sensors Article
Optical Analog to Electromagnetically Induced Transparency in Cascaded Ring-Resonator Systems Yonghua Wang, Hua Zheng, Chenyang Xue * and Wendong Zhang Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China; [email protected] (Y.W.); [email protected] (H.Z.); [email protected] (W.Z.) * Correspondence: [email protected]; Tel: +86-351-392-1756 Academic Editor: Vittorio M. N. Passaro Received: 23 June 2016; Accepted: 21 July 2016; Published: 25 July 2016
Abstract: The analogue of electromagnetically induced transparency in optical methods has shown great potential in slow light and sensing applications. Here, we experimentally demonstrated a coupled resonator induced transparency system with three cascaded ring coupled resonators in a silicon chip. The structure was modeled by using the transfer matrix method. Influences of various parameters including coupling ratio of couplers, waveguide loss and additional loss of couplers on transmission characteristic and group index have been investigated theoretically and numerically in detail. The transmission character of the system was measured by the vertical grating coupling method. The enhanced quality factor reached 1.22 ˆ 105 . In addition, we further test the temperature performance of the device. The results provide a new method for the manipulation of light in highly integrated optical circuits and sensing applications. Keywords: coupled resonator induced transparency; electromagnetically induced transparency; ring resornator; silicon waveguide
1. Introduction The electromagnetically induced transparency (EIT) effect is a nonlinear effect which occurs in the interaction process between light and material [1]. Due to strong material dispersion caused by quantum interference, a transparency peak will emerge in the absorption curve and the group velocity of light can be rapidly slowed down [2–4] and therefore the EIT effect has shown great potential in various promising applications, including slow light control, quantum information processing and sensing technology [5,6]. However, the realization of EIT in atomic systems is a tough task since some restrictions must be strictly fulfilled. Recently, researchers have found that the EIT-like spectrum can also be generated in some other structures which are easier to realize, such as optical resonators [7–9] and Fano metamaterials [10–15]. For the case of EIT, the transparency window is caused by the reduced absorption, due to the quantum destructive interference between the transitions from the two dressed states, into a common energy level. Similarly, the EIT-like effect generated by optical resonators works by means of coherent interference between the resonating modes which produces optical transparency inside the absorption window. Compared to the EIT in atomic systems, the analogue of electromagnetically induced transparency with optical resonators has many remarkable advantages such as simpler structure, smaller device size and being easier to design, which mean it has enormous potential for applications in optical sensors [16,17] and optical delay lines [18,19]. The optical EIT-like effect has been experimentally realized in many optical structures including coupled fiber systems [20], coupled fused-silica spheres [21] and optical parameter oscillator cavities [22]. In these structures, the linewidths of the induced window can be extremely narrow. The drawback of these devices is the bulky and incompact structure which is hardly present for integrated applications. Sensors 2016, 16, 1165; doi:10.3390/s16081165
www.mdpi.com/journal/sensors
Sensors 16, 1165 1165 Sensors 2016, 2016, 16,
22 of of 10 10
hardly present for integrated applications. The on-chip integrated all-optical analogue of EIT effect has realized in photonic crystals [23,24]ofand microrings [8,25]. in However, to the[23,24] small The been on-chip integrated all-optical analogue EITsilicon effect has been realized photonicdue crystals size of these structures, it is However, challenging to todetune optical for controlling the resonant and silicon microrings [8,25]. due the small size cavity of these structures, it isofchallenging to interaction between the two optical pathways. For instance, the two paralleled require detune optical cavity for controlling of the resonant interaction between the resonators two optical[26] pathways. an nm perimeter the[26] tworequire rings, an which is normally challenging to the control For~8 instance, the twodifference paralleledbetween resonators ~8 nm perimetervery difference between two in the fabrication. rings, which is normally very challenging to control in the fabrication. Here, we analog to to EIT onon a chip in we theoretically theoreticallyand andexperimentally experimentallydemonstrate demonstrateananall-optical all-optical analog EIT a chip ainthree-cascaded-ring system. The mathematical a three-cascaded-ring system. The mathematicalmodel modelwas wasestablished establishedby byusing using transfer transfer matrix method. The The bandwidth bandwidth of of the central transmission peak and maximum group index was analyzed with various parameters. By optimizing the coupling angular deviation and the coupling strength of the three resonators, a significant transparency window has been experimentally obtained. The effect of the coupling strength between the resonators has been demonstrated, indicating that the EIT-like good sensitivity sensitivity to to the the temperature temperature and andstress. stress. The Theexperimentally experimentallymeasured measuredquality quality window has a good factor of the transparency system has reached 1.22 ˆ × 10 1055,, which which is is much much larger larger than than the the Q factor in single resonators and in the two-paralleled-ring EIT-like EIT-like systems. In In this this three-cascaded-ring three-cascaded-ring system, system, the EIT-like spectrum is much easier to achieve since we can change the coupling angular deviation and the coherent interference between the the resonators, which can the coupling couplingdistance distancetotoobtain obtaina good a good coherent interference between resonators, which make up for thethe deficiency in in the can make up for deficiency thefabrication. fabrication.Compared Comparedtotothe the parallel parallel double-ring double-ring coupled resonator, narrowertransmission transmission spectrum higher group has achieved been achieved in our resonator, aanarrower spectrum andand higher group indexindex has been in our system, system,means whichameans a better sensitivity and alight slower light velocity for applications. sensing applications. which better sensitivity and a slower velocity for sensing StructuralDesign Design 2. Structural Figure 1 shows the schematic structure of three-cascaded-ring system which consists of two straight waveguides and three microrings. The radius of microrings is 20 µm. μm. E0 is the input optical field, E11 is is the the output output of of the through port and E77 is is the the output output of of the the drop drop port. port.
θ
Figure Figure 1. 1. Schematic Schematic of of three-ring three-ring coupled coupled resonator. resonator.
The transmission matrix of this structure could be written as: The transmission matrix of this structure could be written as: « ff E « E ff «A « ff A12 Eff 6 0 11 0 E6 P4Q3 P3Q2 P2Q1 P1 E0 A11 A12 E0 “ P4 Q3 P3 Q2 P2 Q1 P1 EE1 1 “ A21A21 A22A22 E1 E1 E7 E7
(1) (1)
a11´kki 11{/?11 ´ rri ff 1 « ´ i i , ki and ri are the coupling coefficient and insert loss of where PPi “ ?1 ? a where , k and ri are the coupling coefficient and insert loss of i 11 ´rrii 11{/ 11 ´kkii i ii kki i ´ «
ff
0 0 e ei´1iθR1 Rβ coupler ii respectively. is the transmission matrix of ring1 and ring3. coupler respectively. QQ11“Q Q 33“ ieiθR2Rβ is the transmission matrix of ring1 and ring3. 0 2 « ff 0 e ´iθ3 Rβ 0 ei 3 R Q2 “ 0iθ4 Rβ e is the transmission matrix of ring2. θ i is the phase shift of the i-th ring, 0 is the transmission matrix of ring2. θi is the phase shift of the i-th ring, Q2 ie R 4 0 β “ n ωce´ ia is propagation constant, n is effective refractive index, ω is the angular frequency of light,
Sensors 2016, 16, 1165
n
c
3 of 10
ia is propagation constant, n is effective refractive index, is the angular frequency of
Sensors 2016, 16, 1165
3 of 10
light, c is speed of light, a is loss of waveguide. The transfer function of through port and drop port can be expressed as: c is speed of light, a is loss of waveguide. The transfer function of through port and drop port can be E A expressed as: Tthrough 1 11 (2) E10 A12 E A 11 (2) Tthrough “ ´ “´ E0 A12
E7
A11 A22
T drop E7 A21 A11 A22 Tdrop “ E0 “ A21 ´ A12 E0 A12
(3) (3)
Figure Figure 2a 2a illustrates illustrates the thepower powertransmission transmissionof ofthree-ring three-ringcoupled coupledresonator resonatorwith withkk11== kk44 == 0.05, 0.1, 0.25. ItItcan canbebeseen seenthat thatthere there would three absorption bands in the transmission. 0.1, 0.15, 0.2, 0.25. would bebe three absorption bands in the transmission. As As coupling coefficient increases, resonant depth would evidently decrease. thethe coupling coefficient increases, resonant depth would evidently decrease. At kAt 1 =k1 k4==k0.25, the 4 = 0.25, the maximum power transmittance central resonancehas hasdiminished diminishedtoto0.46. 0.46. Figure Figure 2b 2b shows the maximum power transmittance of of central resonance the effect effect of of waveguide-microring waveguide-microring coupling coupling coefficient on the the FWHM FWHM (full (full width width at at half half maximum) maximum) of of the the central central resonance resonance and and maximum maximum group group index. index. With With an an increase increase of of the the coupling coupling coefficient, coefficient, both both FWHM FWHM and and maximum maximum group group index indexwould wouldincrease. increase.
