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Abstract
Squeezing light to nanoscale is the most vital capacity of nanophotonic circuits processing on-chip optical signals that allows to significantly enhance light–matter interaction by stimulating various nonlinear optical effects. It is well known that plasmon can offer an unrivaled concentration of optical energy beyond the optical diffraction limit. However, the progress of plasmonic technology is mainly hindered by its ohmic losses, thus leading to the difficulty in building large-area photonic integrated circuits. To significantly increase the propagation distance of light, we develop a new waveguide structure operating at the telecommunication wavelength of 1,550 nm. It consists of a nanostructured hybrid plasmonic waveguide embedded in a high-index-contrast slot waveguide. We capitalize on the strong mode confinement of the slot waveguide and reduce mode areas with the nanostructured hybrid plasmonic configuration while maintaining extremely low ohmic losses using a nanoscale metal strip. The proposed design achieves a record propagation distance of 1,115 µm while comparing with that of other designs at a mode area of the order of 10−5 A0 (A0 is the diffraction-limited area). The mode characterization considering fabrication imperfections and spectral responses show the robustness and broadband operation range of the proposed waveguide. Moreover, we also investigated the crosstalk to assess the density of integration. The proposed design paves the way for building nanophotonic circuits and optoelectronic devices that require strong light–matter interaction.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The ever-increasing demand for data transmission capacity drives the development of photonic integrated circuits (PICs) to overcome the inherent limitations of transmission bandwidth. In current nanoscale electronic circuits, these limitations are attributed to the signal delay and heat dissipation [1,2]. Nevertheless, the fundamental optical diffraction limit hinders the realization of controlling light in nanophotonic devices [3]. In addition, shrinking light mode size is also crucial for multiple applications, such as the enhancement of light–matter interaction [4,5], the resolution of spectroscopy techniques [6], and the accuracy of sensing devices [7,8]. To date, the most promising approach to breaking the diffraction limit is to couple light with free electrons in noble metals. This approach allows forming of a coupled mode called surface plasmon polariton (SPP) [9] that propagates along dielectric–metal interfaces in visible and near-infrared ranges. Some potential applications using SPP mechanism include plasmon-controlled fluorescence technology in biology [10], light emission enhancement in quantum-dot-doped nanofibers [11], plasmon-mediated whispering-gallery-mode emission [12], optical energy transfer from quantum-dot-doped polymer photonic to plasmonic nanowires [13], light coupling efficiency. Rapid advancements of modern micro/nanofabrication technologies resulted in a variety of SPP-based waveguides (also called plasmonic waveguides). These waveguides featured carefully designed material geometries that paved the way for building subwavelength waveguides and components with distinct degrees of light confinements [14–17]. However, the generation of nanoscale modes in plasmonic waveguides was accompanied by significant metallic ohmic losses [18,19], thus leading to the high propagation losses of light.
To significantly improve the figure of merit (FoM) between the mode size and ohmic losses in plasmonic waveguides, the hybrid plasmonic waveguides (HPWs) were independently proposed by Alam et al. [20,21] and Zhang’s group [22]. Instead of adopting the coupling between two SPP modes in the conventional plasmonic waveguides, a lossless dielectric waveguide mode was coupled with an SPP mode to form an HPW mode that possessed a moderately increasing mode area while retaining lower ohmic losses. Following the pioneering theoretical work [22], experimental low-loss optical waveguide [23] and nanolasers [24,25] with nanoscale spot sizes and low pumping thresholds were fabricated. Inspired by the HPW structure, multiple modified designs were reported [26–39]. The modified HPWs [26–39] can be categorized on the basis of mode area and propagation length. Accordingly, two types of HPWs can be specified featuring (1) smaller mode areas of 10−3 to 10−5 A0 with propagation length of several tens to several micrometers [26–33], respectively, and (2) longer propagation length of several millimeters to several hundreds of micrometers with mode areas of 10−2 to 10−3 A0 [34–39], where A0 is the diffracted-limit mode area. Therefore, HPWs of types (1) and (2) are beneficial for implementing high-density and low-loss photonic devices, respectively. Note that type (2) requires a symmetric HPW structure because the longitudinal component of the electric field in the metal should be minimized, thus substantially lowering ohmic dissipation.
