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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 6 — Mar. 24, 2014
  • pp: 6778–6790
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Fano resonances in a multimode waveguide coupled to a high-Q silicon nitride ring resonator

Dapeng Ding, Michiel J. A. de Dood, Jared F. Bauters, Martijn J. R. Heck, John E. Bowers, and Dirk Bouwmeester  »View Author Affiliations


Optics Express, Vol. 22, Issue 6, pp. 6778-6790 (2014)
http://dx.doi.org/10.1364/OE.22.006778


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Abstract

Silicon nitride (Si3N4) optical ring resonators provide exceptional opportunities for low-loss integrated optics. Here we study the transmission through a multimode waveguide coupled to a Si3N4 ring resonator. By coupling single-mode fibers to both input and output ports of the waveguide we selectively excite and probe combinations of modes in the waveguide. Strong asymmetric Fano resonances are observed and the degree of asymmetry can be tuned through the positions of the input and output fibers. The Fano resonance results from the interference between modes of the waveguide and light that couples resonantly to the ring resonator. We develop a theoretical model based on the coupled mode theory to describe the experimental results. The large extension of the optical modes out of the Si3N4 core makes this system promising for sensing applications.

© 2014 Optical Society of America

1. Introduction

Integrated optical circuits consist of waveguides and beamsplitters that can transport and distribute optical signals on a chip. The addition of resonant structures, such as ring resonators, adds important functionality to integrated circuits. On resonance, light can be coupled from a waveguide into a ring resonator and vice versa via evanescent fields. The interference between light in a single-mode waveguide and a ring resonator generates a symmetric resonance dip (that can be approximated as a Lorentzian function in the vicinity of the minimum) in the transmission spectrum of the waveguide. The resonant energy transfer between the waveguide and ring resonator leads to numerous applications such as light storage [1

1. F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007). [CrossRef]

], add/drop filters [2

2. B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999). [CrossRef]

], integrated switches [3

3. V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004). [CrossRef] [PubMed]

] and sensors [4

4. A. Ksendzov and Y. Lin, “Integrated optics ring-resonator sensors for protein detection,” Opt. Lett. 30, 3344–3346 (2005). [CrossRef]

].

The symmetric transmission spectrum is significantly modified by introducing an additional optical channel into the system. The interference between the direct and indirect transport channels gives rise to an asymmetric, Fano-like transmission lineshape. So far the realization of an additional transport channel leading to the Fano resonance includes, but is not limited to, the use of two partial reflecting elements in the waveguide [5

5. S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80, 908–910 (2002). [CrossRef]

, 6

6. C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83, 1527–1529 (2003). [CrossRef]

], multimode waveguides [7

7. A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, and K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett. 86, 261106 (2005). [CrossRef]

9

9. A. C. Ruege and R. M. Reano, “Multimode waveguide-cavity sensor based on fringe visibility detection,” Opt. Express 17, 4295–4305 (2009). [CrossRef] [PubMed]

], multimode ring resonators [10

10. B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011). [CrossRef]

,11

11. Y.-F. Xiao, L. He, J. Zhu, and L. Yang, “Electromagnetically induced transparency-like effect in a single polydimethylsiloxane-coated silica microtoroid,” Appl. Phys. Lett. 94, 231115 (2009). [CrossRef]

] and multiple ring resonators [12

12. B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012). [CrossRef]

]. When multimode waveguides are used, the Fano resonances appear and the degree of asymmetry is determined by the coupling of the different modes of the waveguide and ring resonator. It has been shown that the degree of asymmetry of the Fano resonances can be tuned by varying the coupling region on the multimode waveguide [7

7. A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, and K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett. 86, 261106 (2005). [CrossRef]

] or by varying the relative phase of the light injected into different modes in the waveguide [8

8. A. C. Ruege and R. M. Reano, “Sharp Fano resonances from a two-mode waveguide coupled to a single-mode ring resonator,” J. Lightwave Technol. 28, 2964–2968 (2010). [CrossRef]

]. Sensing applications have been demonstrated in a system where light is coupled into a ring resonator via a multimode waveguide and coupled out via multiple single-mode waveguides [9

9. A. C. Ruege and R. M. Reano, “Multimode waveguide-cavity sensor based on fringe visibility detection,” Opt. Express 17, 4295–4305 (2009). [CrossRef] [PubMed]

].

In this article we explore the tunability of the Fano resonances in a multimode waveguide coupled to a multimode ring resonator. The waveguide and the ring resonator consist of a high-aspect-ratio silicon nitride (Si3N4) core embedded in silicon dioxide (SiO2) cladding. The mode selectivity is achieved by positioning and butt-coupling single-mode fibers to the multimode waveguide at both ends. We observe the Fano resonance with various degree of asymmetry when the two fibers are independently scanned along the core width direction. Advantages and limitations of this system and the Fano resonance scheme for sensing applications are discussed.

