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Abstract
A waveguide-connected deformed circular-side triangular microresonator is proposed and fabricated. Room temperature unidirectional light emission is experimentally demonstrated in the far-field pattern with a divergence angle of 38°. Single mode lasing at 1545.4 nm is realized at an injection current of 12 mA. The emission pattern changes drastically upon the binding of a nanoparticle with radius down to several nanometers, predicting applications in electrically pumped, cost-effective, portable and highly sensitive far-field detection of nanoparticles.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Whispering-gallery mode (WGM) optical microcavities owing high quality (Q) factors and small mode volumes provide an ideal platform for the exploration of novel physical phenomena including exceptional points [1–3], nonreciprocal light transmission [4,5], and symmetry breaking [6,7]. At the same time, WGM microcavities have found a wide range of practical applications such as nonlinear optics [8–11], cavity quantum electrodynamics [12,13], highly sensitive bio/chemical sensing [14–18], all-optical flip-flops [19,20], and - in particular - microlasers [21–23]. Up to date, WGM microlasers of various shapes have been realized including microspheres [24,25], microdisks [26,27], microtoroids [28,29], and so on.
However, light emission is isotropic in a traditional WGM microlaser due to rotational symmetry. To realize efficient extraction and collection of light, the emission should be tailored into narrowly defined directions. Highly directional or even unidirectional light emission has been reported in microcavities with defects or boundary deformation, such as the limacon cavity [30], the circular resonator with a point scatterer [31], the shortegg cavity [32], the D-shaped microcavity [33], the THCS-type microcavity [34], etc. The Q factors reduced drastically for cavities with defects, which limits the potential application. Nevertheless, the chiral symmetry is not destroyed for those cavity modes that contain both clockwise (CW) and counterclockwise (CCW) modes.
Semiconductor polygonal microcavities, including regular triangle, square and hexagon microcavities, represent another kind of deformed microcavity. Directly connected with a waveguide, directional output has been reported with semiconductor polygonal microcavities [35–37], benefiting the integration with other optoelectronic devices. Unlike the limacon microcavity which provides an ideal platform for the study of ray dynamics and chaos, the mode field distributions within the semiconductor polygonal microcavities are much simpler and more predictable. By substituting the straight sides with circular sides, light can be concentrated at the midpoints of the arc-edges, reducing the field distribution near the corners [38,39]. Chirality plays a key role for the applications of directional light emission [40], all-optical flipflops [19,20], and nonreciprocal light propagation [4,5]. Recently, unidirectional emission with chirality approaching 1 has been theoretically proposed in a deformed circular square resonator [41]. However, the scheme is only suitable for materials with refractive index ratio (the ratio of the refractive index n of the cavity material to the peripheral limiting material) around 2.08. In this letter, for the widely adopted cavity material of AlGaInAs quantum wells, a waveguide-connected deformed circular-side triangular microresonator (CTM) is designed and fabricated. Unidirectional light emission with chirality close to 1 is experimentally reported in the far-field pattern with a divergence angle of 38°, and the mode Q factor is 105 for the fundamental mode. Numerical simulation predicts sharp change of the far-field emission pattern upon the adsorption of nanoparticles. Direct integration of the triangular microresonator and the waveguide provides a convenient and robust scheme not only for unidirectional light emission but also for far-field nanoparticle detection based on chirality [42]. The advantages of electrical pumping, simple structure, and low-cost may greatly inspire the development of integrated portable sensing devices.
2. Numerical simulations
The proposed circular-side triangular microresonator is shown in Fig. 1(a). The microcavity with straight side length a is fabricated on a InP wafer, laterally confined by air. The radii of the three circular-sides marked by 1, 2, and 3 are r1, r2, and r3. The deformation parameter ${\delta} \;\ =\ \;\ {r}\ -\ \sqrt {{{r}^\textrm{2}}\textrm{ - }{{a}^\textrm{2}}\textrm{/4 }}$ denotes the distance from the straight side to the top of the circular side. The resonator is connected to a waveguide with width w and length l.
Fig. 1. (a) Schematic diagram of the waveguide connected circular triangular microresonator laterally confined by air. A, B, and C represent the three vertices. The radii corresponding to the three circular sides marked by 1, 2, and 3 are r1, r2, and r3. The straight side length is a. $\mathrm{\delta }$ is the deformation parameter. (b) Poincaré SOS of the CTM with a = 15 µm, r1= 14.5 µm, r2 = r3 = 15.5 µm.
