1. Introduction

Highly confined at a metal-dielectric interface, surface plasmon has been considered as a promising solution to overcome the wavelength barrier for miniaturization, and bridge the gap between nanoscale electronics and microscale photonics [1]. In the past decade, the area of plasmonics has witnessed an explosion of interest and tremendous progress in fundamental science and technological applications. Especially, surface plasmon lasers, the counterparts of classical photonic lasers, generating stimulated emission of surface plasmons instead of photons [2], have attracted increasing attention recently [3–7]. Compared with classical lasers, surface plasmon lasers show distinct features such as strongly confined electromagnetic fields, enhanced light-matter interactions, mode sizes beyond the diffraction limit, and ultra-fast response time [5]. As coherent, nanoscale, and ultrafast light sources, surface plasmon lasers provide the prospect of exciting applications in optoelectronic integrated circuits [8, 9], sensors [10], ultra-high-resolution biomedical diagnostics [11], and ultrafast spectroscopy [12, 13].

Although the fundamental physics has been widely investigated and is rather well understood [14–17], demonstrating plasmonic lasing remains challenging. In various configurations for surface plasmon lasers [18–26], the metal-insulator-semiconductor (MIS) design [27–30] supporting hybrid surface plasmon polariton (SPP) mode, as illustrated in Figs. 1(a)-1(b), becomes very popular due to its natural integration of semiconductor nanomaterials. Quite recently, all-color [31], ultra-violet [32, 33] and near-infrared [34] surface plasmon lasers have been demonstrated with various semiconductor nanomaterials. Compared with the MIS Fabry-Pérot (F-P) type cavity, which utilizes a nanowire and is of very low quality factor (the Q factor ~10), the MIS whispering-gallery mode (WGM) cavity using a square nanobelt takes advantage of total internal reflection of SPPs to mitigate the radiation loss, enabling relatively high Q factor approaching 100 and room temperature operation of plasmonic lasing [5]. Because the plasmonic mode suffers from high dissipative loss and relatively low Q factor, conventional photonic lasing of lower threshold may be triggered and misinterpreted as plasmonic lasing [35]. As a result, in order to claim plasmonic lasing, there is a prerequisite that all the possible photonic lasing modes must be suppressed. One way to address this issue is to strictly restrict the semiconductor thickness so that photonic modes are cut off by the waveguide structure. For example, it was believed that the nanobelt thickness should be smaller than 60 nm for a square cavity of length ~1 μm in [28].

 

Fig. 1 (a) and (d) are schematic diagrams, and (b) and (e) are waveguide mode profiles of the MIS and the DMIS hybrid designs, respectively. The thicknesses of layers 'D', 'M', 'I' and 'S' are t_D, t_M, t_I, t_S, respectively. (c) and (f) show comparisons of the DMIS and MIS designs on normalized propagation lengths L_m and normalized vertical mode sizes h_m for the plasmonic modes. The calculations were performed with parameters stated in the text.

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In this work, we turn to novel cavity design instead of the waveguide mode cutoff thickness to suppress possible photonic lasing modes and relieve the nanobelt thickness restriction for purified plasmonic lasing. Before addressing this challenge, let us retrospect the cavity design of classical polarized lasers, recalling that the directions of polarization for plasmonic and photonic waveguide modes are perpendicular to each other. It is well known that linearly-polarized laser emissions in gas lasers or typical Ti:Sapphire lasers are usually obtained by utilizing Brewster windows. Inspired by the polarization selectivity by reflection of Brewster windows, here we propose a dielectric-metal-insulator-semiconductor (DMIS) hybrid design, as illustrated in Fig. 1(d), to achieve our goal. Compared with the MIS design, we will show that there exists strong polarization selectivity by reflection effect in the proposed DMIS design. The matching condition for this effect will be clarified and a simple theoretical method to achieve the matching condition will be developed. A WGM cavity based on the DMIS design will be a purified plasmonic cavity because photonic modes leaks out of the cavity at early stage via a specially designed channel, which functions as the Brewster window in classical linearly-polarized lasers. Using these cavities, we will experimentally demonstrate purified plasmonic lasers with relieved restriction on the semiconductor nanobelt thickness. Approaches for further improving the purified plasmonic lasing performance such as the Q factor, the lasing threshold, and the cavity mode volume will also be discussed.

