Low dispersion broadband integrated double-slot microring resonators optical buffer

Abstract

Microring resonator optical buffer is attractive in high-speed optical network system, but ordinary microring resonator use strip waveguide as its basic light guide medium, which cannot provide small footprint, low dispersion and high delay-bandwidth product (DBP) simultaneously. Double-slot waveguide structure was first proposed to construct racetrack-microring resonators. It was found that cascading multiple microrings can increase the delay-bandwidth and lower the dispersion of the resonators by optimizing the structure parameters. Optical buffer cascaded by 8 microrings with flat bandwidth of 20 GHz provided the delay of 150 ps and the dispersion of ~${10}^{-7}$ ps/nm over 1530−1630 nm, and the footprint of each microring was about 51$$. This study can provide design methods and theoretical basis support for practical application.

Keywords

optical buffer / microring / resonator / delay / slot / waveguide / dispersion

1 Introduction

To achieve photonic circuits with ultra-high integration density, it has been desired for a long time to have nano-scale optical waveguides with strong confinement of light. Three kinds of typical nanophotonic waveguides have been developed in the past years, which includes nanophotonic wires (strip nano-waveguide) [1,2], photonic-crystal waveguides [3] and nanoplasmonic waveguide [4-16]. The former two nanophotonic waveguides, which utilize nano-structures with ultra-high index contrast, cannot be beyond the diffraction limit. In contrast, a nanoplasmonic waveguide can break the diffraction limit and enable deep subwavelength confinement and waveguiding of light, which makes it become a very attractive candidate for ultra-high integration density. A nanoplasmonic waveguide also offers a way to merge electronics and photonics [17] so that it is potential to realize ultra-small optoelectronic integrated circuits (OEICs) for low power-consumption and high speed signal generation, processing as well as detection. Several years ago, some nanoplasmonic waveguides supporting ultra-highly localized fields were proposed and demonstrated, including metal nano-slot waveguides [8-10,15,16] and metal V-groove waveguides [11,12]. However, these nanoplasmonic waveguides have large losses and their propagation distance is very limited (usually ~µm).

More recently hybrid plasmonic waveguides [18-21], which consist of a high-index region, a metal region and a low-index nano-slot between them, have been paid intensive attention to Refs. [22-43] It has been shown that hybrid plasmonic waveguides have the potential to achieve a nano-scale light confinement as well as relatively long propagation distance simultaneously. In 2007, Alam et al. proposed the initial form of a hybrid plasmonic waveguide including a lossy dielectric nanowire adjacent to a metal surface [18]. It was shown that a super-mode exists due to the coupling between a surface-plasmonic mode and a dielectric-waveguide mode. The mode properties of this super-mode were investigated in the wavelength range from 0.5 to 1.2 µm (which is not the transparent window of silicon and out of the telecommunication window) and the calculated full width at half maximum (FWHM) of the demonstrated supermode is about 400 nm (~λ/3 when operating at 1.2 µm), which is not as small as that achieved by those hybrid nanoplasmonic waveguide proposed later [19-21]. In Ref. [19], the name of hybrid plasmonic waveguide was proposed formally and a hybrid plasmonic waveguide operating at 1550 nm was obtained by putting a dielectric cylinder above a metal surface, for which the mode area was as small as λ²/400. With this kind of hybrid plasmonic waveguide, a nano-laser emitting 489 nm light was demonstrated in 2009 [43]. In comparison with the hybrid plasmonic waveguide with a cylinder, a nano-waveguide with a rectangular cross section would be more useful from a view point of fabrication and integration [20,21]. In Ref. [20], the authors has given an analyses for the dispersion relation and loss of the modes in several types of metal-GaAs nanoplasmonic waveguides, including a rectangular GaAs strip above Ag-substrate (which is very similar to that shown in Refs. [18,19]), and a lateral GaAs-gap-Ag strip on a SiO₂ substrate (which is not easy to fabricate). For these early hybrid plasmonic waveguides [18,19], the surface plasmonic effect occurs at the top-surface of the metal thin film and unfortunately the metal top-surface is usually quite rough, which would introduce some notable scattering loss.

As it well known, silicon photonics have become very popular because of the compatibility with mature complementary metal oxide semiconductor (CMOS) technologies with low cost and excellent processing control. And silicon-on-insulator (SOI) nanowires are usually used for silicon nanophotonic integrated circuits. Therefore, it would be attractive to develop a silicon hybrid nanoplasmonic waveguide which is SOI-compatible so that it can be fabricated on a standard SOI wafer by using CMOS-compatible processes. In our previous paper, we have presented a SOI nanowire with a metal cap which is used for a submicron-heater [22], and there is a low-index region (e.g., SiO₂) between the silicon core and the metal cap. When the SiO₂ layer becomes very thin (e.g., several tens of nanometers), a silicon hybrid nanoplasmonic waveguide (with a metal cap) is achieved, as proposed first in Ref. [21]. This silicon hybrid nanoplasmonic waveguide has a field enhancement at the thin low-index region for the hybrid plasmonic mode (transverse magnetic (TM) polarization) and the spot size can be as small as 50 nm × 5 nm when operating at 1550 nm. Particularly, for this silicon hybrid nanoplasmonic waveguide, the surface plasmonic effect occurs at the metal bottom-surface, which is as smooth as the top surface of the low-index thin film. This is important and helpful to obtain low scattering loss of surface. This might make it more attractive than those hybrid plasmonic waveguide on a metal surface. Furthermore, the SOI-compatibility of the proposed silicon hybrid nanoplasmonic waveguide makes the fabrication simplified, and it becomes feasible to integrate a nanoplasmonic circuits and a silicon nanophotonic circuit on the same chip conveniently. Therefore, the silicon hybrid nanoplasmonic waveguide has been attracting lots of attention and various hybrid nanoplasmonic waveguides with some modifications have been proposed in the following years [44-65]. Silicon hybrid nanoplasmonic waveguide for transverse electric (TE) polarization can also be obtained by e.g., introducing double low-index vertical nano-slots at both sides of a high-index region [49-55]. In Section 2.2, various hybrid nanoplasmonic waveguides will be reviewed and compared.

