Quasi-BIC laser enabled by high-contrast grating resonator for gas detection

2.1 Structure design

The schematic diagram of proposed double-HCG resonant structure is shown in Figure 1. The structure is designed to support a quasi-BIC at wavelength of 570 nm. The active region consists of 215 nm thick SiO₂ layer doped with Rhodamine 6G (R6G), as shown in Figure 1(a). A similar gain medium has been reported in a previous work [28]. The R6G layer is surrounded by Si₃N₄ stripes with a symmetric arrangement along z direction, and the refractive index of Si₃N₄ is 2.0. The HCG parameters are described by the thickness of grating layer T, filling factor (the grating width divided by the period) F and the period Λ. We consider the dimensions of whole device in x- and y-direction are infinite, as exhibited in Figure 1(b). The detail parameters of materials are shown in Table 1.

Figure 1:

Schematic of proposed resonator based on HCGs:

(a) single unit cell of two dimensional resonator; (b) whole structure with the organic R6G thin layer. The dark green downward arrow represents optical pump, the light green arrows on both sides of resonator are emitted light from the resonator.

In the point of fabrication view, although there may exist several technical challenges, several experiments on the similar grating structure have been reported [29, 30]. A freestanding cascade grating fabrication technique, based on positive resist e-beam lithography (EBL) and ion coupling plasma, is supposed to be feasible to fabricate the designed structure. The SiO₂ layer doped with R6G can be made by using sol–gel technique, which is a suitable method for incorporating organic molecules into inorganic solid hosts. The low-temperature process involving the hydrolysis and condensation reactions of metal alkoxides enables us to dope different molecules with a poor thermal stability into coating films [31]. The fabrication process mainly includes thin film deposition and grating pattern. The Si₃N₄ thin film is uniformly coated with SiO₂ doped R6G sol solution, and then cover another Si₃N₄ thin film on the other side. The grating structures can be separately patterned on both sides by using EBL and ICP with CHF₃ gas [32]. A similar sandwiching structure consisting of two aluminum gratings and a Si₃N₄ membrane has been reported recently [33].

2.2 Theory and simulation

A semi-quantum framework is adopted to simulate the interaction between the electromagnetic fields and gain medium. The organic dye molecules in this work are well described as a four-energy-level system, and the population inversion is generated between the electronic level of L₂ state and L₁ state. As shown in Figure 2, which presents the population dynamics of the four relevant electronic levels of the molecule, such as the ground state, L₀, and the three excited states, L₁, L₂, and L₃. The molecular polarization given by spontaneous and stimulated transitions are described through the following equation [34]:

where Δω_i,j and ω_i,j are the bandwidth and frequency of the transition between states i and j, κi,j=6πε0c3/ωi,j2⋅τi,j [35], τ_i,j represents the lifetime of the spontaneous emission. ΔN_i,j(t) is the difference of population density between two energy states of the interest. E⃗(t) is the total electric field, and can be calculated by solving the curl Maxwell equations [36]:

Figure 2:

Energy level diagram and parameters used for modelling the dye molecules in FDTD simulations. The transition energies are E₃₀ = E₃ − E₀ and E₂₁ = E₂ − E₁. Since the transition from L₃ to L₂ is much faster than the transition from L₃ to L₀, the excitation quickly decay to L₂, leading to a population inversion for the transition from L₂ to L₁.

In order to solve for the fields in a self-consistent fashion, it is necessary to couple the molecular polarization P⃗i,j to the electromagnetic fields via the rate equations of the four-level system describing the gain medium [37]. Such rate equations describe the time evolution of the energy states’ population densities, and are given by Ref. [38]. The time evolution of each energy state density is described by their respective spontaneous decay processes N _i /(τ_i,j) and stimulated processes (E⃗(t)⋅dP⃗i,j/dt). The field involved in the rate equations is the total field and accounts for the effects of any local optical intensity on the dynamics of the population densities.

The FDTD method is adopted to solve the coupled equations. A plane wave in 4 ps pump pulse normally incident on the device along z-direction, as shown by the dark green downward arrow in Figure 1(b), and its center wavelength is λ_P = 512 nm. For the case of R6G-doped SiO₂, we set that the absorption transition: λ_a = 512 nm and Δλ_a = 35 nm; the emission transition: λ_e = 570 nm and Δλ_e = 50 nm; the concentration of dye molecule: C = 1 × 10¹⁹ cm⁻³, which is comparable to the concentrations previously reported in the same material host [28]; and the lifetimes: τ₃₂ = τ₁₀ = 5 × 10⁻¹⁴s, τ₃₀ = 1 × 10⁻⁹ s, τ₂₁ = 1.8 × 10⁻⁹ s. Finally, the calculated emission cross section is around 3 × 10⁻¹⁶ cm², which is also consistent with the experimental report [39].