To get large-area nanophotonic circuits, waveguides capable of transmitting light for sufficiently long distances and featuring nanoscale mode sizes are crucial. To the best of our knowledge, shrinking the waveguide mode area below 10−3 A0 while maintaining a millimeter-scale propagation length has not been achieved yet. In this study, we propose a novel waveguide structure operating at the optical communication wavelength of 1,550 nm using a nanostructured HPW (NHPW) embedded in a high-index-contrast slot waveguide (SW) [40,41] referred to as NHPWSW. This structure capitalizes on the strong mode confinement in a low-index gap of SW and further shrinks the mode area with the NHPW to approximately 10−4 to 10−5 A0 while possessing millimeter-scale propagation lengths. The geometry parameters and fabrication tolerances of the present NHPWSW are extensively analyzed to demonstrate superior performances compared with those of previously reported HPWs. Moreover, we also investigate the dependence of mode characteristics on the wavelength to assess the broadband operation. Finally, we consider mode crosstalk to demonstrate the degree of integration of the present design for building nanoscale PICs.
2. Waveguide design principle and mode characterization
The schematic of the proposed NHPWSW composed of an NHPW embedded in the gap of a high-index-contrast SW is shown in Fig. 1(a), and its front view is shown in Fig. 1(b). The NHPW consists of a silver (Ag) nanostrip (yellow), a low-index slot layer filled with porous silicon dioxide (SiO2) [42,43] shown with translucent color, and a silicon (Si) nanoridge with a semi-circular top. The SW covered by conventional SiO2 consisted of a porous SiO2 slot layer sandwiched between two high-index Si strips. Choosing a medium with lower refractive index for the slot region can increase the confinement strength resulted from enhancing the electric field amplitude inside the slot region. To date, the porous SiO2 thin film is the lowest refractive index, thus making the highest contrast of refractive index to Si. The design principle of the NHPWSW combines two guiding mechanisms from an NHPW and SW. By coupling the NHPW mode with the SW mode, the resultant hybrid mode shows not only extremely tight mode confinement but also ultra-low propagation loss. Different from the reported HPW structures [26–28,31,33,34,38] adopting metal as a substrate or occupying a significant part of HPW structures, the proposed NHPWSW uses nanoscale Ag strip, thus substantially reducing ohmic losses.
Fig. 1. (a) A schematic of nanostructured hybrid plasmonic waveguide slot waveguide (NHPWSW) covered by SiO2. It consists of a nanostructured hybrid plasmonic waveguide (NHPW) embedded in a high-index-contrast slot waveguide (SW). Here, the NHPW includes a silver (Ag) nanostrip (yellow), a low-index slot layer filled with porous silicon dioxide (SiO2), and a silicon (Si) nanoridge with a semi-circular top. (b) The front view of (a).
To evaluate the performances of a plasmonic waveguide, three key indices, including the normalized mode area Am = Ae/A0 [22], propagation length Lp = λ/[4πIm(ne)], and $FoM = {L_p}/2\sqrt {{A_m}/\pi } $ [22] should be considered. Here A0 = λ2/4 (λ is the working wavelength in vacuum) is the diffraction-limited mode area; Im(ne) is the imaginary part of effective refractive index, ne; and Ae is given by Eq. (1) and corresponds to the ratio of the total mode energy, Wm, and the peak energy density, W(r), defined by Eq. (2).