With these proposed hybrid plasmonic waveguides, some ultracompact functionality elements have been realized, including directional couplers [59-63], power splitters [64-68] and grating reflectors [69]. Since the hybrid plasmonic waveguide enables a submicron bending radius [53,64,70,71], one can realize ultra-compact resonators, including submicron rings/donuts [65,66,71-75], disks [76,77] and photonic-crystal cavities [78-80], as the well-known versatile elements in photonic integrated circuits. Such resonators have ultra-compact footprint as well as good performances (e.g., acceptable quality factor and large Purcell efficiency [77]). Furthermore, as it well known, hybrid plasmonic waveguides are very polarization-sensitive, which is helpful for realizing ultrasmall polarization-handling devices, including polarizers [81-86], polarization-beam splitters (PBS) [87-92], and polarization rotators [93-95]. These will be also reviewed in Section 3.4.

Regarding that a hybrid plasmonic waveguide is still not a good option for long-distance (e.g., 10³-10⁴µm) optical interconnects if there is no assistance from gain mediums [50], it might be a promising way to combine a silicon hybrid nanoplamonic waveguide and a low-loss SOI nanowire [72]. This way, the low-loss SOI nanowire enables a long-distance optical interconnect while the hybrid nanoplamonic waveguide is used locally to realize some functionality elements with ultrasmall footprints. To realize the seamless integration between hybrid plasmonic circuits and silicon nanophotonic circuits, two coupling approaches can be utilized. One is the evanescent coupling structure designed according to the phase-matching condition [63] and the other is the butt-coupling structure (which provides an efficiency of 70%-80% with a very short mode converter [96]).

To compensate the intrinsic loss of hybrid plasmonic waveguides, a general way is to introduce some gain medium, in which way active hybrid plasmonic devices can be also realized. For example, a deep subwavelength plasmonic laser has been demonstrated experimentally, by using a hybrid plasmonic waveguide with a CdS cylinder above a silver plate [43]. For silicon hybrid plasmonics, the nano-slot can be filled in with some low-index gain medium, e.g., Er-doping, quantum dots, Si nano-crystals, etc. Due to the field enhancement in the low-index nano-slot region, some gain enhancement is observed [47]. In Section 4.1, we will give a discussion on the loss isspue of silicon hybrid nanoplamonic waveguide. Furthermore, the field enhancement in the nano-slot also makes the hybrid plasmonic waveguide very promising for the applications including highly-efficient optical modulation [97-102], nonlinear optical effects (like optical parametric amplifier [103]), optical sensing with high sensitivity [104-106], and enhanced optical forces [107,108]. This will be summarized in Section 4.2.

2 Silicon hybrid nanoplasmonic waveguidest

2.1 Principle of silicon hybrid nanoplasmonic waveguides

To understand the guided-mode mechanism for a hybrid nanoplasmonic waveguide (which usually consists of a high refractive-index (RI) region, a metal layer and a low-RI region between them), first we consider a hybrid slab waveguide with the same layer structure for which the analytical expressions for the eigen-modes can be obtained. The hybrid slab waveguide has a low-index cladding, a high-index layer, a low-index layer and the metal layer, as shown in Fig. 1(a). According to Maxwell’s equation, the electric field distribution of the TM fundamental mode for the slab waveguide is given as

(1)$$E_y={\displaystyle \frac{\mathrm{1}}{n_M^2}}{A}_M\exp (-{\gamma }_M(y-t_L)),t_{\mathrm{L}}<y+\infty ,$$

(2)$$E_y={\displaystyle \frac{\mathrm{1}}{n_L^{\mathrm{2}}}}[A_{L1}\exp ({\gamma }_L(y-t_L))+A_{L2}\exp (-{\gamma }_{L}y)],\mathrm{0}<y<t_{\mathrm{L}},$$

(3)$$E_y={\displaystyle \frac{\mathrm{1}}{n_L^2}}{A}_H\cos (k_{H}y\mathrm{-}\phi ),-t_{\mathrm{H}}<y<\mathrm{0},$$

(4)$$E_y={\displaystyle \frac{\mathrm{1}}{n_S^{\mathrm{2}}}}{A}_S\exp ({\gamma }_S(y+t_H)),y<-t_{\mathrm{H}},$$

where the constants A_M, A_L1, A_L2, A_H, and A_S are determined according to the boundary conditions at the corresponding interfaces between adjacent layers. And the complex propagation constant can be achieved by solving the following eigen-equations

