Here we present a novel waveguide providing > 70% optical power confinement in a relatively small area, 0.12μm2, which could be used to fabricate quantum dot or other sub-wavelength-sized active regions, modulators or detectors on Si. This structure forms a novel, low-index waveguide which can be engineered to have properties similar to high-index or slot waveguides, showing that there is in fact a continuum between these two waveguides.
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Interconnect (IC) delay has become a significant impediment to processor performance since decades of scaling have both reduced transistor delay and increased IC delay, and the most mature technology to address this issue is optical ICs[1, 2]. Recently, IBM has demonstrated an integrated, Si-based, nanophotonic chip with the ultimate goal of increasing integrated chip speed. To accomplish this goal, several on-chip, optical waveguide (WG) structures can be utilized including, for example, ridge and slot waveguides.
Starting with a silicon-on-insulator (SOI) wafer, ridge waveguides have been the standard waveguide structure for guiding light on a Si platform. Ridge waveguides (traditional WGs) utilize the well-known phenomenon of guiding light through a high index material using total internal reflection. Another technique to guide light on Si has been proposed and demonstrated, the slot waveguide[4, 5], which counter-intuitively guides light within a low-index, sub-wavelength (typically ∼ 50 nm) region. Though a slot waveguide has a very small mode area, enabling a lower threshold albeit with lower power, it also has, unfortunately, a low power confinement factor. Here we develop a low-index waveguide that enable light confinement within a low-index core with a small mode area and high confinement factor by engineering the high-index cladding thickness of the waveguide. The novel aspect of guiding light through a low-index medium has advantages of enabling devices design whose active region has a lower index than that of Si, thus enabling on-chip optical devices by possibly using erbium-doped SiO2 or other oxides or metamaterials, for example, quantum dots within an insulating matrix as an active region. Such a multi-QD-based device would be analogous to a gaseous laser, where the gain medium (QDs or the gas) is of a sub wavelength size and is contained within an external optical cavity.
The proposed, low-index WG, requires a low-index material cladded by two thin, high-index layers which are then surrounded by a low-index material, an example of such a structure is shown in Fig. 1. The WG’s core, in this case, is composed of, an alloyed material made of QDs (e.g. GaSb, InAs, InN, Ge) in a low-index matrix (e.g. oxide or polymers) and confined between two cladding layers of Si surrounded by SiO2. The WG is optimized to guide 1.55μm light, this large wavelength (in comparison to the size of the QDs) is favorable to reduce scattering events. The WG confines light in its core in two different directions using two different mechanisms; in Fig. 1, light is confined in the x-direction through the novel WG structure and in the y-direction through traditional index-contrast.
2. 1D analytic model
Figure 2(a) presents a simplified, 1D model of the WG focusing on the novel, optical-confinement mechanism, and is used to introduce the basic confinement concepts. The structure is such that nlow < ncore < nclad and, for this paper, we shall use nlow = nSi02 = 1.5, nclad = nSi = 3.5 and ncore = 2.25. A core index of 2.25 can be achieved through an alloy, ∼ 50% by volume, of a high-index material (e.g. III–V, II–IV, nanowires) and of a low-index material (e.g. SiO2, polymer). Our proposed, low-index waveguide is optimized to guide light at 1.55 μm but other wavelengths could be considered, keeping in mind that longer wavelengths will be more tolerant, scatter less, to index variations (surface roughness, QDs, etc.).
The magnitude of the electric field (Ex) for the 1D case, calculated by solving analytically the Maxwell’s equations for the transverse mode (TM), is depicted in Figs.2(b) and (c) for two different cladding thicknesses, hclad = 130 nm and 100 nm, for a constant core thicknesses of 300 nm. These solutions present the approximately highest field overlap of Ex with the core region and were optimized after several iterations of the core (hcore) and cladding (hclad) thicknesses. In varying hclad from 100 to 130 nm, the electric field within the core changes from an evanescent to a sinusoidal shape, electric fields typically associated with slot and traditional, index-contrasted WGs, respectively.
The changing profile can be understood by comparing the effective refractive indices for the 130 nm (neff = 2.29) and 100 nm (neff = 2.19) core thicknesses, which is greater and less than ncore, respectively. This change of the neff explains the variation of the mode’s shape, keeping in mind that Ex can be expressed as:
An important metric which assesses the quality of the optical mode’s overlap with the core (i.e. gain or active region) is the power confinement (Γ), which can enhance the device’s (lasers, modulators, and detectors) efficacy. The power confinement is usually defined as the ratio between power (E × H*) in the core to the overall power in the WG (core and claddings). For the structures described in Figs.2(b) and (c), Γ = 76% and Γ = 80%, respectively, and are considerably higher than that of typical slot waveguides, ∼ 30 – 45 % [4, 6].
3. 2D finite difference model
To understand the behavior of the full structure depicted in Fig.1, a 2D, finite-element model, was solved for Ex and the results are shown in Fig.3. This 2D WG offers additional confinement in the y-direction through traditional index contrast between the core and the filling polymer material. The model is numerically solved for various thicknesses of hclad at a fixed hcore = 300 nm and core widths wcore = 350 nm. The WG parameters are optimized in order to maximize the confinement ratio defined by the following:Eq. (2) leads to better confinement predictions, especially for designs which highly-confine light. Figures 3(a) and (b) depict the magnitude of Ex over the waveguide’s cross-section and illustrate the quality of the mode’s overlap with the core for two different values of hclad, 130 nm and 350 nm, respectively. The cladding thickness that approximately optimizes Γ′ is represented in Fig.3(a), where hclad = 130 nm, similar to the 1D model. Light confinement within the core significantly reduces with increasing hclad, as can be seen by moving from point (a) (Γ′ = 0.68) to point (b) (Γ′ = 0.22) along the curve depicted in Fig.3(d). For the case of a hclad = 350 nm (shown in Fig.3(b)), one can see that the modes evolve into two separate, ridge-like WGs, where the light is primarily guided in the clad itself. This reduced confinement within the core demonstrates the importance of maintaining small hclad. If one now takes the geometry shown in Fig.3(b) and, keeping all else constant, reduces the core thickness, the traditional, index-contrasted WG reverts to the familiar slot-WG, with high confinement within a narrow, low-index region. This variation in geometries, shows that there is actually a continuum of properties between a slot, low-index and ridge WGs, with many properties of the the proposed low-index WG between that of the slot and ridge WGs.
We have shown that hclad strongly affects the mode’s profile for fixed hcore and wcore. These two parameters only slightly affect the confinement ratios when hcore and wcore are in the vicinity of 350 nm and 300 nm, respectively, as shown in Fig.4. Larger core dimensions do provide enhanced confinement but they are not single mode.
Strong light confinement can be both beneficial and detrimental to laser operation because both enhanced spontaneous emission and wavelength dispersion can arise. As taken into account by the Purcell factor, small mode areas alter the density of optical states which effectively result in enhanced spontaneous emission from the emitters within the guided mode. The mode area of the optimized low-index WG (Fig. 3(a)) is 0.12μm2, about an order of magnitude higher than the ∼ 0.01μm2 mode areas of slot waveguides; however, with a high Q-factor cavity, enhanced spontaneous emission could still result. Such an phenomenon would enable, for example, low-threshold lasing. The WG-dispersion of the optimized low-index WG is relatively small, two times smaller than the bulk dispersion of silicon, as shown in Fig. 5, suggesting that WG-dispersion is negligible and that global dispersion would be dictated by the materials composing the WG. Indeed, WG-dispersion can become significant for small mode-area waveguides such as the ones seen in plasmonics and, to a laser extent, in slot-waveguides and such a WG-dispersion can overcome the material dispersion. However, the light in the low-index WG depicted in Fig. 3(a), is not confined enough to be highly WG-dispersive.
Table 1 summarizes the low-index WG properties in comparison to standard, index-contrasted WGs and slot-waveguides. In addition to the characteristics previously discussed, the light coupling either in or out of the WG is facilitated by its geometry and could be achieved by properly engineering a standard, SOI-based WG. As can be seen in this table, many of the properties of the low-index WG is in between that of the slot and index-contrasted WGs.
Here we have demonstrated a novel, low-index waveguide. In addition, this waveguide possesses a high power confinement ratio (∼ 70%) allowing good device (laser, detector and modulator) efficiencies. The small mode-area of the cavity (∼ 0.1 μm) would also enable low-threshold lasing and the WG has been shown to have low dispersion. Finally, we showed that slot and ridge waveguides are special cases, optimized under different conditions, of the proposed WG structure and that there is a continuum of properties between the slot and ridge waveguides.
References and links
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