To predict the light emission pattern, ray dynamics is calculated and the Poincaré surface of section (SOS) is depicted in Fig. 1(b) for the asymmetric deformed CTM. Whenever the light ray hits the cavity boundary, the distance S from vertex A along the arc in the counterclockwise direction and the corresponding reflection angle ${\chi}$ are recorded. Smax denotes the perimeter of the CTR. The position S/Smax = 0 corresponds to vertex A. The red horizontal dashed line given by $\mathrm{sin}\chi \;\ =\ {{n}_\textrm{1}}/{{n}_\textrm{2}}$ shows the critical condition for total internal reflection. The refractive indices are n1 = 1 and n2 = 3.2 for the surrounding air and the InP based microcavity, respectively. 360 light rays with random initial conditions above the red line are traced. From the perspective of phase space, three islands at S/Smax = 0.1685, 0.4955 and 0.8321 corresponding to reflections from the arc sides 2, 3 and 1 are imbedded in the chaotic sea, shown in Fig. 1(b). Only the light rays below the red line can escape. It should be noted that for a deformed CTM with r1 < r2, r3, light emits only from the arc side 1 [43]. The waveguide is located in the chaotic sea between the two stable islands as shown by the vertical blue dashed lines in Fig. 1(b), causing asymmetric scattering of the light rays in the chaotic region. Correspondingly, the chirality in the chaotic sea is passed to the stable islands through the tunneling effect.
Finite-element method (FEM, COMSOL Multiphysics 4.3b) is applied to simulate the electromagnetic field distribution of the microresonator. Two-dimensional simulation in the x − y plane with the effective refractive index neff has been verified as a reasonable simplification for such whispering gallery mode microcavities [2,38]. Only the TE modes are simulated considering the transverse-electric (TE)-dominant gain in the compressively-stressed AlGaInAs/InP multiple quantum wells epitaxial wafer. The perfectly matched layer (PML) is applied to absorb the outgoing waves by surrounding the region of interest by a layer of virtual domains with the boundary condition of perfect electric conductor. The eigenfrequency module was applied to solve the resonant frequencies and field distributions of the modes. The smallest mesh sizes of the cavity and the surrounding air are set to be λ/neff/20 and λ/10, respectively, where λ = 1550 nm. The partial differential equation can be written as
Mode field distributions |Hz| of the fundamental modes and the corresponding far field patterns are illustrated in Fig. 2 for three CTMs with different parameters. The eigenfrequencies are 194.58 THz, 195.85 THz and 195.85 THz in Figs. 2(a), (c) and (e). For the symmetric CTM with r1 = r2 = r3 shown in Fig. 2(a), light escapes from the midpoints of all the three circular sides in both clockwise (CW) and counter-clockwise (CCW) directions due to rotational symmetry, resulting in the far-field emission pattern in Fig. 2(b). For the asymmetric CTM with r1 < r2 = r3 (Fig. 2(c)), rotational symmetry is partially broken. As a result, light rays escape only from the arc side 1, but still in both the CW and CCW directions. Correspondingly, the CW and CCW modes exit from the midpoint of the arc edge 1 at angles of 15° and 165° as shown in Fig. 2(d). Special notice should be paid to the waveguide-connected asymmetric CTM with r1 < r2, r3 where unidirectional light emission only in the CW direction is obtained (Fig. 2(e-f)). By connecting a waveguide at vertex A, light emission in the CCW direction is reflected back by the waveguide and interacts with the CW mode in the cavity, enhancing the CW emission. The FEM simulation results agrees well with the prediction from ray dynamics.
Fig. 2. Near field and far field emission patterns of the fundamental TE mode in the circular sided triangular microcavity with a = 15 µm. (a-b) For the symmetric CTM with r1 = r2 = r3 = 15.5 µm, light escapes from the three sides in both clockwise (CW) and counter-clockwise (CCW) directions. (c-d) For the asymmetric CTM with r1 = 14.5 µm, r2 = r3 = 15.5 µm, light escapes in both CW and CCW directions only from the arc side 1. (e-f) For the waveguide connected asymmetric CTM with r1 = 14.5 µm, r2 = r3 = 15.5 µm, unidirectional light emission only in the CW direction is obtained. The width and length of the waveguide are 1.5 µm and 4.5 µm, respectively.