(5)$$k_H{t}_L=n\pi +{\tan }^{-\mathrm{1}}\left({\displaystyle \frac{{\gamma }_S{n}_H^2}{k_H{n}_S^2}}\right)-{\tan }^{-\mathrm{1}}\left({\displaystyle \frac{{\gamma }_L{n}_H^2}{k_H{n}_L^2}}{\displaystyle \frac{\mathrm{1}-{\displaystyle \frac{{\gamma }_L{n}_M^2+{\gamma }_M{n}_L^2}{{\gamma }_L{n}_M^2-{\gamma }_M{n}_L^2}}\exp (\mathrm{2}{\gamma }_L{t}_H)}{\mathrm{1}+{\displaystyle \frac{{\gamma }_L{n}_M^2+{\gamma }_M{n}_L^2}{{\gamma }_L{n}_M^2-{\gamma }_M{n}_L^2}}\exp (\mathrm{2}{\gamma }_L{t}_H)}}\right),$$

where, n_M, n_L, n_H, and n_S are the indices for metal, the low-index layer, the high-index layer, and the substrate, respectively,

$$k_0^{\mathrm{2}}{n}_H^{\mathrm{2}}-k_H^{\mathrm{2}}=k_0^{\mathrm{2}}{n}_M^{\mathrm{2}}+{\gamma }_M^{\mathrm{2}}=k_0^{\mathrm{2}}{n}_L^{\mathrm{2}}+{\gamma }_L^{\mathrm{2}}=k_0^{\mathrm{2}}{n}_S^{\mathrm{2}}+{\gamma }_S^{\mathrm{2}}={\beta }^{\mathrm{2}},$$

in which k₀ is the wavenumber of the light in vacuum.

Figures 1(b)–1(d) show the profiles for the electric field E_y of the fundamental mode in the hybrid slab waveguide as the low-index-layer thickness t_L decreases. As mentioned in the introduction, it is promising to choose SOI wafers for the hybrid plasmonic structure. Therefore, in this example Si and SiO₂ are chosen as the materials for the high-index layer and the low-index layer, respectively. The wavelength λ = 1550 nm and the corresponding refractive indices for all the involved materials as n_metal = 0.1453+ 11.3587i (Ag) [19], n_SiO2 = 1.445, and n_Si = 3.455. The thickness of the silicon layer is assumed to be 220 nm. One should realize there are two eigen modes in such a hybrid slab waveguide. One is the dielectric mode confined well in the Si region and the other one is the surface plasmonics mode at the interface between SiO₂-metal.

When the thickness of the low-index (e.g., SiO₂) layer between Si and metal is large (e.g., 0.5 µm), these two eigen modes are little overlapped and the dielectric mode confined in the silicon region is influenced by metal very slightly, as shown in Fig. 1(b). In this case, the dielectric mode is used usually for the photonic integrated circuits, which is the case of using metal heater for thermal tuning. One should note that there are field enhancements at the top and bottom surfaces of the SiO₂ layer. The field enhancement at the Si-SiO₂ interface is due to a strong discontinuity of the normal component of the electric field, which is the same as that in a pure-dielectric horizontal slot waveguide [2]. On the other hand, at the SiO₂-metal interface, surface-plasmonic wave is excited. The electric field of the excited surface-plasmonic wave decays exponentially at both sides of the interface and has a peak at the interface. As shown in Eq. (2), the field distribution in the thin SiO₂ layer (0<y<t_L) is as the sum of two exponential functions. Therefore, when the SiO₂ thickness becomes less than the penetration depth of the evanescent wave (e.g.,<100 nm), the dielectric mode and the surface plasmonic mode become overlapped and coupled. And there is a field enhancement in the low-index layer, as shown in Fig. 1(d) and the mode is confined tightly in the low-index region.

Fig.1 (a) Configuration for a hybrid slab waveguide; the electric field Ey in a hybrid slab waveguide when (b) tL = 500 nm; (c) tL = 150 nm; (d) tL = 50 nm

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2.2 Structures of silicon hybrid nanoplasmonic waveguides

Fig.2 (a) Cross section of a hybrid plasmonic waveguide with a metal cap; (b) calculated field distribution for the major component Ey(x,y) of the quasi-TM fundamental mode of the hybrid plasmonic waveguide with wco = 200 nm and hslot = 50 nm. In this figure, the field distributions Ey(0, y) and Ey(x, 0) are also shown [21]

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Similarly, a silicon hybrid nanoplasmonic waveguide shown in Fig. 2(a) has a significant field enhancement in the low index region, as shown by the curve of E_y(0, y) in Fig. 2(b). In this example, the wavelength λ = 1550 nm and the geometrical dimensions are chosen as follows: w_co = 200 nm, h_m = 100 nm, h_slot = 50 nm, and h_rib= H = 300 nm. In Ref. [21], it has shown that a silicon hybrid nanoplasmonic waveguide has a spot-size as small as 50 nm × 5 nm even when operating at 1550 nm and the propagation distance is as long as several tens of microns. It can be seen that a hybrid plasmonic waveguide provide a promising platform to realize ultra-dense photonic integration. In the past years (from 2009 to 2014), people have developed various hybrid plasmonic waveguides [24-42,44-58] . In principle, a hybrid plasmonic waveguide can be formed with e.g., a cylindrical wire [19] or a rectangular cross section [20]. The cylindrical one is pretty successful when it was proposed first in 2008 [19] and a hybrid plasmonic waveguide with a silicon cylinder were also demonstrated later [26,27]. On the other hand, a nano-waveguide with a rectangular cross section would be more useful than a cylindrical hybrid plasmonic waveguide regarding the fabrication and integration [21]. Therefore, here we focus on the silicon hybrid nanoplasmonic waveguides with rectangular structures as summarized in Table 1.

