We investigate theoretically and experimentally Fano resonances in integrated silicon Bragg reflectors. These asymmetric resonances are obtained by interference between light reflected from the Bragg waveguide and from the end facet. The Bragg reflectors were designed and modeled using the 1D transfer matrix method, and they were fabricated in standard silicon wafers using a CMOS-compatible process. The results show that the shape and asymmetry of the Fano resonances depend on the relative phase of the reflected light from the Bragg reflectors and end facet. This phase relationship can be controlled to optimize the lineshapes for sensing applications. Temperature sensing in these integrated Bragg reflectors are experimentally demonstrated with a temperature sensitivity of 77pm/°C based on the thermo-optic effect of silicon.
© 2013 Optical Society of America
Asymmetric Fano lineshapes in integrated photonic devices has received considerable attention due to their potential for applications in optical switching, modulation, and sensing [1–4]. Of particular interest are coupled waveguide-resonator systems, in which asymmetric lineshapes can be obtained by interference between a broadband background signal and a narrow resonance signal. Several photonic devices have been proposed to demonstrate asymmetric lineshapes in integrated photonics [1–7]. In , waveguides with partially reflecting elements were coupled to photonic crystal cavities, creating sharp and asymmetric lineshapes. Asymmetric Fano resonances were also observed in  by offsetting the coupling waveguides in ring resonators. Recently [4–6], it has been shown that asymmetric lineshapes can be controlled by changing the optical phase with a ring-resonator-coupled Mach-Zehnder interferometer. In addition, asymmetric lineshapes have been observed in coupled systems consisting of a single mode ring resonator and a multimode waveguide .
These previous studies have focused on side-coupled photonic devices, while few studies have addressed direct-coupled structures. Unlike side-coupled devices that usually require transmission measurements, direct-coupled devices enable data extraction from reflection measurements. This feature simplifies packaging by minimizing input and output coupling of the waveguides, and minimizes the required number of phase-control elements, making the devices compact and suitable for high density arrays .
Many integrated photonics platforms have been proposed for implementation of these photonic devices, but interest in silicon photonics has rapidly grown due to its compatibility with electronics and due to the wide range of applications it can support [8–10]. Most silicon photonic devices are fabricated on silicon-on-insulator (SOI) wafers to facilitate vertical field confinement [8–11]. However, SOI photonics suffer from several limitations due to the varying buried oxide (BOX) thickness [12, 13], and due to the fact that SOI is not the standard in the electronics industry. Monolithic silicon photonics in standard silicon simplifies integration of electronics and photonics and is a possible alternative to SOI photonics [14–18].
Among various applications, Fano resonances are especially interesting for sensor applications because the slope sensitivity can be increased by sharp asymmetric lineshapes . Additionally, these optical sensors offer the advantages of robustness and immunity to electromagnetic interference (EMI). One study has reported the potential use of asymmetric lineshapes for biomedical sensing specifically in ring resonators . However, few studies have investigated the use of asymmetric lineshapes in other types of sensors such as temperature sensors.
In this paper, we present theoretical and experimental studies of asymmetric Fano resonances in direct-coupled integrated silicon Bragg reflectors [14, 15]. These reflectors are fabricated as monolithic photonic devices in standard silicon wafers. We demonstrate that we can control the resonance lineshapes by controlling the relative phase of the light reflected from the Bragg reflector and the chip facet, and that these asymmetric lineshapes can be optimized for sensing applications. Subsequently, we report on an experimental study of integrated silicon photonic temperature sensors based on these Bragg reflectors with the asymmetric Fano Lineshapes.
2. Device design and modeling
2.1 Device design
Our silicon Bragg reflectors consist of two parts: an air-cladding silicon rib waveguide and a periodic array of hole that allows underetching for field confinement and formation of the Bragg periodicity, as shown in Fig. 1. The waveguides are designed to provide strong field confinement and to operate in single mode. An SOI substrate is not required because the vertical confinement is achieved by underetching the silicon substrate. Waveguide widths of 700nm and 800nm, and rib height of 250nm were simulated using the alternating direction implicit (ADI) beam propagation method (BPM) in OptiFDTD. The refractive index of silicon was set to 3.5. The results show that our waveguides support single-mode operation for both the TE and TM polarizations.
