1. Introduction

Ultrafast lasers are a topic of focus in quantum electronics because of their wide-ranging applications in military, scientific, medical, and industrial field [1–3]. Since the 1960s, numerous approaches have been proposed and successfully demonstrated to construct mode-locked lasers [4–6]. Compact and low-cost passively mode-locked lasers based on saturable absorbers (SAs) have become crucial tools to generate ultrafast laser pulses with pulse widths ranging from picoseconds to femtoseconds [7–9]. In general, saturable absorption (SA) is a special nonlinear phenomenon that quenches the optical absorption under high-intensity light. The properties of SAs, such as their modulation depth and saturation intensity, influence the amplitude and shape of the incident light. Consequently, Q-switching or mode-locking can be realized. Layered SAs have been a noteworthy topic since graphene was first used in a pulsed fiber laser in 2009 [10]. The successes with graphene encouraged researchers to investigate the photonic applications of other 2D materials [15].

In recent years, some 2D materials (e.g., transition metal dichalcogenides [11,12], black phosphorous [13,14], Antimonene [16] and MXene [17]) have been successfully used as SAs in ultrashort pulse lasers [18]. Compared with the above-mentioned materials which the saturable intensities were at least up to MW/cm², topological insulators (TIs) possessed ultralow saturation intensities (below 1 kW/cm²) result from bulk state quickly saturation [19]. The ultrasensitive optical nonlinearity led to over-saturation behavior as the pump power increases and limited the application in pulse lasers. However, by employing proper cavity engineering to prevent over-saturation, the first continuous-wave (CW) mode-locking solid state laser based on Bi₂Te₃ sheet was successfully demonstrated with a repetition rate of approximately 1 GHz [20–21]. Of note, TIs exhibit long-term stability and special properties due to their intrinsic bulk states, which typically have ultrafast relaxation time (about few ps) [22]. In addition, short pulse mode-locking laser with graphene-Bi₂Te₃ heterostructure absorber was realized, and the pulse duration can reach as narrow as hundreds of fs [23]. With careful lasing design, Bi₂Te₃ (or TIs) can be a potential material for mode-locked light sources with very high repetition rates and ultra-short pulse.

Recently, mode locking lasers with GHz-level repetition rates have been realized and shown their role for application [24]. In addition, by using the techniques of harmonic or rational harmonic mode-locking (HML/RHML), tens of GHz operation were also reported [25–27]. However, compared with typical mode-locking approaches, the pulse quality of the RHML approach is limited. Fortunately, rapid improvements in semiconductor processes have increased the practicality of microcavities, which has led to mode spacing of tens or hundreds of GHz within cavities. Therefore, repetition rates at the GHz or even higher levels have become an important issue and have attracted significant attention [28–30].

Among the various approaches, high-quality microdisk cavity lasers have been of particular interest for applications in photonic integrated circuits due to their promising and versatile optical functions [31–33]. Moreover, cavities with whispering gallery modes (WGMs) have become one class of excellent candidates for compact semiconductor lasers for chip-scale integrated systems. For mode-locking operation, Matsko et al. demonstrated the first active mode-locking WGM laser with a repetition rate at tens of GHz [34]. Unfortunately, there has not been additional progress regarding WGM-based pulsed lasers.

Generally speaking, without tip or waveguide coupling, the pumping efficient is somehow low in microdisk cavity laser. Consequently, the output of WGM is weak as well. This indicates that the saturable intensity of the SAs covered on the microdisk should be low enough for successfully modulating the intensity inside the microdisk to achieve the requirement for mode-locking. In this study, by using Bi₂Te₃ as ultrasensitive SAs, we investigated InGaAsP multiple quantum wells (MQWs) WGM-locking behavior. Under optical excitation, multi-lasing with equal spectral spacing was observed and attributed to mode-locking behavior. A repetition rate over 4 THz was accordingly estimated from the spectrum. Additionally, clear degenerate breaking was observed with a frequency shift of approximately 1 THz. To the best of our knowledge, this is the first demonstration of a passively mode-locked behavior WGM, which may find applications in dual-comb devices.

