1. Introduction

Optical microresonators can support whispering-gallery modes (WGMs) with high quality (Q) factors due to the total internal reflection at the resonator surface. The properties of small mode volumes and high-Q factors for the WGM optical microresonators enable their wide applications in the photonic integrated circuits [1–3]. With the merits of compact size, low threshold and planar integration capability, WGM microlasers with circular shapes have been widely investigated as compact coherent light sources for on-chip optical interconnection [4–6]. The cavity modes were manipulated through parity-time symmetry-breaking and spatial gain profile engineering, and hence single-mode lasing was realized [7, 8]. To realize directional emission, deformed circular microresonators have been proposed and studied [9–13]. Square resonators have also been proposed to fabricate directional-emission microlasers due to their unique mode properties [14–20]. Single-mode lasing with tunable wavelengths was realized for the square microlaser with a waveguide connected to the middle-point of one side [21]. However, the mode Q factors of the square microresonators are limited by the inevitable radiation loss from the vertices of the square resonator. Recently, we have proposed a novel circular-side square resonator (CSR), with the flat-sides replaced by circular arcs as concave reflectors to enhance the mode confinement for the four-bounced WGMs [22]. The concave reflectors can converge the mode light rays along a narrow transmission path, which results in ultrahigh-Q WGMs due to the elimination of the radiation losses from the vertices. However, multiple peaks relative to high-order transverse modes appear in the lasing spectra, which limit the application of the CSR microlasers.

In this paper, we control the lasing spectra of the CSR microlasers by carefully designing the structure of the CSR. The waveguide connection angle is changed to optimize the mode Q factor and suppress the undesired high-order transverse modes. Dual-mode lasing CSR microlasers with controllable and variable mode intervals ranging from 0.54 to 5.4 nm are demonstrated experimentally, with the lasing spectra in good agreement with the simulation results. These results indicate that the CSR microlasers can be utilized for millimeter wave or terahertz wave generation by optical heterodyne technique [23]. In addition, low-threshold single-mode CSR microlasers are realized with a smaller resonator size and a slight deformation, which indicate an enhancement of mode confinement compared with the non-deformed square microlasers. Therefore, the lasing spectra of the CSR microlasers are successfully engineered by optimizing the size and the deformation parameter of CSRs.

2. Dual-mode lasing with variable mode intervals

2.1 Numerical simulation

Figure 1(a) shows a two-dimensional (2D) schematic diagram of the CSR surrounded by the bisbenzo-cyclobutene (BCB), where the flat sides (dashed lines) are replaced by circular arcs. The deformation parameter δ is defined as the distance between the flat side and the top of arc satisfying$\delta =r-\sqrt{r^2-{(a/2)}^2}$, where a is the flat-side length and r is the radius of the circular arc. Different from the structure given in [22], the waveguide angle is changed to make it parallel to the tangential of one circular side, which is used to optimize the mode Q factors and the output coupling efficiency. The characteristics of the transverse-electric (TE) modes are investigated by solving 2D wave equation in the x-y plane using the finite element method (FEM) (COMSOL Multiphysics 5.0). In the numerical simulation, the refractive indices of the CSR and BCB are set to 3.2 and 1.54, respectively, and the maximum grid size is set to one-eighth of the mode wavelength in each region to ensure the computation accuracy. The z-directional magnetic field $H_z(x,y,t)=\psi (x,y)exp(-i\omega t)$ can be obtained by the FEM, and the mode Q factor is then calculated from the complex eigen frequency ω as Q = Re(ω)/|2Im(ω)|.

 

Fig. 1 (a) Schematic diagram of the 2D circular-side square microresonator. (b) Simulated mode wavelengths and corresponding Q factors versus the deformation parameter δ. The 0th-order and 1st-order transverse modes are marked by circle and triangle symbols, respectively. The distributions of |H_z| for the (c) 0th-order and (d) 1st-order transverse modes as δ = 2.5 μm.