The emission pattern can also be explained by expanding the wave function in cylindrical harmonics,
Fig. 3. (a) $\textrm{|}{\mathrm{\alpha }_{m}}{\textrm{|}^\textrm{2}}$ of different angular quantum numbers for a CTM with and without a connecting waveguide. a = 15 µm, r1 = 14.5 µm, r2 = r3 = 15.5 µm. (b-c) Husimi distribution map in a deformed CTM without waveguide (b) and connected to a waveguide with width w = 1.5 µm, length l = 4.5 µm (c).
By designing the cavity parameters, the mode distribution and the light emission pattern can be engineered. The directivity parameter U describes the directionality of the far-field distribution
where I(θ) is the far-field distribution intensity at the polar angle θ. Influences of the length l and width w of the waveguide on the mode quality factor Q and the directionality U are studied and the results are illustrated in Fig. 4. With the increase of l, Q remains above 105 and changes within less than 10%. With the increase of w, Q increases while U decreases. U remains at about 0.733 for the wide range of 4 µm < l < 6 µm and 0.5 µm < w < 3.5 µm, indicating a high tolerance for device fabrication.Fig. 4. Q factor and directionality under different values of waveguide length l (a) and waveguide width w (b) in a waveguide-connected CTM with a = 15 µm, r1 = 14.5 µm, r2 = r3 = 15.5 µm.
When a nanoparticle adsorbs to the boundary of the microcavity, both the chirality and the far field emission patterns will change as shown in Fig. 5, promising application in ultrasensitive nanoparticle detection based on far field pattern. The refractive index of the nanoparticle is set to 1.5 to simulate the situation of polystyrene and most biological particles. The parameters of the resonator are set to be a = 15 µm, r1 = 14.5 µm, r2 = r3 = 15.5 µm, l = 4.5 µm, w = 1.5 µm. Drastically different values of chirality are expected when the nanoparticle binds at different positions. Three vertices A, B, C are marked both in the figure and the inset of Fig. 5(a). The most evident change happens when θ = 68.1°, corresponding to the hot spot of mode field distribution as shown in Fig. 2(e). Backscattering induced by the nanoparticle also influences the Q factor. To achieve the highest sensitivity, the nanoparticle is supposed to bind to the hot spot. The far field emission pattern and corresponding electromagnetic field distribution change with the adsorption of nanoparticles with different sizes, as can be found in Fig. 5(b). When there is no nanoparticle, unidirectional light emission in CW direction is obtained; when a nanoparticle with r = 6 nm adsorbs, bidirectional emission happens; when r = 9 nm, bidirectional emission with almost equal CW and CCW intensity is realized; when r = 12 nm, CCW mode at the emission angle of 165° dominates.
Fig. 5. (a) Chirality and Q factor change with the adsorption of nanoparticle with radius of 8 nm. The inset is the structure of the CTR with a nanoparticle. (b) Far-field emission patterns and corresponding near-field mode distribution under different nanoparticle sizes.
3. Experimental results
Waveguide connected deformed circular-side triangular microcavities are fabricated using the AlGaInAs/InP multiple quantum wells (MQWs) wafer. The straight length is a = 15 µm and three circular side radii are r1 = 14.5 µm, r2 = r3 = 15.5 µm. The width and length of the waveguide are w = 1.5 µm and l = 4.5 µm. The active region consists of six compressively strained 6-nm-thick quantum wells and seven 9-nm-thick barrier layers, sandwiched between two 100 nm AlGaInAs separate confinement layers. Contacting photolithography and inductively coupled plasma (ICP) etching techniques are employed to transfer the microcavity patterns onto the SiO2 layer. Smooth and steep sidewalls with a deep etching depth of 4.6 µm are obtained by a second ICP etching process to ensure significant optical confinement [46]. A 150-nm SiO2 layer is deposited to prevent oxidation of the active layer. Afterward, a Ti/Pt/Au p-electrode is deposited by e-beam evaporation and lift-off process, and an Au/Ge/Ni metallization layer is deposited by magnetron sputtering as the n-electrode. To benefit light emission, the p-electrode is designed graphical to ensure that the side wall of the emitting edge (arc side 1) is free of metal coverage. Scanning electron microscope (SEM) image of the deformed CTR laser after ICP etching is shown in Fig. 6(a), and the microscopic image is presented in Fig. 6(b).