2. Theoretical model

Fig. 1 Schematic drawing of a multimode waveguide coupled to a multimode ring resonator via a coupling region (CR). Light is coupled into and out of the waveguide using single-mode fibers (SM) with optical powers Pin and Pout through the fibers, respectively. Both the input and output fiber positions are tunable with respect to the center of the waveguide. The length of the waveguide section from the input (output) to the coupling region is L1 (L2). The electric fields at different positions are denoted by E1E5. The radius of the ring resonator is R.

By combining Eq. (2), Eq. (3) and Eq. (4), and solving equations for Aj and Bj, one obtains an input-output relation of the form
Bj=tjAjkakrkjlrlkAlexp(i2πβkR)aktk.
(6)

In the experiment, one can selectively pump and probe variable superpositions of the Eigenmodes of the waveguide by coupling light into and out of the multimode waveguide with single-mode fibers. At the input port of the waveguide, a single-mode fiber with a Gaussian mode profile h(x, y) couples to each of the Eigenmodes of the waveguide. The coupling efficiency to the jth order Eigenmode of the waveguide ηj is
ηj(x,y)=fj(x,y)h(xx,yy)dxdy,
(7)
where (x′, y′) are the coordinates of the center of the input coupling fiber. These Eigenmode components of the waveguide propagate from the input port to the coupling region and gain different phase factors, therefore
Aj(x,y)=ηj(x,y)Pinexp(iβjL1),
(8)
where Pin is the power through the input fiber, β′j is the propagation constant of the jth order Eigenmode of the waveguide, L1 is the distance from the input port to the coupling region of the waveguide, and the waveguide is assumed to be lossless. The total field at the output port of the waveguide is
E5(x,y,x,y)=jBj(x,y)exp(iβjL2)fj(x,y),
(9)
where L2 is the distance from the coupling region to the output port of the waveguide. At the output port of the waveguide, a single-mode fiber with the same field profile as the input coupling fiber couples to the output field. The power through the output fiber Pout is then
Pout(x,y,x,y)=|E5(x,y,x,y)h(xx,yy)dxdy|2|jSj(x,y)Bj|2,
(10)
where (x″, y″) are the coordinates of the center of the output coupling fiber and Sj(x″, y″) = ηj(x″, y″)exp(−iβ′jL2). Eventually, the power transmission through the input-output fibers is given by
T(x,y,x,y)=PoutPin=|jSjBj|21Pin.
(11)
By using the explicit form of Bj in Eq. (6) and βk in Eq. (5), the power transmission T becomes
T(Δν,x,y,x,y)=|jSjtjAjkakj,lSjrkjrlkAlexp[iek(ν0+Δν)]aktk|21Pin,
(12)
where ek = 4π2npk(ν)R/c and Δν is frequency detuning with respect to a reference frequency ν0. Note that AjPin as given in Eq. (8) and thus Pin cancels out in Eq. (12).

For the jth order Eigenmode of the ring resonator, resonances occur when
ej(ν0+Δν)=2mπ,
(13)
with m being an integer. The resonant frequency detunings of the jth order Eigenmode of the ring resonator are
Δν0j=2mπejν0=mc2πnpj(ν)Rν0.
(14)
The free spectral range (FSR) of the jth order Eigenmode of the ring resonator is defined as the frequency difference between two adjacent resonant frequencies. If one assumes linear dispersion relations of the materials within one FSR (typically tens of GHz for a ring resonator), the FSR can be expressed as
FSRj=c2πngj(ν)R,
(15)
where ngj(ν) = npj(ν) + ν (dnpj(ν)/dν) is the effective group index of the jth order Eigenmode of the ring resonator at frequency ν. In the experiment, we will use Eq. (15) to extract effective group indices from measured FSRs.

Equation (12) can be simplified under the assumption that the resonances of the modes are narrow enough to be well separated in frequency domain. In the vicinity of the resonant frequency detuning of the jth order Eigenmode Δν0j, the terms for the other Eigenmodes in the summation in Eq. (12) are slowly varying functions with respect to Δν and might be approximated as complex functions qk (kj). qk is not a function of Δν, but still a function of (x′, y′) and (x″, y″). Under this simplification, Eq. (12) reads
T(Δν,x,y,x,y)|qbjexp[iej(ν0+Δν)]ajtj|2,
(16)
where q=(jSjtjAjkjqk)/Pin and bj=ajk,lSkrjkrljAl/Pin are complex and dimensionless functions of (x′, y′) and (x″, y″). The exponential term in Eq. (16) can be further simplified by the Taylor expansion with respect to Δν0j and keeping (Δν − Δν0j) up to the second power:
T(Δν,x,y,x,y)ζj+αj[ϕj2(ΔνΔν0j)2+2ϕjθjγj(ΔνΔν0j)+θj2γj2(ΔνΔν0j)2+γj2],
(17)
where ζj, αj, ϕj and θj are real and dimensionless functions of (x′, y′) and (x″, y″) that characterize the profile of the transmission spectra (see below). Their explicit expressions in terms of the coefficients in Eq. (16) are tedious and not given here. The expression of γj is simple:
γj=1ajtjejajtj.
(18)
Equation (17) will be used to analyze our experimental data. We note that Eq. (17) and Eq. (18) are also valid for the coupling of a multimode waveguide to a single-mode ring resonator.

