical-cavity surface-emitting laser(VCSEL)-like diode that exhibits WG modes with unusual photonic quantum ring(PQR) characteristics such as µA-range threshold currents and spectral √ Tdependence, in addition to the usual VCSEL mode. We will thus illustrate and analyze the two-threshold behavior of successive lasings, first the PQR and then the VC-SEL as well. Indeed, the quantum wire behavior of the PQR is vividly demonstrated in the √ T -dependent spectral peak shift data. We note that the quantum-ring-like WG modes are naturally formed in the circumferential Rayleigh band region [5] of the active microdisk of a regular multi-quantum-well VCSEL-like structure but without any intentional and real quantum ring patterning.The PQR device differs from the previous WG lasers [ [1][2][3][4]6] in that the vertical confinement is improved by the top and bottom DBR layers, and that stripe or segmented top electrodes are used for vertical output coupling. The metal-organic vapor-phase epitaxy-grown device employs a one-λ thick active layer with four 80 A Al 0.11 Ga 0.89 As quantum wells(QWs), whose details have been described elsewhere [8,9,12]. In the active disk plane, the PQR region is defined by Rayleigh's bandwidth, W Rayleigh = (φ/2)(1 − n ef f /n), where the WG mode occurs, which is well described in Ref. [7]: Rayleigh's annular band is defined by the active disk's radius R(= φ/2) for outer boundary and the inner reflection point r in = Rn M /n, where n is the refractive index of the active medium and n M is the effective refractive An exploded segment shows the effective toroidal structure of the PQR, where R is the index-guided outer limit and rin is the inner reflection limit which may also be reinforced by gain guiding. The radial evanescent field results from forward and backward helical traveling waves, and its intensity peaks at a distance t ≤ 1 µm from the outer boundary.The calculated profile of the annular WG emission based on Rayleigh's Bessel function analysis is shown in Fig. 1(a) for our device with R = 7.5 µm. The azimuthal mode number is rather large here, M = 2πRn ef f /λ = 188, and hence the 376 azimuthal peaks are not well distinguishable, unlike the i...

Photonic Quantum Ring Laser of Whispering Cave Mode

“…N 1D is the 1D transparency carrier density, τ the carrier lifetime, η the quantum efficiency, and I i stands for internal loss (Ahn et al, 1999;Kwon et al, 2006). The PQR formulae are now compared with the actual data in Fig.…”

“…A tremendous intensity build-up occurred after increasing injection currents, so that appropriate neutral density filters had to be used for intensity attenuation. PQR lasing occurs along the perimeter of the active disk called the Rayleigh bandwidth, 0.63 μm width for Φ = 20 μm (Ahn et al, 1999), while LED emission occurs in the central bulk region of the PQR mesa. A threshold of 28 μm (= 11 A/cm2), observed through ring pattern schemes as shown in Fig.…”

“…(Wiersig & Hentschel, 2008) On the other hand, when we employ a new micro-cavity of vertically reflecting distributed Bragg reflector (DBR) structures added below and above quantum well (QW) planes, say a few active 80Å (Al) GaAs QWs, a 3D toroidal cavity is formed giving rise to helix standing waves in 3D whispering cave modes (WCMs) as shown Fig. 1 (Ahn et al, 1999). The photonic quantum ring (PQR) laser of WCMs is thus born without any intentionally fabricated ring pattern structures, which will be elaborated later.…”

Hole emitter whispering galleries of photonic quantum ring

“…3, inset) [9]. Now the helical WG standing wave manifold, or more exactly double LaguerreGaussian helix modes, dynamically induces concentric PQRs for imminently recombinant carriers in the quantum well Rayleigh region.…”

“…To overcome the above bottleneck issues with micro-to-nano ampere emitter capabilities, we propose and analyze 3D WG lasers of helix mode, activated by recombinant photonic quantum rings (PQRs) naturally generated in the "concave or convex" WG region of active quantum well planes without any artificial etching for the ring definition. We have earlier reported on the PQR microresonators of concave 3D WG modes made of cylindrical mesas, or traditional micropillars with smoothly etched sidewalls, fabricated mostly from wafers consisting of a few 80 Å (Al)GaAs quantum well active planes between p-type top and n-type bottom GaAs/AlAs Bragg reflectors for vertical optical confinement [9]. As shown previously these devices exhibit ultralow threshold and transparency currents reducible to the micro-to-nano ampere regime, and thermal stabilities at operating temperatures due to T -dependent quantum wire spectral shift, which are crucial for mega-to-giga pixel chip operations, and also extendible to nanoemitter developments to enable the bottom-up nanosystem paradigm as discussed later.…”