Fig. 6. (a) SEM image of the circular side triangular microlaser after ICP etching. (b) Microscopic image of the CTM with p-electrode. (c) Integral ball output power and voltage versus continuous-wave injection current. The inset shows the wavelength of the main lasing mode versus the injection current. (d) Lasing spectra at injection currents of 4, 6, and 12 mA. The inset shows the detailed spectra at 4 mA near the wavelength of 1543.15 nm.
Lasing characteristics for the proposed CTR laser at the thermoelectric cooler (TEC) temperature of 287 K are illustrated in Figs. 6(c-d). Fig. 6(c) shows the output power P and the voltage V versus the injection current I. The threshold current is 4 mA with a threshold current density of 2.5 kA/cm2, and the maximum power coupled to a multimode fiber (MMF) is 46 µW at 12 mA. For I below threshold, slight blue shift happens due to the increase of carrier density. The main lasing mode has a red shift from 1543.29 to 1545.41 nm as I increases from 5 to 12 mA, as plotted in the inset of Fig. 6(c). The redshift rate is 0.3 nm/mA, and the corresponding temperature rise is about 18.4 K from 5 to 12 mA based on the red shift rate of 0.115 nm/K [47].The red-shift is mainly caused by the heating effect of the injection current due to the saturation of the carrier density above the threshold. Detailed lasing spectra for $I\; = \; 4,\; 6$ and $ 12\; \textrm{mA}$ are plotted in Fig. 6(d). At the threshold current of 4 mA, the measured FWHMs of the lasing mode is 0.13 nm at the wavelength of 1543.15 nm, corresponding to an actual Q factor of 1.19 × 104. The slight degrade from the simulated value may result from the vertical radiation loss or the loss induced by the roughness of the cavity side wall. At the injection current of 12 mA, single-mode lasing with the side mode suppression ratio (SMSR) of 28.2 dB is realized. The longitudinal mode interval around 1550 nm is 19.8 nm. The free spectral range of the deformed CTR is 23.3 nm. The transverse mode interval in simulation is 3.37 nm which is consistent with that in experiment, which reveals that the experimentally observed mode is localized on the period-3 islands chain.
The far field light emission pattern is illustrated in Fig. 7. The microcavity is fixed on a AlN submount, and the detector rotates along the cavity boundary at the distance of 9 cm away. Fig. 7(b) is the detailed experimental far field pattern for I = 12 mA. Unidirectional light emission from arc side 1 with a divergence angle of about 38° is obtained. Slight deviation between the simulation and experimental far field emission patterns may be induced by the unavoidable roughness during the fabrication process.
Fig. 7. (a) Schematic diagram of the experimental far field light emission test. (b) Experimental (black) and theoretical (red) far field pattern at the injection current of 12 mA.
4. Conclusion
We have demonstrated both theoretically and experimentally that a waveguide connected deformed circular triangular microresonator can realize unidirectional laser emission with high chirality. By designing ${{r}_{{1\; }}} \ne {\; }{{r}_\textrm{2}}{,\; }{{r}_\textrm{3}}$, rotational symmetry is broken and light emits only through the arc side $\textrm{1}\; $ but in both CW and CCW directions. The connecting waveguide improves the chirality drastically through backscattering of the CCW mode component. Unidirectional light emission from arc side 1 only in the CW direction is predicted from ray dynamics, FEM simulation and wave analysis. Experimentally, unidirectional light emission with a divergence angle of 38° is obtained, and single mode lasing with high SMSR is realized. The experimental emission patterns agree with the theoretical predictions well. The simulated far field emission pattern of the CTM changes drastically with the adsorption of a nanoparticle with radius down to several nanometers, predicting applications in highly sensitive bio/chemical sensing and nanoparticle detection. Compared with previous reports on single nanoparticle detection based on microcavities, this scheme can remove the dependence of expensive tunable lasers with narrow linewidth. Moreover, far field detection eliminates the need for evanescent coupling and optical spectrum analyzer. This research will shed light on unidirectional laser sources. The priorities of electrically driven, simple structure of only a single microcavity, together with far-field detection promise an efficient scheme for low-cost, integrated, and highly sensitive optical sensor.
Funding
National Key Research and Development Program of China (2021YFB2800600); National Natural Science Foundation of China (12274403, 11974341, 11704375).
Disclosures
The authors declare no conflicts of interests.
Data Availability
Data supporting the findings of this study are not publicly available at this time but may be obtained from the authors upon reasonable request.
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