The mode profiles of our rib waveguides at 1310nm wavelength at the cross sections marked with dashed lines in Fig. 1(b) are plotted in Fig. 2 for the TE and TM polarizations. Compared to conventional SOI rib waveguides, our waveguides possess different mode profiles due to the underetching of the waveguides. It can be seen that for the TE polarization the effective index is 3.40 at the AA’ cross section and 3.43 at the BB’ cross section, while for the TM polarization the effective index is 3.39 at AA’ and 3.42 at BB’.
2.2 Device modeling: transfer matrix method
Based on the geometry of the silicon Bragg reflectors (see Fig. 1), the region from the chip facet to the periodic structure can be modeled as a phase plate. The rest of the region with periodic structure can then be modeled as a 1D distributed Bragg reflector (DBR) with a period of the hole arrays Λ and an array of refractive indices that gradually change between neff1 and neff2, as shown in Fig. 3. The reflection spectrum is determined by interference between the light reflected from the front surface and from the silicon DBR.
The DBRs determine the spectral response of the Fano resonance, reflecting narrow-band light at the resonant wavelengths. The relationship between the waveguides and the periodic hole arrays can be described through the Bragg condition:
In addition, the device facet reflects broad-band light due to a ~55% field reflectivity from the silicon-air interface. The interference between the DBR-reflected light at these wavelengths and the facet-reflected light results in asymmetric lineshapes. Different lineshapes can be obtained by changing the relative phase of the two reflections. Given a phase plate thickness d and the effective index of the phase plate neff, the relative phase can be calculated by the difference in optical path length:Eq. (2) that the relative phase can be controlled by the thickness and effective index of the phase plate; furthermore, the change of the relative phase is periodic with a periodicity of λB/2neff in terms of the phase plate thickness, resulting in the same lineshape repeating every λB/2neff.
The Bragg reflectors are numerically simulated using the 1D transfer matrix method. One period of the DBR is decomposed into N segments, and is modeled by the piecewise constant index approximation, in which the refractive indices gradually change between neff1 and neff2 based on a step function. N is chosen to be at least 100 so that the structures can be correctly modeled. This number could be reduced by using the piecewise linear index approximation and the Airy function . Each segment is then represented by a 2 x 2 matrix :Eq. (3) by changing the thickness to d and using the appropriate effective indices. The reflectivity is then calculated from MTOT = MDBRMPP.
Figure 4 illustrates the transfer matrix simulations of the silicon Bragg reflectors for different phase plate thickness obtained by using neff1 = 3.43 and neff2 = 3.40 for the case of 800nm waveguide width. As can be seen, the transfer matrix method shows a resonance wavelength at 1366nm, which is consistent with Eq. (1). Different asymmetric Fano lineshapes are obtained by varying the thickness of the phase plate from 650nm to 800nm. It also follows that the change of the lineshapes is periodic with a periodicity of about 200nm in terms of the phase plate thickness. This periodicity can be accounted for by Eq. (2) that the phase plate with an effective index of 3.40 and a thickness of 200nm results in a 400nm round-trip distance and a 2π phase difference required to repeat the lineshapes at resonance wavelength of 1366nm.
3. Device fabrication and testing
3.1 Device fabrication
Our waveguide Bragg reflectors were fabricated by the Generation Of PHotonic Elements by RIE (GOPHER) process [14–18]. A layer of SPR955 0.7μm photoresist was spun on standard silicon wafers, and the waveguides were patterned using an ASM-L i-line stepper. The rib waveguide structures were then transferred into the silicon substrate by directional silicon reactive ion etching etch (Fig. 5(a)). To fabricate the hole array, a 800nm thick LPCVD low temperature oxide was deposited on top of the rib waveguides to serve as a hard mask (Fig. 5(b)). A second lithography step was used to define the hole array, followed by the directional oxide etch and directional silicon etch to transfer the pattern into the silicon substrate (Fig. 5(c)). Next, thermal oxidation was performed to form sidewall protection, and, subsequently, the bottom oxide in the hole array was etched (Fig. 5(d)). Another directional silicon etch was conducted to etch the holes further into the substrate. The waveguides were then underetched by an isotropic silicon plasma etch using SF6 (Fig. 5(e)). This isotropic etch shapes our waveguides by timed etching, resulting in etch profiles that may vary depending on the Bragg hole size and periodicity. Etching recipes, including etch time, pressure and gas flows, should therefore be optimized for different Bragg designs. Finally, the wafer was cleaved into a 1cm long (10000 periods) chip for testing. An SEM of the completed structure is shown in Fig. 5(f).