Prior to mode characterization, we examined the combined effect of the NHPWSW from the NHPW and SW structures. In particular, we first considered mode properties of the NHPW with the geometry parameters hnr = 15 nm, hAg = 10 nm, and wnr = 10 nm and obtained Re(ne) = 5.496, Lp = 1.41 µm, Am = 9.2 × 10−7, and FoM = 1,302. These results clearly demonstrated that the NHPW supported an HPW mode with extremely high localization and ohmic losses. Note that the radius of curvature of Si nanoridge is assumed as wnr/2. In contrast, we obtained Re(ne) = 1.642 and Am = 3.1 × 10−2 for the SW structure with hSi = 220 nm, wSi = 150 nm, and gap thickness of 25 nm (that is the addition of hnr = 15 nm and hAg = 10 nm). Note that the propagation length of the SW can be considered infinite for using all-dielectric materials. Combining the NHPW with SW resulted in NHPWSW possessing exceptional mode properties of Re(ne) = 1.7348, Lp = 1,115 µm, Am = 5.6 × 10−5, and FoM = 132,046. Compared with the NHPW mode with Lp = 1.41 µm, although the NHPWSW mode achieves an extremely long propagation length Lp = 1,115 µm by means of larger normalized mode area, Am, the obtained Am = 5.6 × 10−5 of the present NHPWSW is still much smaller than that of most previously reported ones [27–30,34–37]. To demonstrate the above-calculated results, we showed relative energy profile, Wn = W(r)/Wmax, along the dashed lines H (at y = hnr, the contacted plane of Ag nanostrip and Si nanoridge, whereas y = 0 is the bottom of Si nanoridge) and V (at x = 0, the middle of Si nanoridge) in Figs. 2(a) and (b), respectively. Here, Wmax is the maximum of W(r) for the corresponding structures (i.e., Wmax’s are different for NHPW and NHPWSW). Figure 2(a) shows that the SW has no significant effect on the mode distribution of NHPW along the x-direction. Note that the significant part of the NHPW mode field penetrates into the region (i.e., y >0; see Fig. 2(b)) of Ag nanostrip due to its small thickness of hAg = 10 nm, leading to extremely high ohmic losses, similar to the results reported in [29] and [30]. Note that the SW leads to significantly enhancing the electric field in the y-direction but not in the x-direction. Therefore, the relative energy profiles, Wn = W(r)/Wmax, along the dashed line H for the two structures are almost overlapping but they show substantially different along the dashed line V. Obviously, the mode field of NHPW in the region of Ag nanostrip is drastically pushed toward the Si nanoridge side after covering the NHPW by an SW, resulting in a significant reduction of ohmic losses.
Fig. 2. Relative energy density, Wn = W(r)/Wmax along the dashed lines (a) H and (b) V in the inset of (b). Wmax’s are the maximum of W(r) for the corresponding structures.
Let us simply compare the modes of a general HPW [22] and the proposed NHPWSW. On the one hand, NHPW and SW attain much tighter mode confinements than dielectric–metal interface and a dielectric waveguide, respectively. On the other hand, the size of a lossless SW is much larger than that of the Ag nanostrip in the present NHPWSW. Oppositely, the size of the dielectric waveguide is much smaller than that of the metal substrate in an HPW. As a result, the proposed NHPWSW features much lower ohmic losses compared with a general HPW. Thus, NHPWSW is able to achieve the millimeter-scale propagation length maintaining extremely tight mode confinement. We believe that the proposed mechanism can be extended and applied in other HPW structures.
To study the dependence of mode characteristics on geometry parameters, we show the Re(ne), Lp, Am, and FoM versus hAg for several values of wnr in Figs. 3(a)–(d), respectively. Here we set hSi = 220 nm, wSi = 150 nm, and hnr = 15 nm. As hAg and wnr increase, we observe that Re(ne) gradually increases. For the Lp, increasing hAg results in a significant decrease, but the variation of wnr has a slight effect on Lp. For wnr = 10 nm, Lp can exceed 1 mm, whereas hAg is smaller than 15 nm. Regulated by the trade-off between Lp and Am for general plasmonic waveguides, Am shrinks as hAg increases. Interestingly, decreasing wnr results in a stronger influence on Am than on Lp, thereby obtaining larger FoM. Figures. 3(a) and (c) demonstrate that larger wnr increases Re(ne) and Am, indicating that more energy is spread into the Si nanoridge, not porous SiO2.
Fig. 3. Mode characterization: (a) real part of effective refractive index Re(ne), (b) propagation length Lp, (c) normalized mode area Am, and (d) FoM versus hAg for several values of wnr. Here, hSi = 220 nm, wSi = 150 nm, and hnr = 15 nm.
