Fano resonance lineshapes in a waveguide-microring structure enabled by an air-hole
Linpeng Gu, Liang Fang, Hanlin Fang, Juntao Li, Jianbang Zheng, Jianlin Zhao, Qiang Zhao, Xuetao Gan
FFano resonance lineshapes in a waveguide-microring structure enabled by an air-hole
Linpeng Gu , Liang Fang , Hanlin Fang , Juntao Li , Jianbang Zheng , Jianlin Zhao , and Qiang Zhao ∗ , Xuetao Gan ∗ MOE Key Laboratory of Material Physics and Chemistry under Extraordinary Conditions,and Shaanxi Key Laboratory of Optical Information Technology,School of Science, Northwestern Polytechnical University, Xi’an 710072, China State Key Laboratory of Optoelectronic Materials and Technologies,School of Physics, Sun Yat-Sen University, Guangzhou, 510275, China and Qian Xuesen laboratory of Space Technology, China Academy of Space Technology, Beijing 100094, China (Dated: July 5, 2019)
We propose and demonstrate, by simply inserting anair-hole in the waveguide side-coupling with a microringresonator (MRR), the transmission spectrum presentsFano lineshapes at all of the resonant modes. Measuredfrom the fabricated devices, Fano lineshapes with sloperates over 400 dB/nm and extinction ratios over 20 dB areobtained. We ascribe it to the air-hole-induced phase-shiftbetween the discrete resonant modes of the MRR andthe continuum propagating mode of the bus-waveguide,which modifies their interference lineshapes from sym-metric Lorentzian to asymmetric Fano. From devices withvaried locations and diameters of the air-hole, differentFano asymmetric parameters are extracted, verifyingthe air-hole-induced phase-shifts. This air-hole-assistedwaveguide-MRR structure for achieving Fano resonancelineshapes has advantages of simple design, compactfootprint, large tolerance of fabrication errors, as wellas broadband operation range. It has great potentials toexpand and improve performances of on-chip MRR-baseddevices, including sensors, switchings and filters.
I. INTRODUCTION
Microring resonators (MRRs) play crucial roles in on-chipinterconnect, signal processing, and nonlinear optics [1–4].Fano resonance lineshapes of MRRs have recently attractedintense interest for improving these chip-integration func-tions [5–8]. As opposed to usual symmetric Lorentzian res-onance lineshapes, they have asymmetric and sharp slopesaround the resonant wavelengths. The wavelength range fortuning the transmission from zero to one is much narrowerin Fano lineshapes, which therefore strengthens the figure ofmerits of power consumption, sensing sensitivity, extinctionratio, etc. [5, 9–11]. Fano resonance is recognized as a gen-eral phenomenon in physical waves and originates from theinterference between continuum state and discrete localizedstate [12]. By considering resonant modes in MRRs as the dis-crete state, Fano resonances were realized by coupling MRRswith other photonic structures, including Mach-Zehnder inter-ferometers [13–15] and Fabry-Perot cavities [16, 17], which ∗ [email protected]; [email protected] provide a quasi-continuum mode. Unfortunately, these inte-grated structures sacrifice the compact footprint of MRRs, andit is challenging to achieve precise structure designs and de-vice fabrications for overlapping MMR’s discrete modes withthe quasi-continuum modes. Also, because of the limitedbandwidth of the quasi-continuum modes, Fano resonancesonly form at certain resonant wavelengths of the MRR, whichis incoordinate with the broadband operation of the MRR-based devices.Here, we report a compact design to realize Fano line-shapes at all of the resonant modes of a MRR, which also haslarge design and fabrication tolerances. In the widely reportedMRR-based devices, the MRR is normally side-coupled witha bus-waveguide to access its resonant modes, as shown inFig. 1(a). Our proposed design is inserting an air-hole in thebus-waveguide around the waveguide-MRR coupling region,as shown in Fig. 1(b). This inserted air-hole functions as aphase-shifter between the discrete resonant mode in MRR andthe continuum propagating mode in the bus-waveguide, whichis experimentally verified by the transmission spectra of thefabricated devices with different air-hole locations and diam-eters. The obtained slope rate (SR) and extinction ratio (ER)of the Fano resonance lineshapes are exceeding 20 dB and 400dB/nm, respectively. II. MODEL AND THEORY
