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OPTICS LETTERS / Vol. 39, No. 20 / October 15, 2014
Liquid sensor based on high-Q slot photonic crystal cavity in silicon-on-insulator configuration Charles Caër,1,2 Samuel F. Serna-Otálvaro,1 Weiwei Zhang,1 Xavier Le Roux,1 and Eric Cassan1,* 1
Institut d’Électronique Fondamentale, Université Paris-Sud CNRS UMR 8622 Bat. 220, Centre scientifique d’Orsay, 91405 Orsay, France 2 Present address: Laboratoire Kastler Brossel, UPMC, ENS, CNRS, Case 74, 4 Place Jussieu, F75252 Paris Cedex 05, France *Corresponding author: eric.cassan@u‑psud.fr Received July 1, 2014; revised September 4, 2014; accepted September 4, 2014; posted September 8, 2014 (Doc. ID 214503); published October 3, 2014 We present the realization of an optical sensor based on an infiltrated high-Q slot photonic crystal cavity in a nonfreestanding membrane configuration. Successive infiltrations by liquids with refractive indices ranging from 1.345 to 1.545 yield a sensitivity S of 235 nm/RIU (refractive index unit), while the Q-factor is comprised between 8000 and 25,000, giving a sensor figure of merit up to 3700. This sensor has a detection limit of 1.25 × 10−5 . The operation of this device on a silicon-on-insulator (SOI) substrate allows a straightforward integration in the silicon photonics platform, while providing a compliant mechanical stability. © 2014 Optical Society of America OCIS codes: (130.3120) Integrated optics devices; (130.6010) Sensors; (230.5750) Resonators; (230.5298) Photonic crystals. http://dx.doi.org/10.1364/OL.39.005792
Photonic crystals cavities (PCCs) offer many advantages for the integration of on-chip optical sensors. First, their ability to confine light in a very small volume enhances their sensitivity to their environment (e.g., by refractive index change or absorption) while minimizing their footprint. Second, their very high optical quality factors and their very high free spectral range (FSR) allow multiplexing of many cavities, which facilitates massive on-chip integration. The unique properties of PCC have enabled the study of cells in vivo [1]. In standard PCC, as well as whispering gallery optical resonators, the interaction of an optical mode with an analyte is only limited to its evanescent part, which limits the sensitivity. The confinement of light in the low index material brings a clear advantage for enhancing the sensitivity of the sensor. This feature can be obtained by forming a hole defect inside the hole lattice [2], or by adding a slot inside the photonic crystal cavity. Slot photonic crystal cavity (SPCC) has been successfully used for chemical and gas sensing with very high sensitivity [3,4]. The SPCCs are mainly formed by locally modulating the waveguide line-defect, either by shifting holes [5] or by stretching the lattice constant [3]. This small perturbation enables very high-Q factors when operating in membrane configuration [6] while minimizing the mode volume. The SPCC has also been employed for coupling optical detection of molecules with a lasing mode [7]. Despite significant progress made on SPCC-based biosensors [8], the current devices are limited by their Q-factor which is degraded when filled by a liquid down to a few thousands (e.g., 4000 in Ref. [3]). Maintaining a high Q-factor is desirable since it enhances the interaction between the analytes and the optical field, and reduces the cavity linewidth, enabling a larger scale for multiplexing detection channels in a given free spectral range. At the same time, an operation without undercutting is preferable since it ensures a better mechanical stability and fewer fabrication steps, thus reducing the manufacturing costs. We have recently reported a high-Q slot photonic crystal cavity in a silicon-on-insulator (SOI) configuration based on a 0146-9592/14/205792-03$15.00/0
two-step heterostructure cavity [9] with a measured quality factor of 23,000. In this Letter, we present a sensor based on our previous work [9] on a filled cavity lying on silica. The design of the SPCC is depicted in Fig. 1. The cavity is formed by a slight stretch of the lattice constant (Δa 10 nm), forming a photon trap in the waveguide. The length of the barriers is 7a0 , a0 being the nominal lattice constant (a0 400 nm), and the other parameters of the SPCC being: r 105 nm, W slot 110 nm.