Tab.1 Reported silicon hybrid nanoplasmonic waveguides with rectangular structures

Ref.	year	configuration	theory/ experiment	features
[18]	2007		theory	structure: Si/SiO2/Ag λ: 500~1200 nm FWHM: 400 nm Lprop: 13.5 µm
[21]	2009		theory	structure: Ag/SiO2/ Si λ: 1550 nm WWG: 50 nm Lprop: ~90 µm
[45]	2010		experimen	structure: Au-SiO2-Si λ: 1550 nm WWG: 250 nm Lprop: 40 µm
[49]	2010		theory	structure: Ag-SiO2-Si-SiO2-Ag λ: 1550 nm Si-core width: 50 nm Aeff: 0.007 µm2 Lprop: ~20 µm
[47]	2011		theory	structure: Ag-SiO2-Si λ: 1550 nm WWG: 70 nm loss: ~0.1 dB/µm Aeff: 0.066 µm2
[51]	2011		theory	structure: Al-SiO2-Si-SiO2-Al λ: 1550 nm Si-core width: 300 nm Lprop: ~31 µm
[53]	2011		experimen	structure: Al-SiO2-Si-SiO2-Al λ: 1550 nm Si-core width: 43-136 nm loss: 1.07-1.63 dB/µm
[54]	2011		experiment	structure: Cu-SiO2-Si-SiO2-Cu λ: 1550 nm Si-core width: 21-134 nm loss: 0.37-0.63 dB/µm
[55]	2011		experiment	structure: Ag-SiO2-Si-SiO2- Ag λ: 1550 nm Si-core width: 300 nm; propagation loss: 1.6 dB/mm
[65]	2012		experiment	structure: Cu-SiO2-Si λ: 1550 nm waveguide width: 160 nm loss: 0.122 dB/µm
[52]	2012		experiment	structure: Cu-SiOx-Si-SiOx-Cu λ: 1554 nm/1318 nm Si-core width: 160-220 nm loss: 0.2-0.3 dB/µm
[57]	2013		experiment	structure: Ag-air-Si λ: 1550 nm Si width: 400 nm loss: 0.14 dB/µm
[56]	2013		theory	structure: Si-Si:nc-Ag-Si-nc-Si λ: 1550 nm slot size: 150 nm × 200 nm loss: 3 × 10-4 dB/µm
[38]	2013		theory	Structure: Ag-Air-Si λ: 1550 nm Aeff: 2.8 × 10-6 λ2 Lprop: 2.6 µm

Fig.17 SEM picture for a sputtering silver surface

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Fig.18 SEM picture for a silicon hybrid nanoplasmonic waveguide with dropped metal [109]

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As shown in Table 1, in 2007 Alam et al. proposed the initial form of a hybrid plasmonic waveguide including a lossy dielectric nanowire adjacent to a metal surface [18] and the calculated FWHM of the supported supermode is about 400 nm (~λ/3 when operating at 1.2 µm), which is much larger than that achieved by those hybrid nanoplasmonic waveguide proposed in the following years [44-55]. Note that the surface plasmonic effect in this hybrid plasmonic waveguide occurs at the top-surface of the metal thin film and unfortunately the metal top-surface is usually quite rough. The roughness for the top surface of the sputtered silver thin film is ~20 nm (see the scanning electron microscope (SEM) picture for a sputtering silver surface shown in Fig. 3). This will introduce some notable scattering loss. Furthermore, for such a hybrid plasmonic waveguide with the metal thin film at the bottom, a standard SOI wafer is not available and one usually needs to deposit amorphous silicon thin film [40]. In 2009, a silicon hybrid nanoplasmonic waveguide with a metal cap is proposed first [21]. For this waveguide, the silicon ridge can be even modified to be a silicon slab so that the fabrication can be simplified further. The spot-size is as small as 50 nm × 5 nm when operating at 1550 nm and the calculated propagation loss is ~0.1 dB/µm. The surface plasmonic effect in this silicon hybrid nanoplasmonic waveguide occurs at the metal bottom-surface, which is as smooth as the top surface of the low-index thin film to help obtain low scattering loss of surface. More importantly, a standard SOI wafer can be used for this hybrid plasmonic waveguide and the SOI-compatibility makes the fabrication simplified. A 250 nm-wide silicon hybrid nanoplasmonic waveguide with such a structure was fabricated in 2010 [45], and the measured propagation length is about 40 µm with a gold cap, which agrees well with the calculation results. For the fabrication of a silicon hybrid nanoplasmonic waveguide, a challenge is to adhere the narrow metal strip on the SiO₂ film tightly. The process of the metal patterning should be careful. Otherwise, the metal strip might be lift-off, as shown in Fig. 4 [109]. A potential solution for this issue is to use the modified structure with a reversed metal ridge on the top for a silicon hybrid nanoplasmonic waveguide, as shown in Fig. 5(a) [47]. Figure 5(b) shows the field profile in a hybrid plasmonic waveguide. It can be seen that there is a significant field enhancement, which is similar to that shown in Ref. [21]. This type of silicon hybrid nanoplasmonic waveguide has been researched theoretically [46] as well experimentally [65]. The measured propagation loss of the fabricated silicon hybrid nanoplasmonic waveguide with copper is ~0.122 dB/µm for a 160 nm-wide waveguide [65]. In Ref. [48], Goykhman et al. demonstrated a silicon hybrid nanoplasmonic waveguide fabricated with the local oxidization process and the measured propagation loss is about 105 cm^-1 for a 310 nm-wide waveguide.

