1. Introduction

In recent years, subwavelength lasers have attracted a great deal of interest as they are promising components for applications in integrated photonic circuits, local chemical or biological sensing and imaging. Efforts have been carried on several fronts to reduce the laser sizes. Photonic crystal cavities provide subwavelength modal volumes, but their physical size must be several times larger than the wavelength in at least one spatial dimension [1]. Metallic structures present another approach of confining light on subwavelength scales by utilizing the surface plasmon resonances [2,3]. In previous research, metallic waveguides have been employed to realize subwavelength terahertz quantum cascade lasers [4], near-infrared metal coated nanocavity lasers [5], nanosphere plasmonic lasers [6] and nanopatch lasers [7] at cryogenic temperatures. By proper incorporation of low-loss dielectric into metallic structures, subwavelength metallo-dielectric cavity lasers were also demonstrated at room temperature under pulsed optical pumping [8]. Semiconductor disk cavities represent another candidate for subwavelength lasers by taking advantage of the high quality (Q) factors of the supported whispering-gallery modes. Microdisk lasers were first realized in the early 1990s for cavities with diameters larger than the emission wavelength [9,10], and recently disk lasers with diameters equal to and less than the lasing wavelength were demonstrated [11–13]. For small size subwavelength disk lasers [12,13], the cavity Q factors degrade rapidly [14,15], and also their underlying pedestals have restricted heat conduction due to the limited dimensions and/or low thermal conductivities [9]. These limited Q factor and thermal conduction render the laser operation in continuous-wave (CW) mode questionable. As such, previous small size disk lasers were reported to operate in pulsed mode only with the thermal effects avoided by using low duty cycle and short pump pulses [11–13].

In this paper, we examine the possibility of CW operation in subwavelength disk lasers. By using InGaAs/AlInAs heterostructures as the gain medium and optimizing the heat dissipation condition, we demonstrate the CW operation of subwavelength disk lasers at telecomm wavelength. A 1.49 µm diameter, 209 nm thick InGaAs/AlInAs disk is shown to lase in single-mode at a wavelength of 1.53 µm under CW optical pumping at 45 K.

2. Laser design and fabrication

The microdisks used in our experiments were fabricated on lattice-matched InGaAs/AlInAs heterostructures grown on InP substrate using solid-source molecular beam epitaxy (MBE) [16]. The designed layer structure is sketched in Fig. 1(a) , which is composed of six 9 nm-thick InGaAs quantum wells separated by 3 nm AlInAs barriers with two 60 nm-thick InGaAs cladding layers. The total thickness of the InGaAs/AlInAs layers is 209 nm. Electron beam lithography was used to define ~3 µm diameter PMMA circles on top of the sample, which acted as an etching mask. The sample was etched in an acid solution composed of HNO₃/HBr/H₂O with the ratio of 1:1:20. After wet-etching for ~40 seconds, which gives an etching depth of ~1.5 µm, disk cavities with diameters between 1.4 and 1.8 µm were formed. In order to avoid coupling of the optical mode into the InP substrate, selective wet-etching in a solution of HCl/H₂O with the ratio of 1:2 was conducted at room temperature for ~1.5 hours to remove the InP around and below the InGaAs/AlInAs disks. A scanning electron microscope (SEM) image in Fig. 1(b) shows the side-view of a representative disk. The disk diameter is 1.49 µm. Its sidewall is vertical and the surfaces are smooth; these features are advantageous for improving the cavity Q factor and minimizing scattering losses. The underlying InP pedestal forms a mountain-like shape with a rough surface. Such a shape is different from multi-faceted shapes reported for quantum cascade disk lasers using the same material system [17,18] due to different etching conditions and sample geometries. Figure 1(c) shows a top-view image of the disk. The pedestal is ~0.84 µm in diameter. This size is chosen as a compromise between effective heat sinking and prevention of optical mode coupling into the substrate.

 

Fig. 1 (a) Schematic epitaxial layer structure of our laser material. (b) Side-view and (c) top-view scanning electron microscope (SEM) images of an InGaAs/AlInAs disk on top of an InP pedestal.