To clearly observe the mode distribution, we show the relative energy profile Wn = W(r)/Wmax along the dashed lines H and V for several values of wnr in Figs. 4(a) and (b), respectively. Here we set hAg = 10 nm and hnr = 15 nm, and Wmax is the peak value of W(r) for wnr = 10 nm. Evidently, the mode distribution is tighter, and the peak value of Wn is higher as wnr decreases, verifying the smaller Am [see Fig. 3(c)].
Fig. 4. Relative energy density, Wn = W(r)/Wmax along the dashed lines (a) H and (b) V for several values of wnr. Here, hAg = 10 nm and hnr = 15 nm, and Wmax is the peak value of W(r) for wnr = 10 nm.
In addition, we also show the relative energy profile, Wn = W(r)/Wmax along the dashed lines H and V for several values of hAg in Figs. 5(a) and (b), respectively. Here, wnr = 10 nm and hnr = 15 nm, and Wmax is the peak value of W(r) for hAg = 10 nm. Although Wmax is the largest for the hAg = 10 nm, the mode profile is looser, thus leading to the larger Am [see Fig. 3(c)]. Thus, we conclude that smaller wnr and larger hAg result in larger Lp and smaller Am and consequently higher FoM. Note that choosing smaller hAg with a higher W(r) peak value is beneficial for achieving a higher Purcell factor and stronger light–matter interaction.
Fig. 5. Relative energy density, Wn = W(r)/Wmax along the dashed lines (a) H and (b) V for several values of hAg. Here, wnr = 10 nm and hnr = 15 nm, and Wmax is the peak value of W(r) for hAg = 10 nm.
The dependence of mode characterization on hnr for several values of wnr are also shown in Fig. 6 at hSi = 220 nm, wSi = 150 nm, and hAg = 10 nm. As hnr increases, we observe that Re(ne) gradually decreases, but Lp and Am are nearly constant, apparently differing from that of varying hAg [see Figs. 3(b) and (c)]. Note that the variations of Re(ne), Lp, and Am for different values of wnr here are the same as that shown in Fig. 3. As a result, varying hnr shows slight dependence on mode properties.
Fig. 6. Mode characterization: (a) Re(ne), (b) Lp, (c) Am, and (d) FoM versus the hnr for several values of wnr at hSi = 220 nm, wSi = 150 nm, and hAg = 10 nm.
The mode profiles of Wn along the dashed lines H and V for several values of hnr are shown in Figs. 7(a) and (b), respectively, at hAg = 10 nm and wnr = 20 nm.
Fig. 7. Relative energy density, Wn = W(r)/Wmax along the dashed lines (a) H and (b) V for several values of hnr. Here, hAg = 10 nm and wnr = 20 nm, and Wmax is the peak value of W(r) for hnr = 15 nm.
Although Wmax of hnr = 15 nm is the largest, its mode profile is the loosest, leading to the nearly constant Am and Lp for different values of hnr. From the results of Figs. 3 and 6, we observe that the mode properties significantly depend on the geometries of hAg and wnr but are only slight variation on varying hnr.
Next, we address the effect of the SW geometry on mode properties. Figures 8(a)–(d) show Re(ne), Lp, Am, and FoM, respectively, versus width of the Si part, wSi, for its several heights, hSi, at wnr = 10 nm, hnr = 15 nm, and hAg = 10 nm. As expected, larger wSi and hSi result in larger Re(ne). However, the dependences of Lp and Am on the parameters wSi and hSi are rather slight, except for the moderate increase of Lp for the smaller value of hSi = 180 nm. The results also imply that most energy concentrates within the nanoscale gap between the Ag nanostrip and Si nanoridge.
Fig. 8. Mode characterization: (a) Re(ne), (b) Lp, (c) Am, and (d) FoM versus the wSi for several values of hSi at wnr = 10 nm, hnr = 15 nm, and hAg = 10 nm.
To demonstrate the superiority of the proposed NHPWSW, we compared the mode characteristics with those of the previously reported results (Table 1). As mentioned in the introduction, types (1) and (2) target smaller Am and longer Lp, respectively.
Table 1. Comparison of modal properties of Am, Lp, and FoM.a
For type (1), although Am’s achieve the orders from 10−3 to 10−5, their Lp’s are smaller than 50 µm. In contrast, Lp’s achieve millimeter-scale distances, but Am’s are limited in the range of 10−2 to 10−3 except in the report by Zheng et al. [38]. In [38], the authors adopted a metal–ridge–slot structure based on a two-dimensional transition metal dichalcogenide (2D TMD) symmetrically embedded into two identical cylindrical dielectric waveguides. In a general symmetrical HPW structure, the longitudinal component of the electric field is zero in the center of the metal region [34–37], thus significantly reducing the ohmic losses but the symmetrical HPW structure is accompanied by larger mode areas. To significantly shrink the mode area, 2D TMD layers are used to cover the metal ridge, thus leading to high propagation losses. Overall, we achieve the same order of magnitude of Am as that in [38] and simultaneously maintain the millimeter-scale Lp = 1,115 µm. The latter implies that the proposed NHPWSW allows overcoming the trade-off between Lp and Am.
3. Fabrication issues and wavelength response
NHPWSW fabrication steps were illustrated schematically in Fig. 9 and included the following:
- (1) deposition of a Si layer with thickness hSi and coating a photoresist (PR) film on a conventional SiO2 substrate;
- (2) definition of the lower Si layer (width wnr) of the SW, followed by PR exposure with ultraviolet (UV) light, development, and an etching process;
- (3) coating a PR film with thickness hnr;
- (4) application of extreme UV lithography to form a rectangular groove with width wnr;
- (5) deposition of a Si film into the groove followed by lifting off the PR to form a Si nanoridge;
- (6) rounding the rectangular top of the Si nanoridge to a semi-circular one using e-beam lithography by carefully controlling the exposure time and scanning speed;
- (7) coating a PR film;
- (8) application of a mask, a PR exposure, and a development to lift out the PR films next to the Si nanoridge;
- (9) evaporation of a porous SiO2 film with thickness hnr using the oblique deposition technique40;
- (10) lifting out the PR film;
- (11) repetition of steps (3) to (5) but coating with a PR film of thickness hAg and sputtering an Ag film to form Ag nanostrip;
- (12) repetition of steps (7)–(10) to evaporate a porous SiO2 film with thickness hAg;
- (13) deposition of a Si film with thickness hSi;
- (14) deposition of a conventional SiO2 film to cover the waveguide structure.
Note that reducing the contact area between the nanostructured Si and Ag increases mode confinement. Therefore, choosing a semi-circular top for both the Si and Ag is able to achieve the smallest contact area. However, we chose an Ag nanostrip with a rectangle to relief the fabrication difficulty in forming an inverse semi-circular top by e-beam lithography. In addition, the difficult step to fabricate the proposed structure is to perfectly obtain the Si nanoridge with a semi-circular top. Here, we suggested adopting e-beam lithography by carefully controlling the exposure time and scanning speed to moderately reduce the imperfections. To evaluate the device robustness, we investigated the fabrication tolerance of the NHPWSW. The investigation revealed that the most critical parameters affecting the mode properties were the dimensions of Ag nanostrip and Si nanoridge. Moreover, the dependences of mode properties on wnr and hAg are analyzed and shown in Fig. 3. Considering both the critical dimensions and the fabrication steps, the alignment between Ag nanostrip and Si nanoridge might be the most difficult to control precisely. Therefore, we analyzed the dependences of Am and Lp on the relative deviation of the Si nanoridge (Δx/wnr) for the Ag nanostrip at hnr = 15 nm, hAg = 10 nm, hSi = 220 nm, and wSi = 150 nm (Fig. 10). Here, Δx is the deviation distance in the x-direction. Evidently, Am and Lp are almost constants across the deviations from Δx/wr = 0 to 0.5, revealing the high fabrication tolerance of the proposed structure on its critical dimensions.
Fig. 10. The dynamics of (a) Am and (b) Lp versus the relative deviation of the Si nanoridge (Δx/wnr) for the Ag nanostrip with several values of wnr and hnr = 15 nm, hAg = 10 nm, hSi = 220 nm, and wSi = 150 nm.
The other crucial parameter that defines device performance is the operating bandwidth. We proceeded in addressing the spectral response on Lp and Am. Considering the dispersion of the material [42,44], Fig. 11 shows plots of Am and Lp versus the working wavelength, λ. We observed that the Am varied from 5.3 × 10−5 to 7.7 × 10−5 in the wavelength range of λ = 1,400 to 1,650 nm, respectively.
Fig. 11. Plots of (a) Am and (b) Lp versus the working wavelength λ at hnr = 15 nm, hAg = 10 nm, hSi = 220 nm, and wSi = 150 nm for several values of wnr.
However, the Lp showed stronger dependence on λ than Am. For instance, Lp values were 677 and 1,505 µm for λ = 1,400 and 1,650 nm, respectively. Within the range of λ = 1,500 to 1,600 nm, Lp showed moderate variation from 930 to 1,310 µm, respectively. The slight variation of Am and Lp across the broadband of 100 nm confirmed the high robustness of the present structure.
Here, we summarize the novelty of the present design compared to the previously published designs [26–31,34–39]. A typical HPW structure [20–22] consisted of a low-index dielectric sandwiched by a high-index dielectric and a metal is adopted by the papers [26–31] despite using different geometries as classified in category 1. The advantage of category 1 shows smaller Am but accompanies with shorter Lp about only tens of micrometers that is impractical to apply in large-area PICs. The other kind of design as classified in category 2 [34–39] are formed by coupling two HPW modes using two typical HPWs with a mirror symmetry arrangement. The longitudinal component of the electric field (dominates the ohmic losses) of the symmetrical HPW structures is nearly zero in the center of the metal medium, thus significantly increasing the Lp. However, the symmetrical HPWs lead to larger mode areas of about Am = 10−2 to 10−3. Among the works [26–31,34–39], the structures are all based on at least a constituting element, namely a typical HPW. In contrast, the mode property of the proposed NHPWSW is formed by coupling two guiding mechanisms including a typical HPW and a high-index-contrast SW that are totally different from that in papers [26–31,34–39]. The resultant guided mode accomplishes a waveguide mode with an Am of the order of 10−5 concurrently with Lp of the order of millimeter by well leveraging Am and Lp. The present results significantly relief the drawbacks of scarifying the mode performances either Am or Lp in papers [26–31,34–39]. We believe that the novel design makes the present work outperform all the other work in literature [26–31,34–39].
Recently, a two-dimensional (2D) monolayer molybdenum disulfide (MoS2) showing strong light-matter interactions and flexible tunability is widely used in building various nanophotonic and optoelectronics devices due to its bound exciton confinement [46]. The exciton modes in monolayer MoS2 result in the resonant coupling with incident photons as similar as the SPP modes in metals via coupling with incident photons. However, they are limited by the low quantum yield for the practical applications such as quantum emitters and photon detection. Yang et al. [47–49] reported various single polyaniline nanowires assembled with quantum dots to improve the performances of light emission and photon detection. To achieve above desirable performances, better light confinement with lower energy loss are two inevitable conditions. Integrating monolayer MoS2 or quantum emitters with high-performance plasmonic structures such as the present NHPWSW provides an additional degree of freedom via exciton-plasmon coupling to tailor light-mater interactions for exciton modulation and photon detection.