2. Theoretical calculations

Compared with the MIS design in Fig. 1(a), the proposed DMIS hybrid design adopts an ultra-thin metal layer and adds a dielectric layer beneath the metal layer, as illustrated in Fig. 1(d). Compared with the symmetric hybrid long-range SPP (LRSPP) waveguide [36, 37], which is referred to as the SIMIS design, the proposed asymmetric design facilitates the fabrication, and more importantly, the dielectric layer of parameters matched to the semiconductor layer allows for strong polarization selectivity by reflection, which will be used to suppress possible photonic lasing modes in the WGM cavity and realize purified plasmonic lasing in this work.

All the numerical calculations throughout this work are performed with the fully-vectorial three-dimensional (3D) Fourier modal method (FMM) [38, 39] at λ = 500 nm. The simulation setup adopts perfectly matched layers (PMLs) in the x direction, and the numbers of Fourier harmonics are set to be N_x = 401 and N_y = 1 (so that the simulation system extends to infinity in the y direction). For both the DMIS and MIS designs, silicon dioxide (SiO₂) is used as the substrate layer with refractive index n_Sub = 1.46, silver (Ag) as the metal layer with n_M = 0.0157 + 3.0848i [40], alumina (Al₂O₃) as the insulator layer with thickness t_I = 10 nm and index n_I = 1.66, and cadmium sulphide (CdS) as the semiconductor layer with thickness t_S = 80 nm and index n_S = 2.5. In the DMIS design, the ultra-thin metal layer is of thickness t_M = 20 nm, which is the smallest thickness we could achieve in experiments so as to greatly reduce the plasmonic mode's propagation loss. The dielectric layer is of thickness t_D = 70 nm and index n_D = 2.5 without special specifications. Note that although the dielectric layer shares the same refractive index as the semiconductor layer, we refer to the design as 'DMIS' instead of 'SMIS' in order to emphasize that the material of the dielectric layer is passive or does not provide gain to the lasing system. In the MIS design, the metal layer is assumed to be optically thick enough (t_M = 200 nm).

As both the DMIS and the MIS WGM cavities could be formed naturally by semiconductor square nanobelts atop of corresponding multilayer substrates, as has been demonstrated in [28], hereafter we refer to the two sides of the cavity interface, with and without the semiconductor layer, as the inside and the outside (of the cavity), respectively.

2.1 Mode properties

Similar to the symmetric SIMIS design, there exist hybrid short-range SPP (SRSPP) mode (the TM₀ mode) and hybrid LRSPP mode (the TM₁ mode) in the DMIS design. Figure 1(c) shows that the propagation length L_m of the hybrid LRSPP mode reaches ~13λ, more than four times larger than that of the MIS plasmonic TM₀ mode (~3λ), whereas that of the hybrid SRSPP is only ~0.5λ. Note that the hybrid SRSPP mode suffers from so high dissipative loss that it will not be considered for plasmonic lasing.

Figures 1(b) and 1(e) show that the hybrid LRSPP mode generally inherits the MIS TM₀ mode in the field profile: electric fields are highly confined in the low-index insulator layers, and of small overlaps with the corresponding plasmonic modes outside the interfaces. Although a small portion of mode energy spreads into the dielectric layer, the DMIS TM₁ mode features subwavelength vertical mode size (~λ/9), which is only a little larger compared with the MIS TM₀ mode (~λ/15), as shown in Fig. 1(f). For the TE-polarized photonic mode, however, the DMIS design is distinct from the MIS design. The photonic modes inside (the TE₀ and TE₁ modes) and outside (the TE_0,out mode) the DMIS interface all show a large portion of mode energy confined in the dielectric layer and thus present very good field overlaps between them under matching conditions, which will be clarified later; whereas there exists no photonic mode outside the MIS interface. According to the mode coupling theory [41], it is expected that the DMIS TM₁ mode, and the MIS TM₀ and TE₀ modes will be efficiently reflected due to very low coupling efficiency across the interface, whereas the DMIS TE₀ and TE₁ modes will transmit through the interface by efficiently coupling to the TE_0,out mode.