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The effects of different pedestal sizes on the 1.49 µm diameter disk cavity are analyzed in Fig. 2 . We used Comsol Multiphysics to calculate the optical modes and the disk temperature under CW optical pumping. The optical mode calculation is based on the weak-form approach [19]. Assuming a refractive index of 3.5 [20] for the disk and 3.1 [21] for the InP pedestal, and using radiation-matching boundary condition, resonant whispering-gallery modes were calculated. For the temperature calculation, we used a 3D steady-state heat conduction model. The thermal conductivities of the disk and the InP pedestal were taken as 5 and 69 W/(m•K), respectively [22]. The thermal power in the disk is 1.4 mW/µm³, which corresponds to an optical pump intensity of approximately 418 W/mm² (slightly above the experimental laser threshold measured in Section 3). The substrate bottom surface is kept at a constant temperature of 45 K, and all other boundaries are treated as thermal insulation. The pedestal is approximated as a cylinder with a height of 1.5 µm. Figure 2(a) shows the optical mode confinement factor (defined as the fraction of the electrical field intensity |E|² confined in the disk), and the cavity Q as a function of the pedestal radius for a representative TE_1,5 mode. It is readily seen that as the pedestal radius increases beyond ~0.5 µm, the confinement factor drops from ~0.4 to 0.05, and the Q factor decreases from ~2000 to 270. This rapid reduction in confinement factor and Q is due to the mode leakage into the pedestal and the substrate as the pedestal size approaches the disk size. Therefore for good lasing properties, sufficiently small pedestal size is needed. However, for the point view of heat dissipation, which is important for CW laser operation as studied in this work, the pedestal serves as a heat sink, and it needs to be as large as possible. Figure 2(b) shows the maximum disk temperature for different pedestal radii. When the pedestal radius decreases below ~0.3 µm, the disk temperature dramatically increases up to ~500 K, which would prevent the laser operation. Considering these effects on the optical mode and the heat dissipation, the pedestal radius between ~0.3-0.5 µm is believed to be an optimum size for achieving CW laser operation. Our fabricated pedestal size as shown in Fig. 1(c) falls in this range. Additionally, the high thermal conductivity of the InP pedestal (~69 W/(m•K)) is more than twice of the thermal conductivity of AlGaAs pedestal in the GaAs-based disk lasers reported in Refs [11]. and [12], and thus enables more efficient heat dissipation in our devices.

 

Fig. 2 (a) Calculated optical mode confinement factor and cavity Q as a function of the pedestal radius for the 1.49 µm diameter disk. The inset shows the profile of magnetic field component normal to the disk plane for a 0.5 µm radius pedestal. (b) Calculated maximum temperature in the disk with different pedestal sizes. The inset shows a cross-section temperature distribution of the disk with a 0.5 µm radius pedestal.

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The microdisks were measured in a micro-photoluminescence (µ-PL) apparatus. The samples were mounted in a low-temperature cryostat cooled with liquid helium. A diode-pumped Nd:yttrium–aluminum–garnet (YAG) laser with relatively long emission wavelength of 1064 nm was chosen as the pump laser for minimizing heat generation. The pump light was focused by a 50 × microscope objective with a 0.42 numerical aperture and a working distance of 1.7 cm to a spot size of ~5 µm on top of a single disk. The scattered light emission from the disk was collected by the same objective and then directed to a Horiba TRIAX spectrometer with a Peltier-cooled InGaAs photodiode array for recording the spectrum. The measurements were performed under CW optical pumping.

3. Testing results and analysis

Figure 3 shows the emission spectra of the 1.49 µm diameter, 209 nm thick disk under different pump intensities at a heat-sink temperature of 45 K. At low pump intensities, spontaneous emission from electron-hole radiative recombination in both the quantum well region and the InGaAs cladding layers are measured in the wavelength range from 1350 to 1550 nm. When the pump intensity increases beyond 276 W/mm², a narrow peak appears at the wavelength of 1530 nm.

 

Fig. 3 Emission spectra of a 1.49 µm diameter, 209 nm thick InGaAs/AlInAs disk at different pump intensities between 11.2 and 477.2 W/mm². The spectra are vertically shifted for clear view.

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By fitting the emission peaks given in Fig. 3 to a Lorentzian function, the linewidths— defined as the full width at half maximum (FWHM)—are obtained and plotted in Fig. 4 a ) as a function of the reciprocal pump intensity. The linewidth decreases from 3.8 to 1.2 nm as the pump intensity increases from 276 to 477.2 W/mm². Figure 4(b) shows the spectrally integrated emission intensity as a function of the pump intensity. The curvature slope changes at the pump intensity of ~300 W/mm², which indicates a threshold behavior. These observed linewidth narrowing and threshold behavior suggest that the emission corresponds to laser action. This laser emission was observed at temperatures up to ~55 K for CW pumping, and ~70 K for optical chopped pumping with 50% duty cycle. The pulsed laser performance with low duty cycle and short pump pulses were not determined in this work as limited by the pump laser source.

 

Fig. 4 (a) Full width at half maximum (FWHM) of the emission peak versus reciprocal pump intensity. (b) Spectrally integrated intensity versus pump intensity. The two solid lines are fitted linear curves.