3.1 BIC modes supported by the passive structure

First, the optical properties of single HCG layer are analyzed. To obtain a perfect mirror for light trapped in a Fabry–pérot BIC system, we carry out FDTD simulations and calculate the structure’s reflectance, for a normally incident plane wave polarized along the y-direction. Figure 3(a) illustrates the results of our simulations as a function of the wavelength and of the grating thickness, taking a grating filling factor F = 0.5. We observe two regions, which we refer to as the dual/multi-mode region (from λ = 530 to 700 nm) and the single-mode region (λ > 700 nm), as suggested by previous nomenclature [40]. For the single mode region, the grating operates in a longer wavelength regime, behaving like a quasi-uniform layer [17], so only Fabry–Pérot modes are supported in this wavelength range. On the other hand, in the dual/multi-modes region, the pattern is quite different, describing contrasting regions with high (>99%) and low reflectance. In addition, we find the localized patterns do not change in an obvious manner when modify the filling factor F, instead, just an overall shifting to the longer wavelength. The reflectance spectrum shown in Figure 3(a) reveals that with a proper selection of the grating parameters (e.g., the thickness T, filling factor F, and period Λ), an ultra-high (>99%) reflectivity over a spectral range is achievable (as shown by the double arrow line).

Figure 3:

Reflectance spectra mapping and electric field distribution profile.

(a) Reflectance spectra mapping as a function of grating thickness when the filling factor F = 0.50; (b) reflectance spectra as a function of the thickness of SiO₂; (c) reflectance contour distribution of the architecture by sweeping the incident angle from −25° to 25°; (d) electric field distribution profiles within four periods corresponding to the places marked by ‘2’.

We proceed now to study the optical properties of the entire passive structure (SiO₂ layer sandwiched by the two HCGs) as a function of the main structural parameters. Figure 3(b) displays the reflectance spectra mapping as function of SiO₂ layer thickness, under the condition of T = 230 nm, F = 0.50, and Λ = 530 nm. We notice there are a series of discrete reflectance vanishing points at the SiO₂ layer thickness of 20, 210, 400, and 590 nm, corresponding to a periodical disappearance of resonance. These singular points break the high reflection continuum, showing the typical feature of Fabry–Pérot BIC. As mentioned before, an HCG layer possesses high reflectivity within a wide range, thus two HCGs layers with a symmetric alignment can make a Fabry–Pérot cavity. Therefore, BICs are formed when the distance between two HCG layers is tuned to make the round-trip phase shifts add up to an integer multiple of 2π [13]. Similar phenomenon was observed in a hybrid structure composed of a subwavelength grating layer and an un-patterned high-refractive-index cap layer [41]. However, the BIC nature of the modes was not identified. In addition, the high Q resonance in such a structure originates from the constructive interference of two Bloch modes in the grating layer, which is fundamentally different from the Fabry–Pérot BIC that exits in double gratings and stacked photonic crystal (PhC) slabs.

To obtain a quasi-BIC mode at wavelength of 566 nm that could be employed in a practical device, we slightly increase the thickness of SiO₂ layer by 5 nm. Figure 3(c) shows the band diagram of the designed structure, which is plotted by varying the angle of incidence (θ, from −25° to 25°) with respect to the z-axis. We observe symmetric patterns relative to the axis of θ = 0° (also Γ point), and the quasi-BIC mode at the position of mode 2, where is marked by the arrow and number ‘2’, is successfully identified. This quasi-BIC mode exhibits a low dispersion near θ = 0° around 566 nm, suggesting a strong resonance in individual unit cell [42]. Apart from mode 2, we also find other BIC modes at θ = 0° (e.g., positions marked by ‘1’ and ‘3’) and 14.8° (e.g., position marked by ‘4’). Those BICs feature vanishing linewidths, suggesting a nonleaky state [4].

To further characterize the quasi-BIC at mode 2, we plot the field distribution profile in (x, z)-plane for this mode under the incident angle θ = 0°, as shown in Figure 3(d). The E _y distribution of mode 2 over the (x, z)-plane shows a strong confinement within the cavity and a symmetric profile along z-direction. Due to the high reflectance of the HCGs and the sub-wavelength thickness of the SiO₂ layer, the first-order standing wave (i.e., one peak across the SiO₂ layer) is observed [43]. Typically, Fabry–Pérot BIC can be generated in systems with two identical resonances coupled to a single radiation channel [13]. Here, the round-trip phase shift between the two resonances in HCGs is 2π, thus the field is constructively interfered and trapped in the cavity while the resonant radiations from the HCGs interfere destructively out side of the cavity, which leads to the formation of Fabry–Pérot BIC.

3.2 Quasi-BIC lasing and characterization

To realize quasi-BIC lasing, we selected the grating parameters (T = 230 nm, F = 0.50, and Λ = 530 nm) which can provide the highest possible reflectivity (as marked in Figure 3), and the SiO₂ thickness is 215 nm. Then, R6G dye molecules are doped into SiO₂ thin layer to compensated the internal losses of resonator. As shown in Figure 1(b), the proposed sandwiched structure recalls conventional VCSELs, however, our design significantly reduces the cavity length. Figure 4(a) shows the gain spectrum of R6G (black curve), the spectrum of the cavity mode (blue curve) and typical lasing spectrum of resonator (red curve). Clearly, the R6G gain spectrum has a broad linewidth with its central region overlapping with the cavity mode peak, a feature guaranteeing a proper compensation of the cavity losses. Interestingly, the cavity mode shows the typical asymmetric line shape of a Fano resonance. This resonance is caused by the interference of radiative (bright) and nonradiative (dark) modes [44, 45]. For Si₃N₄-based HCG resonator, dark mode is associated with the Bragg scattering induced by HCG in the lateral direction, which results in a resonant mode with narrow bandwidth. On the other hand, the bright mode is associated with the weak Fabry–Pérot mode induced by the index difference in the vertical direction, which results in a mode with nearly flat-band spectrum. The interference of these two modes result in an asymmetric line shape of the spectrum [46, 47]. Moreover, this phenomenon could confine the optical mode in the structure well and result in a high Q factor, which is beneficial for the BIC laser operation with very narrow linewidth (red curve).

Figure 4:

Lasing characterization results.

(a) Gain spectrum of R6G (black curve), cavity mode spectrum (blue curve), and typical emission spectrum of laser (red curve) operated above threshold; (b) input–output function curve (black) and spectrum linewidth changing as a function of input energy (blue); (c) near field intensity distribution of laser in (x, y) plane at z = 612.5 nm; (d) electric field intensity distribution in (x, z) plane at y = 0 nm. Both near fields are calculated at the peak laser emission wavelength, and the pump beam size in the simulation is 7.6 μm × 5.0 μm.

Figure 4(b) shows the detail characterizations of lasing behaviour. The black curve is the conventional plot of output power as a function of pump energy density, so we can estimate the threshold is around 17 μJ/cm², and the output power can reach to more than 40 μW when the pump is 25 μJ/cm², which is close to the power of practical device. The blue curve represents the corresponding optical spectrum linewidth (the full-width at half-maximum of the peak, FWHM) changing, the sharp narrowing of spectrum also indicates a coherence emission is achieved when the laser is operated above threshold. Both results are clear indications of lasing. We notice the linewidth is pump power modulated, and it becomes broader in far above threshold region. Such behavior has been reported in several experimental investigations on plasmonic laser systems [48, 49], and can be attributed to the dependence of refractive index on pump power.

Figure 4(c) and (d) are the electric field intensity distributions of resonator in (x, y) and (x, z) planes, respectively. When the resonator is operated above threshold, a large mode overlaps with the input pump contributing to a simple and efficient coupling of the input light, as suggested by the high intensity interfere fringes. In addition, the far field observation indicates a single mode lasing, which makes the laser device is more attractive. From the side view (Figure 4(d)), it is clear how the light is predominantly confined within the grating bars and there is exactly one intensity lobe within the interval of neighboring bars. In the middle, higher intensity stripe indicates the gain medium region, where we can find the vertical confinement of this device is much stronger than the confinement typically found in conventional DBRs-based vertical cavity emitting lasers. Since the double gratings provide the largest power reflectance, all diffraction orders disappear except the 0th order. In addition, the HCGs bring a higher effective refraction index and much higher than the surrounding environment, leading to strong lateral confinement for the lateral modes.