Fig. 1. (a) Upper left: scanning electron micrograph of the SPCC. The scale bar is 2 μm. Right: scheme of the slot photonic crystal cavity based on a two-step heterostructure with a superposition of the E y field computed with 3D FDTD. The holes in the stretched lattice regions are colored for clarity. a0 , a1 , and a2 denote lattice constants of 400, 410, and 420 nm, respectively. (b) Transmission spectrum of the photonic crystal waveguide containing the SPCC filled by a liquid (nliq 1.448), showing a resonance at λ 1582.9 nm. © 2014 Optical Society of America
October 15, 2014 / Vol. 39, No. 20 / OPTICS LETTERS
Details on the fabrication procedure are reported in Ref. [10], involving electron beam lithography and inductively coupled plasma etching. The experimental setup consists of a tunable laser diode (TLD) emitting light in a fiber passing through a polarization controller and a TE filter. The light flows through a polarization maintaining fiber and is injected in the sample by a lensed fiber. The light is collimated at the output through an objective lens, filtered with a TE polarizer, and then focused by a second lens onto a fiber coupler sending light to a photodetector. The transmission spectrum is obtained by driving the TLD with a component tester and sweeping the laser wavelength (resolution of 1 pm). The measurements are performed after covering the sample with different liquids (Cargille), ranging from 1.35 to 1.55. The refractive index of each liquid is tabulated by the manufacturer at visible wavelengths, and therefore has to be corrected with the Sellmeier equation for telecom wavelengths. The refractive indices for the set of liquids are: 1.345, 1.41, 1.448, 1.45, 1.516, and 1.55. The linear transmission spectra of the cavity filled by four liquids ranging from 1.41 to 1.545 are depicted in Fig. 2. Normalization has been done by averaging the transmission in the waveguide with an input laser power of 5 mW, and no filtering is applied to the data. The different spectra indicate a progressive increase of the transmission on resonance when increasing the refractive index, as well as a shift of the resonant wavelength. At the same time, the cavity linewidth broadens when the liquid refractive index increases from 1.448 to 1.545. We attribute this to both asymmetry induced by the vertical index mismatch and modification of the coupling coefficient between the access waveguides and the cavity. This effect is even more pronounced for the smallest refractive index, where the resonant mode is hardly distinguishable from the noise in the photonic bandgap. This is because of a lesser confinement and poor coupling efficiency; therefore, the device is more efficient when the refractive index in the slot is close to or higher than the refractive index of silica. The resonant modes of the SPCC for each liquid are shown in Fig. 3(a). The cladding refractive index change tunes the resonant wavelength over a range of 50 nm with a linear shift. The measured Q-factors deduced from the
Fig. 2. Normalized transmission spectrum for different values of the liquid refractive index, showing the translation of the fundamental mode of the cavity (colored).
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Fig. 3. (a) Resonant spectra of the cavity for successive infiltrations by a liquid with an increasing refractive index (squares) and associated Lorentzian fits (solid line). The resonant wavelength drifts linearly with the refractive index (dotted line). Each resonance is normalized by its maximum value. (b) Resonant wavelength as a function of the refractive index, showing a linear dependence yielding a sensitivity of 235 nm/RIU, and quality factor as a function of the refractive index, showing a maximum value of 25,000 around nliq 1.44.
Lorentzian fits [Fig. 3(a)] are plotted as a function of the liquid refractive index in Fig. 3(b). As expected, the lowest Q-factor is obtained for the smallest index (Q 8000 for nliq 1.345) and the highest Q-factor is achieved when the liquid refractive index perfectly matches the index of silica, yielding to the very high value of Q 25; 000, which even exceeds the value reported in our previous work [9]. For a higher refractive index, the Q-factor decreases but remains higher than 12,000 for nliq 1.545, suggesting that Q-factors higher than 104 with a polymer infiltration and a transmission on resonance near 20% are within reach. A linear fit of the resonant wavelength as a function of the refractive index is traced in Fig. 3(b). By defining the sensitivity S as S dλ∕dn, the SPCC yields a sensitivity of 235 nm/RIU. This value is smaller than those reported previously in other SPCC systems [3,4], but it should be pointed out that the SPCC lies on a buried silica layer and has a narrower slot, reducing the overlap between the liquid and the cavity light field. This explains the reduced sensitivity. However, this SPCC has a better mechanical stability, a higher Q-factor, and the hydrophilic behavior of the silica helps the wetting of the liquid on the sample. We also underline that the coupling efficiency in this SPCC yields a transmission on resonance up to 25% for the highest refractive index, which makes this device practical for an integration in silicon photonics and gives a very high signal to noise ratio. Referring to the figure of merit of real-time and label-free sensors [11] as FOM S∕FWHM, the values range from 1200 to 3700. Based on the definition in Ref. [12], we have calculated the detection limit of our device. The definition of the
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sensitivity of our device enables us to discriminate a refractive index shift of only 2 × 10−3 , indicating that a cladding refractive index change of only 2.9 × 10−4 will switch a signal circulating in the cavity from an ON/OFF state. The small footprint of our device will enable the integration of many cavities connected through the same bus waveguide for multiplexing sensing applications.
Fig. 4. Resonant spectra of the cavity for nliq 1.448 (blue) and nliq 1.45 (red) with Lorentzian fits (solid lines), showing a wavelength shift of 0.75 nm.
sensor resolution given by White and Fan shows that our device resolution is limited by the spectral resolution of the tunable laser (1 pm), giving a detection limit DL 1.25 × 10−5 . We also studied the wavelength shift for small variations of the refractive index. In Fig. 4, we can see a wavelength shift of 0.75 nm for a liquid refractive index change of only 0.002 RIU. This wavelength shift represents approximately 10 times the full width at half-maximum (FWHM). This figure shows that the device allows a fine estimation of the concentration of an analyte in the liquid, which relates to the measured sensitivity of the sensor. On the other hand, the device is compatible with an integration of multiple cavities coupled to the same waveguide [13], which will enable the multiplexing of many detection channels in a compact device [14]. In conclusion, we have demonstrated a liquid sensor with a sensitivity of 235 nm/RIU and a detection limit of 1.25 × 10−5 based on a slot photonic crystal cavity on SOI and covered by a liquid. The quality factor moves from 8000 to 25,000 for a liquid refractive index comprised between 1.35 and 1.55, a maximum Q-factor of 25,000 being achieved at nliq 1.44, which enhances the sensor figure of merit up to 3700. The very-high
C. Caër and S. F. Serna-Otálvaro acknowledge scholarships from the Ministry of Higher Education and Research (France). This project is partly supported by the ANR (Agence Nationale de la Recherche) through the POSISLOT project. Fabrication was conducted in the IEF clean room facilities (CTU/MINERVE), part of RENATECH network. References 1. G. Shambat, S.-R. Kothapalli, J. Provine, T. Sarmiento, J. Harris, S. S. Gambhir, and J. Vučković, Nano Lett. 13, 4999 (2013). 2. M. R. Lee and P. M. Fauchet, Opt. Lett. 32, 3284 (2007). 3. A. Di Falco, L. O’Faolain, and T. F. Krauss, Appl. Phys. Lett. 94, 063503 (2009). 4. J. Jágerská, H. Zhang, Z. Diao, N. Le Thomas, and R. Houdré, Opt. Lett. 35, 2523 (2010). 5. T. Yamamoto, M. Notomi, H. Taniyama, E. Kuramochi, Y. Yoshikawa, Y. Torii, and T. Kuga, Opt. Express 16, 13809 (2008). 6. A. H. Safavi-Naeini, T. P. Mayer Alegre, M. Winger, and O. Painter, Appl. Phys. Lett. 97, 181106 (2010). 7. S. Kita, S. Hachuda, K. Nozaki, and T. Baba, Appl. Phys. Lett. 97, 161108 (2010). 8. M. G. Scullion, A. F. Di Falco, and T. F. Krauss, Biosens. Bioelectron. 97, 161108 (2010). 9. C. Caer, X. Le Roux, and E. Cassan, Appl. Phys. Lett. 103, 251106 (2013). 10. C. Caer, X. Le Roux, and E. Cassan, Opt. Lett. 37, 3660 (2012). 11. L. J. Sherry, S. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, Nano Lett. 5, 2034 (2005). 12. I. M. White and X. Fan, Opt. Express 16, 1020 (2008). 13. S. Mandal and D. Erickson, Opt. Express 16, 1623 (2008). 14. Y. Takahashi, T. Asano, D. Yamashita, and S. Noda, Opt. Express 22, 4692 (2014).
OPTICS LETTERS / Vol. 39, No. 20 / October 15, 2014
Liquid sensor based on high-Q slot photonic crystal cavity in silicon-on-insulator configuration Charles Caër,1,2 Samuel F. Serna-Otálvaro,1 Weiwei Zhang,1 Xavier Le Roux,1 and Eric Cassan1,* 1
Institut d’Électronique Fondamentale, Université Paris-Sud CNRS UMR 8622 Bat. 220, Centre scientifique d’Orsay, 91405 Orsay, France 2 Present address: Laboratoire Kastler Brossel, UPMC, ENS, CNRS, Case 74, 4 Place Jussieu, F75252 Paris Cedex 05, France *Corresponding author: eric.cassan@u‑psud.fr Received July 1, 2014; revised September 4, 2014; accepted September 4, 2014; posted September 8, 2014 (Doc. ID 214503); published October 3, 2014 We present the realization of an optical sensor based on an infiltrated high-Q slot photonic crystal cavity in a nonfreestanding membrane configuration. Successive infiltrations by liquids with refractive indices ranging from 1.345 to 1.545 yield a sensitivity S of 235 nm/RIU (refractive index unit), while the Q-factor is comprised between 8000 and 25,000, giving a sensor figure of merit up to 3700. This sensor has a detection limit of 1.25 × 10−5 . The operation of this device on a silicon-on-insulator (SOI) substrate allows a straightforward integration in the silicon photonics platform, while providing a compliant mechanical stability. © 2014 Optical Society of America OCIS codes: (130.3120) Integrated optics devices; (130.6010) Sensors; (230.5750) Resonators; (230.5298) Photonic crystals. http://dx.doi.org/10.1364/OL.39.005792
Photonic crystals cavities (PCCs) offer many advantages for the integration of on-chip optical sensors. First, their ability to confine light in a very small volume enhances their sensitivity to their environment (e.g., by refractive index change or absorption) while minimizing their footprint. Second, their very high optical quality factors and their very high free spectral range (FSR) allow multiplexing of many cavities, which facilitates massive on-chip integration. The unique properties of PCC have enabled the study of cells in vivo [1]. In standard PCC, as well as whispering gallery optical resonators, the interaction of an optical mode with an analyte is only limited to its evanescent part, which limits the sensitivity. The confinement of light in the low index material brings a clear advantage for enhancing the sensitivity of the sensor. This feature can be obtained by forming a hole defect inside the hole lattice [2], or by adding a slot inside the photonic crystal cavity. Slot photonic crystal cavity (SPCC) has been successfully used for chemical and gas sensing with very high sensitivity [3,4]. The SPCCs are mainly formed by locally modulating the waveguide line-defect, either by shifting holes [5] or by stretching the lattice constant [3]. This small perturbation enables very high-Q factors when operating in membrane configuration [6] while minimizing the mode volume. The SPCC has also been employed for coupling optical detection of molecules with a lasing mode [7]. Despite significant progress made on SPCC-based biosensors [8], the current devices are limited by their Q-factor which is degraded when filled by a liquid down to a few thousands (e.g., 4000 in Ref. [3]). Maintaining a high Q-factor is desirable since it enhances the interaction between the analytes and the optical field, and reduces the cavity linewidth, enabling a larger scale for multiplexing detection channels in a given free spectral range. At the same time, an operation without undercutting is preferable since it ensures a better mechanical stability and fewer fabrication steps, thus reducing the manufacturing costs. We have recently reported a high-Q slot photonic crystal cavity in a silicon-on-insulator (SOI) configuration based on a 0146-9592/14/205792-03$15.00/0
two-step heterostructure cavity [9] with a measured quality factor of 23,000. In this Letter, we present a sensor based on our previous work [9] on a filled cavity lying on silica. The design of the SPCC is depicted in Fig. 1. The cavity is formed by a slight stretch of the lattice constant (Δa 10 nm), forming a photon trap in the waveguide. The length of the barriers is 7a0 , a0 being the nominal lattice constant (a0 400 nm), and the other parameters of the SPCC being: r 105 nm, W slot 110 nm.
Fig. 1. (a) Upper left: scanning electron micrograph of the SPCC. The scale bar is 2 μm. Right: scheme of the slot photonic crystal cavity based on a two-step heterostructure with a superposition of the E y field computed with 3D FDTD. The holes in the stretched lattice regions are colored for clarity. a0 , a1 , and a2 denote lattice constants of 400, 410, and 420 nm, respectively. (b) Transmission spectrum of the photonic crystal waveguide containing the SPCC filled by a liquid (nliq 1.448), showing a resonance at λ 1582.9 nm. © 2014 Optical Society of America
October 15, 2014 / Vol. 39, No. 20 / OPTICS LETTERS
Details on the fabrication procedure are reported in Ref. [10], involving electron beam lithography and inductively coupled plasma etching. The experimental setup consists of a tunable laser diode (TLD) emitting light in a fiber passing through a polarization controller and a TE filter. The light flows through a polarization maintaining fiber and is injected in the sample by a lensed fiber. The light is collimated at the output through an objective lens, filtered with a TE polarizer, and then focused by a second lens onto a fiber coupler sending light to a photodetector. The transmission spectrum is obtained by driving the TLD with a component tester and sweeping the laser wavelength (resolution of 1 pm). The measurements are performed after covering the sample with different liquids (Cargille), ranging from 1.35 to 1.55. The refractive index of each liquid is tabulated by the manufacturer at visible wavelengths, and therefore has to be corrected with the Sellmeier equation for telecom wavelengths. The refractive indices for the set of liquids are: 1.345, 1.41, 1.448, 1.45, 1.516, and 1.55. The linear transmission spectra of the cavity filled by four liquids ranging from 1.41 to 1.545 are depicted in Fig. 2. Normalization has been done by averaging the transmission in the waveguide with an input laser power of 5 mW, and no filtering is applied to the data. The different spectra indicate a progressive increase of the transmission on resonance when increasing the refractive index, as well as a shift of the resonant wavelength. At the same time, the cavity linewidth broadens when the liquid refractive index increases from 1.448 to 1.545. We attribute this to both asymmetry induced by the vertical index mismatch and modification of the coupling coefficient between the access waveguides and the cavity. This effect is even more pronounced for the smallest refractive index, where the resonant mode is hardly distinguishable from the noise in the photonic bandgap. This is because of a lesser confinement and poor coupling efficiency; therefore, the device is more efficient when the refractive index in the slot is close to or higher than the refractive index of silica. The resonant modes of the SPCC for each liquid are shown in Fig. 3(a). The cladding refractive index change tunes the resonant wavelength over a range of 50 nm with a linear shift. The measured Q-factors deduced from the
Fig. 2. Normalized transmission spectrum for different values of the liquid refractive index, showing the translation of the fundamental mode of the cavity (colored).
5793
Fig. 3. (a) Resonant spectra of the cavity for successive infiltrations by a liquid with an increasing refractive index (squares) and associated Lorentzian fits (solid line). The resonant wavelength drifts linearly with the refractive index (dotted line). Each resonance is normalized by its maximum value. (b) Resonant wavelength as a function of the refractive index, showing a linear dependence yielding a sensitivity of 235 nm/RIU, and quality factor as a function of the refractive index, showing a maximum value of 25,000 around nliq 1.44.
Lorentzian fits [Fig. 3(a)] are plotted as a function of the liquid refractive index in Fig. 3(b). As expected, the lowest Q-factor is obtained for the smallest index (Q 8000 for nliq 1.345) and the highest Q-factor is achieved when the liquid refractive index perfectly matches the index of silica, yielding to the very high value of Q 25; 000, which even exceeds the value reported in our previous work [9]. For a higher refractive index, the Q-factor decreases but remains higher than 12,000 for nliq 1.545, suggesting that Q-factors higher than 104 with a polymer infiltration and a transmission on resonance near 20% are within reach. A linear fit of the resonant wavelength as a function of the refractive index is traced in Fig. 3(b). By defining the sensitivity S as S dλ∕dn, the SPCC yields a sensitivity of 235 nm/RIU. This value is smaller than those reported previously in other SPCC systems [3,4], but it should be pointed out that the SPCC lies on a buried silica layer and has a narrower slot, reducing the overlap between the liquid and the cavity light field. This explains the reduced sensitivity. However, this SPCC has a better mechanical stability, a higher Q-factor, and the hydrophilic behavior of the silica helps the wetting of the liquid on the sample. We also underline that the coupling efficiency in this SPCC yields a transmission on resonance up to 25% for the highest refractive index, which makes this device practical for an integration in silicon photonics and gives a very high signal to noise ratio. Referring to the figure of merit of real-time and label-free sensors [11] as FOM S∕FWHM, the values range from 1200 to 3700. Based on the definition in Ref. [12], we have calculated the detection limit of our device. The definition of the
5794
OPTICS LETTERS / Vol. 39, No. 20 / October 15, 2014
sensitivity of our device enables us to discriminate a refractive index shift of only 2 × 10−3 , indicating that a cladding refractive index change of only 2.9 × 10−4 will switch a signal circulating in the cavity from an ON/OFF state. The small footprint of our device will enable the integration of many cavities connected through the same bus waveguide for multiplexing sensing applications.
Fig. 4. Resonant spectra of the cavity for nliq 1.448 (blue) and nliq 1.45 (red) with Lorentzian fits (solid lines), showing a wavelength shift of 0.75 nm.
sensor resolution given by White and Fan shows that our device resolution is limited by the spectral resolution of the tunable laser (1 pm), giving a detection limit DL 1.25 × 10−5 . We also studied the wavelength shift for small variations of the refractive index. In Fig. 4, we can see a wavelength shift of 0.75 nm for a liquid refractive index change of only 0.002 RIU. This wavelength shift represents approximately 10 times the full width at half-maximum (FWHM). This figure shows that the device allows a fine estimation of the concentration of an analyte in the liquid, which relates to the measured sensitivity of the sensor. On the other hand, the device is compatible with an integration of multiple cavities coupled to the same waveguide [13], which will enable the multiplexing of many detection channels in a compact device [14]. In conclusion, we have demonstrated a liquid sensor with a sensitivity of 235 nm/RIU and a detection limit of 1.25 × 10−5 based on a slot photonic crystal cavity on SOI and covered by a liquid. The quality factor moves from 8000 to 25,000 for a liquid refractive index comprised between 1.35 and 1.55, a maximum Q-factor of 25,000 being achieved at nliq 1.44, which enhances the sensor figure of merit up to 3700. The very-high
C. Caër and S. F. Serna-Otálvaro acknowledge scholarships from the Ministry of Higher Education and Research (France). This project is partly supported by the ANR (Agence Nationale de la Recherche) through the POSISLOT project. Fabrication was conducted in the IEF clean room facilities (CTU/MINERVE), part of RENATECH network. References 1. G. Shambat, S.-R. Kothapalli, J. Provine, T. Sarmiento, J. Harris, S. S. Gambhir, and J. Vučković, Nano Lett. 13, 4999 (2013). 2. M. R. Lee and P. M. Fauchet, Opt. Lett. 32, 3284 (2007). 3. A. Di Falco, L. O’Faolain, and T. F. Krauss, Appl. Phys. Lett. 94, 063503 (2009). 4. J. Jágerská, H. Zhang, Z. Diao, N. Le Thomas, and R. Houdré, Opt. Lett. 35, 2523 (2010). 5. T. Yamamoto, M. Notomi, H. Taniyama, E. Kuramochi, Y. Yoshikawa, Y. Torii, and T. Kuga, Opt. Express 16, 13809 (2008). 6. A. H. Safavi-Naeini, T. P. Mayer Alegre, M. Winger, and O. Painter, Appl. Phys. Lett. 97, 181106 (2010). 7. S. Kita, S. Hachuda, K. Nozaki, and T. Baba, Appl. Phys. Lett. 97, 161108 (2010). 8. M. G. Scullion, A. F. Di Falco, and T. F. Krauss, Biosens. Bioelectron. 97, 161108 (2010). 9. C. Caer, X. Le Roux, and E. Cassan, Appl. Phys. Lett. 103, 251106 (2013). 10. C. Caer, X. Le Roux, and E. Cassan, Opt. Lett. 37, 3660 (2012). 11. L. J. Sherry, S. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. Xia, Nano Lett. 5, 2034 (2005). 12. I. M. White and X. Fan, Opt. Express 16, 1020 (2008). 13. S. Mandal and D. Erickson, Opt. Express 16, 1623 (2008). 14. Y. Takahashi, T. Asano, D. Yamashita, and S. Noda, Opt. Express 22, 4692 (2014).