(a)
(b) Figure 2. Effect of waveguide-microring coupling coefficient: (a) on transmission spectrum Figure 2. Effect of waveguide-microring coupling coefficient: (a) on transmission spectrum (b) on (b) on FWHM (full width at half maximum) of central resonance and maximum group index. FWHM (full width at half maximum) of central resonance and maximum group index.
Sensors 2016, 16, 1165 Sensors 2016, 16, 1165
4 of 10 4 of 10
The relation between spectrum is The between microring-microring microring-microring coupling coupling coefficient and transmission transmission spectrum shown Figure Figure 3a. 3a. It It can can be seen that with the increase resonance is shown increase of of kk22==kk3,3the , theposition positionofofcentral central resonance almost unchanged, but the move away central gradually.gradually. Figure 3b is almost unchanged, but two the side-resonances two side-resonances movefrom away fromresonance central resonance shows 3b theshows effectthe of effect microring-microring coupling coefficient on FWHM of central resonant and Figure of microring-microring coupling coefficient on FWHM of central resonant maximum group index. After increasing of of k2 k=2 k and maximum group index. After increasing =3,k3the , theFWHM FWHMofofcentral centralresonance resonance was quickly extended while while the the maximum maximum group group index index was was raised raisedat atfirst firstand andthen thendeclined. declined. extended
(a)
(b) Figure 3. Effect of ring-ring coupling coefficient: (a) on transmission spectrum (b) on FWHM of Figure 3. Effect of ring-ring coupling coefficient: (a) on transmission spectrum (b) on FWHM of central central resonance and maximum group index. resonance and maximum group index.
Figure 4a shows the transmission of the three-ring coupled resonator with different waveguide Figure 4abe shows theseen transmission of the three-ring coupled resonator with different waveguide losses. It can clearly that, as the waveguide loss increases, the resonant depth of the three losses. It can be clearly seen that, as the waveguide loss increases, the resonant depth of the three resonances would decrease. Figure 4b shows the effect of the optical waveguide loss on FWHM of resonances would decrease. Figure 4b shows the effect of the optical waveguide loss on FWHM of the the central resonance and maximum group index. With the increase of optical waveguide loss, the central and maximum Withand, the in increase of optical waveguide loss,index the FWHM FWHMresonance of the central resonance group wouldindex. increase, contrast, the maximum group would of the central resonance would increase, and, in contrast, the maximum group index would decrease. decrease.
Sensors 2016, 16, 1165 Sensors 2016, 16, 1165
5 of 10 5 of 10
(a)
(b) Figure 4. Effect of waveguide loss: (a) on transmission spectrum (b) on FWHM of central resonance Figure 4. Effect of waveguide loss: (a) on transmission spectrum (b) on FWHM of central resonance and maximum group index. and maximum group index.
3. Device Fabrication and the Experiment 3. Device Fabrication and the Experiment The scanning electron microscopy (SEM) graphs of three-ring coupled resonators are shown in The scanning electron microscopy graphs ofwafers, three-ring coupled resonators Figure 5. The device was fabricated on(SEM) commercial SOI having a silicon thicknessare of shown 220 nm in Figure The device was fabricated onElectron commercial wafers, having a silicon 220 nm and a5.buried-oxide thickness of 3 μm. beamSOI lithography (JBX5500ZA) andthickness inductionof coupler andplasma a buried-oxide thickness of 3 µm. Electron beam lithography (JBX5500ZA) and induction coupler etching process (STS HRM ICP) were used to fabricate the three-ring coupled resonator. The plasma etching process (STScascaded HRM ICP) were used to were fabricate three-ring resonator. bus waveguide and the ring resonators fullythe etched, with coupled a depth of 220 nm The and bus a waveguide resonatorstransverse were fullyelectric etched,(TE) withlight. a depth 220 nm andtwo a width width ofand 450 the nm,cascaded to guidering single-mode Theofradii of the ring of 450resonators nm, to guide transverse electric (TE)oflight. Thewaveguide, radii of thea two resonators were weresingle-mode designed to be 20 μm. At both ends the bus pair ring of grating couplers was fabricated with a 600 nm period, in order to couple light in and out of the devices. The distance designed to be 20 µm. At both ends of the bus waveguide, a pair of grating couplers was fabricated between the period, straight in waveguide the light microring was which is the with a 600 nm order to and couple in and out110 of nm, the devices. Theoptimum distance distance betweenasthe proven from past experience. The gap between microring designed 70 nm straight waveguide and the microring was 110the nm, which isand themicroring optimumwas distance as from proven from to 200 nm. The coupling angular deviation θ was designed from 0° to 60°. To decrease the loss of the past experience. The gap between the microring and microring was designed from 70 nm to 200 nm. 300 °C deviation to 1200 °Cθthermal oxidation procedure used. Subsequently, thewaveguide, Buffered Thewaveguide, coupling angular was designed from 0˝ to 60˝was . To decrease the loss of the Oxide Etch and 1000 °C annealing with nitrogen were used to obtain a smoother waveguide 300 ˝ C to 1200 ˝ C thermal oxidation procedure was used. Subsequently, the Buffered Oxidesurface, Etch and ˝ 1000 C annealing with nitrogen were used to obtain a smoother waveguide surface, which means a
Sensors 2016, 16, 1165
6 of 10
Sensors 2016, 16, 1165
6 of 10
higher Q means factor. aThe enlarged views ofenlarged Figure 5aviews showofthat the straight and waveguides the rings have which higher Q factor. The Figure 5a showwaveguides that the straight good surface roughness. and the rings have good surface roughness.
(a)
(b) Figure 5. SEM of the cascaded rings and the gratings: (a) rings and straight waveguide (b) the grating Figure 5. SEM of the cascaded rings and the gratings: (a) rings and straight waveguide (b) the couplers. grating couplers.