2.2 Strong polarization selectivity by reflection

To evaluate the polarization selectivity by reflection at the interface, we quantitatively calculate the reflection efficiencies for the plamsonic and photonic waveguide modes of both the MIS and DMIS designs, rather than qualitatively compare the effective refractive index differences between inside and outside modes, or equivalently the amounts of momentum to undergo total internal reflection [28]. Here we are only interested in the incidence angle of θ = 45° as it results in closed-loop trajectories in square-shaped WGM cavities [42].

Figure 2(a) shows that, the interface reflection of the MIS plasmonic TM₀ mode is almost perfect (close to 100%), and that of the photonic TE₀ mode reaches ~80%, resulting in small polarization ratio of 1.25:1. In other words, both the MIS plasmonic TM₀ and photonic TE₀ mode are efficiently reflected by the interface. In the DMIS design, however, whilst the reflection efficiency of the hybrid plasmonic TM₁ mode is large (> 80%), those of the photonic modes are all very small (< 20%) when the parameters of the semiconductor and the dielectric layers are matched, leading to high polarization ratio up to 4:1, as shown in Fig. 2(b). Recall that there are four interfaces of a square WGM cavity, according to the cavity round-trip trajectories, the overall polarization ratio for reflection by the cavity could be roughly estimated to be the fourth power of the polarization ratio for reflection by a single interface. This gives rise to overall polarization ratio of 256:1 for the DMIS WGM cavity, one order of magnitude larger than that for the MIS WGM cavity (~24.4:1). Such strong polarization selectivity by reflection in favor of the plasmonic mode makes the DMIS design more favorable for realizing purified plasmonic lasing.

 

Fig. 2 (a) and (b) are calculated modal reflection efficiencies R versus t_S for the MIS design and the DMIS design, respectively. (c) are calculated effective refractive indices n_eff for the DMIS design and (d) are their differences |Δn_eff| for the TE₀ and TE₁ modes compared with the TE_0,out mode. The vertical arrows in (b) and (d) indicate the matching condition.

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Note that all the above-calculated reflection properties agree well with our previous speculations based on mode profile overlaps and the mode coupling theory. These properties are also well explained with the effective refractive index differences between inside and outside modes. For example, the smaller interface reflection of the MIS TE₀ mode was attributed to its insufficient momentum to undergo total internal reflection in [28]. Similarly, the well suppressed reflection efficiencies for the DMIS TE₀ and TE₁ modes correspond to their very small effective refractive index differences compared with the TE_0,out mode, as shown in Fig. 2(c).

To achieve high polarization ratio or strong polarization selectivity by reflection, both the DMIS TE₀ and TE₁ modes should be efficiently coupled into the TE_0,out mode. The transmission efficiency or the coupling efficiency depends on the field overlap integral, or equivalently the phase mismatch parameter between the inside and outside waveguide modes being coupled, $\delta ={\beta }_{\text{in}}-{\beta }_{\text{out}}=k_0\left(n_{\text{eff,in}}-n_{\text{eff,out}}\right)$ [41]. As a result, high transmission and concurrently low reflection for both the DMIS TE₀ and TE₁ modes will be obtained when these modes are matched, as much as possible, to the TE_0,out mode. This can be done by minimizing |Δn_eff| for both the TE₀ and TE₁ modes compared with the TE_0,out mode, which are expressed as $\left|n_{{\text{eff,TE}}_0}-n_{{\text{eff,TE}}_{0\text{,out}}}\right|$ and $\left|n_{{\text{eff,TE}}_1}-n_{{\text{eff,TE}}_{0\text{,out}}}\right|$, respectively. Comparison of Figs. 2(b) and 2(d) shows that, reflection efficiencies of the DMIS TE₀ and TE₁ modes feature exactly the same trends of the corresponding |Δn_eff|, and the matching dielectric thickness for the optimized polarization ratio is accurately predicted by the crossover point of |Δn_eff| for both modes (the prediction error is only 5 nm). In other words, we develop a very simple and efficient method to maximize the polarization selectivity by reflection effect for the DMIS design. We should emphasize that, given the semiconductor layer thickness and even when the dielectric and semiconductor layers are of different materials and refractive indices, the matching semiconductor thickness for strong polarization selectivity by reflection effect is also predicted accurately using the as-developed method, as illustrated in Fig. 3. Under matching conditions, the polarization ratios are also as high as 4:1, and the prediction errors on the semiconductor or dielectric thickness are only about 5 nm, which is within the tolerance of thin film deposition methods such as evaporation or sputtering.

