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Sensitivity optimization of a photonic crystal ring resonator for gas sensing applications
Accepted Manuscript Title: Sensitivity Optimization of a Photonic Crystal Ring Resonator for Gas Sensing Applications Authors: R. Jannesari, C. Ranacher, C. Consani, T. Grille, B. Jakoby PII: DOI: Reference:
S0924-4247(17)31435-8 http://dx.doi.org/doi:10.1016/j.sna.2017.08.017 SNA 10271
To appear in:
Sensors and Actuators A
Received date: Revised date: Accepted date:
3-2-2017 27-6-2017 5-8-2017
Please cite this article as: R.Jannesari, C.Ranacher, C.Consani, T.Grille, B.Jakoby, Sensitivity Optimization of a Photonic Crystal Ring Resonator for Gas Sensing Applications, Sensors and Actuators: A Physicalhttp://dx.doi.org/10.1016/j.sna.2017.08.017 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Sensitivity Optimization of a Photonic Crystal Ring Resonator for Gas Sensing Applications R.Jannesaria, C. Ranacherb, C. Consanib, T. Grillec, B. Jakobya a. Institute for Microelectronics and Microsensors, Johannes Kepler University, Linz, Austria b. Carinthian Tech Research AG, Villach, Austria c. Infineon Technologies Austria AG, Villach, Austria
HIGHLIGHTS
A design for high Q factor photonic crystal ring resonator (PCRR) is presented. The PCRR is based on 2D pillar type photonic crystals. The high quality factor (3.85×105) of the cavity, along with strong overlap between analyet and the field of the resonance mode of PCRR, which have low group velocity, consequence into enhance sensitivity for gas sensing applications. Most of the works that focused on the utilization of the slow light phenomenon until now, dealt with the slow light effect in the high-refractive area of the PhC structure. In contrast, in this work, we illustrate a new concept to enhance the sensitivity of gas sensors for optical sensing by enhancing the light-matter interaction in low refractive area of the PhC, which corresponds to the region filled by the analyte. Abstract In this work we report on a computational study regarding the enhancement of the absorption of mid infrared (MIR) light for gas sensing applications. In order to address this goal, a photonic crystal ring resonator (PCRR) with a quality factor of more than 3.85×105 was designed. The considered PCRR is based on 2D pillar type photonic crystals, which consist of a hexagonal array of silicon rods. The high quality factor of the cavity, along with strong overlap between the field of the resonant mode and the analyte (0.76) and low group velocity of PCRR modes consequence into enhance sensitivity for gas sensing.
Keywords: photonic crystal ring resonator; gas sensor; resonators; integrated optics 1.
Introduction
Measuring the optical properties of fluids plays a central role in chemical analysis. An optical sensor operates by measuring the changes in a property of light as it passes through an analyte. In this framework, photonic technology has significantly enhanced fluid sensing performance, particularly in the area of light-analyte interaction, multiplexing and device miniaturization. Different integrated optical sensors have been proposed, such as micro-ring resonators [1] and photonic crystals [2] [3]. Over the past few years, photonic crystals triggered a lot of interest in lab-on-chip optical technology in connection with their significant potential with respect to, e.g., confinement of light in small volumes, possibility of convenient integration with waveguides, and achievable ultra-high quality factors in case of resonators [4]. Photonic crystals have a wide range of applications including antennas [5], sensors [6], filters [7], etc. PhC-based sensors have been also proposed as gas sensors in mid infrared (MIR), since many gases (e.g., CO2, CH4, CO) exhibit characteristic absorption lines in mid-IR wavelength region which is why this region is often referred to as “figure print” region. A review of gas and liquid sensors based on PhC is presented by Y. Zhao et.al. at 2011 [8]. This work introduces a photonic crystal ring resonator (PCRR) for gas sensing in the mid infrared region. The general sensing mechanism is based on designing a resonator featuring electromagnetic fields in the analyte, which occupies part of the resonator volume, such that the characteristics of the device are affected by the absorption in the sample (a gas, for instance). PCRRs were first introduced in 2002 to realize a hexagonal waveguide ring laser [9]. A PhC sensor based on a ring resonator cavity has been, e.g., proposed for monitoring the level of seawater salinity between 0% to 40% in 2012 [10]. In a review paper, Robinson et.al. present an overview on photonic crystal ring resonators [11]. In this paper we particularly address the utilization of the slow light phenomenon corresponding to waveguide modes featuring very low group velocities. Most of the works that focused on the utilization of the slow light phenomenon until now, dealt with the slow light effect in the high-refractive area of the PhC structure. In contrast, in
this work, we illustrate a new concept to enhance the sensitivity of gas sensors for optical sensing by enhancing the light-matter interaction in low refractive area of the PhC, which corresponds to the region filled by the analyte. The structure of the PCRR is optimized by properly changing the radius of silicon pillars constituting the PhC structure. Simulation results indicate that a very high filling factor of 0.758 and a low group velocity of 7×10-4c could be achieved. The PhC structures in our design utilize silicon thus enabling fabrication in standard MEMS technology. 2.