The performance of the device was tested by vertical grating coupling method. The experimental system is illustrated in Figure 6a. The generation of the transparency curve is obtained by sweeping the frequency of the tunable laser (New Focus TLB-6728-P, Irvine, CA, USA, linewidth is less than 200 kHz) with the resolution of 0.01 nm. Light export from the tunable laser source is polarization-tuned by a polarization controller and injected into the grating coupler using a 75˝ lensed fiber and aligning by a precision translation stage (New Focus M-461-XYZ-M). The output light is detected by a photoelectric detector (New Focus 1811) and displayed on the digital oscilloscope (Tektronix MDO3054, Beaverton, OR, USA). Figure 6b shows the transmission spectrum from the through port of the structure with θ = 30˝ and the gap between the resonators of 110 nm. In the theoretical analysis, the coupling angular deviation θ has no influence on the transparency (a) (b) window, but in the actual fabrication it can change the destructive interferences between the responses Figure 6. (a) Device measurement setup andand (b) scanning curve of the of structures with θ = 30°. Utilizing of the three rings due to the scattering loss the bending loss the waveguide. this character, we have fabricated different coupling angular deviation and obtained a significant The performance was tested vertical grating coupling method. The experimental transparency peak with of thethe θ =device 30˝ . One of the by transparency windows in the wavelength axis with the system is illustrated in Figure 6a. The generation of the transparency curve is obtained by sweeping theoretical fitting curves is shown in Figure 7. It can be observed that the transmission peak splits into thenarrow frequency ofin the tunable laser (New TLB-6728-P, CA,theoretical USA, linewidth is we lessobserve than three peak both the through portFocus and the drop port.Irvine, From the analysis 200 kHz) with the resolution of 0.01 nm. Light export from the tunable laser source is polarizationthat the transmission character of our system is extremely sensitive to the radius of the microring.
Sensors 2016, 16, 1165
7 of 10
Due to machined error, there would be slight differences between the radius of the microrings which Sensors 2016, 16, 1165 7 of 10 would lead to the asymmetry of the two side-resonance. The FWHM of the central resonance is 5 as narrow as 0.0125 nm, corresponding to a quality of 1.22 ˆ 10 . The red line in Figure 7 (b)thefactor tuned by a polarization controller and injected into grating coupler using a 75° lensed fiber and is the theoretical fitting with k = k = 0.15, k = 0.108, k = r1 =output 20 µm, r2 is = 19.997 µm and 1 rings 4 and 2 3 and0.15, aligning by a5.precision stage (New Focus M-461-XYZ-M). The light Figure SEM of thetranslation cascaded the gratings: (a) rings straight waveguide (b) thedetected grating by r3 =a 20.0072 µm, which shows good agreement with the experimental result. photoelectric couplers. detector (New Focus 1811) and displayed on the digital oscilloscope (Tektronix MDO3054, Beaverton, OR, USA). Figure 6b shows the transmission spectrum from the through port of the structure with θ = 30° and the gap between the resonators of 110 nm. In the theoretical analysis, the coupling angular deviation θ has no influence on the transparency window, but in the actual fabrication it can change the destructive interferences between the responses of the three rings due to the scattering loss and the bending loss of the waveguide. Utilizing this character, we have fabricated different coupling angular deviation and obtained a significant transparency peak with the θ = 30°. One of the transparency windows in the wavelength axis with the theoretical fitting curves is shown in Figure 7. It can be observed that the transmission peak splits into three narrow peak in both the through port and the drop port. From the theoretical analysis we observe that the transmission character of our system is extremely sensitive to the radius of the microring. Due to machined error, there would be slight differences between the radius of the microrings which would lead to the asymmetry of the two side-resonance. The FWHM of the central (b) × 105. The red line in resonance is as narrow as (a) 0.0125 nm, corresponding to a quality factor of 1.22 Figure 7 isFigure the theoretical fitting with k1 =setup k4 = and 0.15,(b) k2scanning = 0.108, k 3 = 0.15, r1 = 20 μm, r2 = 19.997 μm and 6. (a) Device measurement curve of the structures with θ = 30°. ˝ Figureμm, 6. (a)which Device measurement setup and (b) the scanning curve ofresult. the structures with θ = 30 . r3 = 20.0072 shows good agreement with experimental The performance of the device was tested by vertical grating coupling method. The experimental system is illustrated in Figure 6a. The generation of the transparency curve is obtained by sweeping the frequency of the tunable laser (New Focus TLB-6728-P, Irvine, CA, USA, linewidth is less than 200 kHz) with the resolution of 0.01 nm. Light export from the tunable laser source is polarization-
(a)
(b) Figure 7. The measured transmission spectrum of (a) the through port and (b) the drop port. The blue
Figure 7. The measured transmission spectrum of (a) the through port and (b) the drop port. line is the experimental result curve and red line is theoretical fitting curve. The blue line is the experimental result curve and red line is theoretical fitting curve.
Sensors 2016, 16, 1165 Sensors 2016, 16, 1165
8 of 10 8 of 10
Since the EIT-like EIT-like window window in our device has a significant sensitivity sensitivity to to the change of the ring perimeter, perimeter, we we are areconvinced convinced that that the the EIT-like EIT-like system system can can be be used used as as a temperature temperature sensor, in which the resonant strength of the transparency window will be changed by the thermal thermal expansion expansion effect. effect. Therefore, further testedtested the response of transparency window in window different temperatures, Therefore, we wehave have further the response of transparency in different as shown in Figure 8. temperatures, as shown in Figure 8.
Figure window in in different different temperatures. temperatures. Figure 8. 8. The The response response of of transparency transparency window
The temperature sensors that use the single resonator have been reported [26,27], in which the The temperature sensors that use the single resonator have been reported [26,27], in which the temperature variation was measured by monitoring the shift in the resonant wavelength of the silicon temperature variation was measured by monitoring the shift in the resonant wavelength of the silicon resonator. However, the temperature variations will induce the thermo-optic effect and the thermal resonator. However, the temperature variations will induce the thermo-optic effect and the thermal expansion effect simultaneously. This means the shift in the resonant wavelength will be influenced expansion effect simultaneously. This means the shift in the resonant wavelength will be influenced by by both the changed effective index and the changed ring perimeter. Since we cannot verify the actual both the changed effective index and the changed ring perimeter. Since we cannot verify the actual effective index and the group index in the fabricated silicon ring resonators, it is not accurate if we effective index and the group index in the fabricated silicon ring resonators, it is not accurate if we only consider the shift in the resonant wavelength. While in our scheme, the temperature not only only consider the shift in the resonant wavelength. While in our scheme, the temperature not only changes the resonant shift, but also changes the resonance strength. Therefore, utilizing our EIT-like changes the resonant shift, but also changes the resonance strength. Therefore, utilizing our EIT-like scheme for temperature sensing is a promising method. scheme for temperature sensing is a promising method. 4. Conclusions 4. Conclusions In summary, EIT-like effect has been demonstrated theoretically and experimentally in the In summary, EIT-like effect has been demonstrated theoretically and experimentally in the cascaded three-ring coupled resonators on a silicon chip. The influence of parameters including cascaded three-ring coupled resonators on a silicon chip. The influence of parameters including coupling coefficient, waveguide loss, addition loss of couplers on EIT-like effect have been studied. coupling coefficient, waveguide loss, addition loss of couplers on EIT-like effect have been studied. EIT-like resonance is experimentally observed in the cascaded three-ring coupled resonator with a EIT-like resonance is experimentally observed in the cascaded three-ring coupled resonator with quality factor of 1.22 × 105. The experimental results agrees with the theoretical analysis well. The a quality factor of 1.22 ˆ 105 . The experimental results agrees with the theoretical analysis well. temperature performance of the device is further studied. This structure is promising for applications The temperature performance of the device is further studied. This structure is promising for in integrated optical sensors and optical delay lines. applications in integrated optical sensors and optical delay lines. Acknowledgments: This This work work was was supported supported by by the the China China National National Funds Funds for for Distinguished Distinguished Young Scientists Acknowledgments: Young Scientists (Grant No. 61525107) and National Natural Science Foundation Foundation of of China China (Grant (Grant No. No. 91123036). 91123036). Author Contributions: Contributions: Y.W., Y.W., H.Z. H.Z. and and conceived conceived and and designed designed the the structure; structure; H.Z. H.Z. performed performed the theoretical simulation. C.X. and and W.Z. W.Z. performed performed the the experiments; experiments; Y.W. Y.W. and and H.Z. H.Z. analyzed analyzed the the data; data; Y.W. Y.W. and simulation. C.X. and H.Z. H.Z. wrote wrote the paper. the paper. Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest.
Sensors 2016, 16, 1165
9 of 10
References 1. 2. 3.
4. 5. 6.
7. 8. 9. 10. 11. 12. 13. 14.
15. 16. 17. 18. 19. 20. 21. 22. 23.
Boller, K.J.; Imamoglu, A.; Harris, S.E. Observation of electromagnetically induced transparency. Phys. Rev. Lett. 1991, 66, 2593–2596. Hau, L.V.; Harris, S.E.; Dutton, Z.; Behroozi, C.H. Light speed reduction to 17 metres per second in an ultracold atomic gas. Nature 1999, 397, 594–598. [CrossRef] Safavi-Naeini, A.H.; Alegre, T.P.M.; Chan, J.; Eichenfield, M.; Winger, M.; Hill, J.T.; Lin, Q.; Chang, D.; Painter, O. Electromagnetically induced transparency and slow light with optomechanics. Nature 2011, 472, 69–73. [PubMed] Longdell, J.J.; Fraval, E.; Sellars, M.J.; Sellars, M.J.; Manson, N.B. Stopped light with storage times greater than one second using electromagnetically induced transparency in a solid. Phys. Rev. Lett. 2005, 95, 063601. Lukin, M.D.; Imamoglu, ˘ A. Controlling photons using electromagnetically induced transparency. Nature 2001, 413, 273–276. Liu, N.; Weiss, T.; Mesch, M.; Langguth, L.; Eigenthaler, U.; Hirscher, M.; Sönnichsen, C.; Giessen, H. Planar Metamaterial Analogue of Electromagnetically Induced Transparency for Plasmonic Sensing. Nano Lett. 2009, 10, 1103–1107. Smith, D.D.; Chang, H.; Fuller, K.A.; Rosenberger, A.T.; Boyd, R.W. Coupled-resonator-induced transparency. Phys. Rev. A 2004, 69, 063804. Xu, Q.; Sandhu, S.; Povinelli, M.L.; Shakya, J.; Fan, S.; Lipson, M. Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency. Phys. Rev. Lett. 2006, 96, 123901. Heebner, J.E.; Boyd, R.W.; Park, Q.H. Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide. Phys. Rev. E 2002, 65, 036619. Singh, R.; Cao, W.; Al-Naib, I.; Cong, L.; Withayachumnankul, W.; Zhang, W. Ultrasensitive terahertz sensing with high-Q Fano resonances in metasurfaces. Appl. Phys. Lett. 2014, 105, 171101. Manjappa, M.; Chiam, S.Y.; Cong, L.; Bettiol, A.A.; Zhang, W.; Singh, R. Tailoring the slow light behavior in terahertz metasurfaces. Appl. Phys. Lett. 2015, 106, 181101. Pitchappa, P.; Manjappa, M.; Ho, C.P.; Singh, R.; Singh, N.; Lee, C. Active Control of Electromagnetically Induced Transparency Analog in Terahertz MEMS Metamaterial. Adv. Opt. Mater. 2016, 4, 541–547. Zhang, S.; Genov, D.A.; Wang, Y.; Liu, M.; Zhang, X. Plasmon-induced transparency in metamaterials. Phys. Rev. Lett. 2008, 101, 047401. Cao, W.; Singh, R.; Zhang, C.; Han, J.; Tonouchi, M.; Zhang, W. Plasmon-induced transparency in metamaterials: Active near field coupling between bright superconducting and dark metallic mode resonators. Appl. Phys. Lett. 2013, 103, 101106. [CrossRef] Cao, W.; Singh, R.; Al-Naib, I.A.; He, M.; Taylor, A.J.; Zhang, W. Low-loss ultra-high-Q dark mode plasmonic Fano metamaterials. Opt. Lett. 2012, 37, 3366–3368. [PubMed] Steinberg, B.Z.; Scheuer, J.; Boag, A. Rotation-induced superstructure in slow-light waveguides with mode-degeneracy: Optical gyroscopes with exponential sensitivity. J. Opt. Soc. Am. B 2007, 24, 1216–1224. Zhang, Y.; Wang, N.; Tian, H.; Wang, H.; Qiu, W.; Wang, J.; Yuan, P. A high sensitivity optical gyroscope based on slow light in coupled-resonator-induced transparency. Phys. Rev. A 2008, 372, 5848–5852. Heebner, J.E.; Wong, V.; Schweinsberg, A.; Boyd, R.W.; Jackson, D.J. Optical transmission characteristics of fiber ring resonators. IEEE J. Quantum Electron. 2004, 40, 726–730. Scheuer, J.; Paloczi, G.T.; Poon, J.K.S.; Yariv, A. Coupled resonator optical waveguides: toward the slowing and storage of light. Opt. Photonics News 2005, 16, 36–40. Smith, D.D.; Lepeshkin, N.N.; Schweinsberg, A.; Gehring, G.; Boyd, R.W.; Park, Q.H.; Chang, H.; Jackson, D.J. Coupled-resonator-induced transparency in a fiber system. Opt. Commun. 2005, 264, 163–168. Kouki, T.; Norihiko, K.; Makoto, T. Slow light in coupled-resonator-induced transparency. Phys. Rev. Lett. 2007, 98, 213904. Ke, D.; Changde, X.; Jing, Z. Coupled-resonator-induced transparency with a squeezed vacuum. Phys. Rev. Lett. 2011, 106, 1486–1503. Yang, X.; Yu, M.; Kwong, D.L.; Wong, C.W. All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities. Phys. Rev. Lett. 2009, 102, 173902.
Sensors 2016, 16, 1165
24.
25. 26. 27.
10 of 10
Yang, X.; Yu, M.; Kwong, D.L.; Wong, C.W. Coupled resonances in multiple silicon photonic crystal cavities in all-optical solid-state analogy to electromagnetically induced transparency. IEEE J. Sel. Top. Quantum Electron. 2010, 16, 288–294. Xu, Q.; Dong, P.; Lipson, M. Breaking the delay-bandwidth limit in a photonic structure. Nat. Phys. 2007, 3, 406–410. Yu, X.; Ma, H.; Jin, Z.; Pan, M.; Hou, L.; Xie, W. Sensitive birefringent temperature sensor based on a waveguide ring resonator. Appl. Opt. 2014, 53, 2748–2753. [PubMed] Lee, H.S.; Park, C.H.; Lee, S.S.; Lim, B.T.; Bae, H.K.; Lee, W.G. Silicon photonic temperature sensor employing a ring resonator manufactured using a standard CMOS process. Opt. Express 2010, 18, 22215–22221. © 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).
Optical Analog to Electromagnetically Induced Transparency in Cascaded Ring-Resonator Systems Yonghua Wang, Hua Zheng, Chenyang Xue * and Wendong Zhang Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China; [email protected] (Y.W.); [email protected] (H.Z.); [email protected] (W.Z.) * Correspondence: [email protected]; Tel: +86-351-392-1756 Academic Editor: Vittorio M. N. Passaro Received: 23 June 2016; Accepted: 21 July 2016; Published: 25 July 2016
Abstract: The analogue of electromagnetically induced transparency in optical methods has shown great potential in slow light and sensing applications. Here, we experimentally demonstrated a coupled resonator induced transparency system with three cascaded ring coupled resonators in a silicon chip. The structure was modeled by using the transfer matrix method. Influences of various parameters including coupling ratio of couplers, waveguide loss and additional loss of couplers on transmission characteristic and group index have been investigated theoretically and numerically in detail. The transmission character of the system was measured by the vertical grating coupling method. The enhanced quality factor reached 1.22 ˆ 105 . In addition, we further test the temperature performance of the device. The results provide a new method for the manipulation of light in highly integrated optical circuits and sensing applications. Keywords: coupled resonator induced transparency; electromagnetically induced transparency; ring resornator; silicon waveguide
1. Introduction The electromagnetically induced transparency (EIT) effect is a nonlinear effect which occurs in the interaction process between light and material [1]. Due to strong material dispersion caused by quantum interference, a transparency peak will emerge in the absorption curve and the group velocity of light can be rapidly slowed down [2–4] and therefore the EIT effect has shown great potential in various promising applications, including slow light control, quantum information processing and sensing technology [5,6]. However, the realization of EIT in atomic systems is a tough task since some restrictions must be strictly fulfilled. Recently, researchers have found that the EIT-like spectrum can also be generated in some other structures which are easier to realize, such as optical resonators [7–9] and Fano metamaterials [10–15]. For the case of EIT, the transparency window is caused by the reduced absorption, due to the quantum destructive interference between the transitions from the two dressed states, into a common energy level. Similarly, the EIT-like effect generated by optical resonators works by means of coherent interference between the resonating modes which produces optical transparency inside the absorption window. Compared to the EIT in atomic systems, the analogue of electromagnetically induced transparency with optical resonators has many remarkable advantages such as simpler structure, smaller device size and being easier to design, which mean it has enormous potential for applications in optical sensors [16,17] and optical delay lines [18,19]. The optical EIT-like effect has been experimentally realized in many optical structures including coupled fiber systems [20], coupled fused-silica spheres [21] and optical parameter oscillator cavities [22]. In these structures, the linewidths of the induced window can be extremely narrow. The drawback of these devices is the bulky and incompact structure which is hardly present for integrated applications. Sensors 2016, 16, 1165; doi:10.3390/s16081165
www.mdpi.com/journal/sensors
Sensors 16, 1165 1165 Sensors 2016, 2016, 16,
22 of of 10 10
hardly present for integrated applications. The on-chip integrated all-optical analogue of EIT effect has realized in photonic crystals [23,24]ofand microrings [8,25]. in However, to the[23,24] small The been on-chip integrated all-optical analogue EITsilicon effect has been realized photonicdue crystals size of these structures, it is However, challenging to todetune optical for controlling the resonant and silicon microrings [8,25]. due the small size cavity of these structures, it isofchallenging to interaction between the two optical pathways. For instance, the two paralleled require detune optical cavity for controlling of the resonant interaction between the resonators two optical[26] pathways. an nm perimeter the[26] tworequire rings, an which is normally challenging to the control For~8 instance, the twodifference paralleledbetween resonators ~8 nm perimetervery difference between two in the fabrication. rings, which is normally very challenging to control in the fabrication. Here, we analog to to EIT onon a chip in we theoretically theoreticallyand andexperimentally experimentallydemonstrate demonstrateananall-optical all-optical analog EIT a chip ainthree-cascaded-ring system. The mathematical a three-cascaded-ring system. The mathematicalmodel modelwas wasestablished establishedby byusing using transfer transfer matrix method. The The bandwidth bandwidth of of the central transmission peak and maximum group index was analyzed with various parameters. By optimizing the coupling angular deviation and the coupling strength of the three resonators, a significant transparency window has been experimentally obtained. The effect of the coupling strength between the resonators has been demonstrated, indicating that the EIT-like good sensitivity sensitivity to to the the temperature temperature and andstress. stress. The Theexperimentally experimentallymeasured measuredquality quality window has a good factor of the transparency system has reached 1.22 ˆ × 10 1055,, which which is is much much larger larger than than the the Q factor in single resonators and in the two-paralleled-ring EIT-like EIT-like systems. In In this this three-cascaded-ring three-cascaded-ring system, system, the EIT-like spectrum is much easier to achieve since we can change the coupling angular deviation and the coherent interference between the the resonators, which can the coupling couplingdistance distancetotoobtain obtaina good a good coherent interference between resonators, which make up for thethe deficiency in in the can make up for deficiency thefabrication. fabrication.Compared Comparedtotothe the parallel parallel double-ring double-ring coupled resonator, narrowertransmission transmission spectrum higher group has achieved been achieved in our resonator, aanarrower spectrum andand higher group indexindex has been in our system, system,means whichameans a better sensitivity and alight slower light velocity for applications. sensing applications. which better sensitivity and a slower velocity for sensing StructuralDesign Design 2. Structural Figure 1 shows the schematic structure of three-cascaded-ring system which consists of two straight waveguides and three microrings. The radius of microrings is 20 µm. μm. E0 is the input optical field, E11 is is the the output output of of the through port and E77 is is the the output output of of the the drop drop port. port.
θ
Figure Figure 1. 1. Schematic Schematic of of three-ring three-ring coupled coupled resonator. resonator.
The transmission matrix of this structure could be written as: The transmission matrix of this structure could be written as: « ff E « E ff «A « ff A12 Eff 6 0 11 0 E6 P4Q3 P3Q2 P2Q1 P1 E0 A11 A12 E0 “ P4 Q3 P3 Q2 P2 Q1 P1 EE1 1 “ A21A21 A22A22 E1 E1 E7 E7
(1) (1)
a11´kki 11{/?11 ´ rri ff 1 « ´ i i , ki and ri are the coupling coefficient and insert loss of where PPi “ ?1 ? a where , k and ri are the coupling coefficient and insert loss of i 11 ´rrii 11{/ 11 ´kkii i ii kki i ´ «
ff
0 0 e ei´1iθR1 Rβ coupler ii respectively. is the transmission matrix of ring1 and ring3. coupler respectively. QQ11“Q Q 33“ ieiθR2Rβ is the transmission matrix of ring1 and ring3. 0 2 « ff 0 e ´iθ3 Rβ 0 ei 3 R Q2 “ 0iθ4 Rβ e is the transmission matrix of ring2. θ i is the phase shift of the i-th ring, 0 is the transmission matrix of ring2. θi is the phase shift of the i-th ring, Q2 ie R 4 0 β “ n ωce´ ia is propagation constant, n is effective refractive index, ω is the angular frequency of light,
Sensors 2016, 16, 1165
n
c
3 of 10
ia is propagation constant, n is effective refractive index, is the angular frequency of
Sensors 2016, 16, 1165
3 of 10
light, c is speed of light, a is loss of waveguide. The transfer function of through port and drop port can be expressed as: c is speed of light, a is loss of waveguide. The transfer function of through port and drop port can be E A expressed as: Tthrough 1 11 (2) E10 A12 E A 11 (2) Tthrough “ ´ “´ E0 A12
E7
A11 A22
T drop E7 A21 A11 A22 Tdrop “ E0 “ A21 ´ A12 E0 A12
(3) (3)
Figure Figure 2a 2a illustrates illustrates the thepower powertransmission transmissionof ofthree-ring three-ringcoupled coupledresonator resonatorwith withkk11== kk44 == 0.05, 0.1, 0.25. ItItcan canbebeseen seenthat thatthere there would three absorption bands in the transmission. 0.1, 0.15, 0.2, 0.25. would bebe three absorption bands in the transmission. As As coupling coefficient increases, resonant depth would evidently decrease. thethe coupling coefficient increases, resonant depth would evidently decrease. At kAt 1 =k1 k4==k0.25, the 4 = 0.25, the maximum power transmittance central resonancehas hasdiminished diminishedtoto0.46. 0.46. Figure Figure 2b 2b shows the maximum power transmittance of of central resonance the effect effect of of waveguide-microring waveguide-microring coupling coupling coefficient on the the FWHM FWHM (full (full width width at at half half maximum) maximum) of of the the central central resonance resonance and and maximum maximum group group index. index. With With an an increase increase of of the the coupling coupling coefficient, coefficient, both both FWHM FWHM and and maximum maximum group group index indexwould wouldincrease. increase.
(a)
(b) Figure 2. Effect of waveguide-microring coupling coefficient: (a) on transmission spectrum Figure 2. Effect of waveguide-microring coupling coefficient: (a) on transmission spectrum (b) on (b) on FWHM (full width at half maximum) of central resonance and maximum group index. FWHM (full width at half maximum) of central resonance and maximum group index.
Sensors 2016, 16, 1165 Sensors 2016, 16, 1165
4 of 10 4 of 10
The relation between spectrum is The between microring-microring microring-microring coupling coupling coefficient and transmission transmission spectrum shown Figure Figure 3a. 3a. It It can can be seen that with the increase resonance is shown increase of of kk22==kk3,3the , theposition positionofofcentral central resonance almost unchanged, but the move away central gradually.gradually. Figure 3b is almost unchanged, but two the side-resonances two side-resonances movefrom away fromresonance central resonance shows 3b theshows effectthe of effect microring-microring coupling coefficient on FWHM of central resonant and Figure of microring-microring coupling coefficient on FWHM of central resonant maximum group index. After increasing of of k2 k=2 k and maximum group index. After increasing =3,k3the , theFWHM FWHMofofcentral centralresonance resonance was quickly extended while while the the maximum maximum group group index index was was raised raisedat atfirst firstand andthen thendeclined. declined. extended
(a)
(b) Figure 3. Effect of ring-ring coupling coefficient: (a) on transmission spectrum (b) on FWHM of Figure 3. Effect of ring-ring coupling coefficient: (a) on transmission spectrum (b) on FWHM of central central resonance and maximum group index. resonance and maximum group index.
Figure 4a shows the transmission of the three-ring coupled resonator with different waveguide Figure 4abe shows theseen transmission of the three-ring coupled resonator with different waveguide losses. It can clearly that, as the waveguide loss increases, the resonant depth of the three losses. It can be clearly seen that, as the waveguide loss increases, the resonant depth of the three resonances would decrease. Figure 4b shows the effect of the optical waveguide loss on FWHM of resonances would decrease. Figure 4b shows the effect of the optical waveguide loss on FWHM of the the central resonance and maximum group index. With the increase of optical waveguide loss, the central and maximum Withand, the in increase of optical waveguide loss,index the FWHM FWHMresonance of the central resonance group wouldindex. increase, contrast, the maximum group would of the central resonance would increase, and, in contrast, the maximum group index would decrease. decrease.
Sensors 2016, 16, 1165 Sensors 2016, 16, 1165
5 of 10 5 of 10
(a)
(b) Figure 4. Effect of waveguide loss: (a) on transmission spectrum (b) on FWHM of central resonance Figure 4. Effect of waveguide loss: (a) on transmission spectrum (b) on FWHM of central resonance and maximum group index. and maximum group index.
3. Device Fabrication and the Experiment 3. Device Fabrication and the Experiment The scanning electron microscopy (SEM) graphs of three-ring coupled resonators are shown in The scanning electron microscopy graphs ofwafers, three-ring coupled resonators Figure 5. The device was fabricated on(SEM) commercial SOI having a silicon thicknessare of shown 220 nm in Figure The device was fabricated onElectron commercial wafers, having a silicon 220 nm and a5.buried-oxide thickness of 3 μm. beamSOI lithography (JBX5500ZA) andthickness inductionof coupler andplasma a buried-oxide thickness of 3 µm. Electron beam lithography (JBX5500ZA) and induction coupler etching process (STS HRM ICP) were used to fabricate the three-ring coupled resonator. The plasma etching process (STScascaded HRM ICP) were used to were fabricate three-ring resonator. bus waveguide and the ring resonators fullythe etched, with coupled a depth of 220 nm The and bus a waveguide resonatorstransverse were fullyelectric etched,(TE) withlight. a depth 220 nm andtwo a width width ofand 450 the nm,cascaded to guidering single-mode Theofradii of the ring of 450resonators nm, to guide transverse electric (TE)oflight. Thewaveguide, radii of thea two resonators were weresingle-mode designed to be 20 μm. At both ends the bus pair ring of grating couplers was fabricated with a 600 nm period, in order to couple light in and out of the devices. The distance designed to be 20 µm. At both ends of the bus waveguide, a pair of grating couplers was fabricated between the period, straight in waveguide the light microring was which is the with a 600 nm order to and couple in and out110 of nm, the devices. Theoptimum distance distance betweenasthe proven from past experience. The gap between microring designed 70 nm straight waveguide and the microring was 110the nm, which isand themicroring optimumwas distance as from proven from to 200 nm. The coupling angular deviation θ was designed from 0° to 60°. To decrease the loss of the past experience. The gap between the microring and microring was designed from 70 nm to 200 nm. 300 °C deviation to 1200 °Cθthermal oxidation procedure used. Subsequently, thewaveguide, Buffered Thewaveguide, coupling angular was designed from 0˝ to 60˝was . To decrease the loss of the Oxide Etch and 1000 °C annealing with nitrogen were used to obtain a smoother waveguide 300 ˝ C to 1200 ˝ C thermal oxidation procedure was used. Subsequently, the Buffered Oxidesurface, Etch and ˝ 1000 C annealing with nitrogen were used to obtain a smoother waveguide surface, which means a
Sensors 2016, 16, 1165
6 of 10
Sensors 2016, 16, 1165
6 of 10
higher Q means factor. aThe enlarged views ofenlarged Figure 5aviews showofthat the straight and waveguides the rings have which higher Q factor. The Figure 5a showwaveguides that the straight good surface roughness. and the rings have good surface roughness.
(a)
(b) Figure 5. SEM of the cascaded rings and the gratings: (a) rings and straight waveguide (b) the grating Figure 5. SEM of the cascaded rings and the gratings: (a) rings and straight waveguide (b) the couplers. grating couplers.