3.2 Testing of silicon Bragg reflectors
The reflection-spectra of the fabricated Bragg reflectors were measured through direct end-facet coupling. This measurement setup, shown in Fig. 6, consists of a broadband light source (1300nm-1380nm), a polarization controller, a 3dB coupler and a lensed fiber. Light from the source is propagated through the polarization controller, the 3dB coupler and the lensed fiber, and then directly coupled into the waveguide Bragg reflector under test. The reflected light from the device is collected by the same lensed fiber. Due to mode mismatch, offset and tilt between the waveguide and the lensed fiber, the coupling loss was estimated to be 5-10 dB/facet. The measured data are then processed with Savitzky–Golay filtering  to smooth out the measurement irregularities. Figure 7 shows the measured reflection spectra and the corresponding SEM images of the waveguide Bragg reflectors. Note that no Fabry-Perot effect is observed in the measurement results because these fabricated devices have a ~50 dB/cm propagation loss that eliminates the Fabry-Perot effect. These losses come from the imperfections of the hole shape and the scatting of the hole array, and could be improved by better lithography, etching and smoothing techniques.
Our measurement results show that tuning of the Fano lineshapes can be achieved by changing the boundary conditions at the facet. Such tuning can be interpreted by the phase plate model, in which different thickness and effective index of the phase plate result in different asymmetric lineshapes. To quantitatively analyze our Bragg reflectors, we also plot in Fig. 7 the calculated reflection spectra based on the transfer matrix model. These calculated spectra are fitted to the measured data by optimizing the effective indices and by extracting the phase plate thicknesses from the SEM images. It follows that neff1 and neff2 are found to be 3.433 and 3.403, respectively, for 800nm waveguides, and 3.423 and 3.393, respectively, for 700nm waveguides. The extracted phase plate thicknesses from Figs. 7(a)–7(d) are 370nm, 800nm, 850nm, and 585nm, respectively. These results show that the transfer matrix can successfully match the experimental results, except for the secondary resonances around 1366nm. These resonances are possibly due to slightly different effective indices for the two polarizations. Furthermore, the resonance wavelengths of the devices in Figs. 7(a) and 7(c) are slightly different: 1363.2nm and 1367.2nm, respectively. The difference in resonance wavelengths is likely due to the difference in effective indices of the 700nm and 800nm waveguide widths.
Since the periodicity of the phase plate is 200nm, it is challenging to control the desired phase plate thickness using standard cleaving methods. Two methods could be applied to precisely control the phase plate thickness. First, the facets can be manufactured by lithography, followed by etching and sidewall smoothing [16, 17, 22], resulting in well-defined facets and phase plate thicknesses. Alternatively, a focused ion beam (FIB) could be utilized to locally shape the phase plate. This method offers the advantage of post-processing the devices.
To further investigate tuning of asymmetric Fano lineshapes on a single device, we locally etch our device facet using the FIB, and we measure the reflection spectrum after each etch. By repeating the procedure several times, we obtain different asymmetric Fano lineshapes on the same device, indicating that different Fano lineshapes can be controlled by varying the phase plate thickness. Figure 8 shows the calculated and experimental spectra and the corresponding SEM images after the FIB etching (see Fig. 7(d) for the spectra and SEM image before the FIB cutting). It follows that given the phase plate thickness our transfer matrix model matches the experimental results well. Furthermore, as depicted in Figs. 8(b) and 8(c), the spectra are almost the same for two facet conditions, in which the facet cut differ by about 398nm. This facet-cut difference is very close to two periods of the periodic lineshape change discussed in section 2.2, thus resulting in very similar spectral results.