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For the CSRs with a = 16 μm and an output waveguide width w of 1.8 μm, the mode wavelengths and Q factors versus δ are plotted in Fig. 1(b) for the fundamental (0th-) and first (1st-) order transverse TE modes around 1550 nm. The initial mode wavelengths are 1544.1 and 1543.3 nm for the 0th-order and 1st-order transverse modes, respectively, as δ = 1.9 μm. Then the wavelengths red-shift with the increase of δ due to the enlarged resonator size, and the shift velocities are about 18.7 and 13.2 nm/μm for the 0th-order and 1st-order transverse modes, respectively. The difference results from the different optical path lengths caused by the deformation. The mode wavelengths are 1559.09 and 1553.86 nm for the 0th-order and 1st-order transverse mode, respectively, as δ = 2.7 μm. The wavelength interval between the 0th-order and 1st-order transverse modes increases from 0.8 to 5.25 nm as δ increases from 1.9 to 2.7 μm. The Q factors of the 0th-order and 1st-order transverse mode are 8.6 × 10⁷ and 3.6 × 10⁶, respectively, as δ = 1.9, then increase to 2.8 × 10⁸ and 1.1 × 10⁷ as δ increases to 2.1 μm, and finally drop to 6.6 × 10⁵ and 6.3 × 10⁴ as δ = 2.7 μm. The Q factors of second-order transverse modes are more than one order of magnitude lower than that of the 1st-order transverse modes, which indicate that high-order transverse modes are suppressed. Considering the vertical radiation loss, the Q factors of the two transverse modes will be close, which enables stable dual-mode lasing [20]. The magnetic field (|H_z|) distributions of the 0th-order and 1st-order transverse modes are shown in Figs. 1(c) and 1(d), respectively, as δ = 2.5 μm, where the fields in the output waveguide are magnified by ten times. The results show that the high Q modes are well confined with narrow beam width due to the converge ability of the circular sides, which can be regarded as concave mirrors. In addition, efficient light output can be obtained from the coupled waveguide.

2.2 Experimental results

The CSR microlasers are fabricated on the compressively-strained multiple-quantum-wells (MQWs) AlGaInAs/InP laser wafer with the same fabrication techniques as in [20]. The resonator patterns are transferred onto the SiO₂ layer using contact photolithography and inductively coupled-plasma (ICP) dry etching techniques, and the laser wafer is then etched to about 4.1 μm using the ICP technique again with the patterned SiO₂ layer as a hard mask. Figure 2(a) shows the scanning electron microscope (SEM) image of a CSR after InP ICP etching. After the planarization with BCB and a SiO₂ isolation layer deposition, a contact window on top of the CSR is opened by photolithography and ICP etching for current injection. Then Ti/Pt/Au and Ni/Ge/Au are deposited as the p- and n-electrode metals, respectively. Figure 2(b) shows the optical microscope image of a fabricated CSR microlaser.

 

Fig. 2 (a) SEM image of a CSR after ICP etching. (b) Optical microscope image of a fabricated CSR microlaser.

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The CSR microlasers with different δ are fabricated, while a and w are maintained at 16 and 1.5 μm, respectively. By butt-coupling a multi-mode fiber to the cleaving facet of the output waveguide, the CSR microlasers are measured on a thermoelectric cooler (TEC) with a fixed temperature of 288 K. For the CSR microlaser with δ = 2.7 μm, the threshold current is 8 mA and the maximum coupled power is about 15 μW, which indicate a poor waveguide coupling efficiency due to the excessive ideal Q value. Figure 3(a) shows the lasing spectrum of the microlaser at an injection current of 36 mA measured by an optical spectrum analyzer (OSA), which indicate a uniform dual-mode lasing with a side-mode suppression-ratio (SMSR) of 25.5 dB. The lasing peaks at 1566.91 and 1561.51 nm correspond to the 0th-order and 1st-order transverse modes, respectively. The mode interval is 5.4 nm, which agrees well with the simulation result of 5.23 nm. Figure 3(b) shows the measured lasing spectra for the CSR microlasers with δ from 1.9 to 2.5 μm, which indicate a purer spectrum than the results in [22]. Dual-mode lasing is realized for all the devices, with the SMSRs above 20 dB. Both the lasing wavelengths and the mode interval gradually increase with the increase of δ, which are consistent with the simulation results. The two modes can realize stable dual-mode lasing due to the totally different mode numbers. The wavelength intervals between the 0th-order and 1st-order transverse modes versus δ are depicted in Fig. 3(c) as the solid circles. The measured transverse mode intervals Δλ₀₁ are varied with δ at the rate of 5.9 nm/μm for the CSR microlasers as 1.9 ≤ δ ≤ 2.5 μm, which agrees well with the numerical result of 5.5 nm/μm depicted by the open squares.