The performance of the device was tested by vertical grating coupling method. The experimental system is illustrated in Figure 6a. The generation of the transparency curve is obtained by sweeping the frequency of the tunable laser (New Focus TLB-6728-P, Irvine, CA, USA, linewidth is less than 200 kHz) with the resolution of 0.01 nm. Light export from the tunable laser source is polarization-tuned by a polarization controller and injected into the grating coupler using a 75˝ lensed fiber and aligning by a precision translation stage (New Focus M-461-XYZ-M). The output light is detected by a photoelectric detector (New Focus 1811) and displayed on the digital oscilloscope (Tektronix MDO3054, Beaverton, OR, USA). Figure 6b shows the transmission spectrum from the through port of the structure with θ = 30˝ and the gap between the resonators of 110 nm. In the theoretical analysis, the coupling angular deviation θ has no influence on the transparency (a) (b) window, but in the actual fabrication it can change the destructive interferences between the responses Figure 6. (a) Device measurement setup andand (b) scanning curve of the of structures with θ = 30°. Utilizing of the three rings due to the scattering loss the bending loss the waveguide. this character, we have fabricated different coupling angular deviation and obtained a significant The performance was tested vertical grating coupling method. The experimental transparency peak with of thethe θ =device 30˝ . One of the by transparency windows in the wavelength axis with the system is illustrated in Figure 6a. The generation of the transparency curve is obtained by sweeping theoretical fitting curves is shown in Figure 7. It can be observed that the transmission peak splits into thenarrow frequency ofin the tunable laser (New TLB-6728-P, CA,theoretical USA, linewidth is we lessobserve than three peak both the through portFocus and the drop port.Irvine, From the analysis 200 kHz) with the resolution of 0.01 nm. Light export from the tunable laser source is polarizationthat the transmission character of our system is extremely sensitive to the radius of the microring.
Sensors 2016, 16, 1165
7 of 10
Due to machined error, there would be slight differences between the radius of the microrings which Sensors 2016, 16, 1165 7 of 10 would lead to the asymmetry of the two side-resonance. The FWHM of the central resonance is 5 as narrow as 0.0125 nm, corresponding to a quality of 1.22 ˆ 10 . The red line in Figure 7 (b)thefactor tuned by a polarization controller and injected into grating coupler using a 75° lensed fiber and is the theoretical fitting with k = k = 0.15, k = 0.108, k = r1 =output 20 µm, r2 is = 19.997 µm and 1 rings 4 and 2 3 and0.15, aligning by a5.precision stage (New Focus M-461-XYZ-M). The light Figure SEM of thetranslation cascaded the gratings: (a) rings straight waveguide (b) thedetected grating by r3 =a 20.0072 µm, which shows good agreement with the experimental result. photoelectric couplers. detector (New Focus 1811) and displayed on the digital oscilloscope (Tektronix MDO3054, Beaverton, OR, USA). Figure 6b shows the transmission spectrum from the through port of the structure with θ = 30° and the gap between the resonators of 110 nm. In the theoretical analysis, the coupling angular deviation θ has no influence on the transparency window, but in the actual fabrication it can change the destructive interferences between the responses of the three rings due to the scattering loss and the bending loss of the waveguide. Utilizing this character, we have fabricated different coupling angular deviation and obtained a significant transparency peak with the θ = 30°. One of the transparency windows in the wavelength axis with the theoretical fitting curves is shown in Figure 7. It can be observed that the transmission peak splits into three narrow peak in both the through port and the drop port. From the theoretical analysis we observe that the transmission character of our system is extremely sensitive to the radius of the microring. Due to machined error, there would be slight differences between the radius of the microrings which would lead to the asymmetry of the two side-resonance. The FWHM of the central (b) × 105. The red line in resonance is as narrow as (a) 0.0125 nm, corresponding to a quality factor of 1.22 Figure 7 isFigure the theoretical fitting with k1 =setup k4 = and 0.15,(b) k2scanning = 0.108, k 3 = 0.15, r1 = 20 μm, r2 = 19.997 μm and 6. (a) Device measurement curve of the structures with θ = 30°. ˝ Figureμm, 6. (a)which Device measurement setup and (b) the scanning curve ofresult. the structures with θ = 30 . r3 = 20.0072 shows good agreement with experimental The performance of the device was tested by vertical grating coupling method. The experimental system is illustrated in Figure 6a. The generation of the transparency curve is obtained by sweeping the frequency of the tunable laser (New Focus TLB-6728-P, Irvine, CA, USA, linewidth is less than 200 kHz) with the resolution of 0.01 nm. Light export from the tunable laser source is polarization-
(a)
(b) Figure 7. The measured transmission spectrum of (a) the through port and (b) the drop port. The blue
Figure 7. The measured transmission spectrum of (a) the through port and (b) the drop port. line is the experimental result curve and red line is theoretical fitting curve. The blue line is the experimental result curve and red line is theoretical fitting curve.
Sensors 2016, 16, 1165 Sensors 2016, 16, 1165
8 of 10 8 of 10
Since the EIT-like EIT-like window window in our device has a significant sensitivity sensitivity to to the change of the ring perimeter, perimeter, we we are areconvinced convinced that that the the EIT-like EIT-like system system can can be be used used as as a temperature temperature sensor, in which the resonant strength of the transparency window will be changed by the thermal thermal expansion expansion effect. effect. Therefore, further testedtested the response of transparency window in window different temperatures, Therefore, we wehave have further the response of transparency in different as shown in Figure 8. temperatures, as shown in Figure 8.
Figure window in in different different temperatures. temperatures. Figure 8. 8. The The response response of of transparency transparency window
The temperature sensors that use the single resonator have been reported [26,27], in which the The temperature sensors that use the single resonator have been reported [26,27], in which the temperature variation was measured by monitoring the shift in the resonant wavelength of the silicon temperature variation was measured by monitoring the shift in the resonant wavelength of the silicon resonator. However, the temperature variations will induce the thermo-optic effect and the thermal resonator. However, the temperature variations will induce the thermo-optic effect and the thermal expansion effect simultaneously. This means the shift in the resonant wavelength will be influenced expansion effect simultaneously. This means the shift in the resonant wavelength will be influenced by by both the changed effective index and the changed ring perimeter. Since we cannot verify the actual both the changed effective index and the changed ring perimeter. Since we cannot verify the actual effective index and the group index in the fabricated silicon ring resonators, it is not accurate if we effective index and the group index in the fabricated silicon ring resonators, it is not accurate if we only consider the shift in the resonant wavelength. While in our scheme, the temperature not only only consider the shift in the resonant wavelength. While in our scheme, the temperature not only changes the resonant shift, but also changes the resonance strength. Therefore, utilizing our EIT-like changes the resonant shift, but also changes the resonance strength. Therefore, utilizing our EIT-like scheme for temperature sensing is a promising method. scheme for temperature sensing is a promising method. 4. Conclusions 4. Conclusions In summary, EIT-like effect has been demonstrated theoretically and experimentally in the In summary, EIT-like effect has been demonstrated theoretically and experimentally in the cascaded three-ring coupled resonators on a silicon chip. The influence of parameters including cascaded three-ring coupled resonators on a silicon chip. The influence of parameters including coupling coefficient, waveguide loss, addition loss of couplers on EIT-like effect have been studied. coupling coefficient, waveguide loss, addition loss of couplers on EIT-like effect have been studied. EIT-like resonance is experimentally observed in the cascaded three-ring coupled resonator with a EIT-like resonance is experimentally observed in the cascaded three-ring coupled resonator with quality factor of 1.22 × 105. The experimental results agrees with the theoretical analysis well. The a quality factor of 1.22 ˆ 105 . The experimental results agrees with the theoretical analysis well. temperature performance of the device is further studied. This structure is promising for applications The temperature performance of the device is further studied. This structure is promising for in integrated optical sensors and optical delay lines. applications in integrated optical sensors and optical delay lines. Acknowledgments: This This work work was was supported supported by by the the China China National National Funds Funds for for Distinguished Distinguished Young Scientists Acknowledgments: Young Scientists (Grant No. 61525107) and National Natural Science Foundation Foundation of of China China (Grant (Grant No. No. 91123036). 91123036). Author Contributions: Contributions: Y.W., Y.W., H.Z. H.Z. and and conceived conceived and and designed designed the the structure; structure; H.Z. H.Z. performed performed the theoretical simulation. C.X. and and W.Z. W.Z. performed performed the the experiments; experiments; Y.W. Y.W. and and H.Z. H.Z. analyzed analyzed the the data; data; Y.W. Y.W. and simulation. C.X. and H.Z. H.Z. wrote wrote the paper. the paper. Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest.