2. Device fabrication

To demonstrate Bi₂Te₃ SA with WGMs, a microcavity laser with two elements, a high-quality microdisk cavity laser as the coherent photon source and a Bi₂Te₃ cluster as the absorber, was prepared. The microdisk cavity was implanted in an InGaAsP layer on the top surface of a sapphire substrate. The InGaAsP layer contained four quantum wells, and the device was designed to support gain in the near-infrared optical communication wavelength regime. The InGaAsP MQW epitaxial wafer was directly bonded on a single-side-polished sapphire wafer at 480°C. The original InP substrate was removed via wet etching in an HCl solution. It provides better optical mode confinement in InGaAsP MQW gain medium due to high-refractive-index InGaAsP placed on low-refractive-index sapphire substrate. Moreover, the high thermal conductivity sapphire substrate supported a higher excitation intensity tolerance, which enabled the lasing cavities to operate under continuous wave (CW) laser excitation at room temperature [30].

For fabricating the lasing cavities, a 240-nm- thick silicon nitride (Si₃N₄) layer was first deposited on the InGaAsP MQW sapphire wafer as a hard etching mask for the plasma-enhanced chemical vapor deposition. The microdisk patterns were defined through electron beam lithography with a poly-methyl methacrylate resist (PMMA, 950 A5, MicroChem) at a 30 keV accelerating voltage. Next, a two-step reactive ion etching was used to transfer the microdisk pattern from the PMMA to the Si₃N₄ and from the Si₃N₄ to InGaAsP MQW at room temperature in an inductively coupled plasma system. A scanning electron microscope (SEM) was used to photograph the InGaAsP MQW microdisk, which was presented in Fig. 1(a). A Bi₂Te₃ powder was prepared by mechanically exfoliating hexagonal Bi₂Te₃ single crystals with uniform morphologies to examine the absorption effects with the cavity lasing modes. We dispersed the powders in ethanol and then subjected them to ultra-sonication for 8 hours to obtain Bi₂Te₃ sheets. The concentration of the Bi₂Te₃ in the dispersion was 3 mg/cm³, and then dropped on the fabricated microdisk cavities and then twice spin coat at 1000 rpm. The Bi₂Te₃ cluster was accordingly placed on the top edge of the 10-µm-diameter microdisk, as demonstrated in the SEM image of Fig. 1(b). These procedures ware similar to our previous studies that for pulsed solid state lasers and the optical damage threshold of Bi₂Te₃ was around 100 MW/cm², the other optical properties were also well characterized [35].

 

Fig. 1. Tilted view SEM images of the same fabricated InGaAsP MQW microdisk on sapphire (a) without and (b) with Bi₂Te₃ cluster.

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3. Results and discussions

3.1 Optical properties of InGaAsP microdisk

As showed in Fig. 2, the microdisk cavity was then optically pumped at room temperature using an 850-nm diode laser at normal incidence under CW condition. The pump beam was reflected by a dichroic mirror, and then focused on the devices through a 100× objective lens. The lasing light was collected with a multimode fiber collimator and the signal which can pass through dichroic mirror was introduced to an optical spectrum analyzer. The photoluminescence (PL) of the fabricated InGaAsP microdisk lasing cavities without Bi₂Te₃ was characterized under optical pumping. The InGaAsP layer contained four quantum wells, which was designed to support gain from 1500 nm to 1650nm in the near-infrared optical communication wavelength regime. As depicted in Fig. 3(a), the dominant resonances emerged at approximately 1586 nm under the current diameter, which the lasing resonance was attributed to TE_1.48 mode and similarly with previous study [36]. The wavelength difference between the simulations and measurements, which was less than 1%, was attributed to fabrication imperfections. With a 7.7 mW normal incident excitation under CW conditions, a lasing peak with a Q value of 15500 was observed by estimating the ratio of the lasing wavelength ($\lambda $) to the linewidth ($\Delta \lambda $). To simulate the optical modes of this microdisk cavity, a three-dimensional finite-element method was applied for the microdisk cavity. The simulated model was consisted of an InGaAsP microdisk laid on sapphire substrate and covered by air. We set the corresponding refractive indices of the materials as ${n_{InGaAsP}} = 3.4$, ${n_{sapphire}} = 1.7$, ${n_{air}} = 1.0$. Figures 3(b) and 3(c) present the simulated $|E |$ mode profile of the TE_1,48 lasing mode [(b) top view and (c) cross-sectional view]. The results reflect the behavior of the first-order WGM lasing mode in the microdisk cavity.

 

Fig. 2. Experimental scheme of optical pumping and coupling.

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Fig. 3. (a) Lasing resonance of the InGaAsP MQW microdisk without Bi₂Te₃ coupling at 1586.4 nm under 7.7 mW CW operation at room temperature. (b) Top view and (c) cross-sectional view of the simulated normalized electric field profile of the TE_1,48 WGM resonance. The intensity color scales in (b) and (c) are identical.

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3.2 Optical properties of InGaAsP microdisk with Bi₂Te₃

To characterize the SA effects between WGM lasing without and with Bi₂Te₃ clusters, the emission spectra of the identical microdisk was accordingly collected. The lasing operating conditions were controlled to be the same as that illustrated in Fig. 2, and the effects after coating the devices with Bi₂Te₃ cluster were be compared. Unlike the single peak illustrated in Fig. 3, the lasing spectra varied dramatically in this case. Figure 4(a) illustrated the background-removed lasing spectra of the identical 10-µm microdisk but with Bi₂Te₃ cluster on top. The top part of Fig. 4(a) included the simulated mode profiles of three adjacent TE-polarized first-order WGMs which are labeled with TE_1,47, TE_1,48 and TE_1,49. By comparing the calculated WGM wavelengths from simulation and the lasing spectra, we can conclude the main peak groups was corresponding to the WGMs of the microdisk cavity. By benefit of SA from Bi₂Te₃ cluster, the modes of TE_1.47 and TE_1.49 were consequently emerged. Typically, degenerate splitting is inevitable for any WGM for a high-Q cavity due to either the clockwise or counterclockwise waveguide dispersion [37,38]. Here, the original WGM split into double peaks in the three emerging modes (denoted as M^L_x for the lower energy peak and M^H_x for the higher energy peak where x is the mode number of WGMs) caused a difference in the observed lasing output of the covered Bi₂Te₃ cluster microdisk. In the measured spectrum, the wavelength spacing between the higher energy peaks were approximately few tens nm, and between the lower and higher energy peak were approximately few nm. The variations in the PL peak intensities and linewidths under different pumping powers were also investigated. Figure 4(b) illustrated the lasing peak intensities the of TE_1.47 (blue) and TE_1.48 (red) modes under various conditions, while Fig. 4(c) exhibits the corresponding variations in the lasing peak linewidths for different pumping powers. The PL peak intensities increasing, the linewidths clearly dropped once the pumping power reached the threshold value of approximately 8 mW. This represents the nominal microdisk lasing behavior at this region. The emission wavelength of the PL peak exhibited a slight blue shift and the distance between the splitting peaks continuously decreased as the pumping power increased. These power dependent wavelength shifting phenomena arose from the same thermal problems as the pumping was increased, the lasing peak intensities decreased after pumping power exceeded 13 mW. In previous works, both low-threshold WGM lasing and degenerate splitting have been reported and studied [39–41]. It is well known that WGMs in microdisk cavities constitute a promising approach to provide light sources for various applications, such as optical communications [42]. The similar phenomenon about which multi-peak emission from microdisk covered by SAs is still less reported and discussed.

 

Fig. 4. (a) Lasing spectra depend on pumping power for identical InGaAsP MQW 10-µm microdisk coupling with Bi₂Te₃ cluster. (b) Lasing peak intensity and (c) Lasing peak linewidth variation of TE_1.47 (blue) and TE_1.48 (red) mode for pumping power.

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To analyze the nature of the emission peaks, we estimated their frequency using the emission spectrum shown in Fig. 4. For the WGM of the TE^H_1.49, TE^H_1.48, and TE^H_1.47, the emission frequencies were readily estimated to be 194.8, 190.2, and 185.7 THz, and the frequency spacing was approximately 4.6 THz. The frequency values of the TE^L_1.49, TE^L_1.48, and TE^L_1.47 modes were 193.7, 189.4, and 185.1 THz, and the frequency spacing was approximately 4.3 THz. Table 1 lists emission wavelength and frequency for all the adjunction modes. Given both the lasing characteristics and the equal spacing of the adjunction modes, the mode-locking phenomenon was considered to be achieved. The repetition rate was accordingly estimated over 4 THz.

Table 1. Emission wavelengths of microdisk lasing without or with Bi₂Te₃.

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To further confirm this observation, we calculated the refractive index from the frequency spacing. Typically, the mode spacing of a WGM is given by c/ (π D n_eff), where, c, D, and n_eff denote the velocity of light in a vacuum, diameter of the microdisk (=10 µm) and refractive index, respectively. The refractive index values of 2.099 and 2.221 for the TE^H_1.48 and TE^L_1.48 energy peaks were calculated (see Table 1) and agree quite well with the results of a related study [43]. These values can explained the nature of the mode-locking mechanism.

3.3 WGM mode-locked application

Despite of that hundreds of GHz or even higher repetition rate mode spacing comb have been realized through nonlinear processes, to the best of our knowledge, this is the first time that the emission spectrum from an active medium disks exhibited a mode-locked like behavior due to the on-top saturable absorber [44,45]. The small differences in the frequency spacing between the high and low energies were attributed to the different waveguide dispersions caused by the inhomogeneous thickness distributions of the covered Bi₂Te₃ cluster. Moreover, this also indicated that the Bi₂Te₃ cluster played a key role in the operational dynamics, a better frequency spacing was expected to be achieved by uniform SA flake. That is, the evanescent electric field of the WGM from the microdisk was modulated by the Bi₂Te₃ cluster. Similar to a previous work that employed a mode-locked fiber laser and a D-shaped fiber covered with a TI-saturable absorber, this study reveals the mode-locking operation due to the pumping power [46].

Recently, WGMs have been demonstrated as a promising method to provide low-threshold coherent light sources. As TIs provided low saturation, this study achieved mode-locking operation with repetition rates of maybe more than THz on microdisk WGMs, see Fig. 5. Although the emission radiation of the demonstration was collected by the fibers, it is emphasized that low-threshold mode-locking microdisk lasers are feasible with TIs as SAs and with waveguide coupling [47]. In addition, the repetition rate can be adjusted by managing the dimensions of the disk. Moreover, the different thickness of the covered TI powders result in the variations of the waveguide dispersion under clockwise (CW) or counter clockwise (CCW), leading to degenerate splitting. Recently, dual-comb light sources have become a notable topic for applications as sensors due to the high speed measurement and broad band optical spectrum [48]. For which several approaches, such as micro-ring-based dual-comb device, have been reported [47–49]. A more compact and cost-efficient light source are achieved by benefit of modulation from SAs, and research combine with dual-comb and SAs must be going on. As a result, a WGM-based dual-comb device with scaling repetition rate will be expectable and should be further developed.

 

Fig. 5. Scheme of degenerate breaking whispering gallery mode (WGM) passive mode-locking operation with TIs.

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4. Conclusion

In summary, on chip frequency comb has been realized a trend because of its wide range applications, such as metrology, sensing and so on. Broadband spectrum output, compactness in space and efficient conversion are main goal for shooting. To date, various nonlinear gain approaches, for example: micro-ring/toroidal resonator or super-continuum generation within nonlinear waveguide, have been proposed and demonstrated. Regarding to the alternative way through real gain, scaling repetition rate and on-chip methods are still less discussed. In this work, Bi₂Te₃ cluster based saturable absorber InGaAsP multiple quantum wells (MQWs) whispering gallery mode (WGM) locking is proposed and demonstrated for fulfilling the requirement of efficient on-chip broadband light source. By benefiting from the low threshold of WGM and ultrasensitive saturation intensity of bulk state within the topological insulators, low threshold multi-peaks lasing action with equal spectral spacing was realized. This could be attribute to mode-locking and the repetition rate as high as an estimated over 4 THz was accordingly achieved. Additionally, clear degenerate breaking was observed with a frequency shift of approximately 1 THz for each lasing mode. To the best of our knowledge, this is the first demonstration of a passively mode-locked WGM. These also exhibit applications potential for dual-comb products.