Fig.19 (a) Cross section of a hybrid plasmonic waveguide with an inverted metal rib; (b) field distribution in a hybrid plasmonic waveguide with the following parameters: nH = 3.455, nL = 1.445, nmetal = 0.1453+ 11.3587i, H = 300 nm, hrib = 250 nm, hslot = 10 nm, hm = 100 nm, and wco = 200 nm [47]

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2.3 Silicon hybrid nanoplasmonic waveguides for TE polarization

Silicon hybrid nanoplasmonic waveguide is usually designed for TM polarization, as shown above. In Ref. [49], we proposed a CMOS-compatible hybrid nanoplasmonic waveguide working for TE polarization, as shown Fig. 6(a). There are double nano-slots formed at both sides of the Si rib while the SiO₂ layer at the top of the Si rib is relatively thick to minimize the metal absorption. When the SiO₂ layer at both sides of the Si rib is thick (e.g., 0.5 µm-thick) and the Si rib is relatively wide (e.g., 400 nm), the fundamental mode field is confined well in the Si region and consequently the metal layer will hardly influence the mode field distribution. In this case, the present structure behaves like a regular SOI nanowire. However, the metal layer will give a significant influence to the guided mode when the SiO₂ thickness becomes small (e.g.,<50 nm). Figure 6(b) shows the calculated field distribution of the major-component E_x(x, y) for the quasi-TE fundamental mode. The field distributions E_x(x, y₀) and E_x(x₀, y) are also shown. It can be seen that the present hybrid plasmonic waveguide provides a very good light confinement even when the waveguide core is as small as 50 nm (or even smaller). The field at the two 10 nm-SiO₂ nano-slots is enhanced greatly, which is similar to that shown in Fig. 5. In the present hybrid plasmonic waveguide, the double nano-slots help to achieve a very high power confinement factor at the low-index regions even when the slot area is very small. The theoretical analysis has shown that there is a very high power density in the SiO₂ nano-slots, e.g.,>120 µm^-2 when w_SiO2 = 10 nm. The effective area A_eff is as small as 0.007 µm² for a 50 nm-wide waveguide with double 10-nm slots. This kind of silicon hybrid nanoplasmonic waveguide with double nano-slots working for TE polarization [49-55] has been investigated extensively. For example, Zhu et al. demonstrated the fabricated Cu-SiO₂-Si-SiO₂-Cu hybrid plasmonic waveguides has a loss of<1dB/µm loss even when the silicon core width is as small as 21 nm [54]. The developed devices (like resonators, modulators) will be reviewed in Section 4.

Fig.20 (a) Cross section of a hybrid plasmonic waveguide with double low-index slots; (b) field distribution for the major component Ex(x, y) of the quasi-TE fundamental mode when wco = 50 nm and wSiO2 = 10 nm. Here the field distributions Ex(x0, y) and Ex(x, y0) are also shown. Here x0 = wSi/2+ wSiO2/2 and y0 = hSi/2 [49]

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In addition to the popular structures of silicon hybrid nanoplasmonic waveguides shown in Table 1, various novel designs have been presented more recently for realizing hybrid plasmonic waveguides with e.g., an additional semiconductor strip [28], multiple layers [29-31], angled sidewalls [32-34], a trench [35] and a silver nanowire [36]. Some extremely compact silicon hybrid nanoplasmonic waveguides have also been presented [37-39]. In Ref. [37], a hybrid plasmonic waveguide with a silicon cylindrical nanowire placed on a metal rib is proposed to achieve a sport size of 4.2 nm × 2.1 nm as well as a 38 µm-long propagation distance. In Ref. [38], the model with the nonlocal effect is used in the analysis for an ultrasmall small hybrid plasmonic waveguide.

According to the reported theoretical and experimental results for various silicon hybrid nanoplasmonic waveguides, it can be seen that silicon hybrid nanoplasmonic waveguides can confine light tightly in nano-scale and the propagation losses have been also verified to be acceptably low, which provides a good platform to realize ultrasmall functionality devices.

3 Silicon hybrid nanoplasmonic devices

3.1 Ultra-sharp bending of silicon hybrid nanoplasmonic waveguides

Figures 7(a)–7(d) show the electrical field distribution E_y(x,y) of the TM fundamental mode for silicon hybrid nanoplasmonic waveguides with different bending radii R. From these figures, it can be seen that there is a field enhancement in the low-index slot region and the light is still confined in the slot region very well even for the bending radius as small as 500 nm (about only 1/3 of the operation wavelength). This is due to the strong light confinement in silicon hybrid nanoplasmonic waveguides [71]. When the radius decreases, the peak of the electrical field shifts outward gradually, as predicted. This causes less field interaction with the inner sidewall, which helps to achieve low scattering loss.

Fig.21 Electrical field distribution Ey(x, y) for the cases of (a) R = 2 µm, (b) R = 1 µm, (c) R = 800 nm, (d) R = 500 nm. The other parameters are: hslot = 20 nm, wco = 400 nm [71]

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Figures 8(a)–8(c) show the calculated loss for a 90°-bending hybrid plasmonic waveguide [71]. The loss is contributed by the intrinsic loss due to the metal absorption (which is proportional to the bending radius) as well as the leakage due to the bending (which increases exponentially as the bending radius decreases). Therefore, there is an optimal bending radius R_opt, which gives a minimal total loss for a 90°-bending, as shown in Figs. 8(a)–8(c). The bending loss for other silicon hybrid nanoplasmonic waveguides has also been studied. For example, Shin et al. gave an analysis for a metal-insulator-silicon-insulator-metal hybrid plasmonic waveguide and the calculated loss for a direct bend with a 220 nm-wide silicon core is 4.5 dB [70]. For Cu-SiO₂-Si-SiO₂-Cu hybrid plasmonic waveguides [64], the measured bending loss is about 0.73 dB/turn (R = 0) when the silicon core width is ~64 nm, which agrees well with the theoretical estimation. The ability for sharp bending makes silicon hybrid nanoplasmonic waveguide very promising to realize ultra-dense devices for photonic integration.