 

Fig. 3 Matching conditions (indicated by vertical arrows) for strong polarization selectivity by reflection in the DMIS design. (a) and (d) are modal reflection efficiencies R, (b) and (e) are effective refractive indices n_eff, and (c) and (f) are effective index differences |Δn_eff| for the TE₀ and TE₁ modes compared with the TE_0,out mode. The calculations were performed with (a)–(c) t_S = 80 nm, n_D = 2.5 (CdS), and (d)–(f) t_S = 100 nm, n_D = 2.4 (GaN).

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Figures 4(a)–4(c) show strong reflection of the plasmonic mode and well suppressed reflection of the photonic modes under a matching condition. Intuitively, the matched dielectric layer in the DMIS design acts as a transmission channel specially designed for the photonic modes only. Note that when t_D is so large that the TM-polarized photonic TM_1,out mode is supported outside the DMIS interface and the effective refractive index differences between the TM₁ mode and the TM_1,out mode are very small, the reflection of the TM₁ mode drops dramatically, as shown in Figs. 3(a)–3(b) and 3(d)–3(e). This is because the dielectric layer, in this case, acts as the transmission channel for both the TM₁ and TE₀ modes, which are efficiently coupled to the photonic TM_1,out and TE_0,out modes, respectively, as shown in Figs. 4(d)–4(e). Note that, Figs. 3(a), 3(d) and 4(d)–4(f) show that the reflection efficiency of the TE₁ mode is larger than those of the TM₁ and TE₀ modes. In other words, the polarization selectivity by reflection effect is shifted to be in favor of the photonic TE₁ mode instead of the original plasmonic TM₁ mode. As a result, t_D should be restricted so as to assure efficient reflection of the TM₁ mode, which is as vital as the matching condition for achieving strong polarization selectivity by reflection in favor of the plasmonic TM₁ mode.

 

Fig. 4 Simulated electric field distributions for the plasmonic and photonic modes reflected by the DMIS interface. (a) and (d) are simulated E_x fields for the hybrid plasmonic TM₁ modes. (b)–(f) are simulated E_y fields for the (b, e) TE₀ and (c, f) TE₁ modes. The incident fields are not shown for clarity. The black lines in the x-z planes outline the DMIS interface and the arrows indicate the reflected or transmitted directions of dominant power flows. The calculations were performed with (a)–(c) t_D = 70 nm, (d)–(f) t_D = 140 nm. Color map of each plot is scaled independently.

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2.3 Purified plasmonic DMIS WGM cavity

A DMIS WGM cavity formed by a semiconductor square nanobelt atop of multilayer substrate, as illustrated in Fig. 5(a), takes advantage of the strong polarization selectivity by reflection effect in favor of the plasmonic TM₁ mode. The photonic TE₀ and TE₁ modes escape the cavity at early stage, while the plasmonic TM₁ mode suffers from limited loss due to relatively long propagation length and efficient reflection at the cavity interfaces. As a result, it is possible to obtain a purified plasmonic WGM cavity based on the DMIS hybrid design. Such an on-chip polarized cavity can be treated as the counterpart of a classical linearly-polarized laser cavity utilizing Brewster windows.

 

Fig. 5 Theoretically estimated performance of a DMIS WGM cavity with L = 5 μm. (a) is the schematic top-view diagram showing that the TE-polarized photonic mode leaks out of the cavity, whereas the TM-polarized plasmonic mode is supported by the cavity. (b)–(d) show Q factors (Q_abs, Q_rad, and Q_tot), (e) are confinement factors Γ_s, and (f) are gain thresholds g_th versus t_S.