By using the etching techniques and 1D transfer matrix model, we can generate different asymmetric lineshapes optimized for various applications. The asymmetric lineshapes in Figs. 7(b), 7(d), 8(b) and 8(c) are especially interesting for the sensing applications because the slope sensitivities of such sensors are greatly improved by Fano resonance compared to those of symmetric resonances . These resonances could also be used to improve the optical switching characteristics .
4. Silicon Bragg reflectors for temperature sensing
The asymmetric Fano lineshapes make our silicon Bragg reflectors well-suited for temperature sensing applications. In such devices, temperature sensing is achieved by the temperature-induced lineshape shifts based on the thermo-optic effect of silicon . According to the 5th order Bragg condition and the thermal-optic coefficient of silicon (~2x10−4 (1/K)) , the temperature sensitivity S of our sensors can be expressed asEq. (4). According to Eqs. (1) and (4), the theoretical temperature sensitivity is 0.080 nm/°C.
To test the devices and to control the temperature, our temperature sensors are mounted on a thermoelectric module (FerroTec) calibrated by a thermal couple. The reflection-spectrum of our temperature sensors is then measured through the edge coupling setup discussed in section 3.2. To ensure that the temperature sensor reaches thermal equilibrium, we chose a time interval of more than 3 minutes between consecutive temperature measurements. Figure 9(a) shows the reflection spectrum for temperatures ranging from 21.5°C to 34.6°C. Starting from 1367nm, the resonance wavelength shifts to longer wavelengths as the temperature increases due to the positive thermo-optic coefficient of silicon. For comparison, we plot in Fig. 9(b) a calculated spectrum based on the 1D transfer matrix method with the thermo-optics effects. The transfer matrix numerically models the asymmetric Fano lineshapes and the wavelength shifts due to the thermo-optic effect, successfully matching the experimental results.
The experimental and calculated resonance wavelength shifts as a function of temperature are shown in Fig. 10, in which the temperature sensitivity can be extracted by the slope of the linear fitting to be 0.077 nm/°C. This experimental result is in good agreement with the theoretical sensitivity from Eq. (4) and the 1D transfer matrix calculations, indicating that the thermo-optic effect dominates over other effects, such as thermal expansion.
Our temperature sensors based on Bragg reflectors offer several important advantages. First, they operate in reflection, which significantly simplifies the overall measurement system in that input and output couplings are not required as in transmission measurements. Furthermore, the sensitivity of our temperature sensors is comparable to other types of integrated optical temperature sensors, such as silicon ring resonators , silicon nitride resonators , and polymer ring resonators . Finally, our temperature sensors are CMOS-compatible, which allow us to leverage not only well-established CMOS processes, but also the new developments in integration of electronics and photonics.
In addition to the temperature sensors, our silicon Bragg reflectors can be applied to other types of sensors such as chemical sensors and biomedical sensors. Since these sensors usually require liquid environments, the hole array and the air cladding layer between the waveguide and the substrate can function as microfluidic channels, facilitating the sensing mechanisms. Moreover, such integrated silicon photonic devices can be easily integrated with other polymer microfluidic channels to form lab-on-a-chip devices.
We describe a silicon-photonic integrated waveguide technology that is compatible with standard processes. This technology only requires standard silicon wafers, eliminating the need for SOI wafers in silicon photonics. Using this technology, we demonstrate asymmetric Fano resonances at 1366nm in integrated silicon Bragg reflectors, and show that the resonances match well with our 1D transfer matrix model. Tuning of the Fano lineshapes was achieved by changing the facet conditions with a periodicity of about 200nm in our Bragg reflectors.
We then demonstrate temperature sensors based on asymmetric Fano resonances in these Bragg reflectors. The temperature sensitivity of our sensors is measured to be 77 pm/°C, in good agreement with our simulations using a 1D transfer matrix method. Such temperature sensors have potentials for applications that require robustness, simplicity, low cost and integration of electronics and photonics. Our results show that this silicon photonic technology and asymmetric Fano resonances can be very useful for a variety of sensing applications.
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