Fig.22 Calculated bending loss for bent hybrid plasmonic waveguides (at 1550 nm). (a) hslot = 10 nm; (b) hslot = 20 nm; (c) hslot = 50 nm [71]

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3.2 Optical couplers/splitters

The ultra-sharp bending can dramatically diminish the overall size of some basic elements based on silicon hybrid nanoplasmonic waveguides (e.g., power splitters/couplers) since 90°-bends or S-bends usually are used as the access parts. In Ref. [68], we presented the design for several types of power splitters with sub-µm² footprints based on a multimode interference (MMI) structures, as well as Y-branches, as shown in Figs. 9(a) and 9(b). The designed sub-µm² power splitter were also shown to work well in a broad wavelength range (1.25-1.7 µm), since the silicon hybrid nanoplasmonic waveguide bending can achieve low loss (e.g.,<0.12 dB/90° with an 800 nm radius) in such a broad band [71]. The experimental results for the ultrasmall power splitters based on the metal-SiO₂-Si-SiO₂-metal hybrid plasmonic waveguides were demonstrated in Ref. [54] and the measured loss for a fabricated 1 × 2 power splitter is ~1.4 dB (which is consistent with the calculation result). Ultracompact directional couplers (DCs) based on silicon hybrid nanoplasmonic waveguides have also been realized in Refs. [40,59,61-63] (see Fig. 9(c)) and the DC demonstrated in Ref. [40] has a coupling length as short as only 1.55 µm with arm widths of ~170 nm.

Fig.23 (a) 1 × 2 3 dB MMI power splitter; (b) 1 × 2 3 dB Y-branch power splitter; (c) 1 × 2 3 dB DC

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3.3 Ultrasmall resonators

As a versatile element for photonic integrated circuits, optical resonators have been attracting lots of attention for many applications, e.g., light sources [110], optical filters [111], optical modulators/switches [112], optical sensing [113], nonlinear optics [114], etc. As mentioned above, a silicon hybrid nanoplasmonic waveguide enables very sharp bending and thus it is promising to develop ultracompact resonators. Table 2 gives a summary for the developed silicon hybrid nanoplasmonic waveguide resonators, including microring resonators, micro-donut resonators, as well as micro-disk resonators.

It can be seen that the demonstrated silicon hybrid nanoplasmonic waveguide resonators have subwavelength or even submicron bending radius and the Q-factor is at the order of 10²-10³. The Purcell factor is expected to be pretty high because of the ultrasmall volume, which is useful for the applications of single photon source, lasing or light-matter interactions. For example, the hybrid-plasmonic microdisk presented in Ref. [77] is with a bending radius ~890 nm and has a Purcell factor as high as 1824. In Ref. [71], we proposed a submicron-donut resonator, which has a pure dielectric access waveguide so that a long-distance optical interconnect is enabled and no additional mode converter is needed to combine the hybrid plasmonic circuits and the pure dielectric waveguides. The temperature-dependence of a silicon hybrid nanoplasmonic waveguide resonator has been analyzed [73] and an athermal resonator is achieved with the assistance of TiO₂ which has a negative thermal-optical coefficient [74]. Silicon hybrid nanoplasmonic waveguides have also been used to realize photonic-crystal cavities [78-80]. The cavity designed in Ref. [79] has a giant Q/V value (~60000 λ^-3), which offers a great opportunity to enhance the light-matter interaction.

Tab.2 Silicon hybrid nanoplasmonic waveguide resonators

Ref.	year	structure	R	extinction ratio	Q	FSR
[71]	2011		800 nm	30 dB	220	148 nm
[77]	2011		890 nm	-	648	140 nm
[75]	2011		910 nm	28 dB	638	143 nm
[65]	2012		1.09 µm	13.7 dB	63	106 nm
[76]	2013		522 nm	12.4 dB	110	210 nm

3.4 Polarization handling devices

Surface plasmonic waveguides are well known for the strong polarization dependence and usually there are surface plasmonic modes supported for only one polarization. Similarly silicon hybrid nanoplasmonic waveguide also has very strong polarization-dependence. Figure 10 shows the dominant electric field for the TE fundamental (TE₀) mode and TM fundamental (TM₀) mode. It can be seen that the TE₀ modal field is mainly confined in the silicon region while the TM₀ modal field has a peak enhancement in the SiO₂ nanoslot. This distinction makes it possible to realize polarization handling devices conveniently, including polarizers, polarization beam splitters (PBSs) as well as polarization rotators, which is very useful for many applications [115].

Polarizer is useful to improve the extinction ratio of polarized light and in recent years various ultra-short polarizers based on silicon hybrid nanoplasmonic waveguides have been proposed [81-86]. In 2012, the polarization-dependence of the mode coupling [84] as well as the mode absorption loss [86] in a silicon hybrid nanoplasmonic waveguide has been utilized to realize compact TE-pass polarizers. For a 30 µm-long polarizer demonstrated, the extinction ratio is ~23 dB and the insertion loss is about 2 dB. Huang et al. proposed a TE-pass polarizer with a 16 dB extinction ratio and a 2.2 dB insertion loss by using a silicon hybrid nanoplasmonic waveguide with double nano-slots [85]. More recently, an ultrasmall TE-pass silicon-hybrid-plasmonic-waveguide polarizer with a broadband (>200 nm band for 15 dB extinction ratio) is proposed with a Bragg grating structure [83]. In a similar way, TM-pass polarizers can also be realized with silicon hybrid nanoplasmonic waveguide [81,82], which plays important role for some applications to improve the extinction ratio of TM polarized light.