αj, ϕj and θj in Eq. (17) are under-determined and extra constraint conditions can be added. In analogy to [14

14. S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003). [CrossRef]

], we impose
ϕj=1θj2andαj,ζj>0,
(19)
which requires 0 < ϕj < 1 and −1 < θj < 1. The term in the square bracket of Eq. (17) describes a lineshape with amplitude in between zero and one. For θj = 0 and ϕj = 1, the lineshape is a normal Lorentzian dip, while for θj = ±1 and ϕj = 0, the lineshape turns into a Lorentzian peak. In between it gives an asymmetric lineshape, with maximum asymmetry for θj2=ϕj2=1/2. Opposite signs of θj result in mirror-symmetric lineshapes. αj and ζj rescale the lineshape, but the degree of asymmetry remains the same. The coefficient θj will be referred to as the Fano parameter, since its absolute value measures the degree of asymmetry of the lineshape and its sign determines one of the two mirror-symmetric lineshapes.

For a specific geometry and materials of the waveguide and the ring resonator and fixed operating wavelength, the parameter γj in Eq. (18) is a constant, while ζj, αj, ϕj and θj vary with the input and output fiber positions. By tuning the input and output fiber positions with respect to the waveguide, it is possible to achieve θj = 0 and ϕj = 1 where the transmission lineshape of the jth order Eigenmode of the ring resonator becomes a Lorentzian function. The quality factor of the Lorentzian lineshape is given by
Qj=ν0+Δν0j2γj=ejajtj(ν0+Δν0j)2(1ajtj),
(20)
which is a function of internal and coupling losses and is independent of the input and output fiber positions. Consequently, when the input and output fiber positions are scanned with respect to the waveguide, the transmission lineshape varies, but the quality factor remains the same. Therefore Eq. (20) is also valid for the Fano resonance. We emphasize that the above assertion is based on the assumption that the resonances of the ring resonator are narrow enough to be well separated in frequency domain and is always valid for a single-mode ring resonator.

For a Lorentzian lineshape (θj = 0 or 1 in Eq. (17)), the slope responsivity of the transmission spectrum defined as |dT/dΔν|max is (33/8)αj/γj(0.65αj/γj), when ΔνΔν0j=±(3/3)γj. In contrast, a Fano lineshape with the maximum asymmetry ( θj=±2/2 in Eq. (17)) has the slope responsivity of the transmission spectrum αjj, when Δν = Δν0j. Thus for the same αj and γj, the Fano resonance with the maximum asymmetry improves the slope responsivity by a factor of 1.54 compared to the Lorentzian resonance.

At off-resonant frequencies, strong fields can not build up in the ring resonator and therefore the transmission in the waveguide is effectively decoupled from the ring resonator, i.e. Aj = Bj. Combining Eq. (7), Eq. (8) and Eq. (11), and using Aj = Bj, we obtain the off-resonance transmission for a given input and output positions of the fibers
Toff(x,y,x,y)=|jfj(x,y)h(xx,yy)dxdyfj(x,y)h(xx,yy)dxdyexp[iβj(L1+L2)]|2.
(21)
Since h(x, y) is an even function and fj(x, y) is either an even or an odd function, it can be proved that Toff is invariant upon the transformation x′x″ and x′ ↔ −x″. Hence x′ = x″ and x′ = −x″ are two symmetry axes of Toff in the coordinate system of (x″, x′). This property will be used in Section 5 to determine the central position of the waveguide.