 

Fig. 3 (a) Lasing spectrum of the CSR microlaser with δ = 2.7 μm at 36 mA. (b) Lasing spectra of the CSR microlasers at different δ. (c) Mode interval between the 0th-order and 1st-order transverse modes versus δ.

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3. Single-mode lasing

In this section, we demonstrate single-mode lasing for the CSR microlasers with smaller size. The square microlasers with a = 10 μm and w = 1.5 μm are considered, where the waveguide is connected to one vertex and the direction is parallel to the diagonal of the square. Figure 4 shows the emission spectra for the square microlasers with δ = 0, 0.1 and 0.2 μm, respectively. For the non-deformed square microlaser with δ = 0, the spectrum measured at 15 mA has apparent resonant peaks at 1514.5, 1537.8 and 1562.4 nm, with the longitudinal mode intervals of 23.3 and 24.6 nm, respectively. However, the full width half maximums (FWHMs) are about 1nm. We have measured three different samples and no lasing can be observed due to their low Q factors. For the CSR microlasers with δ = 0.1 and 0.2 μm, evident lasing is obtained at 2.8 and 2.2 mA with the FWHMs of 0.16 and 0.14 nm for the main peaks marked by circles, and the corresponding Q factors are 9.5 × 10³ and 1.1 × 10⁴, respectively. In fact, we find that the CSR microlasers with a slight deformation can lase easily compared with the non-deformed square microlasers by measuring several devices with the same parameters.

 

Fig. 4 Emission spectra of the CSR microlaser with a = 10 μm, w = 1.5 μm and δ = 0, 0.1 and 0.2 μm, at the current of 15, 2.8 and 2.2 mA, respectively.

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The lasing spectrum of the CSR microlaser with δ = 0.1 μm at 15 mA is plotted in Fig. 5(a), which shows a single-mode lasing at 1547 nm with a SMSR of 32.1 dB. Three longitudinal modes can be clearly observed, where the three narrow linewidth peaks at 1523.8, 1546.9 and 1570.9 nm are the 0th-order transverse modes. For comparison, the simulated mode wavelengths and Q factors obtained by FEM are plotted as open symbols, where the 0th-order, 1st-order and 2nd-order transverse modes are marked by circular, triangular and square symbols, respectively. The mode spacing obtained in experiment is smaller than the simulated value, as the dispersion is not considered in the numerical simulation using a fixed refractive index n [24]. In order to match the peak positions, the scale of top-X axis is slightly different from that of the bottom-X axis. The 0th-order modes have the highest Q factors to lase, which agree well with the experiment results. For the CSR microlaser with δ = 0.2 μm at 16 mA, the lasing spectrum is measured and plotted in in Fig. 5(b), which shows a single-mode lasing at 1552.5 nm with a SMSR of 36.2 dB. The Q factors of the high-order modes are greater than the values in Fig. 5(a), which are consistent with the FWHMs of the mode peaks in the experimental spectrum. The mode intervals Δλ₀₁ are 5.7 and 10.2 nm as δ = 0.1 and 0.2 μm, respectively. Therefore, low-threshold single-mode lasing laser can be obtained for the CSR microlasers with a smaller size and a slight deformation for enhancing mode confinement.

 

Fig. 5 Lasing spectra of the CSR microlaser with (a) δ = 0.1 and (b) δ = 0.2 μm. Top-X and right-Y indicate the simulated mode wavelengths and Q factors with the open symbols.

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4. Conclusion

In conclusion, we have designed CSR microlasers with output waveguide parallel to the tangential of one circular side, and demonstrated spectra engineering by adjusting the device size and deformation parameter. The circular sides can enhance the optical confinement and the mode interval simultaneously as concave mirrors. Dual-mode lasing with variable mode spacing is achieved by changing the deformation parameter, which can be used for the optical heterodyne THz wave generation. The devices need further optimization to achieve efficient waveguide output by comprehensively considering the material loss, fabrication process, and resonator structure. In addition, single-mode lasing is realized by reducing the resonator size and implanting a slight deformation to enhance the mode Q factors. The CSR microlasers with a robust output coupling scheme suitable for planar integration will be a versatile component in photonic integrated circuits for optical communication and storage.