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In order to understand the lasing behavior, we measured the photoluminescence from an unpatterned sample without a microdisk cavity. This spectrum is shown in the black curve in Fig. 5(a) . There are two emission peaks. The one covering wavelengths between ~1450-1600 nm is attributed to the emission from the InGaAs cladding layers, since this emission range agrees with the bandgap of bulk InGaAs at ~0.82 eV (1512 nm) [22]. The second peak covering shorter wavelengths between ~1350-1500 nm is attributed to the emission from the InGaAs/AlInAs quantum wells, which have sizes resulting in quantum-confinement and therefore blue-shifted emission. The observed lasing at 1530 nm for the subwavelength disk laser with diameter of 1.49 µm, shown in the red spectrum in Fig. 5(a), appears at the longer wavelength shoulder of the InGaAs cladding emission peak. Therefore, the main contribution to optical gain is believed to be from the InGaAs claddings for this subwavelength laser. For a second disk laser with slightly larger diameter of 1.54 µm, its emission at 1454 nm as given by the blue spectrum appears at longer wavelength shoulder of the quantum well emission, which indicates that the quantum wells mainly contribute to the optical gain for this slightly larger disk. Therefore both quantum wells and cladding layers in our structure can provide optical gain for the lasing depending on the resonant wavelength position of the cavity modes.

 

Fig. 5 (a) Photoluminescence of the laser material without cavity (black) and lasing spectra of two microdisks with diameter of 1.49 (red) and 1.54 (blue) µm. The triangles, referred to the right y-axis, are the calculated Q factors for TE_1,6 and TE_1,5 modes in the 1.49 (red) and 1.54 (blue) µm diameter disks. (b) Calculated spatial distribution of electrical field radial component in the cross-section of the disk and pedestal, and (c) magnetic field normal component in the disk plane for the TE_1,5 mode in the 1.49 µm diameter disk.

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We next identified the optical modes using finite element analysis as described in Section 2. Here we only considered TE-polarized modes with first radial mode number and different azimuthal mode number (m), which have the highest Q factors and are most favorable for lasing as suggested in previous studies on microdisk lasers and cavities [14,15]. The calculated resonant wavelengths and radiation-limited Q factors for different TE_1,m modes, which have overlap with the spontaneous emission, are plotted as triangle symbols in Fig. 5(a) for the disks with different diameters of 1.49 and 1.54 µm. As seen from the red triangles for the 1.49 µm diameter subwavelength laser, the TE_1,5 mode has a resonant wavelength of 1522 nm, which matches well with the measured lasing wavelength at 1530 nm as given by the red spectrum, and thus is attributed as the lasing mode. Figure 5(b) shows the calculated spatial distribution of electrical field for this TE_1,5 mode, where the field is mostly concentrated on the disk edge with little penetration into the InP pedestal. The effective modal volume is calculated as ~2.12(λ/n)³. Figure 5(c) shows the magnetic field profile in the disk plane, where five field maxima and five minima are present. The calculated Q for this TE_1,5 mode is ~1800, which is more than three times of the experimental Q ~510 as estimated by the lasing linewidth near threshold. This large discrepancy is likely due to the roughness scattering, especially on the pedestal as evidenced by rough surface shown in Fig. 1(b) and the fairly large amount of field distribution near the pedestal surface as shown in Fig. 5(b). A further optimization on the pedestal fabrication would improve this surface scattering. For the slightly larger disk with diameter of 1.54 µm, the lasing mode is assigned as TE_1,6 mode as given by the blue triangle in Fig. 5(a), whose calculated resonant wavelength is 1410 nm and is in reasonable agreement with the observed lasing at 1454 nm as given by the blue spectrum.

Also shown in Fig. 5(a) is that as the azimuthal mode number m decreases from 6 to 5, the calculated Q factors quickly drop from ~6000-10000 to ~1800-2600, which is in agreement with the exponential decay of Q factor with decreasing m as suggested in previous studies [14,15]. For even smaller m of less than 5, our calculated Q factor is less than ~500. Considering this dramatic decrease in Q factor with decreasing m, the TE_1,5 mode is believed to be the most promising cavity mode for further performance optimization in subwavelength lasers since it allows for subwavelength device dimension in a cavity with relatively high Q factor on the order of 10³, approximately one order magnitude higher than the Q factors of the metallic structures studied in previous research [4–7]. With further optimization in the layered structure for better carrier confinement and for matching the TE_1,5 mode with the quantum well emission, we expect to improve the laser properties for high temperature and possibly electrical injection operation. Another aspect which is of interest about the subwavelength disk lasers is their output power. For the disk laser studied in this work, the measured optical power into the collection objective placed on top of the disk is ~140 pW at a pump intensity of ~477 W/mm². As the disk cavity radiates in a wide range of solid angles with the major fraction in the disk plane and small fractions into the substrate and the disk vertical direction, developing directional emission cavities and integrated laser array would be a promising approach for scaling up the laser power.

4. Conclusion

By using an InGaAs/AlInAs layered structure on an InP substrate and optimizing the heat dissipation condition, subwavelength microdisk lasers have been demonstrated at telecom wavelength under CW optical pumping and at a heat-sink temperature of 45 K. The spectral narrowing and threshold behavior were presented as evidences of the lasing action. Our simulation indicates that the lasing mode is the TE_1,5 whispering-gallery mode with a modal volume of ~2.12(λ/n)³. The InGaAs cladding layers were shown to contribute to the optical gain in the subwavelength laser.