4. Waveguide crosstalk
To assess the degree of device integration, crosstalk between adjacent waveguides is a fundamental index. Therefore, we analyzed the mode crosstalk of a coupled waveguide system consisting of two present NHPWSWs with a center-to-center distance, s, as shown in Fig. 12(a). Mode profiles, Ey, of the symmetric and asymmetric modes are shown in Figs. 12(b) and (c), respectively. Here we set hSi = 220 nm, wSi = 250 nm, wnr = 10 nm, hnr = 15 nm, and hAg = 10 nm. In coupled mode theory [50], the coupling length, Lc, of a coupled waveguide system is used to evaluate the crosstalk strength and is determined by Lc = λ/[2(ne − no)], where ne and no are the effective refractive indices of symmetric and asymmetric modes, respectively. The coupling length, Lc, versus s for several pairs of hSi and wSi are shown in Fig. 12(d), and that for the pairs of wnr and hAg are shown in Fig. 12(e). As can be seen in Fig. 8(c), variations of hSi and wSi have an insignificant effect on Am. Simultaneously, Re(ne) increases substantially with hSi and wSi [see Fig. 8(a)].
Fig. 12. (a) Schematic of a coupled waveguide system consisting of two NHPWSWs with a center-to-center separation, s. Mode profiles Ey of the (b) symmetric and (c) asymmetric modes for the parameters’ values of s = 500 nm, hSi = 220 nm, wSi = 250 nm, wnr = 10 nm, hnr = 15 nm, and hAg = 10 nm. Coupling length Lc versus s for several pairs of (d) hSi and wSi, and (e) wnr and hAg. (f) Comparison of Lc for the present structure with that for other reported results.
It indicates that more energy is concentrated in the Si nanoridge, although Am is almost invariant, resulting in weaker crosstalk and thus larger coupling length, as shown in Fig. 12(d). Note that the effect of hSi is more significant than that of wSi because larger hSi makes mode distribution tighter than that of larger wSi. For hSi = 220 nm and wSi = 250 nm, the slop of Lc to s is 187 µm/100 nm, and Lc achieves 1,881 µm at s = 1.5 µm. For the pairs of wnr and hAg, Lc shows a smaller variation [Fig. 12(e)]. Additionally, as can be seen from Figs. 3(a) and (c), larger hAg results in larger Re(ne) and smaller Am, thus leading to larger Lc. In contrast, although larger wnr results in larger Re(ne), Am also increases. Therefore, the coupling length is almost invariant with s [Fig. 12(e)]. To demonstrate the possibility of constructing highly integrated nanophotonic circuits, we compared the coupling length of the proposed NHPSW (at hSi = 220 nm, wSi = 250 nm, wnr = 30 nm, hnr = 15 nm, and hAg = 50 nm) with that of other previously reported results in Fig. 12(f). We observe that the crosstalk of our structure is lower than that in [27] and [30]. Compared to [29], the present structure shows lower (higher) crosstalk, while s is greater (smaller) than 1.0 µm. However, the coupling lengths of the three structures with a few tens of micrometers are much shorter than those (Lp >1,000 µm) of our structure. The results demonstrate that the present design not only features extremely low propagation losses but also allows building high-density nanophotonic circuits.
5. Summary
We have integrated an NHPW with a high-index-contrast SW to obtain a novel waveguide structure operating at the telecommunication wavelength of 1,550 nm. It has featured a record millimeter-scale propagation distance with ultra-deep subwavelength mode size of the order of 10−5, achieving an FoM of the order of 105. Compared with the state-of-art HPWs, our design achieves 10 to 40 times the propagation length at the same order of mode area. In addition, the mode area of the present structure is two orders of magnitude smaller than that of the symmetric HPWs with a millimeter-scale propagation length. Besides, the proposed structure is not limited by the stringent structural and material symmetries, alleviating the required fabrication precision of the symmetric HPWs. We have confirmed structure robustness implying its practical implementation, performed mode characterization, and investigated the effects of fabrication imperfections on waveguide performance. Finally, the crosstalk between waveguides was assessed to demonstrate the ability to build ultra-compact photonic components. In addition to being beneficial for forming large-scale nanophotonic circuits, the deep-subwavelength mode confinement also has a significant impact on the enhancement of light–matter interaction. More specifically, it allows improving the accuracy of optical sensors, power consumption for optical modulators, and the resolution of near-field optical probes.
Funding
Ministry of Science and Technology, Taiwan (109-2112-M-005-005).
Acknowledgments
The authors would like to thank Enago (https://www.enago.tw) for the English language review.
Disclosures
The author declares no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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