Fig.29 Cross section of a silicon hybrid nanoplasmonic waveguide and the filed distributions for the TE0 and TM0 modes

Full size|PPT slide

To realize compact PBSs, which are used to separate or combine TE and TM polarizations, an asymmetrical coupling system has been proved to be a good candidate [115]. Particularly, asymmetrical couplers consisting of a silicon hybrid nanoplasmonic waveguide and silicon nanowires has been proposed to realize ultrasmall PBS [87-91]. The PBS length can be even shortened with a MMI coupler proposed in Ref. [92]. In this design, a metal strip is partially covered on the MMI section to form a Si hybrid plasmonic waveguide, as shown in Fig. 11(a). For TM polarization, the fundamental mode in the MMI section is excited dominantly due to the hybrid plasmonic effect so that the MMI effect does not happen almost. Consequently the TM-polarized light outputs from the through port (as shown in Fig. 11(b)). On the other hand, for TE polarization, the metal on the top influences the light propagation very slightly because there is no hybrid plasmonic effect, and thus the MMI length is chosen optimally to form a mirror image at the cross port (as shown in Fig. 11(b)). With such a design, the MMI section for the PBS is as short as only 1.1 µm, and the PBS has a broad bandwidth of ~80 nm for an extinction ratio of>10 dB. The insertion losses are only 0.32 and 0.88 dB for TE and TM polarizations, respectively.

Fig.30 Configuration (a) and light propagation (b) of a PBS with a MMI coupler on Si HPW platform [92]

Full size|PPT slide

Polarization rotation is another key to realize polarization-handling [115]. Generally, an on-chip polarization rotator based on pure-dielectric optical waveguides can be realized with the mechanism of the mode evolution [116] as well as the hybrid-mode interference [117]. Similarly, for the case with silicon hybrid nanoplasmonic waveguides, low-loss compact polarization rotators [93-95] can also be obtained by utilizing the mode evolution [94], and the hybrid-mode interference [95]. For example, a 3.2 µm-long polarization rotator is presented with a conversion efficiency of 99.5% and an insertion loss of 1.38 dB [95].

As a summary, it can be concluded that a silicon hybrid nanoplasmonic waveguide provide a very promising platform to realize ultrasmall on-chip polarization-handling devices, which is attractive for the future large-scale photonic integrated circuits.

4 Discussion on the issue and applications of silicon hybrid nanoplasmonic waveguides

4.1 Loss issue

Even though a silicon hybrid nanoplasmonic waveguide has a relatively low loss and a relatively long propagation distance is enabled, the intrinsic loss of the metal is still a hinder for the applications of silicon hybrid nanoplasmonic waveguides.

A potential solution is using silicon hybrid nanoplasmonic waveguides locally on the chip with the assistance from low-loss pure dielectric waveguides (SOI nanowires [118]) for long-distance interconnects. This kind of hybrid integration has been used to realize ultrasmall devices [71,87-92]. For example, we proposed a silicon hybrid nanoplasmonic resonant donut with pure dielectric access waveguides [71]. To realize the seamless integration between hybrid plasmonic circuits and silicon nanophotonic circuits, there are usually two ways for light coupling, e.g., the butt-coupling [67,96,119] and the evanescent-coupling [63,120,121]. The butt-coupling way has an efficiency of>55% in a wavelength band as large as 200 nm [96]. For the evanescent-coupling way, one should design the silicon hybrid nanoplasmonic waveguide and the silicon nanowire according to the phase matching condition and the coupling efficiency can be up to 94% [63].

Another potential way to overcome the intrinsic loss of hybrid plasmonic waveguides is introducing gain medium. Table 3 gives a brief summary for gain mediums used in the gain-assisted plasmonic waveguides [47,122-133]. In Ref. [122], a net gain of 85.5 dB/cm for long-range surface plasmonic waveguides has been demonstrated by using a dipolar gain medium with a gain coefficient of ~420 cm^-1. For silicon hybrid nanoplasmonic waveguides, either high-index or low-index gain medium could be used in the high-index region or in the low-index region respectively. For example, semiconductor materials have been used to act as the high-index layer as well as the gain medium for hybrid plasmonic waveguide [134-136]. Particularly, for a silicon hybrid nanoplasmonic waveguide with a metal strip on a slab waveguide [21], the theoretical gain coefficient required to compensate the metal loss can be as low as 3.8 cm^-1 [137], which makes it possible to achieve silicon hybrid nanoplasmonic waveguides with net gain. When a net gain is achieve with the assistance of gain medium, a deep subwavelength laser based on hybrid plasmonic waveguides has been realized [43], and the laser can operates even at the room temperature [138]. As shown in Table 3, there are also some options of low-index gain medium available for silicon hybrid nanoplasmonic waveguides, e.g., silicon nano-crystals [132], Er-doped oxide [124,125] or polymer with quantum dots [129]. The theoretical analysis in Ref. [47] shows that it is possible to compensate the intrinsic loss and even achieve a pure gain with a moderate gain medium.

Tab.3 Gain reported in literatures [47]

Ref.	gain medium	gain	wavelength
[122]	IR140 dye molecules (Sigma Aldrich)	360 cm-1	882 nm
[123]	PMMA with Rhodamine 6G dye (R6G)	420 cm-1	594 nm
[124]	Er-doped phosphate glass	1 cm-1	1532 nm
[125]	Er-doped Al2O3	0.3 cm-1	1530 nm
[126]	sulfide (PbS) QDs	150 cm-1	1525 nm
[127]	GaInAsP	1200 cm-1	1500 nm
[128]	PbS semiconductor quantum dots	1700 cm-1	1250 nm
[129]	PMMA with PbS QDs	17 cm-1	1160 nm
[130]	dye solution	-	633 nm
[131]	PbS QDs	200 cm-1	860 nm
[132]	silicon nanocrystals	100 cm-1	800 nm
[133]	MDMO-PPV:PSF	90 cm-1	600 nm

4.2 Applications of silicon hybrid nanoplasmonic waveguides

The field enhancement in the low-index nano-slot makes silicon hybrid nanoplasmonic waveguides very useful for many applications (e.g., optical modulation, optical nonlinearity, optical sensing, optical force, etc), when filling some functionality medium into the nano-slot region.