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To quantitatively evaluate the polarization selectivity of plasmonic or photonic modes by the DMIS WGM cavity, we theoretically estimate its Q factors, confinement factor Γ_s, and gain thresholds g_th. The total Q factor of a WGM cavity is theoretically calculated with $Q_{\text{tot}}=2\pi n_{\text{eff}}/\left(\lambda {\alpha }_{\text{tot}}\right)$, where n_eff is the effective refractive index of the waveguide mode, ${\alpha }_{\text{tot}}={\alpha }_{\text{abs}}+{\alpha }_{\text{rad}}+{\alpha }_{\text{scat}}$, α_abs is related to the intrinsic dissipative loss, α_rad is the average radiation loss arising from the interface reflection, and α_scat is introduced by the scattering at rough surfaces inside the cavity. As α_scat is usually much smaller than α_abs and α_rad for a smoothly layered structure, it is neglected at the moment. The total Q factor is then expressed as $Q_{\text{tot}}^{-1}=Q_{\text{abs}}^{-1}+Q_{\text{rad}}^{-1}$ with $Q_{\text{abs}}^{-1}=\lambda {\alpha }_{\text{abs}}/\left(2\pi n_{\text{eff}}\right)$ and $Q_{\text{rad}}^{-1}=\lambda {\alpha }_{\text{rad}}/\left(2\pi n_{\text{eff}}\right)$. Similar to the F-P type cavity, we approximately estimate the average radiation loss for a square WGM cavity with ${\alpha }_{\text{rad}}=-\left(\log R_y^2{R}_z^2\right)/\overline{l}$, where $\overline{l}=2\sqrt{2}L$ is the minimum round-trip cavity length with L being the cavity edge length, and R_y and R_z, which are assumed to be $R_y=R_z=R\left(\theta =\pi /4\right)$ here, are the reflection efficiencies at cavity interfaces in the y and z directions, respectively. As a result, Q_rad is proportional to the cavity edge length L. The confinement factor of the semiconductor gain layer is expressed as ${\Gamma }_{\text{s}}=n_{\text{s}}c{\epsilon }_0{\displaystyle {\int }_{\text{S}}{\left|E\right|}^2\text{d}x}/{\displaystyle {\int }_{\infty }\mathrm{Re}\left\{E\times H^{*}\right\}\cdot \widehat{z}\text{d}x}$ [43, 44], where ${\displaystyle {\int }_{\text{S}}•\text{d}x}$ means the integration over the semiconductor layer in the x direction. To achieve lasing, the threshold condition requires that the modal gain per unit length should be larger than the modal dissipative loss per unit length and the average reflection loss per unit length [44]. The bulk semiconductor gain threshold is then theoretically estimated by $g_{\text{th}}={\alpha }_{\text{tot}}/{\Gamma }_{\text{s}}$ with ${\alpha }_{\text{tot}}\approx {\alpha }_{\text{abs}}+{\alpha }_{\text{rad}}$.

Figure 5(b) shows that Q_abs of the plasmonic TM₁ mode is almost comparable to those of the photonic TE₀ and TE₁ modes thanks to the adoption of the ultra-thin metal layer. On the other hand, Fig. 5(c) reveals that Q_rad of the plasmonic mode is one order of magnitude larger than those of the photonic modes. The strong polarization selectivity by reflection of the WGM cavity qualitatively agrees with our previous rough estimation of the overall polarization ratio (256:1) based on a round-trip trajectory with four times interface reflections. As Q_tot obtained with $Q_{\text{tot}}^{-1}=Q_{\text{abs}}^{-1}+Q_{\text{rad}}^{-1}$ is mainly determined by the smaller value of Q_abs and Q_rad, comparison of Figs. 5(b) and 5(c) shows that Q_tot of the photonic modes will be mainly determined by their Q_rad, which inherit exactly the same trends of the corresponding R in Fig. 2(b). This means that the suppression of photonic modes' reflection by the interface plays a key role in the prohibition of photonic lasing modes in the cavity, although photonic modes suffer from very low dissipative loss. Consequently, Q_tot of the TM₁ mode is much larger than those of the TE₀ and TE₁ modes over a very wide range of thickness t_S when L = 5 μm, as shown in Fig. 5(d). In other words, the plasmonic mode is supported much better than the photonic modes in the DMIS WGM cavity, even when the semiconductor layer is as thick as 120 nm. Because a portion of modal energy spreads into the dielectric layer in Fig. 1(e), the confinement factor of the DMIS TM₁ mode is only ~0.5, as shown in Fig. 5(e). Theoretically estimated gain thresholds in Fig. 5(f) reveal that only plasmonic lasing will be triggered when a nanobelt's thickness is smaller than 95 nm. This is because photonic lasing modes are well suppressed due to their much higher thresholds than the plasmonic lasing mode. For thicker nanobelts, however, photonic lasing may be triggered instead due to lower threshold. As a result, the DMIS WGM cavity greatly alleviates the MIS design's strict restriction [28] on the semiconductor thickness for purified plasmonic lasing.

3. Experimental demonstration

Encouraged by the theoretical calculations, we decided to fabricate surface plasmon laser devices based on DMIS WGM cavities and test the lasing performance in real situation. The fabrication processes are described as follows. First of all, a very smooth Al₂O₃/Ag/CdS/SiO₂ multilayer film, which assures trivial scattering loss α_scat of the WGM cavity, was prepared with multi-step processes of thin film deposition. A CdS film with a thickness of 70 nm was first deposited onto a 300 nm SiO₂/Si substrate by magnetron sputtering process. Then a 1 nm Al₂O₃ film was deposited with low-temperature atomic layer deposition (ALD) method to facilitate the deposition of ultra-thin Ag film on the sputtered CdS film. 1 nm copper (Cu) as the wetting layer and then 20 nm Ag film were deposited in sequence using thermal evaporation [45]. At last, another layer of 10 nm Al₂O₃ was deposited with low-temperature ALD. Figures 6(a) and 6(b) show the respective scanning electron microscope (SEM) and atomic force microscope (AFM) images of the as-deposited multilayer film. AFM measurements revealed that the as-deposited film is very smooth, and the root mean square surface roughness is only ~1.0 nm. The CdS nanobelts were synthesized through the chemical vapor deposition method, followed by a solution-based ultra-sonication cleaving process, and were then deposited from solution on the as-deposited film.

 

Fig. 6 (a) SEM and (b) AFM images of the as-deposited multilayer film. (c)–(d) SEM images of typical lasing samples with CdS square or quasi-square nanobelts of size about 5 μm × 5 μm atop of the as-deposited multilayer film. Note that there were no holes in the as-deposited multilayer film at the time of lasing characterization experiments, and the holes are due to corrosion of the Al₂O₃ layer after a long-term exposure in air. (e) Comparison of theoretically estimated gain thresholds g_th (lines), which is part of Fig. 5(f), and experimental lasing thresholds P_IN,th (scattered dots).

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A Coherent Libra regenerative amplifier (50 fs, 1 kHz, 800 nm) seeded by a Coherent Vitesse oscillator (50 fs, 80MHz) was used to characterize the lasing performance of the as-fabricated nanolasers. The 400 nm wavelength laser pulses were obtained with a BBO crystal from the regenerative amplifier's output. A × 20 objective lens (numerical aperture = 0.4) was used to focus the pump beam to a ~27 μm diameter spot onto the sample and collect the lasing emissions from the sample. All lasing experiments were carried out at room temperature. After lasing experiments, the thicknesses of the nanobelts were measured by AFM, and the sizes were measured by calibrated SEM.

Experiments with numerous CdS nanobelts of various sizes, thicknesses and shapes showed that, no lasing actions could be observed for too thin (t_S < 30 nm) or too small (L < 4 μm) square nanobelts probably because of insufficient gain, and square-shaped nanobelts presented lower lasing thresholds than rectangle-shaped ones. For square nanobelts of about 5 μm × 5 μm in size (allowing for small deviations on the shape and the size), as illustrated in Figs. 6(c)-6(d), lasing actions were observed as the nanobelt's thickness increases from 30 nm to more than 100 nm, as shown in Fig. 6(e). Strikingly, experimental lasing thresholds P_IN,th feature exactly the same trends as theoretically estimated gain thresholds g_th. According to the theoretical calculations, there is a distinct transition from plasmonic lasing to photonic lasing as t_S increases. The plasmonic lasing thresholds are very high for too thin nanobelts (t_S < 40 nm), and decrease slowly as t_S increases from 40 nm to 95 nm. As a comparison, the photonic lasing thresholds for nanobelts of t_S > 95 nm decrease more quickly as t_S increases. The remarkably excellent agreement between theoretical estimations and experimental data on lasing thresholds validates the as-developed theoretical models on estimating Q factors and gain thresholds for WGM square cavities. We notice that there are kinks at t_S = 40 nm for theoretical and experimental thresholds in Fig. 6(e). This is because a large portion of the plasmonic TM₁ mode energy is leaked into the air when t_S < 40 nm (not shown), resulting in very large scattering loss or equivalently too small reflection efficiency at the cavity interface, and accordingly too small quality factors, as shown in Figs. 2(b) and 5(c)-5(d), respectively. Because rigorous 3D simulation of such a large sized cavity is very challenging, this simple theoretical model is very efficient and useful although there may exist some deviations due to edge scattering.

The observations of lasing oscillations well above thresholds were confirmed by the sharp lifetime shortening behaviors (not shown), the emission linewidth evolutions and the nonlinear responses of the integrated emission intensity to the pump power, as shown in Fig. 7. As the pump power exceeds a threshold, the spontaneous emission of linewidth ~20 nm evolves into laser oscillation of linewidth 5−6 nm for t_S < 95 nm or 1−2 nm for t_S > 95 nm, as shown by Figs. 7(a)-7(d) and 7(e)-7(f), respectively, and the integrated emission intensity increases rapidly with the pump power (insets of Fig. 7). According to Fig. 6(e), purified plasmonic lasing and photonic lasing are differentiated based on the nanobelt thickness. In other words, plasmonic lasing features much broader linewidth than photonic lasing. As a result, the differentiation of plasmonic lasing and photonic lasing based on the lasing emission spectrum linewidth gives rise to exactly the same result as that based on the nanobelt thickness.

 

Fig. 7 Power-dependent emission spectra evolution of (a)–(d) purified plasmonic lasing and (e)–(f) photonic lasing. The insets are log-log plots of integrated emission intensity (blue dots, with the line to guide the eyes) versus the pump power. The thicknesses of nanobelts from (a) to (f) are 30 nm, 50 nm, 75 nm, 87 nm, 98 nm, and 104 nm, respectively.

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We should emphasize that it was easier to observe purified plasmonic lasing actions using thicker nanobelts provided t_S < 95 nm. This is because the modal loss, the confinement factor and the threshold of the DMIS plasmonic TM₁ mode are almost independent from the semiconductor thickness, as shown in Figs. 1(c), 5(e) and 5(f), respectively. As a result, a thicker nanobelt leads to more effective gain and thus stronger emission intensity of plasmonic lasing. On the other hand, the vertical mode size of the DMIS design holds to be beyond the optical diffraction limit (~λ/9), as shown in Fig. 1(f). These merits of allowing for thicker nanobelts are very attractive for developing purified plasmonic lasers with new semiconductor nanomaterials.

4. Approaches for plasmonic lasing performance improvement

We should note that there is large space to further improve the plasmonic lasing performance, such as the Q factors, the threshold, and the effective cavity mode volume.

Although the dissipative loss of the DMIS design has been reduced a lot compared with the MIS design, as shown in Fig. 1(f), the lasing thresholds of surface plasmon nanolasers based on both designs and using the same semiconductor material are comparable to each other, and the DMIS design requires much larger nanobelt size than the MIS design to realize purified plasmonic lasing actions [28]. This is mainly caused by two reasons. One major reason lies in the fact that, the interface reflection of the DMIS TM₁ mode is only 80%, whereas that of the MIS TM₀ mode is almost perfect (approaching 100%), as shown by Figs. 2(b) and 2(a), respectively. The insufficient reflection leads to small Q_rad, and requires large cavity size, which further results in high dissipative loss within the cavity. To reduce both the lasing threshold and the cavity size for purified plsmonic lasing based on the DMIS design, it is vital to achieve perfect interface reflection of the TM₁ mode. This can be done by introducing circular Bragg structures [46] or plasmonic crystal patterns in the insulator layer, where most of the TM₁ mode power is confined. Note that these patterns will have little influences on the reflection of the DMIS photonic modes because only a small portion of the photonic modes' powers are confined in the insulator layer. As a result, the polarization ratio or the polarization selectivity by reflection in favor of the TM₁ mode will be further improved. Another advantage of introducing patterns is that, the effective cavity mode volume of the obtained annular Bragg resonator or the plasmonic crystal cavity could be reduced into subwavelength scale in all the three dimensions [47, 48]. The other important reason for high threshold and large nanobelt size in our experiments is that, the confinement factor Γ_s for the DMIS TM₀ mode is only half of that for the MIS TM₀ mode. As the confinement factor determines the effective gain of the semiconductor medium harvested by the plasmonic lasing mode, both the lasing threshold and the nanobelt size could be further reduced by increasing Γ_s. By reexamining the DMIS TM₁ mode profile in Fig. 1(e), we notice that if the dielectric layer also utilizes the same active material as the semiconductor layer to provide additional gain, the plasmonic lasing threshold for the obtained SMIS WGM cavity will be reduced almost by half beneficiating from the doubled confinement factor, as shown in Fig. 8.

 

Fig. 8 Theoretically estimated (a) confinement factors Γ_s and (b) gain thresholds g_th of the SMIS WGM cavities with L = 5 μm. Γ_s of the DMIS TM₁ mode and the MIS TM₀ mode are also compared in (a).

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Moreover, the choice of materials makes a difference on the plasmonic lasing threshold. Several experiments based on the MIS hybrid design have showed that, the plasmonic lasing thresholds could be reduced by several orders of magnitude simply by replacing CdS nanowires [27] with GaN nanowires [30, 33]. This is mainly because the gain coefficient of GaN material is expected to be as large as ~10,000 cm⁻¹ [49], which is about a factor of 50 larger than that of CdS material [30]. Moreover, compared with evaporated or sputtered metallic film, the epitaxially grown metallic film of atomic smoothness was shown to be crucial for reducing the plasmonic dissipative loss and lasing threshold [30]. In addition, the plasmonic dissipative loss and lasing threshold could be further reduced for longer wavelength operation [50], or by taking advantage of recent advances in exploring alternative plasmonic materials [51, 52]. This is because Q_tot of the DMIS plasmonic TM₁ mode is mainly limited by its Q_abs, as shown by Figs. 5(b)-5(d).

5. Conclusions

In conclusion, we have proposed a DMIS design featuring strong polarization selectivity by reflection effect, and demonstrated purified plasmonic lasing with relaxed semiconductor thickness using DMIS WGM cavities. A simple method based on minimizing the effective refractive index differences for both the TE₀ and TE₁ modes compared with the TE_0,out mode, has been developed and shown to be very accurate to achieve the matching condition for strong polarization selectivity by reflection. High polarization ratio of 4:1 in favor of the plasmonic mode has been obtained for the interface reflection in the DMIS design compared with only 1.25:1 in the MIS design. As a result, DMIS WGM cavities taking advantage of the strong polarization selectivity by reflection effect have been shown to support the plasmonic TM₁ mode much better than photonic modes over a wide range of semiconductor thicknesses. Especially, it has been revealed that Q_rad of the DMIS plasmonic mode is one order of magnitude larger than those of the photonic modes. We have designed experiments to demonstrate relaxed semiconductor thicknesses for purified plasmonic lasing with square CdS nanobelts. Comparisons of theoretical estimations and experimental data have not only demonstrated purified plamsonic lasing when CdS nanobelts are of thickness smaller than 95 nm, but also validated the as-developed theoretical model on estimating Q factors and gain thresholds for large-sized WGM square cavities. We have also discussed some potential approaches to further improving the purified plasmonic lasing performance, including the Q factors, the threshold, and the cavity's physical size and effective mode size. We expect that the proposed DMIS hybrid design has great potential for the development of better surface plasmon nanolasers using new semiconductor nanomaterials. By varying the thickness of the dielectric layer, we have also shifted the polarization selectivity by reflection effect from being in favor of the TM-polarized plasmonic mode into being in favor of the TE-polarized photonic mode. As a result, we believe that the concept of the strong polarization selectivity by reflection effect will also find applications in on-chip polarization manipulation devices, simply by extending the selectivity between plasmonic and photonic modes into that between TE- and TM-polarized waveguide modes.