Sensors 2016, 16, 1165
9 of 10
References 1. 2. 3.
4. 5. 6.
7. 8. 9. 10. 11. 12. 13. 14.
15. 16. 17. 18. 19. 20. 21. 22. 23.
Boller, K.J.; Imamoglu, A.; Harris, S.E. Observation of electromagnetically induced transparency. Phys. Rev. Lett. 1991, 66, 2593–2596. Hau, L.V.; Harris, S.E.; Dutton, Z.; Behroozi, C.H. Light speed reduction to 17 metres per second in an ultracold atomic gas. Nature 1999, 397, 594–598. [CrossRef] Safavi-Naeini, A.H.; Alegre, T.P.M.; Chan, J.; Eichenfield, M.; Winger, M.; Hill, J.T.; Lin, Q.; Chang, D.; Painter, O. Electromagnetically induced transparency and slow light with optomechanics. Nature 2011, 472, 69–73. [PubMed] Longdell, J.J.; Fraval, E.; Sellars, M.J.; Sellars, M.J.; Manson, N.B. Stopped light with storage times greater than one second using electromagnetically induced transparency in a solid. Phys. Rev. Lett. 2005, 95, 063601. Lukin, M.D.; Imamoglu, ˘ A. Controlling photons using electromagnetically induced transparency. Nature 2001, 413, 273–276. Liu, N.; Weiss, T.; Mesch, M.; Langguth, L.; Eigenthaler, U.; Hirscher, M.; Sönnichsen, C.; Giessen, H. Planar Metamaterial Analogue of Electromagnetically Induced Transparency for Plasmonic Sensing. Nano Lett. 2009, 10, 1103–1107. Smith, D.D.; Chang, H.; Fuller, K.A.; Rosenberger, A.T.; Boyd, R.W. Coupled-resonator-induced transparency. Phys. Rev. A 2004, 69, 063804. Xu, Q.; Sandhu, S.; Povinelli, M.L.; Shakya, J.; Fan, S.; Lipson, M. Experimental realization of an on-chip all-optical analogue to electromagnetically induced transparency. Phys. Rev. Lett. 2006, 96, 123901. Heebner, J.E.; Boyd, R.W.; Park, Q.H. Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide. Phys. Rev. E 2002, 65, 036619. Singh, R.; Cao, W.; Al-Naib, I.; Cong, L.; Withayachumnankul, W.; Zhang, W. Ultrasensitive terahertz sensing with high-Q Fano resonances in metasurfaces. Appl. Phys. Lett. 2014, 105, 171101. Manjappa, M.; Chiam, S.Y.; Cong, L.; Bettiol, A.A.; Zhang, W.; Singh, R. Tailoring the slow light behavior in terahertz metasurfaces. Appl. Phys. Lett. 2015, 106, 181101. Pitchappa, P.; Manjappa, M.; Ho, C.P.; Singh, R.; Singh, N.; Lee, C. Active Control of Electromagnetically Induced Transparency Analog in Terahertz MEMS Metamaterial. Adv. Opt. Mater. 2016, 4, 541–547. Zhang, S.; Genov, D.A.; Wang, Y.; Liu, M.; Zhang, X. Plasmon-induced transparency in metamaterials. Phys. Rev. Lett. 2008, 101, 047401. Cao, W.; Singh, R.; Zhang, C.; Han, J.; Tonouchi, M.; Zhang, W. Plasmon-induced transparency in metamaterials: Active near field coupling between bright superconducting and dark metallic mode resonators. Appl. Phys. Lett. 2013, 103, 101106. [CrossRef] Cao, W.; Singh, R.; Al-Naib, I.A.; He, M.; Taylor, A.J.; Zhang, W. Low-loss ultra-high-Q dark mode plasmonic Fano metamaterials. Opt. Lett. 2012, 37, 3366–3368. [PubMed] Steinberg, B.Z.; Scheuer, J.; Boag, A. Rotation-induced superstructure in slow-light waveguides with mode-degeneracy: Optical gyroscopes with exponential sensitivity. J. Opt. Soc. Am. B 2007, 24, 1216–1224. Zhang, Y.; Wang, N.; Tian, H.; Wang, H.; Qiu, W.; Wang, J.; Yuan, P. A high sensitivity optical gyroscope based on slow light in coupled-resonator-induced transparency. Phys. Rev. A 2008, 372, 5848–5852. Heebner, J.E.; Wong, V.; Schweinsberg, A.; Boyd, R.W.; Jackson, D.J. Optical transmission characteristics of fiber ring resonators. IEEE J. Quantum Electron. 2004, 40, 726–730. Scheuer, J.; Paloczi, G.T.; Poon, J.K.S.; Yariv, A. Coupled resonator optical waveguides: toward the slowing and storage of light. Opt. Photonics News 2005, 16, 36–40. Smith, D.D.; Lepeshkin, N.N.; Schweinsberg, A.; Gehring, G.; Boyd, R.W.; Park, Q.H.; Chang, H.; Jackson, D.J. Coupled-resonator-induced transparency in a fiber system. Opt. Commun. 2005, 264, 163–168. Kouki, T.; Norihiko, K.; Makoto, T. Slow light in coupled-resonator-induced transparency. Phys. Rev. Lett. 2007, 98, 213904. Ke, D.; Changde, X.; Jing, Z. Coupled-resonator-induced transparency with a squeezed vacuum. Phys. Rev. Lett. 2011, 106, 1486–1503. Yang, X.; Yu, M.; Kwong, D.L.; Wong, C.W. All-optical analog to electromagnetically induced transparency in multiple coupled photonic crystal cavities. Phys. Rev. Lett. 2009, 102, 173902.
Sensors 2016, 16, 1165
24.
25. 26. 27.
10 of 10
Yang, X.; Yu, M.; Kwong, D.L.; Wong, C.W. Coupled resonances in multiple silicon photonic crystal cavities in all-optical solid-state analogy to electromagnetically induced transparency. IEEE J. Sel. Top. Quantum Electron. 2010, 16, 288–294. Xu, Q.; Dong, P.; Lipson, M. Breaking the delay-bandwidth limit in a photonic structure. Nat. Phys. 2007, 3, 406–410. Yu, X.; Ma, H.; Jin, Z.; Pan, M.; Hou, L.; Xie, W. Sensitive birefringent temperature sensor based on a waveguide ring resonator. Appl. Opt. 2014, 53, 2748–2753. [PubMed] Lee, H.S.; Park, C.H.; Lee, S.S.; Lim, B.T.; Bae, H.K.; Lee, W.G. Silicon photonic temperature sensor employing a ring resonator manufactured using a standard CMOS process. Opt. Express 2010, 18, 22215–22221. © 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).