3. Sample description

The ring resonator is fabricated by a combination of chemical vapor deposition (CVD), lithography and etching. Details of the sample design, fabrication and basic characterization at 1.5 μm wavelength are reported elsewhere [15

15. J. F. Bauters, M. J. R. Heck, D. John, D. Dai, M.-C. Tien, J. S. Barton, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Ultra-low-loss high-aspect-ratio Si3N4 waveguides,” Opt. Express 19, 3163–3174 (2011). [CrossRef] [PubMed]

, 16

16. M.-C. Tien, J. F. Bauters, M. J. R. Heck, D. T. Spencer, D. J. Blumenthal, and J. E. Bowers, “Ultra-high quality factor planar Si3N4 ring resonators on Si substrates,” Opt. Express 19, 13551–13556 (2011). [CrossRef] [PubMed]

]. We give a brief summary of the properties that are important to this work. Both the ring resonator and the waveguide share the same cross-sectional structure and it is shown in Fig. 2(a), which is a high-aspect-ratio Si3N4 core embedded in SiO2 cladding material. For the particular sample measured in the present work, the Si3N4 core has a width of 5.25 μm and a thickness of 50 nm. The radius of the ring resonator is 6 mm and the gap between the waveguide and the ring resonator is 3 μm. The thicknesses of the top and bottom cladding are both 15 μm.

Fig. 2 Cross-sectional drawing (a) of a Si3N4 waveguide with a width of 5.25 μm and a thickness of 50 nm in SiO2 cladding and calculated TM ((b) TM0 and (c) TM1, y-component electric field or Ey) and TE ((d) TE0, (e) TE1 and (f) TE2, x-component electric field or Ex) mode profiles of this waveguide at 978 nm wavelength. The refractive indices of the Si3N4 core and SiO2 cladding are assumed to be 1.9885 and 1.4507, respectively. The simulation is implemented by the finite element method (FEM) using COMSOL.

Since the radius of the ring resonator is much larger than the width of the Si3N4 core, we assume that the modes of the ring resonator can be approximated by the modes of the straight waveguide, i.e. fj(x, y) ≃ gj(x, y). If one assumes that the refractive index of the thin Si3N4 core is equal to that of bulk amorphous Si3N4 (n = 1.99) and that the refractive index of the SiO2 cladding is 1.45 at 978 nm wavelength, the waveguide modes can be calculated by the finite element method (FEM) using COMSOL (COMSOL Inc.). The FEM simulation shows two transverse magnetic (TM, polarized along the core thickness, or y-direction) modes (TM0 and TM1) with effective phase indices of 1.4576 and 1.4530 and three transverse electric (TE, polarized along the core width, or x-direction) modes (TE0, TE1 and TE2) with effective phase indices of 1.4768, 1.4703, 1.4600, respectively. We note that the effective phase indices of the fundamental TM and TE modes calculated by the effective index method [17

17. R. M. Knox and P. P. Toulios, “Integrated circuits for the millimeter through optical frequency range,” in Proceedings of the Symposium on Submillimeter Waves, (Polytechnic Press, 1970), pp. 497–516.

] are 1.4578 and 1.4770, respectively, in good agreement with the FEM simulations. The possibility to use the effective index method greatly facilitates design and optimization of such waveguides with a high aspect-ratio. The calculated mode profiles are shown in Fig. 2. Due to much smaller dimension of the Si3N4 core in the y-direction compared to the wavelength, the waveguide shows single-mode properties in the y-direction and multimode properties in the x-direction.

Using dispersion relations of fused silica and amorphous Si3N4 the effective group indices are also calculated by the FEM. The results of the two TM modes are 1.4895 and 1.4866 and those of the three TE modes are 1.5478, 1.5502, 1.5504, respectively. Nevertheless, we do not expect a detailed agreement of the calculated effective group indices with the experiment because the actual effective group indices depend on the stress-optic effect and changes in Si3N4 refractive index and thickness due to the annealing process [18

18. J. F. Bauters, M. J. R. Heck, D. D. John, J. S. Barton, C. M. Bruinink, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Planar waveguides with less than 0.1 dB/m propagation loss fabricated with wafer bonding,” Opt. Express 19, 24090–24101 (2011). [CrossRef] [PubMed]

].

4. Experimental method

A schematic of the setup used to measure the transmission properties of the multimode waveguide coupled to a ring resonator is shown in Fig. 3. Two cleaved bare single-mode fibers (980-HP, Nufern Inc.) with a mode field diameter of 4.2 μm at 980 nm wavelength are used to butt-couple light in and out of the waveguide structure. To this end, both fibers are mounted on xyz-translation stages. The two translation stages are motorized in the x-direction to scan along the core of the waveguide.

Fig. 3 Schematic of the experimental setup for measuring the transmission of the multimode waveguide and ring resonator system. Abbreviations: ECDL (External Cavity Diode Laser), FBS (Fiber Beamsplitter), FPI (Fabry-Perot Interferometer), PD (Photodetector), DAQ (Data Acquisition) and HV-Amp (High Voltage Amplifier). Black lines denote single mode optical fibers and purple lines denote electrical wirings.

Light from a tunable, narrow-linewidth laser (DL pro, TOPTICA Photonics AG) is distributed over three single-mode fibers using two cascaded fiber beamsplitters (FBS1 and FBS2). One of the outputs is used as a power monitor (by PD2), while another part of the light is sent to a Fabry-Perot interferometer (FPI) and a photodetector (PD3) to monitor the frequency detuning of the laser during the scan. The remaining light is sent through a fiber polarization controller (FPC) and is used to measure the transmitted power of the waveguide coupled to the ring resonator by PD1. The normalized transmission is then obtained by dividing the signal of PD1 by the signal of PD2. The FPC is used to maximize transmission contrast of a specific resonance. All fiber connections, except those used for butt-coupling to the waveguide, are either angle-cleaved or filled with index-matching liquid to minimize back reflection.

The laser operates at ∼978 nm wavelength and is tuned over approximately 20 GHz around this central wavelength. The detuning is monitored by a computer controlled data acquisition (DAQ) system that generates a voltage VS to control the frequency detuning and records the signals on PD1, PD2 and PD3 as functions of VS. The laser frequency detuning Δν as a function of the voltage VS can be well approximated by a quadratic relation. The coefficients of this quadratic function can be found by fitting to the scan voltages corresponding to maximum transmission of the FPI, using known FSR of 4.00 GHz of the FPI. From this transmission spectra as a function of the frequency detuning of the laser are obtained.

5. Results and discussion

A typical transmission spectrum at certain input and output fiber positions is shown in Fig. 4. The data consists of repetitive sets of resonances labeled by numbers 1, 2 and 3. The measured FSRs of resonance 1, 2 and 3 are 5.39, 5.29 and 5.29 (±0.01) GHz corresponding to effective group indices of 1.475, 1.505 and 1.505 (±0.003), respectively. By optimizing an individual resonance using the FPC and then measuring the polarization of the transmitted light, we find that resonances 1 and 3 correspond to TM and TE modes, respectively. The polarization of resonance 2 is difficult to measure because of its low contrast. As anticipated the effective group indices derived from the measurement systematically deviate from the calculated values (see Section 3). This deviation is due to the stress and diffusion of the Si3N4 core caused by the annealing process [18

18. J. F. Bauters, M. J. R. Heck, D. D. John, J. S. Barton, C. M. Bruinink, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Planar waveguides with less than 0.1 dB/m propagation loss fabricated with wafer bonding,” Opt. Express 19, 24090–24101 (2011). [CrossRef] [PubMed]

].

Fig. 4 Measured transmission as a function of laser frequency detuning over a 20 GHz range. The free spectral range (FSR) of the ring resonator is approximately 5.3 GHz and the measurement range includes four sets of three resonances spaced by one FSR.

Figure 5 shows a more detailed measurement of resonances 1, 2 and 3. The red curve through the data is a fit to Eq. (12) in the form of
T(Δν)=|pj=13bjexp[iej(Δν+ν0j)]dj|2,
(22)
where p, ν0j and dj are real coefficients, bj are complex coefficients, and ej are fixed parameters calculated by the effective phase indices. The three resonances demonstrate different degree of asymmetry in their lineshapes. Although Eq. (12) is derived under the assumption that only modes with one polarization are excited, we can prove that fitting Eq. (12) to the transmission data with modes in two orthogonal polarizations gives correct parameters ajt′j and hence correct quality factors. The quality factors that can be extracted from the fit (see Eq. (20), where ajt′jdj) are (8.1 ± 0.2)×106, (1.9±0.1)×107 and (6.9±0.2)×106 for resonances 1, 2 and 3, respectively. We attribute resonance 1 to the TM0 mode (mode profile in Fig. 2(b)) and resonances 2 and 3 to the TE0 mode (lower coupling and bending losses, therefore higher quality factor; mode profile in Fig. 2(d)) and TE1 mode (mode profile in Fig. 2(e)), respectively. Resonances of other modes can not be recognized in the transmission measurements due to their low contrasts.

Fig. 5 Detailed transmission measurement as a function of laser frequency detuning (blue dots) showing three resonances. The red curve through the data is a fit to Eq. (12). The three resonances labeled by 1, 2 and 3 correspond to the three resonances in Fig. 4 with the same labels. Inset: magnified plot of the main figure for resonance 2.

Because of the single-mode property of the waveguide in the y-direction (see Fig. 2), moving the coupling fibers along the y-direction changes the overall coupling efficiency, but hardly affects the relative weight of different modes excited and collected in the waveguide given that the confinement in the y-direction only very weakly depends on the mode. As a consequence, we observe that the transmission lineshape and Fano resonances are independent of the fiber positions in the y-direction. Therefore in the experiment both of the input and output fibers are aligned to the center of the waveguide in the y-direction (y = y′ = 0) by maximizing the transmission amplitude and are only scanned in the x-direction.

We will focus on resonance 1 which has the highest contrast, indicating that this mode is closest to critical coupling. The FPC is set to maximize the contrast of resonance 1 from here on. Under such a polarization condition, only the two TM modes are excited and the TE modes are negligible. In the vicinity of the resonant frequency, Eq. (17) is applicable. Because resonance 1 is far detuned from other resonances in the frequency domain, the physical origin of the Fano resonance is the coupling of the multimode waveguide to a single resonance of the ring resonator. Figure 6 shows the measured transmission of resonance 1 at four different input-output fiber positions together with the fits to Eq. (17). The slope responsivity (|dT/dν|max) of the four transmission spectra are 4.23, 4.90, 5.35 and 0.22 GHz−1, respectively. From the fits, the Fano parameter θ is extracted and the off-resonant transmission Toff is obtained as
Toff=ζ+αϕ2.
(23)

Figure 7 shows a contour plot of Toff as a function of the input and output fiber positions (x′ and x″, respectively) on a logarithmic scale. By using the symmetric property of Toff (Eq. (21)), two symmetry axes, x′ = x″ and x′ = −x″, are determined and shown as dashed lines in Fig. 7. The intersection of the two symmetry axes corresponds to the center of the waveguide and is defined as the origin of the input and output fiber positions (x′ = x″ = 0). Close to the edges of Fig. 7, the TM1 mode of the waveguide is more strongly excited or more efficiently collected because of its larger spatial extent. Consequently, valley I can be understood as follows: the TM0 mode is weakly excited, while the output fiber only couples to this mode (the TM1 mode is orthogonal to the fiber mode). Similarly, at valley II, only the TM0 mode is strongly excited while the output fiber couples weakly to this mode.

Fig. 6 Measured transmission of resonance 1 as a function of frequency detuning (blue dots). The red curves through the data are fits to Eq. (17) for four different input-output fiber positions. The Fano parameter θ obtained from the fit is shown for each transmission curve. A value of θ close to unity corresponds to a transmission dip (a), while θ close to zero corresponds to a transmission peak (d). θ close to ±2/2(0.707) gives maximum negative (b) and positive (c) asymmetry. The slope responsivity defined as |dT/dν|max are 4.23, 4.90, 5.35 and 0.22 GHz−1, respectively.
Fig. 7 Contour plot of the measured log10 Toff as a function of the input and output fiber positions. The two dashed lines are symmetry axes of the Toff data. The origin of the plot is defined as the intersection of the two symmetry axes. The points marked by (a) – (d) are positions where the transmission (a) – (d) in Fig. 6 are measured, respectively.

Fig. 8 Contour plot of the measured absolute value of the Fano parameter θ as a function of the input and output fiber positions. The points marked by (a) – (d) are positions where the transmission (a) – (d) in Fig. 6 are measured, respectively. The four valleys III and IV yield symmetric transmission peaks with |θ| close to zero.

6. Potential application

The main goal of this article is to investigate the Fano resonance and its tunability in a new structure (high-aspect-ratio core) and a new scheme (two single-mode fibers coupled to a multimode waveguide and a ring resonator). In this section, we will however reflect on the possible advantages and limitations of the system and the Fano resonance scheme for applications.

First, we would like to point out that this system can be optimized for potential sensing applications. The high-aspect-ratio waveguide design makes most of the mode field extend out of the Si3N4 core (see Fig. 2). By using thin top cladding, the mode field of the ring resonator can interact with the environment very efficiently. We have fabricated low-loss waveguides and ring resonators with thin top cladding as an intermediate step before wafer bonding [18

18. J. F. Bauters, M. J. R. Heck, D. D. John, J. S. Barton, C. M. Bruinink, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Planar waveguides with less than 0.1 dB/m propagation loss fabricated with wafer bonding,” Opt. Express 19, 24090–24101 (2011). [CrossRef] [PubMed]

]. These devices with very low scattering losses on the top cladding surface are in principle suitable for sensing applications.

Both high quality factor and high transmission contrast are crucial in sensing applications to achieve high slope responsivity. In the present system, the quality factor and transmission contrast of a specific resonance can be simultaneously optimized. For instance, resonance 2 with the highest quality factor (1.9 × 107) has the lowest transmission contrast. Analysis of losses of resonance 2 compared with resonances 1 and 3 indicates that resonance 2 is over-coupled to the waveguide. Therefore by increasing the coupling distance between the waveguide and the ring resonator in the fabrication process, resonance 2 can be optimized to critical coupling with the maximum contrast and a higher quality factor (> 1.9 × 107).

The method of using single-mode fibers coupled to a multimode waveguide to generate and to tune the Fano resonances implies that only part of the incident light is detected. This seems to limit the use of the Fano resonance for sensing applications. For example the slope responsivity of the Fano resonance shown in Fig. 6(c) is 5.35 GHz−1, while the maximum slope responsivity of the system is 34.37 GHz−1 obtained from a symmetric lineshape when both the input and output fibers are aligned to the center of the waveguide. However one should realize that the light that is not recorded in the Fano resonance is still available and also carries information on the resonance of the ring resonator. A more detailed analysis considering detecting all the output power of the waveguide is needed to investigate whether there can be an overall gain in sensitivity compared to a single-mode-waveguide-ring-resonator configuration. However this is beyond the scope of this article.

7. Conclusion

In summary, we measured transmission through a multimode Si3N4 waveguide coupled to a high-Q Si3N4 ring resonator at 978 nm wavelength. By scanning the positions of single-mode fibers at both input and output ports of the waveguide, we selectively excite and probe combinations of the modes in the waveguide. Fano resonances are observed as a function of the input and output fiber positions, which originates from the interference between the modes in the waveguide after mixing by the ring resonator. We developed a theoretical model based on the coupled mode theory to describe the system. We also showed that the effective index method is a good approximation in calculating the modes of our high-aspect-ratio Si3N4 waveguide. With the large spatial extent of the mode out of the Si3N4 core, our Si3N4 ring resonator is of interest for sensing applications.

Acknowledgments

This work is part of the research programme of the Foundation for Fundamental Research on Matter (FOM), which is part of the Netherlands Organisation for Scientific Research (NWO). This work was supported by NWO VICI Grant No. 680-47-604, NSF DMR-0960331, NSF PHY-1206118 and DARPA IPHOD contract HR0011-09-C-0123.

References and links

1.

F. Xia, L. Sekaric, and Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007). [CrossRef]

2.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999). [CrossRef]

3.

V. R. Almeida, C. A. Barrios, R. R. Panepucci, and M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004). [CrossRef] [PubMed]

4.

A. Ksendzov and Y. Lin, “Integrated optics ring-resonator sensors for protein detection,” Opt. Lett. 30, 3344–3346 (2005). [CrossRef]

5.

S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80, 908–910 (2002). [CrossRef]

6.

C.-Y. Chao and L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83, 1527–1529 (2003). [CrossRef]

7.

A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, and K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett. 86, 261106 (2005). [CrossRef]

8.

A. C. Ruege and R. M. Reano, “Sharp Fano resonances from a two-mode waveguide coupled to a single-mode ring resonator,” J. Lightwave Technol. 28, 2964–2968 (2010). [CrossRef]

9.

A. C. Ruege and R. M. Reano, “Multimode waveguide-cavity sensor based on fringe visibility detection,” Opt. Express 17, 4295–4305 (2009). [CrossRef] [PubMed]

10.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, and Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011). [CrossRef]

11.

Y.-F. Xiao, L. He, J. Zhu, and L. Yang, “Electromagnetically induced transparency-like effect in a single polydimethylsiloxane-coated silica microtoroid,” Appl. Phys. Lett. 94, 231115 (2009). [CrossRef]

12.

B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, and Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012). [CrossRef]

13.

P. Rabiei and W. H. Steier, “Polymer microring resonators,” in Optical Microcavities, K. Vahala, eds. (World Scientific, 2005), pp. 321–324.

14.

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003). [CrossRef]

15.

J. F. Bauters, M. J. R. Heck, D. John, D. Dai, M.-C. Tien, J. S. Barton, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Ultra-low-loss high-aspect-ratio Si3N4 waveguides,” Opt. Express 19, 3163–3174 (2011). [CrossRef] [PubMed]

16.

M.-C. Tien, J. F. Bauters, M. J. R. Heck, D. T. Spencer, D. J. Blumenthal, and J. E. Bowers, “Ultra-high quality factor planar Si3N4 ring resonators on Si substrates,” Opt. Express 19, 13551–13556 (2011). [CrossRef] [PubMed]

17.

R. M. Knox and P. P. Toulios, “Integrated circuits for the millimeter through optical frequency range,” in Proceedings of the Symposium on Submillimeter Waves, (Polytechnic Press, 1970), pp. 497–516.

18.

J. F. Bauters, M. J. R. Heck, D. D. John, J. S. Barton, C. M. Bruinink, A. Leinse, R. G. Heideman, D. J. Blumenthal, and J. E. Bowers, “Planar waveguides with less than 0.1 dB/m propagation loss fabricated with wafer bonding,” Opt. Express 19, 24090–24101 (2011). [CrossRef] [PubMed]

OCIS Codes
(060.2310) Fiber optics and optical communications : Fiber optics
(130.0130) Integrated optics : Integrated optics
(230.5750) Optical devices : Resonators
(230.7370) Optical devices : Waveguides

ToC Category:
Integrated Optics

History
Original Manuscript: December 16, 2013
Revised Manuscript: March 5, 2014
Manuscript Accepted: March 7, 2014
Published: March 17, 2014

Citation
Dapeng Ding, Michiel J. A. de Dood, Jared F. Bauters, Martijn J. R. Heck, John E. Bowers, and Dirk Bouwmeester, "Fano resonances in a multimode waveguide coupled to a high-Q silicon nitride ring resonator," Opt. Express 22, 6778-6790 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-6-6778


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References

  1. F. Xia, L. Sekaric, Y. Vlasov, “Ultracompact optical buffers on a silicon chip,” Nat. Photonics 1, 65–71 (2007). [CrossRef]
  2. B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, E. Ippen, “Vertically coupled glass microring resonator channel dropping filters,” IEEE Photon. Technol. Lett. 11, 215–217 (1999). [CrossRef]
  3. V. R. Almeida, C. A. Barrios, R. R. Panepucci, M. Lipson, “All-optical control of light on a silicon chip,” Nature 431, 1081–1084 (2004). [CrossRef] [PubMed]
  4. A. Ksendzov, Y. Lin, “Integrated optics ring-resonator sensors for protein detection,” Opt. Lett. 30, 3344–3346 (2005). [CrossRef]
  5. S. Fan, “Sharp asymmetric line shapes in side-coupled waveguide-cavity systems,” Appl. Phys. Lett. 80, 908–910 (2002). [CrossRef]
  6. C.-Y. Chao, L. J. Guo, “Biochemical sensors based on polymer microrings with sharp asymmetrical resonance,” Appl. Phys. Lett. 83, 1527–1529 (2003). [CrossRef]
  7. A. Chiba, H. Fujiwara, J. Hotta, S. Takeuchi, K. Sasaki, “Fano resonance in a multimode tapered fiber coupled with a microspherical cavity,” Appl. Phys. Lett. 86, 261106 (2005). [CrossRef]
  8. A. C. Ruege, R. M. Reano, “Sharp Fano resonances from a two-mode waveguide coupled to a single-mode ring resonator,” J. Lightwave Technol. 28, 2964–2968 (2010). [CrossRef]
  9. A. C. Ruege, R. M. Reano, “Multimode waveguide-cavity sensor based on fringe visibility detection,” Opt. Express 17, 4295–4305 (2009). [CrossRef] [PubMed]
  10. B.-B. Li, Y.-F. Xiao, C.-L. Zou, Y.-C. Liu, X.-F. Jiang, Y.-L. Chen, Y. Li, Q. Gong, “Experimental observation of Fano resonance in a single whispering-gallery microresonator,” Appl. Phys. Lett. 98, 021116 (2011). [CrossRef]
  11. Y.-F. Xiao, L. He, J. Zhu, L. Yang, “Electromagnetically induced transparency-like effect in a single polydimethylsiloxane-coated silica microtoroid,” Appl. Phys. Lett. 94, 231115 (2009). [CrossRef]
  12. B.-B. Li, Y.-F. Xiao, C.-L. Zou, X.-F. Jiang, Y.-C. Liu, F.-W. Sun, Y. Li, Q. Gong, “Experimental controlling of Fano resonance in indirectly coupled whispering-gallery microresonators,” Appl. Phys. Lett. 100, 021108 (2012). [CrossRef]
  13. P. Rabiei, W. H. Steier, “Polymer microring resonators,” in Optical Microcavities, K. Vahala, eds. (World Scientific, 2005), pp. 321–324.
  14. S. Fan, W. Suh, J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003). [CrossRef]
  15. J. F. Bauters, M. J. R. Heck, D. John, D. Dai, M.-C. Tien, J. S. Barton, A. Leinse, R. G. Heideman, D. J. Blumenthal, J. E. Bowers, “Ultra-low-loss high-aspect-ratio Si3N4 waveguides,” Opt. Express 19, 3163–3174 (2011). [CrossRef] [PubMed]
  16. M.-C. Tien, J. F. Bauters, M. J. R. Heck, D. T. Spencer, D. J. Blumenthal, J. E. Bowers, “Ultra-high quality factor planar Si3N4 ring resonators on Si substrates,” Opt. Express 19, 13551–13556 (2011). [CrossRef] [PubMed]
  17. R. M. Knox, P. P. Toulios, “Integrated circuits for the millimeter through optical frequency range,” in Proceedings of the Symposium on Submillimeter Waves, (Polytechnic Press, 1970), pp. 497–516.
  18. J. F. Bauters, M. J. R. Heck, D. D. John, J. S. Barton, C. M. Bruinink, A. Leinse, R. G. Heideman, D. J. Blumenthal, J. E. Bowers, “Planar waveguides with less than 0.1 dB/m propagation loss fabricated with wafer bonding,” Opt. Express 19, 24090–24101 (2011). [CrossRef] [PubMed]

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