Photonic crystal
A photonic crystal (PhC) can be described as a periodic modification of a dielectric medium featuring a period (in the order of the wavelength) which can effectively control light propagation [12]. This periodic array can be a onedimensional (1D), two-dimensional (2D) or three-dimensional (3D) array. Similar to crystalline materials, in which the presence of a periodic potential for electrons results in electronic energy bands, in photonic crystals, a periodic refractive index results in photonic bands facilitating photon propagation and forbidden bands (gaps) in between. A complete photonic band gap forbids the transmission of photons with certain frequencies or wavelengths in all directions. Another feature of PhCs is the creation of local states in the band gap by locally adding or removing material (“crystal defects”) [13]. For sensing applications, especially when the concentration of the analyte or its variation is low, efficient interaction between the analyte and light plays an important role; since it not only determine the size of the devise, but also sensitivity of the sensor. In optical absorption spectroscopy, an analyte can be detected not only by changing the position of the frequency respond but also by the variation of light intensity due to absorption in the analyte. The working principle underlying a photonic crystal gas sensor is the enhancement of interaction between analyte and IR-light that, in turn, leads to enhancement of effectively detected gas absorption. The Lambert–Beer law provides the theoretical basis of optical absorption spectroscopy by describing the change in intensity when light passes through an absorbing medium: 𝐼 = 𝐼0 𝑒𝑥 𝑝(−𝛾𝛼𝐶𝐿). (1) Here I0 and I are the intensities of the input and output light respectively, α is the gas absorption coefficient, 𝐶 is the gas concentration, L is the absorption length and γ is the dimensionless parameter of slow light enhanced absorption [14]. The unique properties of photonic crystals such as the presence of photonic band gaps, photonic localization, or slow light phenomena, can be used for gas sensing. This can be, e.g., obtained by utilizing a mode with low group velocity, which features particularly strong light-matter interaction. When the PhC slow light structure is introduced to the sample, the interaction of the light and matter will be enhanced so the absorption coefficient can be greatly increased. In particular, we have [15] ⟨𝐸 | 𝜀 | 𝐸 ⟩ γ=αPhC /α≈f c/vg , 𝑓 ≡ ⟨𝐸 |𝜀𝑎𝑛𝑎𝑙𝑦𝑡𝑒 , (2) |𝐸 ⟩ where, αPhC is the effective absorption factor of the gas-filled PhC, c is the speed of light in vacuum, vg is the group velocity of light in the PhC and f is the so called filling factor of optical field in the analyte. The integral in the nominator of the filling factor is restricted to the region contained the analyte while the integral in the denominator extends over the entire cross section of photonic crystal [16]. To maximize the sensitivity, the portion of electromagnetic field associated with the mode located in the low index region has to be as large as possible. The PhC parameters should be designed to support a mode that has a low group velocity and spectrally overlaps with absorption frequency of interested gas. In addition, features high electric field strengths in the region filled by the analyte (which, in general, features a lower refractive index than the PhC material, i.e. silicon in our case). Photonic crystal resonant micro cavities are another feature of PhCs. Corresponding devices are fabricated by introducing localized defects in perfect periodicity of a photonic crystal. In this way, a series of defects in photonic crystals will break the existing symmetry of the photonic crystal and a narrow defect mode is created in the photonic band gap. The corresponding mode is confined to the defect. The guided slow light enhances light matter interaction so absorption coefficient can be greatly increased [17]. This technology offers a potential for the miniaturization of devices [16]. There are varieties of different cavities that can be produced in photonic crystals. In this work, we consider the use of a photonic crystal ring resonator to obtain a compact and low cost absorption spectroscopy gas sensor. Preliminary results of this work were presented at the Eurosensors 2016 conference [18].
3.
Photonic crystal ring resonator(PCRR)
The photonic crystal ring resonator is formed by removing a number of silicon rods in the PhC structure characterized by triangular distribution of silicon rods in air or the gas to be sensed (i.e. we have high dielectric index pillars embedded in a low dielectric index medium). The schematic view of this cavity is shown in Fig.1. The lattice constant a and the radii r of the rods are tuned to obtain a resonance peak in desired frequency range. An input and an output waveguide are placed in horizontal direction with two lines of silicon rods separating it from the PCRR. Ring resonator based devices yield several advantages including flexibility in mode design and scalability in size, where the choice of ring size can be adjusted to the desired resonance wavelength and leads to a tradeoff between the Q-factor and mode volume [2]. In addition, ring resonators have been designed in order to exhibit different and unique resonant wavelengths, thus allowing multiplexed detection with a single waveguide. It is to be noted that, optical confinement by a photonic band gap is more efficient than by utilizing total internal reflection [8]. Therefore, the PCRR modes have the same properties as photonic crystal modes; modes below the light line are well confined inside the slab, which means that they undergo low loss. The air space in this PCRR will be filled by the analyte when performing sensing tasks. In this design, the gas is in contact with PCRR modes to enhance interaction between guided mode and analyte. The dotted lines in Fig.2(a) shows the band diagram of 2D photonic crystal which supports quasi-transverseelectric (TE) modes (electric field dominantly aligned along the axes of the silicon rods) with a band gap that ranges from 0.2774(a/λ) to 0.4482(a/λ) (shadow area). The hexagonal defect creates additional bands in the band gap of the unperturbed crystal as shown Fig.2 (a) by red lines. The slope of a band in the photonic band structure corresponds to the group velocity of light vg, 𝑣𝑔 =
𝜕𝜔 𝜕𝑘
.
(3)
The flat PCRR modes feature a very low group velocity as indicated by the small slope. When the PhC slow light structure is in contact with the sample, the interaction of the light and matter will be enhanced so the absorption coefficient can be greatly increased [15]. The Plane Wave Expansion (PWE) method is used to calculate the photonic band gap and propagating modes of structure. The used simulation parameters are as follows. The lattice constant a is 1.6µm and the radius of silicon rods r is 0.2a. The lattice constant and radius of photonic crystal rods always have to be chosen in a way such that the desired mode is in the frequency range of absorption peak of analyte. The simulated electric field profile given in terms of the field component Ey (y is Perpendicular to the PhC surface) of cavity modes is shown in Figs. 2(b) through 2(g), respectively. Achieving strong confinement of light intensity in the low index region is the advantage of this PCRR. The mode we selected for sensing is the forth-created band inside the gap (M4), which is rather flat. This mode has most of the electromagnetic field energy in the region of the lowindex material; see Fig. 2(e) yielding the above-mentioned enhanced interaction. Furthermore, this mode is well separated from neighboring bands, which has the advantage that impinging light with specified frequency has less possibility to couple to other modes with the same frequency, which would spuriously decrease the amount of energy coupled to the desired mode. Table 1 summarizes the simulated value for filling factor and normalized frequency for all 6 PCRR modes. The forth mode (M4) has the highest filling factor. Fig.3 shows the normalized group velocity of the PCRR modes.
In this work, the radius of 12 rods at the outer and inner PhC, indicated by blue (dr 1) and cyan (dr2) color in Fig. 1, were tuned to enhance the quality factor of PCRR in vacuum. The Q-factor of forth mode (M4) rises up to more than 3.8×105 for the radii, dr1=0.22µm and dr2=0.19µm. Fig.4(a) shows the calculated Q-factor of the cavity mode as a function of dr1 and dr2. The maximum allowed fabrication tolerance for the pillars radius to keep the Q-factor as high as 3.85×105 is less than 100nm. More variation reduces the Q-factor. Though the lower Q-factor results in a broader peak, since the sensing process is not based on frequency shift of the peak but on the absorption, this does not change the sensitivity of the sensor. Variations of the radii (dr1 and dr2) have only a small effect on the group velocity vg and the filling factor of the mode M4. In these simulations, the absorption in the silicon rods is not considered, i.e. this value for the Q-factor characterizes the PCRR as a non-ideal cavity resonator. Therefor the Q-factor decreases by about one order of magnitude when the PCRR is coupled to waveguide. With this optimization the group velocity of the corresponding mode goes down to the 7×10 -4c where c denotes the free-space velocity of light. Structure optimization is performed by using the finite difference time domain (FDTD) method. The corresponding electric field profile confirms that the cavity mode is strongly confined within the PCRR, having an effective mode volume
equal to Veff =4.36µm3 and the overlap between electric field intensity and the fluid medium to be sensed, is 0.758, calculated using Eq. (2). The effective mode volume is defined as [19]: ∫ 𝜀(𝑟)𝐸 2 (𝑟)𝑑𝑣
𝑉𝑒𝑓𝑓 = [𝜀(𝑟)𝐸2 (𝑟)]
𝑚𝑎𝑥
.
(3)
In this way, the absorption is maximized and the linewidth of the absorption peak is kept narrow. Most competing devices reported in the literature have a larger group velocity compared to the results presented in this work [20]. A photonic crystal waveguide is formed by removing one line of silicon rods creating a series of defects. If the waveguide passes close to the PCRR, coupling is achieved. There are two lines of silicon rods separating the waveguide and PCRR, see Fig.1. Calculated dispersion curve of the photonic crystal waveguide is shown by blue line in Fig.2(a). A Gaussian input signal is launched into input port and at resonance frequency, the propagating mode is coupled from input waveguide into ring and finally to the output waveguide. The transmission efficiency is detected by monitoring the E-field intensity at output port of waveguide. Fig. 4(b) simulated the transmission spectra of the photonic crystal waveguide (blue curve) and spectral position of the PCRR resonance modes (red curve). In the absence of PCRR, the waveguide has uniform transmission in the range of 0.347-0.445(a/λ) within the bandgap of photonic crystal. In the presence of the ring, the transmission spectrum contains pronounced dips. This is due to coupling of waveguide power to the ring at specific wavelengths [21]. The FDTD method was used to calculate transmission spectra of the waveguide coupled to the PCRR. The dips in the transmission spectrum can be utilized to sense the absorption taking place in the PCRR, which will be the subject of future research. Future work will also include the fabrication of device. Simulation results for this work consider an aspect ratio around 15 for the silicon pillars on top of the silicon slab. This aspect ratio represents a challenge in the fabrication of this device. There are a variety of processes that could be considered, such as deep reactive ion etching (DRIE, “Bosch process”). Our suggestion for fabrication is as follows. The first step in the fabrication is the mask processing using the deep ultraviolet (DUV) lithography method to pattern the photonic crystal cavity mask on the resist, after defining the photonic crystal pattern on the resist a thin layer of a metal, such as gold or chromium, is deposited on the sample. By performing a lift-off process, the PhC pattern is created on the metal hard mask. The pattern of the structure is transferred to Si with the DRIE process. Finally, the metal layer is removed in a wet etch process. 4.
Conclusion
We presented a design for a PCRR featuring a very high Q factor. A simulated Q factor of more than 3.85×105 and group velocity of 7×10-4c has been achieved by slightly tuning of radius of twelve silicon rods in the inner and outer corners of the PCRR. The PCRR is simulated by using the PWE and 2D FDTD methods. We have demonstrated a large overlap of the high Q photonic crystal ring resonator mode with the analyte, which indicates the potential for highly effective absorption sensing. The small size of the PCRR makes it suitable for parallel or multiplex detection.
Acknowledgment The authors acknowledge the support of the Austrian COMET program (Linz Center of Mechatronics and Austrian Smart Systems Integration Research Center). References [1] F. Dell’Olio, V. M. N. Passaro, "Optical sensing by optimized silicon slot waveguides," OPTICS EXPRESS, vol. 15, no. 8, p. 4977, 2007. [2] Y. Zhang,C. Zeng,D.Li,G. Gao,Z. Huang,J. Yu and J. Xia, „High-quality-factor photonic crystal ring resonator,“ OPTICS LETTERS, Bd. 39, Nr. 5, p. 1282, 2014. [3] V. M. Lavchiev, B. Jakoby, U. Hedenig, Th. Grille, J. M. R. Kirkbride and G.A.D. Ritchie, „M-line spectroscopy on mid-infrared Si photonic crystals for fluid sensing and chemical imaging,“ OPTICS EXPRESS , Bd. 24, Nr. 1, pp. 262-271, 2016. [4] M. Notomi, „Theory of light propagation in strongly modulated photonic crystals:Refractionlike behavior in the vicinity of the photonic band gap,“ Physical Review B, Bd. 62, 15 OCTOBER 2000. [5] A. Ghaffari, F. Monifi, M. Djavid, and M. S. Abrishamian, „Photonic crystal bends and power splitters based on
ring resonators,“ Optics Communications , Bd. 281, p. 5929, 2008. [6] T. T. Mai, F.L. Hsiao, C. Lee, W. Xiang, C.C. Chen, W. K. Choi, „Optimization and comparison of photonic crystal resonators for silicon microcantilever sensors,“ Sens. Actuators A Phys., Bd. 165, pp. 16-25, 2011. [7] F. Monifi, M. Djavid, A. Ghaffari, M. Abrishamian, „Three output port channel-drop filter based on photonic crystals,“ APPLIED OPTICS, Bd. 48, Nr. 4, p. 804, 2009. [8] Y. Zhao , Y. Zhang, Q. Wang, „Research advances of photonic crystal gas and liquid sensors,“ Sensors and Actuators B: Chemical, Bd. 160, p. 1288–1297, 2011. [9] H. R. H. P. G. K. Y. C. Y. a. J. K. S.H. Kim, Appl. Phys. Lett., Bd. 81, 2002. [10] S.Robinson, R. Nakkeeran, , „Photonic Crystal based sensor for sensing the salinity of seawater.,“ IEEE – International Conference On Advances In Engineering Science and Management (ICAESM), pp. 495-499, 2012. [11] S. Robinson,R. Nakkeeran, „Photonic crystal ring resonator-based add drop filters: a review,“ Optical Engineering , Bd. 52, Nr. 6, p. 060901, 2013. [12] Joannopoulos,J. D. ,Johnson, S. G. ,Winn, J. N. , Meade,R. D., Photonic Crystals: Molding the Flow of Light, Princeton University, 2011. [13] E. Yablonovitch, T. J. Gmitter, and K. M. Leung, „Photonic band structure: The face-centered-cubic case employing nonspherical atoms," , vol. 67,,“ Physical Review Letters, Bd. 67, pp. 2295-2298, 1991.. [14] Y. Zhang, Y. Zhao , D.i Wu and Q. Wang, „Theoretical research on high sensitivity gas sensor due to slow light in slotted,“ Sensors and Actuators B, Bd. 173, pp. 505-509, 2012. [15] Y. Zhao ,Y. Zhang , Q. Wang, „High sensitivity gas sensing method based on slow light in photonic crystal waveguide,“ Sensors and Actuators B, Bd. 173, p. 28–31, 2012. [16] N. A. Mortensena and S.i Xiao, „Slow-light enhancement of Beer-Lambert-Bouguer absorption,“ APPLIED PHYSICS LETTERS, Bd. 90, p. 141108, 2007. [17] D. Pergande, T. M. Geppert, A. von Rhein, S.L. Schweizer,R. B. Wehrspohn, S. Moretton, A. Lambrecht, „Miniature infrared gas sensors using photonic crystals,“ JOURNAL OF APPLIED PHYSICS , Bd. 109, p. 083117, 2011. [18] R.Jannesari, C. Ranacher, C. Consani, V. Lavchiev, T. Grille, B. Jakoby, „High-Quality-Factor Photonic Crystal Ring Resonator with Applications for Gas Sensing,“ in Procedia Engineering, Budapest, 2016. [19] Jean Michel Gerard , Bruno Gayral, „Strong Purcell Effect for InAs Quantum Boxes in Three-Dimensional Solid-State Microcavities,“ JOURNAL OF LIGHTWAVE TECHNOLOGY, Bd. 17, Nr. 11, p. 2089, 1999. [20] N. Zhu, Y. Li, C. Chen, S. Yan, „Slow light in dual-periodic photonic crystals based slotted-waveguidecoupled cavity,“ Optics & Laser Technology , Bd. 83, pp. 125-130, 2016. [21] V. Dinesh Kumar, T. Srinivas, A. Selvarajan, „Investigation of ring resonators in photonic crystal circuits,“ Photonics and Nanostructures – Fundamentals and Applications , Bd. 2, pp. 199-206, 2004.
Biographies Reyhaneh Jannesari received her M.Sc. degree in Solid State physic from the Isfahan University, Isfaha, Iran in 2003. In 2007 she worked as a research assistant at Christian Doppler Laboratory for Surface Optics at the Johannes Kepler University, Linz, Austria. From 2010 to 2014 she worked as a research assistant at the Institute of semiconductor and Solid State Physics physic, JKU where she obtained her Ph.D degree with research focused on ‘Experimental and numerical investigations of Si-based photonic crystals with ordered Ge quantum dots emitters’. Since 2015, she is working as a research assistant at the Institute for Microelectronics and Microsensors, JKU, Linz, Austria. Her focus is on application of Photonic crystal on fluid sensing.
Christian Ranacher was born in Lienz, Austria in 1989. He received the B.Sc. and the Dipl.-Ing. (M.Sc.) in technical physics from Graz University of Technology, Austria, in 2012 and 2014, respectively. After his studies he was working as product and process integration engineer at Infineon Technologies Austria AG and in late 2015 he joined the Carinthian Tech Research AG as a researcher in the field of microsystem technologies. Since 2016 he is also working towards a PhD degree in the field of optical micro fluid sensing at the Institute for Microelectronics at the Johannes Kepler University Linz, Austria.
Cristina Consani was born in Spilimbergo, Italy in 1983. She received her Bachelor and Master Degree in condensed matter physics from the University of Trieste, Italy, in 2005 and 2007, respectively. In 2007 she joined the Institute of Chemical Sciences and Engineering at the EPFL Lausanne, Switzerland, where she obtained her PhD in 2012 with her work on Ultrafast One- and Two-Dimensional UV Transient Absorption Spectroscopy of Haem Proteins. From 2012 to 2015 she worked as a post-doc scientist at the University of Würzburg, where she performed ultrafast two-dimensional spectroscopy and coherent control studies on several molecular systems. In 2016 she joined the Carinthian Tech Research AG as a researcher in the photonics department. Her current research interests include spectroscopy, scattering models and integrated photonics.
Bernhard Jakoby obtained his Dipl.-Ing. (M.Sc.) in Communication Engineering and his doctoral (Ph.D.) degree in electrical engineering from the Vienna University of Technology (VUT), Austria, in 1991 and 1994, respectively. In 2001 he obtained avenia legendi for Theoretical Electrical Engineering from the VUT. From 1991 to1994 he worked as a Research Assistant at the Institute of General Electrical Engi-neering and Electronics of the VUT. Subsequently he stayed as an Erwin Schrödinger Fellow at the University of Ghent, Belgium, performing research on the electrodynamics of complex media. From 1996 to 1999 he held the position of a Research Associate and later Assistant Professor at the Delft University of Technology, The Netherlands, working in the field of microacoustic sensors. From 1999 to 2001 he was with the Automotive Electronics Division of the Robert Bosch GmbH, Germany, where he conducted development projects in the field of automotive liquid sensors. In 2001 he joined the newly formed Industrial Sensor Systems group of the VUT as an Associate Professor. In 2005 he was appointed Full Professor of Microelectronics at the Johannes Kepler University Linz, Austria. He is currently working in the field of liquid sensors and monitoring systems.
2r
a
Input
√3a
Output
Fig.1 A layout configuration of PCRR structure of silicon rods with r=0.2a, where r is radius of rods and a is lattice period. The radius of 6 silicon rods at the corners of the outer PhC, indicated by blue circles (dr1), and 6 silicon rods at the corners of inner PhC, indicate by cyan circles (dr2), is tuned to obtain higher Q factor.
(a)
(b)
(c)
(d)
M1 (e)
M2 (f)
M3 (g)
M4
M5
M6
Fig. 2: (a) The TE band structure of the considered PhC (doted lines) shown together with the PCRR cavity modes (red lines) and dispersion curve of the PhC waveguide (blue line). The light line is shown in gray. The shadow zone represents the photonic band gap of the unperturbed crystal. So called flat bands created by the defects correspond to modes with low group velocity labelled b to g. (b)-(g) The simulated Ey intensity profiles for the PCRR cavity modes.
Γ
Γ
Fig. 3: Normalized group velocity for the PCRR modes with respect to the in-plane wavevector.
b
a
Fig.4: (a) Calculated Q-factor of the cavity mode as a function of dr1and dr2 which are indicated in Fig.1.(b) Simulated spectral position of the PCRR resonance modes (red curve) and transmission spectra of the PhC waveguide (blue curve).
Table1. Frequency and filling factor of PCRR modes.
Mode Frequency(a/λ) Filling factor(f)
M1 0.3428 0.585
M2 0.3466 0.637
M3 0.3655 0.658
M4 0.3806 0.758
M5 0.3933 0.71
M6 0.4222 0.697
S0924-4247(17)31435-8 http://dx.doi.org/doi:10.1016/j.sna.2017.08.017 SNA 10271
To appear in:
Sensors and Actuators A
Received date: Revised date: Accepted date:
3-2-2017 27-6-2017 5-8-2017
Please cite this article as: R.Jannesari, C.Ranacher, C.Consani, T.Grille, B.Jakoby, Sensitivity Optimization of a Photonic Crystal Ring Resonator for Gas Sensing Applications, Sensors and Actuators: A Physicalhttp://dx.doi.org/10.1016/j.sna.2017.08.017 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Sensitivity Optimization of a Photonic Crystal Ring Resonator for Gas Sensing Applications R.Jannesaria, C. Ranacherb, C. Consanib, T. Grillec, B. Jakobya a. Institute for Microelectronics and Microsensors, Johannes Kepler University, Linz, Austria b. Carinthian Tech Research AG, Villach, Austria c. Infineon Technologies Austria AG, Villach, Austria
HIGHLIGHTS
A design for high Q factor photonic crystal ring resonator (PCRR) is presented. The PCRR is based on 2D pillar type photonic crystals. The high quality factor (3.85×105) of the cavity, along with strong overlap between analyet and the field of the resonance mode of PCRR, which have low group velocity, consequence into enhance sensitivity for gas sensing applications. Most of the works that focused on the utilization of the slow light phenomenon until now, dealt with the slow light effect in the high-refractive area of the PhC structure. In contrast, in this work, we illustrate a new concept to enhance the sensitivity of gas sensors for optical sensing by enhancing the light-matter interaction in low refractive area of the PhC, which corresponds to the region filled by the analyte. Abstract In this work we report on a computational study regarding the enhancement of the absorption of mid infrared (MIR) light for gas sensing applications. In order to address this goal, a photonic crystal ring resonator (PCRR) with a quality factor of more than 3.85×105 was designed. The considered PCRR is based on 2D pillar type photonic crystals, which consist of a hexagonal array of silicon rods. The high quality factor of the cavity, along with strong overlap between the field of the resonant mode and the analyte (0.76) and low group velocity of PCRR modes consequence into enhance sensitivity for gas sensing.
Keywords: photonic crystal ring resonator; gas sensor; resonators; integrated optics 1.
Introduction
Measuring the optical properties of fluids plays a central role in chemical analysis. An optical sensor operates by measuring the changes in a property of light as it passes through an analyte. In this framework, photonic technology has significantly enhanced fluid sensing performance, particularly in the area of light-analyte interaction, multiplexing and device miniaturization. Different integrated optical sensors have been proposed, such as micro-ring resonators [1] and photonic crystals [2] [3]. Over the past few years, photonic crystals triggered a lot of interest in lab-on-chip optical technology in connection with their significant potential with respect to, e.g., confinement of light in small volumes, possibility of convenient integration with waveguides, and achievable ultra-high quality factors in case of resonators [4]. Photonic crystals have a wide range of applications including antennas [5], sensors [6], filters [7], etc. PhC-based sensors have been also proposed as gas sensors in mid infrared (MIR), since many gases (e.g., CO2, CH4, CO) exhibit characteristic absorption lines in mid-IR wavelength region which is why this region is often referred to as “figure print” region. A review of gas and liquid sensors based on PhC is presented by Y. Zhao et.al. at 2011 [8]. This work introduces a photonic crystal ring resonator (PCRR) for gas sensing in the mid infrared region. The general sensing mechanism is based on designing a resonator featuring electromagnetic fields in the analyte, which occupies part of the resonator volume, such that the characteristics of the device are affected by the absorption in the sample (a gas, for instance). PCRRs were first introduced in 2002 to realize a hexagonal waveguide ring laser [9]. A PhC sensor based on a ring resonator cavity has been, e.g., proposed for monitoring the level of seawater salinity between 0% to 40% in 2012 [10]. In a review paper, Robinson et.al. present an overview on photonic crystal ring resonators [11]. In this paper we particularly address the utilization of the slow light phenomenon corresponding to waveguide modes featuring very low group velocities. Most of the works that focused on the utilization of the slow light phenomenon until now, dealt with the slow light effect in the high-refractive area of the PhC structure. In contrast, in
this work, we illustrate a new concept to enhance the sensitivity of gas sensors for optical sensing by enhancing the light-matter interaction in low refractive area of the PhC, which corresponds to the region filled by the analyte. The structure of the PCRR is optimized by properly changing the radius of silicon pillars constituting the PhC structure. Simulation results indicate that a very high filling factor of 0.758 and a low group velocity of 7×10-4c could be achieved. The PhC structures in our design utilize silicon thus enabling fabrication in standard MEMS technology. 2.
Photonic crystal
A photonic crystal (PhC) can be described as a periodic modification of a dielectric medium featuring a period (in the order of the wavelength) which can effectively control light propagation [12]. This periodic array can be a onedimensional (1D), two-dimensional (2D) or three-dimensional (3D) array. Similar to crystalline materials, in which the presence of a periodic potential for electrons results in electronic energy bands, in photonic crystals, a periodic refractive index results in photonic bands facilitating photon propagation and forbidden bands (gaps) in between. A complete photonic band gap forbids the transmission of photons with certain frequencies or wavelengths in all directions. Another feature of PhCs is the creation of local states in the band gap by locally adding or removing material (“crystal defects”) [13]. For sensing applications, especially when the concentration of the analyte or its variation is low, efficient interaction between the analyte and light plays an important role; since it not only determine the size of the devise, but also sensitivity of the sensor. In optical absorption spectroscopy, an analyte can be detected not only by changing the position of the frequency respond but also by the variation of light intensity due to absorption in the analyte. The working principle underlying a photonic crystal gas sensor is the enhancement of interaction between analyte and IR-light that, in turn, leads to enhancement of effectively detected gas absorption. The Lambert–Beer law provides the theoretical basis of optical absorption spectroscopy by describing the change in intensity when light passes through an absorbing medium: 𝐼 = 𝐼0 𝑒𝑥 𝑝(−𝛾𝛼𝐶𝐿). (1) Here I0 and I are the intensities of the input and output light respectively, α is the gas absorption coefficient, 𝐶 is the gas concentration, L is the absorption length and γ is the dimensionless parameter of slow light enhanced absorption [14]. The unique properties of photonic crystals such as the presence of photonic band gaps, photonic localization, or slow light phenomena, can be used for gas sensing. This can be, e.g., obtained by utilizing a mode with low group velocity, which features particularly strong light-matter interaction. When the PhC slow light structure is introduced to the sample, the interaction of the light and matter will be enhanced so the absorption coefficient can be greatly increased. In particular, we have [15] ⟨𝐸 | 𝜀 | 𝐸 ⟩ γ=αPhC /α≈f c/vg , 𝑓 ≡ ⟨𝐸 |𝜀𝑎𝑛𝑎𝑙𝑦𝑡𝑒 , (2) |𝐸 ⟩ where, αPhC is the effective absorption factor of the gas-filled PhC, c is the speed of light in vacuum, vg is the group velocity of light in the PhC and f is the so called filling factor of optical field in the analyte. The integral in the nominator of the filling factor is restricted to the region contained the analyte while the integral in the denominator extends over the entire cross section of photonic crystal [16]. To maximize the sensitivity, the portion of electromagnetic field associated with the mode located in the low index region has to be as large as possible. The PhC parameters should be designed to support a mode that has a low group velocity and spectrally overlaps with absorption frequency of interested gas. In addition, features high electric field strengths in the region filled by the analyte (which, in general, features a lower refractive index than the PhC material, i.e. silicon in our case). Photonic crystal resonant micro cavities are another feature of PhCs. Corresponding devices are fabricated by introducing localized defects in perfect periodicity of a photonic crystal. In this way, a series of defects in photonic crystals will break the existing symmetry of the photonic crystal and a narrow defect mode is created in the photonic band gap. The corresponding mode is confined to the defect. The guided slow light enhances light matter interaction so absorption coefficient can be greatly increased [17]. This technology offers a potential for the miniaturization of devices [16]. There are varieties of different cavities that can be produced in photonic crystals. In this work, we consider the use of a photonic crystal ring resonator to obtain a compact and low cost absorption spectroscopy gas sensor. Preliminary results of this work were presented at the Eurosensors 2016 conference [18].
3.
Photonic crystal ring resonator(PCRR)
The photonic crystal ring resonator is formed by removing a number of silicon rods in the PhC structure characterized by triangular distribution of silicon rods in air or the gas to be sensed (i.e. we have high dielectric index pillars embedded in a low dielectric index medium). The schematic view of this cavity is shown in Fig.1. The lattice constant a and the radii r of the rods are tuned to obtain a resonance peak in desired frequency range. An input and an output waveguide are placed in horizontal direction with two lines of silicon rods separating it from the PCRR. Ring resonator based devices yield several advantages including flexibility in mode design and scalability in size, where the choice of ring size can be adjusted to the desired resonance wavelength and leads to a tradeoff between the Q-factor and mode volume [2]. In addition, ring resonators have been designed in order to exhibit different and unique resonant wavelengths, thus allowing multiplexed detection with a single waveguide. It is to be noted that, optical confinement by a photonic band gap is more efficient than by utilizing total internal reflection [8]. Therefore, the PCRR modes have the same properties as photonic crystal modes; modes below the light line are well confined inside the slab, which means that they undergo low loss. The air space in this PCRR will be filled by the analyte when performing sensing tasks. In this design, the gas is in contact with PCRR modes to enhance interaction between guided mode and analyte. The dotted lines in Fig.2(a) shows the band diagram of 2D photonic crystal which supports quasi-transverseelectric (TE) modes (electric field dominantly aligned along the axes of the silicon rods) with a band gap that ranges from 0.2774(a/λ) to 0.4482(a/λ) (shadow area). The hexagonal defect creates additional bands in the band gap of the unperturbed crystal as shown Fig.2 (a) by red lines. The slope of a band in the photonic band structure corresponds to the group velocity of light vg, 𝑣𝑔 =
𝜕𝜔 𝜕𝑘
.
(3)
The flat PCRR modes feature a very low group velocity as indicated by the small slope. When the PhC slow light structure is in contact with the sample, the interaction of the light and matter will be enhanced so the absorption coefficient can be greatly increased [15]. The Plane Wave Expansion (PWE) method is used to calculate the photonic band gap and propagating modes of structure. The used simulation parameters are as follows. The lattice constant a is 1.6µm and the radius of silicon rods r is 0.2a. The lattice constant and radius of photonic crystal rods always have to be chosen in a way such that the desired mode is in the frequency range of absorption peak of analyte. The simulated electric field profile given in terms of the field component Ey (y is Perpendicular to the PhC surface) of cavity modes is shown in Figs. 2(b) through 2(g), respectively. Achieving strong confinement of light intensity in the low index region is the advantage of this PCRR. The mode we selected for sensing is the forth-created band inside the gap (M4), which is rather flat. This mode has most of the electromagnetic field energy in the region of the lowindex material; see Fig. 2(e) yielding the above-mentioned enhanced interaction. Furthermore, this mode is well separated from neighboring bands, which has the advantage that impinging light with specified frequency has less possibility to couple to other modes with the same frequency, which would spuriously decrease the amount of energy coupled to the desired mode. Table 1 summarizes the simulated value for filling factor and normalized frequency for all 6 PCRR modes. The forth mode (M4) has the highest filling factor. Fig.3 shows the normalized group velocity of the PCRR modes.
In this work, the radius of 12 rods at the outer and inner PhC, indicated by blue (dr 1) and cyan (dr2) color in Fig. 1, were tuned to enhance the quality factor of PCRR in vacuum. The Q-factor of forth mode (M4) rises up to more than 3.8×105 for the radii, dr1=0.22µm and dr2=0.19µm. Fig.4(a) shows the calculated Q-factor of the cavity mode as a function of dr1 and dr2. The maximum allowed fabrication tolerance for the pillars radius to keep the Q-factor as high as 3.85×105 is less than 100nm. More variation reduces the Q-factor. Though the lower Q-factor results in a broader peak, since the sensing process is not based on frequency shift of the peak but on the absorption, this does not change the sensitivity of the sensor. Variations of the radii (dr1 and dr2) have only a small effect on the group velocity vg and the filling factor of the mode M4. In these simulations, the absorption in the silicon rods is not considered, i.e. this value for the Q-factor characterizes the PCRR as a non-ideal cavity resonator. Therefor the Q-factor decreases by about one order of magnitude when the PCRR is coupled to waveguide. With this optimization the group velocity of the corresponding mode goes down to the 7×10 -4c where c denotes the free-space velocity of light. Structure optimization is performed by using the finite difference time domain (FDTD) method. The corresponding electric field profile confirms that the cavity mode is strongly confined within the PCRR, having an effective mode volume
equal to Veff =4.36µm3 and the overlap between electric field intensity and the fluid medium to be sensed, is 0.758, calculated using Eq. (2). The effective mode volume is defined as [19]: ∫ 𝜀(𝑟)𝐸 2 (𝑟)𝑑𝑣
𝑉𝑒𝑓𝑓 = [𝜀(𝑟)𝐸2 (𝑟)]
𝑚𝑎𝑥
.
(3)
In this way, the absorption is maximized and the linewidth of the absorption peak is kept narrow. Most competing devices reported in the literature have a larger group velocity compared to the results presented in this work [20]. A photonic crystal waveguide is formed by removing one line of silicon rods creating a series of defects. If the waveguide passes close to the PCRR, coupling is achieved. There are two lines of silicon rods separating the waveguide and PCRR, see Fig.1. Calculated dispersion curve of the photonic crystal waveguide is shown by blue line in Fig.2(a). A Gaussian input signal is launched into input port and at resonance frequency, the propagating mode is coupled from input waveguide into ring and finally to the output waveguide. The transmission efficiency is detected by monitoring the E-field intensity at output port of waveguide. Fig. 4(b) simulated the transmission spectra of the photonic crystal waveguide (blue curve) and spectral position of the PCRR resonance modes (red curve). In the absence of PCRR, the waveguide has uniform transmission in the range of 0.347-0.445(a/λ) within the bandgap of photonic crystal. In the presence of the ring, the transmission spectrum contains pronounced dips. This is due to coupling of waveguide power to the ring at specific wavelengths [21]. The FDTD method was used to calculate transmission spectra of the waveguide coupled to the PCRR. The dips in the transmission spectrum can be utilized to sense the absorption taking place in the PCRR, which will be the subject of future research. Future work will also include the fabrication of device. Simulation results for this work consider an aspect ratio around 15 for the silicon pillars on top of the silicon slab. This aspect ratio represents a challenge in the fabrication of this device. There are a variety of processes that could be considered, such as deep reactive ion etching (DRIE, “Bosch process”). Our suggestion for fabrication is as follows. The first step in the fabrication is the mask processing using the deep ultraviolet (DUV) lithography method to pattern the photonic crystal cavity mask on the resist, after defining the photonic crystal pattern on the resist a thin layer of a metal, such as gold or chromium, is deposited on the sample. By performing a lift-off process, the PhC pattern is created on the metal hard mask. The pattern of the structure is transferred to Si with the DRIE process. Finally, the metal layer is removed in a wet etch process. 4.
Conclusion
We presented a design for a PCRR featuring a very high Q factor. A simulated Q factor of more than 3.85×105 and group velocity of 7×10-4c has been achieved by slightly tuning of radius of twelve silicon rods in the inner and outer corners of the PCRR. The PCRR is simulated by using the PWE and 2D FDTD methods. We have demonstrated a large overlap of the high Q photonic crystal ring resonator mode with the analyte, which indicates the potential for highly effective absorption sensing. The small size of the PCRR makes it suitable for parallel or multiplex detection.
Acknowledgment The authors acknowledge the support of the Austrian COMET program (Linz Center of Mechatronics and Austrian Smart Systems Integration Research Center). References [1] F. Dell’Olio, V. M. N. Passaro, "Optical sensing by optimized silicon slot waveguides," OPTICS EXPRESS, vol. 15, no. 8, p. 4977, 2007. [2] Y. Zhang,C. Zeng,D.Li,G. Gao,Z. Huang,J. Yu and J. Xia, „High-quality-factor photonic crystal ring resonator,“ OPTICS LETTERS, Bd. 39, Nr. 5, p. 1282, 2014. [3] V. M. Lavchiev, B. Jakoby, U. Hedenig, Th. Grille, J. M. R. Kirkbride and G.A.D. Ritchie, „M-line spectroscopy on mid-infrared Si photonic crystals for fluid sensing and chemical imaging,“ OPTICS EXPRESS , Bd. 24, Nr. 1, pp. 262-271, 2016. [4] M. Notomi, „Theory of light propagation in strongly modulated photonic crystals:Refractionlike behavior in the vicinity of the photonic band gap,“ Physical Review B, Bd. 62, 15 OCTOBER 2000. [5] A. Ghaffari, F. Monifi, M. Djavid, and M. S. Abrishamian, „Photonic crystal bends and power splitters based on
ring resonators,“ Optics Communications , Bd. 281, p. 5929, 2008. [6] T. T. Mai, F.L. Hsiao, C. Lee, W. Xiang, C.C. Chen, W. K. Choi, „Optimization and comparison of photonic crystal resonators for silicon microcantilever sensors,“ Sens. Actuators A Phys., Bd. 165, pp. 16-25, 2011. [7] F. Monifi, M. Djavid, A. Ghaffari, M. Abrishamian, „Three output port channel-drop filter based on photonic crystals,“ APPLIED OPTICS, Bd. 48, Nr. 4, p. 804, 2009. [8] Y. Zhao , Y. Zhang, Q. Wang, „Research advances of photonic crystal gas and liquid sensors,“ Sensors and Actuators B: Chemical, Bd. 160, p. 1288–1297, 2011. [9] H. R. H. P. G. K. Y. C. Y. a. J. K. S.H. Kim, Appl. Phys. Lett., Bd. 81, 2002. [10] S.Robinson, R. Nakkeeran, , „Photonic Crystal based sensor for sensing the salinity of seawater.,“ IEEE – International Conference On Advances In Engineering Science and Management (ICAESM), pp. 495-499, 2012. [11] S. Robinson,R. Nakkeeran, „Photonic crystal ring resonator-based add drop filters: a review,“ Optical Engineering , Bd. 52, Nr. 6, p. 060901, 2013. [12] Joannopoulos,J. D. ,Johnson, S. G. ,Winn, J. N. , Meade,R. D., Photonic Crystals: Molding the Flow of Light, Princeton University, 2011. [13] E. Yablonovitch, T. J. Gmitter, and K. M. Leung, „Photonic band structure: The face-centered-cubic case employing nonspherical atoms," , vol. 67,,“ Physical Review Letters, Bd. 67, pp. 2295-2298, 1991.. [14] Y. Zhang, Y. Zhao , D.i Wu and Q. Wang, „Theoretical research on high sensitivity gas sensor due to slow light in slotted,“ Sensors and Actuators B, Bd. 173, pp. 505-509, 2012. [15] Y. Zhao ,Y. Zhang , Q. Wang, „High sensitivity gas sensing method based on slow light in photonic crystal waveguide,“ Sensors and Actuators B, Bd. 173, p. 28–31, 2012. [16] N. A. Mortensena and S.i Xiao, „Slow-light enhancement of Beer-Lambert-Bouguer absorption,“ APPLIED PHYSICS LETTERS, Bd. 90, p. 141108, 2007. [17] D. Pergande, T. M. Geppert, A. von Rhein, S.L. Schweizer,R. B. Wehrspohn, S. Moretton, A. Lambrecht, „Miniature infrared gas sensors using photonic crystals,“ JOURNAL OF APPLIED PHYSICS , Bd. 109, p. 083117, 2011. [18] R.Jannesari, C. Ranacher, C. Consani, V. Lavchiev, T. Grille, B. Jakoby, „High-Quality-Factor Photonic Crystal Ring Resonator with Applications for Gas Sensing,“ in Procedia Engineering, Budapest, 2016. [19] Jean Michel Gerard , Bruno Gayral, „Strong Purcell Effect for InAs Quantum Boxes in Three-Dimensional Solid-State Microcavities,“ JOURNAL OF LIGHTWAVE TECHNOLOGY, Bd. 17, Nr. 11, p. 2089, 1999. [20] N. Zhu, Y. Li, C. Chen, S. Yan, „Slow light in dual-periodic photonic crystals based slotted-waveguidecoupled cavity,“ Optics & Laser Technology , Bd. 83, pp. 125-130, 2016. [21] V. Dinesh Kumar, T. Srinivas, A. Selvarajan, „Investigation of ring resonators in photonic crystal circuits,“ Photonics and Nanostructures – Fundamentals and Applications , Bd. 2, pp. 199-206, 2004.
Biographies Reyhaneh Jannesari received her M.Sc. degree in Solid State physic from the Isfahan University, Isfaha, Iran in 2003. In 2007 she worked as a research assistant at Christian Doppler Laboratory for Surface Optics at the Johannes Kepler University, Linz, Austria. From 2010 to 2014 she worked as a research assistant at the Institute of semiconductor and Solid State Physics physic, JKU where she obtained her Ph.D degree with research focused on ‘Experimental and numerical investigations of Si-based photonic crystals with ordered Ge quantum dots emitters’. Since 2015, she is working as a research assistant at the Institute for Microelectronics and Microsensors, JKU, Linz, Austria. Her focus is on application of Photonic crystal on fluid sensing.
Christian Ranacher was born in Lienz, Austria in 1989. He received the B.Sc. and the Dipl.-Ing. (M.Sc.) in technical physics from Graz University of Technology, Austria, in 2012 and 2014, respectively. After his studies he was working as product and process integration engineer at Infineon Technologies Austria AG and in late 2015 he joined the Carinthian Tech Research AG as a researcher in the field of microsystem technologies. Since 2016 he is also working towards a PhD degree in the field of optical micro fluid sensing at the Institute for Microelectronics at the Johannes Kepler University Linz, Austria.
Cristina Consani was born in Spilimbergo, Italy in 1983. She received her Bachelor and Master Degree in condensed matter physics from the University of Trieste, Italy, in 2005 and 2007, respectively. In 2007 she joined the Institute of Chemical Sciences and Engineering at the EPFL Lausanne, Switzerland, where she obtained her PhD in 2012 with her work on Ultrafast One- and Two-Dimensional UV Transient Absorption Spectroscopy of Haem Proteins. From 2012 to 2015 she worked as a post-doc scientist at the University of Würzburg, where she performed ultrafast two-dimensional spectroscopy and coherent control studies on several molecular systems. In 2016 she joined the Carinthian Tech Research AG as a researcher in the photonics department. Her current research interests include spectroscopy, scattering models and integrated photonics.
Bernhard Jakoby obtained his Dipl.-Ing. (M.Sc.) in Communication Engineering and his doctoral (Ph.D.) degree in electrical engineering from the Vienna University of Technology (VUT), Austria, in 1991 and 1994, respectively. In 2001 he obtained avenia legendi for Theoretical Electrical Engineering from the VUT. From 1991 to1994 he worked as a Research Assistant at the Institute of General Electrical Engi-neering and Electronics of the VUT. Subsequently he stayed as an Erwin Schrödinger Fellow at the University of Ghent, Belgium, performing research on the electrodynamics of complex media. From 1996 to 1999 he held the position of a Research Associate and later Assistant Professor at the Delft University of Technology, The Netherlands, working in the field of microacoustic sensors. From 1999 to 2001 he was with the Automotive Electronics Division of the Robert Bosch GmbH, Germany, where he conducted development projects in the field of automotive liquid sensors. In 2001 he joined the newly formed Industrial Sensor Systems group of the VUT as an Associate Professor. In 2005 he was appointed Full Professor of Microelectronics at the Johannes Kepler University Linz, Austria. He is currently working in the field of liquid sensors and monitoring systems.
2r
a
Input
√3a
Output
Fig.1 A layout configuration of PCRR structure of silicon rods with r=0.2a, where r is radius of rods and a is lattice period. The radius of 6 silicon rods at the corners of the outer PhC, indicated by blue circles (dr1), and 6 silicon rods at the corners of inner PhC, indicate by cyan circles (dr2), is tuned to obtain higher Q factor.
(a)
(b)
(c)
(d)
M1 (e)
M2 (f)
M3 (g)
M4
M5
M6
Fig. 2: (a) The TE band structure of the considered PhC (doted lines) shown together with the PCRR cavity modes (red lines) and dispersion curve of the PhC waveguide (blue line). The light line is shown in gray. The shadow zone represents the photonic band gap of the unperturbed crystal. So called flat bands created by the defects correspond to modes with low group velocity labelled b to g. (b)-(g) The simulated Ey intensity profiles for the PCRR cavity modes.
Γ
Γ
Fig. 3: Normalized group velocity for the PCRR modes with respect to the in-plane wavevector.
b
a
Fig.4: (a) Calculated Q-factor of the cavity mode as a function of dr1and dr2 which are indicated in Fig.1.(b) Simulated spectral position of the PCRR resonance modes (red curve) and transmission spectra of the PhC waveguide (blue curve).
Table1. Frequency and filling factor of PCRR modes.
Mode Frequency(a/λ) Filling factor(f)
M1 0.3428 0.585
M2 0.3466 0.637
M3 0.3655 0.658
M4 0.3806 0.758
M5 0.3933 0.71
M6 0.4222 0.697