For example, in order to realize optical modulator, the nano-slot region can be filled in with some electro-optic (EO) material like HfO₂ [97], Vandium dioxide [98], and EO polymer [99,100]. For EO-polymer, the EO coefficient can be very high (~500 pm/V [101]). The field enhancement in the nano-slots filled by EO-polymer helps obtain an ultra-short π-phase-shifter (e.g., ~13 µm-long with a 2.5 V voltage [102]). The compactness makes it possible to achieve a very high modulation speed of up to 100 GHz as well as very low power consumption of 9 fJ/bit [102]. The power consumption can be even reduced further to e.g. 5 fJ/bit (~100 GHz) by utilizing a silicon hybrid nanoplasmonic resonator (e.g., a nano-disk resonant, R = 510 nm) [100]. When the low-index material is with negative thermal coefficient, an athermal modulator with silicon hybrid nanoplasmonic waveguides can also be achieved [139]. The temperature-insensitivity of an optical modulator indeed benefits from the strong confinement in the low-index region with negative thermal coefficient, regarding that the low-index layer (TiO₂) is as thin as ~ 58 nm.

When the nano-slots are filled with some nonlinear optical material (e.g., nonlinear polymer), an enhanced optical nonlinear effect can be obtained. Zhou et al. presented a silicon hybrid nanoplasmonic waveguide offering an ultra-high nonlinear coefficient γ = 4.7 × 10⁹ W^-1km^-1, which is 4 orders larger than conventional silicon waveguides [25]. An optical parametric amplifier (OPA) is also presented theoretically with a signal gain 14 dB over a 200 nm broad-band [0]. With the nonlinearity of a silicon hybrid nanoplasmonic waveguide, one can also achieve efficient phase-matched second harmonic generation (SHG) from mid-infrared (IR) to near-IR and the SHG yield is as large as 8.8% for a pumping power of 100 mW [141]. In Refs. [142] and [143], more details for the nonlinearity in the silicon hybrid nanoplasmonic waveguides have been given. The enhanced nonlinearity in hybrid plasmonic waveguide enables all-optical switching [144], optical logic gate [145], and signal-format converters [146].

A silicon hybrid nanoplasmonic waveguide is also advantageous for optical sensing because of the high sensitivity due to the field enhancement [104,105]. A subwavelength resonator based on silicon hybrid nanoplasmonic waveguides has been proposed as a biosensor [106] and the sensitivity is ~580 nm/RIU, which is much higher than that for a dielectric nanoslot-waveguide resonator. The compactness of such a sensor also makes it possible to achieve ultra-high integration density and high spatial resolution for a sensor array.

Recently it has shown that enhanced optical forces can be realized by using silicon hybrid nanoplasmonic waveguides [57,107,108]. In comparison with pure dielectric optical waveguides, the optical force in silicon hybrid nanoplasmonic waveguides is enhanced several times, which makes it useful to realize nano-scale optical tweezers [107].

More applications for hybrid plasmonic waveguides are still being explored, including light concentration [147], wavelength division multiplexing (WDM) system [148], electrically induced transparency (EIT) [149], optical filters [150], light controlling [151-153], meta-material [154], detectors [155] and terahertz waveguides [156]. These attempts to extend the applications of silicon hybrid nanoplasmonic waveguide are beneficial to develop complicated ultra-dense integrated photonic circuits in the future.

5 Conclusions

In this paper, we have given a review for recent progresses on silicon hybrid nanoplasmonic waveguides and devices. It has shown that silicon hybrid nanoplasmonic waveguides have attracted lots of attention in the past years (especially since 2009) because of the ability to achieve a nano-scale confinement of light as well as long propagation distance (~10² µm). This is beneficial for realizing ultra-dense photonic integrated circuits in the future. For example, sub-µm² silicon hybrid nanoplasmonic integrated devices have been demonstrated, including power splitters, nano-donut resonators, polarization-handling devices. As a general solution for the loss issue of hybrid plasmonic waveguides, low-index or high-index gain medium have been introduced to compensate the intrinsic loss. In comparison with the conventional nanoplasmonic waveguide, an advantage of hybrid plasmonic waveguide is that the gain medium does not need a high gain coefficient because of the relatively low intrinsic loss, which makes loss compensation feasible in practice. The combination of silicon hybrid nanoplasmonic waveguides for local functionality elements with ultra-small footprints and low-loss pure dielectric waveguides for long-distance interconnect also provides a promising way to alleviate the loss issue, which has been used for silicon hybrid nanoplasmonic resonators, PBSs, etc. The field enhancement in a silicon hybrid nanoplasmonic waveguide makes it very useful. The application of silicon hybrid nanoplasmonic waveguides has been extended to the fields including nonlinear optics, optical modulation, optical sensing, and optical force. It is expected to explore more applications for silicon hybrid nanoplasmonic waveguides, like active plasmonics, quantum plasmonics, etc.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 61107051) and National High-tech R&D Program (No. SS2012AA010407).

RIGHTS & PERMISSIONS

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg