We propose a cladding-free, efficiently tunable, high-quality factor (Q) nanobeam cavity with subwavelength-period nanotentacles (NT), adequately investigate the performance of the cavity, and study the directional heat transfer. By virtue of the excellent heat transfer of Si nanotentacles, a tuning range of more than 6 nm wavelength, with 24mW and 10 KHz switching rate, and 13 μs raising time is experimentally obtained. This result is about twentyfold better than the previous work by Fegadolli [ACS Photon. 2, 470-474 (2015)]. A potential 12nm tuning range with identical power is also theoretically suggested by modifying the silicon structure. With an optimized design, these nanotentacles are demonstrated to have a minimal effect to the cavity and are available to serve as photonic waveguides. This cladding-free design, with a simple fabrication process, is comparable to other proposals in which deep etching, suspended treatment, and troublesome heterogeneous-integration may be needed. Finally but importantly, this smart design can be applied to other photonic cavities, particularly cavities such as ring/disk resonators, in which we reasonably predict a better tuning efficiency due to the thermal circulation. We believe this design is fairly suitable for applications in which light-matter interaction is of primary importance, such as sensing, particle trapping, cavity quantum electrodynamics (CQED), and III-V/Si hybrid lasers with external cavities.
© 2017 Optical Society of America
Over the past decades, silicon has been determined to be the most promising platform for on-chip optical interconnect and nanophotonics. The technology for passive devices on the silicon-on-insulator (SOI) platform such as beam splitters, polarization rotators, resonators, gratings for wavelength division multiplexing (WDM), and active devices like Si/Germanium modulators and Raman laser has matured substantially. However, unwanted discrepancy between design and fabrication may sometimes hinder the fabricated devices and require more laborious fabrication processes. Though post-fabrication trimming technologies such as thermal oxidation , electron beam induced compaction , and superstrate adjustment  can solve these problems without duplicated fabrication processes, the process is time-consuming and difficult to control. In addition, devices such as filters, routers, sensors, and other narrow-band devices require tunability to enhance their availability. There is a pressing need, therefore, for an efficiently tunable method for these two phenomena. Mechanisms such as the electro-optic effect , the free-carrier plasma-dispersion effect , and the thermal-optic effect  have been applied to these tunable devices. Among these mechanisms, the thermal-optic effect is overwhelmingly preferred for low switching-rate devices and those requiring simple fabrication and a large tuning range based on SOI due to the large thermal conductivity (~150W/m·K) and thermal-optical coefficient (~1.8 × 10-4/K). In these devices, usually a low-index cladding is deposited on the silicon to reduce the loss from the upper metal heater. Unfortunately, these low-index layers, such as silicon dioxide, BCB, aluminum oxide, and various polymers usually have poor conductivity, which undoubtedly reduces the thermal efficiency and decreases the switching rate for waveguide-type devices [6–9] such as a Mach Zehnder Interferometer (MZI). Closed cavities with heat circulation, such as ring/disk resonators [10, 11], may be more efficient and are widely used for devices. Deep etching  and suspending treatments  are additionally applied to further improve the thermal efficiency. However, all of these designs require upper insulators or more complicated fabrication, which are not suitable for situations where light-matter interaction is important and upper cladding is prohibited. Surprisingly, cladding-free tunable cavities reliant on side-direction heat injection by silicon beams  and graphene sheet  are proposed. However, the design in  is a special case that is not applicable to other cavities or waveguide occasions because of heat transfer through the waveguide terminal, while that suggested in  may introduce troublesome fabrication processes and introduce additional loss into the resonator.
In this work, we propose a novel, cladding-free nanobeam cavity with excellent thermal efficiency. Compared to traditional tunable cavities, the design introduced in this paper provides a new method for efficient thermal tuning, in which upper cladding for the heater and complicated fabrication techniques such as deep etching and suspended treatment are not needed. This nanotentacle-asssisted tunable nanobeam cavity exhibits a 6.2nm tuning range with 24mW and 10 KHz switching rate and a 13 μs raising time, far surpassing those of previous work . We systematically study the effect of NTs on the cavity, the waveguide, and heat transference and indicate further potential for optimization (at least double the current proposed efficiency can be theoretically attained). This smart design is applicable to other photonic cavities, particularly other closed cavities with heat circulation, such as ring/disk resonators, for which we reasonably predict a better tuning efficiency. Such a tunable cavity is quite useful for applications such as dynamic routers, optomechanical devices, particle trapping, cavity quantum electrodynamics (CQED) and so on.
2. Design and fabrication
Compared to the ring/disk cavity, the photonic crystal (PhC) cavity offers unique advantages such as single-mode operation and small mode volume. In particular, the proposed nanobeam cavity inherits the high performance of a 2D PhC cavity and exhibits flexible coupling ability, such as direct butt coupling [16, 17], all pass coupling , and add-drop type coupling . However, a high quality nanobeam cavity usually requires a high core/cladding index contrast, thus the cladding-free tunable cavity design is quite useful for nanobeam cavities. The schematic of our design is shown in Fig. 1. This cavity consists of a traditional nanobeam cavity (directly connected to a feeding waveguide) and a densely-packed nanotentacle (NT) array (served as side-cladding) connected with a slab on one side. A metal strip is deposited on the slab to generate heat. The details of this cavity are shown Fig. 2(a), in which the radius of the holes, the period and width of the PhC WG, the length, and the period and width of the NT are labeled. Transverse electric (TE) polarization is considered for this proposed cavity. Since the NT array is also a periodic structure, it is difficult to analyze an aperiodic waveguide if the period of the NT and that of the nanobeam are unequal. In our design, we set the relation that NT period = PhC period/2 and use the FDTD model (Lumerical Inc.) to calculate the band diagram, in which a Bloch boundary condition is applied around a unit cell. Therefore, the unit cell here contains two NTs and a single-hole waveguide segment. To obtain a high coupling between feeding waveguide and PhC waveguide, the effective mode index in the feeding waveguide and in the PhC waveguide, indicated by the Bragg condition, should be matched such that Λ = λ/(2·neff), where λ, neff, and Λ are the wavelength in vacuum, the effective index in the feeding waveguide, and the period of the nanobeam. The silicon thickness in this design is 150nm, which results in a 1.8 – 2.6 range for neff, with a common waveguide width of 400 nm – 800 nm. A moderate PhC period of 370 nm is chosen for the nanobeam, and subsequently, a waveguide width of 700nm results according to the above relation.
Compared to the traditional nanobeam waveguide, the NTs here indeed introduce perturbation to the confined mode. However, we should note that the period of the NT is much smaller than both that of the PhC’s and the minimum effective wavelength (λ/nSi), which is about 440nm, and is thereby the resolution limit. The combination of the NT array and the air gap in between can be treated as an effective material with an intermediate index. Such a scope is common in metasurface  and subwavelength research [21, 22]. The effective index of such a boundary along the waveguide direction is calculated according to the volume relation  that , in which η is the volume fraction and n the material index. Because the index of silicon is much larger than that of air, nb increases rapidly with NT width, as in Fig. 2(b). Even the NT width we use, 60nm, is no more than 1/3 of the NT period, nb easily rises to 2.2, higher than the index of silicon dioxide. This high boundary index should account for the degradation of the Q value since the bandgap of PhC will narrow as the index contrast decreases. We thus do not recommend a higher duty cycle of NT when index contrast is critical for device performance. The calculated transmission loss and insertion loss of the NT-assisted waveguide (without PhC holes) are shown in Fig. 2(c). Though the transmission loss of the NT-assisted waveguide is larger than a traditional photonic waveguide (about 10−1 dB/cm), this is small enough for photonic integration, for which a waveguide is usually in the millimeter and centimeter scale. In particular, we control the NT width within 60nm, which helps the waveguide present a transmission loss of no more than 1.5dB/cm. Compared to the transmission loss, the insertion loss has a large rate of change around 60nm and increases rapidly with NT width, which also indicates a proper use range of below 60nm. A method  for analyzing the increase of insertion loss around 60 nm NT is depicted in Fig. 2(g). Here three mode distributions at different positions of a waveguide with 60 nm NT width are chosen for calculating the mode overlap. These tree positions are the strip-mode position, steady-state position (the center of 40th NT), and unsteady-state position (the center of 5th NT, around the junction), respectively, and the mode distributions are shown in Fig. 2(d)-2(f). Obviously, there’s a relatively large mode mismatch between the NT-assisted waveguide (Fig. 2(e) and 2(f)) and the strip waveguide (Fig. 2(f)). In addition, there’s also a small difference between the distribution of steady-state position and the unsteady-state one. This results from the abrupt connection of NT-assisted waveguide and the strip waveguide. Mode overlaps to a strip mode for mode at steady-state position and unsteady-state position with different NT widths are presented in Fig. 2(h) by blue and red lines, respectively. The difference between the slow change of red line and quick decrease of blue line when increasing the NT width is the reason of the rapid increase of insertion loss in Fig. 2(c). These results also give an optimized structure with tapered NT width around the junction.
To obtain a high-quality factor, two radius-tapered, period-fixed mirrors are arranged at both sides, with 0 nm of extra cavity length (such that the pitch of the two central holes is equal to the period) according to previous work by Quan  as in Fig. 1. The calculated band diagram using 3D FDTD (Lumerical Inc.) is presented in Fig. 3(a). The upper band and the designed dielectric mode band are labeled in red and black, respectively. The solid and dashed lines are for nanobeams with a 120 nm radius and a 70 nm radius, respectively. The hole radii at the center and the terminal of the mirror are therefore set to 120 nm and 70 nm, respectively, thus serious reflectivity can be obtained at the terminal of the mirror according to the mode gap effect . The calculated quality factor (Q) of these cavities with different lengths are presented in Fig. 3(b). The Q value for a raw cavity (without NT) with a 35-hole mirror can be up to 107 and decreases with the increasing NT width. Interestingly, even as the NT width reaches 80nm, the Q value is reduced by no more than an order of magnitude, and trend of the Q value with the mirror length is similar for different NT widths (0-80 nm). We choose a moderate mirror length (20 holes) for fabrication because a longer mirror will experimentally have a greater effect on the transmission of the cavity, though a high transmission value up to 95% for 35-hole mirror can be calculated in theory. A NT width of 60nm is also chosen for a moderate Q value of 5 × 104, which is more than enough for filtering or sensing applications. The energy profiles of the resonant modes in these two cavities (with and without NT) are shown in Fig. 3(d) with similar energy distributions. We see that the mode energy of the 60nm-NT cavity has a large amount of energy located outside the Si waveguide, but not leaking to the Si slab. The length of NT we have chosen is 2 μm, which is long enough to cancel the overlap with the energy in the Si slab. The energy confinements of the resonant mode with different NT widths in waveguide or NT are summarized in Fig. 3(c), respectively. Though the energy inside the NT increases with the NT width, the total amount of energy is small for the total cavity. Besides the study on the effect from of NT width, we also provide further results of different density in Fig. 3(e). Two cases with fixed filling factor or fixed nanotentacles (NT) width are depicted by blue lines with triangles and circles, respectively. When decreasing the NT period from 340nm with fixed filling factor, the quality factor (Q) increases quickly at the beginning, and latter tends to be saturated when the NT period is less than 260nm, as the blue line with triangles. This is because the NT period is far smaller than the resonant wavelength. In the meanwhile, as shown by blue line with circles, the Q factor of a cavity with fixed NT width keeps approaching the result (around 105) of the case without NT in Fig. 3(b) when increasing the NT period. This is because of the decreased effective index of air/silicon hybrid boundary which contributes to the bandgap enlargement of photonic crystal. The corresponding waveguide confinement for these two cases are also shown in the figure below. As shown by the red line with triangles, the confinement of a cavity with a fixed filling factor shows identical saturated trend on the denser side. The light confinement of the cavity with a fixed NT width rapidly decreases when the NT period decreases from 180nm, as indicated by the redline with circles. This results from a rapid decrease of the filling factor when NT period is less than 180nm. The information in Fig. 3 demonstrates good confinement of this cavity and indicates the small effect of the NT on the cavity performance.
The calculated relation between index shift and wavelength shift, which is nearly linear, is presented in Fig. 4(a). The effect on wavelength is separately calculated from the waveguide, NT, and both, as in Fig. 4(a) in red, blue and black, respectively. The red is obtained by changing the index in the waveguide while keeping it fixed in NT, while the blue is obtained under opposite conditions. Compared to the black (both), obviously the waveguide constitutes the bulk of the effect on the wavelength shift. This is quite reasonable when considering that, referring to Fig. 3(c), most of the energy is confined within the waveguide. The total wavelength responsivity considering both the waveguide and NT is about 391.2nm/RIU. A Comsol model of heat transfer is built to monitor the heat flux with 25 mW input power. The upper limit of input power is limited by the material and footprint of heater in practice. Since the material we use for heater is Titanium, and the effective length of heater is about 6 μm, we then chose such a moderate value, which is common in thermal-optic tunable devices. An adequately large silicon dioxide and silicon substrate is used for accurate heat accumulation with fixed a 293K temperature bottom. The width of Silicon slab and heater we chose is 3 μm and 1.5μm, respectively, which is to release the alignment during heater overlap. The static temperature distribution of the proposed cavity is shown in Fig. 4(b). Since the silicon has a much larger heat conductivity (150 W/(m·K)) than the titanium (14.63 W/(m·K)), silica (7.6 W/(m·K)) and air (0.02 W/(m·K)), most of the generated heat is dispersed into the silicon structure and subsequently to the waveguide through the NTs. Thermal capacity values used for silicon, titanium, silica, and air are 700 J/(kg·K), 520 J/(kg·K), 966 J/(kg·K) and 1004 J/(kg·K), respectively. The simulated temperature in the center of the cavity is about 370K, which indicates an index change about 0.0135 and wavelength shift about 5.3 nm. The heat flux map, described by arrows, is presented in Fig. 4(c). The direction and density of arrows indicate the direction and magnitude of heat flux. Obviously, though the Si slab has a higher temperature distribution, the generated heat is directionally transferred to the nanobeam.
3. Results and discussion
To fabricate this proposed device, 220nm SOI from SOITEC is first cleaned and oxidized in a 1050 °C O2 environment for 300 minutes to generate a silicon dioxide layer with a thickness of about 140nm (70nm silicon is sacrificed). HF solution treatment is used to remove the upper oxide layer. Standard Electron beam lithography (EBL) and RIE-ICP etching are used for fabricating the cavity structures. 100nm Titanium and 4nm gold for the heater and the electrode are deposited on the sample through electron beam evaporation, followed by lift-off process. The microscope picture of the fabricated device with the parameters discussed above is presented in Fig. 5(a). The black spots on the electrode (yellow area) result from the unoptimized control of pressure during the deposition process and can be improved by better process control. The images by scanning electron microscopy (SEM) are shown in Fig. 5(b)-5(d), with different scales. Figure 5(b) shows the two focused gratings for coupling the source light to the SOI waveguide. The grating period, grating etching depth, and duty cycle of this focused grating are 560 nm, 150 nm, and 0.65, respectively. Such a focus grating can give a −8dB coupling efficiency with negative 38-degree fiber incidence angle. A square electrode pair with 100 μm length and 16 μm gap are connected to the heater through a 20 μm taper. The length of the straight section is 4μm, as in Fig. 5(c). The standing rough edge is formed by removing the polymer in the lift-off process. The insertion loss we observe experimentally is no more than 0.5dB. Such a low insertion loss will not have much effect on the input power. Since the NTs around the terminal contribute a little to the heat transfer, smaller insertion loss can be obtained by tapering the NT width at the terminal .
A tunable laser (Agilent 81940), polarization control, sample, and spectrometer (Yokogawa 6370D) are connected in sequence to obtain the transmission spectrum. Next, a sourcemeter (Keithley 2400), prober (Everbeing), photodetector (Thorlabs DET10D/M), and digital oscilloscope (InfiniiVision 3000T) are added to the circuit to observe the tuning performance and switch rate. The connection schematic is presented in Fig. 6(a). The transmission spectrum was normalized to a straight waveguide (identical length, grating, NT but without the PhC holes). The transmission spectrum without electron injection is shown in Fig. 6(b), labeled in black. The normalized transmission of such a cavity is about 35% and 3dB linewidth Δλ, respectively. Such a linewidth, with more than 40dB extinction ratio, results in a Q value of 9200 according to Q = λ/∆λ. The imperfections resulting from fabrication such as radius shift, sidewall roughness, and unclean surfaces should account for this deviant value compared to the simulation. Next, electric power from low to high is applied to the electrode for tuning the resonant wavelength. Up to a 6.2nm wavelength shift can be obtained with 23.84mW (1.5V, 15.89mA) input power, as in Fig. 6(b). These results indicate a maximum index change of about 0.01585 and an averaged efficiency of 0.27nm/mW, as in Fig. 6(c), which are well coincident to the simulation. An index responsivity of 5 × 10−4 RIU/mW can be acquired according to Fig. 4(a). The temperature of the Si waveguide before damage can thus be estimated to be 100 °C according to the index change. Such a tuning range and efficiency are obviously superior to those in traditional waveguide-type devices with heaters on oxide, in which no more than a 3nm tuning range and dozens of milliwatts are common. Especially compared to the previous work  on tunable nanobeams with up to 550mW for a 6.8nm range, our design presents a better tuning efficiency and, most importantly, demonstrates a new solution for cladding-free heat tuning and offers much freedom for cavity design. We should note that the data of tuning performance were all acquired before the heater was damaged and melted, thus the largest tuning range around the damage point is not shown. In other words, the tuning range in such a cavity is first limited by the fabrication quality of the heater rather than the cavity. A straightforward solution for raising the damage threshold of the heater is to deposit a thicker layer of titanium and design a longer heater, which will decrease the current density. The optimization on fabrication relies on better lift-off technology and thicker resistors, which we believe is beyond the scope of this letter. The switch response with 10 kHz modulation rate and 1 mW power is shown in Fig. 6(d). The input power of 1 mW with a low modulation rate is first verified by a spectrometer for the realization of a high extinction ratio, then switched to a photodetector for high-rate observation. Details of the raising edge are shown in Fig. 6(e), where a raising time of 13μs for 10%-90% transition is labeled. Note that in the transmission and switching measurement the resonance transmission is varied as the wavelength is tuning thermally. This intensity fluctuation is due to the wavelength-dependent coupling efficiency from the fiber to the grating coupler.
To further study the thermal behavior, thermal models with different NT width are analyzed (other parameters are kept fixed). The energies in the NT and waveguide are integrated separately, as in Fig. 7(a). The integrated energy in both increase as the NT width and the total energy stored in NT are, several-fold to the increase in energy of the waveguide since it is the tunnel for heat transferring. Reference models where 1.5 μm silicon dioxide and heater are placed on the cavity in turn are also evaluated (dashed). Though the energy efficiency in both the NT and waveguide are small compared to input power in our case, they are really much higher than the reference case, as seen in other work.
The energy efficiency in the entire silicon structure and waveguide with a fixed NT width and different slab widths are also presented in Fig. 7(b). Two cases, with the heater on the center and on the edge of the slab, are independently analyzed. First, no matter what case or what parameters, the energy efficiency of the total silicon structure is much higher than the waveguide because of the direct contact of the silicon slab and the heater. As the slab size decreases, the silicon slab tends to gain energy, while the waveguide loses energy. This is easy to understand: according to the second law of thermodynamics, the added volume of the silicon slab can be treated as a cold body, and the original a hot body. Since there is no thermal perturbation around these two bodies, the heat from the hot body will naturally transfer to the cold body and realize a new thermal balance. When the silicon slab shrinks, the increasing energy density will push the energy to the surroundings, especially the NTs. These two solid lines in Fig. 7(b) unambiguously indicate the room for optimizing the energy efficiency. It should be particularly noted that for the slab width we used (3μm), the corresponding energy efficiency (0.0135) is nearly half of that observed for a width of 1.6μm (0.0255). That is to say, without any optimization of the heater, an approximate 12nm tuning range with the same power can be predicted, which further demonstrates the superiority of our design. Interestingly, the energy efficiency in the waveguide and total silicon structure of case where the heater is on the edge is larger than the case for which the heater is in the center, and the difference between these two cases for the waveguide is larger than the difference for the entire structure. Taking the 4μm slab as an example, the differences in efficiency for the waveguide and the entire silicon structure are 0.011 and 0.02, respectively. This means that extra energy, about 0.009, is obtained from either the heater or the silicon dioxide. To summarize, a heater located close to the cavity with a shrunken silicon slab will help improve the heat efficiency. The heat distributions for three cases (where the heater is on the center of the 4μm slab, the heater is on the edge of the 4μm slab, and the heater is on a 1.6μm slab where the center and edge are the same) are presented in Figs. 7(c)-7(e). The color in Figs. 7(e) is brighter than in Figs. 7(c) and 7(d), consistent with the data in Figs. 7(a) and 7(b).
To further study the effect of thicker/thinner electrode on thermal performance, we perform similar calculation in terms of the energy efficiency. The results are shown in Fig. 7 (f). The energy efficiencies in waveguide and NT both tend to de slightly affected by a thicker electrode, which is also attributed to the same reason for the silicon slab. Thanks to the excellent heat conductivity and large thermal capacity of silicon, the deviation of efficiency in waveguide for a thickness range of 20-300 nm is less than 20%, which is of good convenience for the practical fabrication and further application. The effects of different NT density on thermal performance are shown below. Energy efficiency in waveguides with a fixed filling factor and a fixed NT width are depicted by the blue lines with triangles and circles, while the efficiencies in NT with a fixed filling factor and a fixed NT width are depicted by the red lines with triangles and circles, respectively. In the case of fixed filling factor (blue and red lines with triangles), both energy efficiencies in waveguide and NT array is almost stable when changing the NT period. This is because the almost unchanged silicon cross section for heat transferring. In the case of fixed NT width (blue and red lines with circles), both efficiencies decrease accordingly when the NT period increases, which results from the decreased filling factor.
We propose a novel cladding-free nanobeam cavity with excellent thermal efficiency. Using this cladding-free, nanotentacles-asssisted, tunable nanobeam cavity, more than a 6 nm tuning range with a 24mW and 10 KHz switching rate and 13 μs raising time is experimentally demonstrated, about twentyfold better performance than the previous work by Fegadolli . Our design demonstrates a new method for efficient thermal tuning, in which upper cladding for the heater and complicated fabrication processes such as deep etching and suspended treatment are not required. We systematically study the effect of NT on the device performance and demonstrate that the NT array is a flexible tool for heat transfer while having only a marginal effect on cavity performance. Further optimization, such as doubling the efficiency by easily adjusting the silicon structure, is also discussed in the thermal model. Thanks to the low loss of the NT-assisted waveguide, this smart design is applicable to any other photonic cavities, especially closed cavities with thermal circulation such as ring/disk resonators, in which we reasonably predict a better tuning efficiency. We believe this tunable method for silicon waveguides is quite useful for applications such as dynamic routers, III-V/Si hybrid lasers with external cavities, particle trapping, cavity quantum electrodynamics (CQED), optomechanical devices, and so on.
National High Technology Research and Development Program (Program 863) of China (No. 2013AA014401); National Natural Science Foundation of China (NSFC) (11621101).
The authors are grateful to Chenlei Li for helping oxidize the SOI wafer during fabrication.
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