To explain the design principle, we first analyse the prop-agation of optical field in the conventional waveguide-MRRcoupling structure shown in Fig. 1(a). When an incident op-tical field E in = E propagates in the bus-waveguide, it willsplit into two parts at the waveguide-MRR coupling regiondue to the evanescent-field coupling. One of them propagatescontinuously in the bus-waveguide with an amplitude of tE after the coupling region, where t is the transmission coeffi-cient of the coupling region. The other part couples into theMRR with an amplitude of i κE , and i κ is the coupling coef-ficient from one waveguide to the other. This part will propa-gate along the MRR and circulate back to the coupling regionwith an amplitude of E = ( iκ ) ae iδ E , where δ = 2 πnL R /λ is the round trip phase delay and a = exp( − αL R ) is the roundtrip amplitude transmission coefficient. Here, n is the effec-tive refractive index of the propagating mode, λ is the operat-ing wavelength, L R is the perimeter of the MRR and α is thelinear loss coefficient. Then, when the optical field E passes a r X i v : . [ phy s i c s . op ti c s ] J u l through the waveguide-MRR coupling region, with the samecoupling mechanism, the part with an amplitude of tE con-tinuously propagates in the MRR, and the other part with anamplitude of i κE couples into the bus-waveguide, which willbe added with the initial propagating field of tE at the outputport of the bus-waveguide. For the part of tE , it will circulatein the MRR and couple partly into the bus-waveguide again atthe coupling region. Under this coupling mechanism, the op-tical fields in the MRR would be added repetitively into thebus-waveguide after each circulation. The total output field ofthe bus-waveguide could be calculated as E out = tE (cid:124)(cid:123)(cid:122)(cid:125) continuum state + iκE + iκE + · · · (cid:124) (cid:123)(cid:122) (cid:125) discrete state = tE + iκ ( iκ ) ae iδ E + iκ ( iκ ) ta e i δ E + · · · = tE + ( iκ ) ae iδ − t n a n +1 e i ( n +1) δ − tae iδ E ( t < , n → ∞ )= ( t − κ ae iδ − tae iδ ) E (1)By assuming there is no loss in the waveguide-MRR cou-pling region, i.e., t + κ = 1 , the final power transmissionspectrum of the coupled system is given by T ( λ ) = (cid:12)(cid:12)(cid:12)(cid:12) E out E in (cid:12)(cid:12)(cid:12)(cid:12) = (cid:12)(cid:12)(cid:12)(cid:12) t − ae i πnL R /λ − tae i πnL R /λ (cid:12)(cid:12)(cid:12)(cid:12) (2)This transmission spectrum has been widely studied andwe plot it in Fig. 1(c) with parameters of t = a = 0 . and nL R = 300 . µ m. It presents periodic Lorentzian dips at thewavelengths that makes phase delay δ = 2 πnL R /λ equal tothe integer multiple of 2 π . At those wavelengths, the opticalfields circulating in the MRR satisfy constructive interferenceand form resonant modes of the MRR. Correspondingly, inEq. 1, the additions after the first term could be considered asa discrete localized state. As discussed above, the first term ofEq. 1 represents the propagating mode of the bus-waveguideafter the coupling region, which is a continuum state of thecoupling system. Hence, around the resonant wavelengths,the output field ( E out ) of the waveguide-MRR is an interfer-ence of a discrete state and a continuum state. The symmetricLorentzian transmission dips (see Fig. 1(c)) of the conven-tional waveguide-MRR structure shown in Fig. 1(a) just arisefrom this interference. Note, in the widely reported Fano res-onances of photonic structures, it has been well recognizedthat the interference of a discrete state and a continuum stateshould give rise to a Fano lineshapes. This contradicts theLorentzian lineshapes of the conventional waveguide-MRR.We ascribe it to the factor of phase-difference between thediscrete state and the continuum state. In the conventionalwaveguide-MRR structure, the incident light splits into theMRR and the bus-waveguide at the coupling region, makingthem having the same initial phase. For the optical field form-ing resonant mode in the MRR, it experiences a phase delay ofinteger multiple of 2 π after it circulates back to the coupling region. Hence, when the discrete resonant modes couple backinto the bus-waveguide, they have phase differences of integermultiple of 2 π relative to the continuum mode propagating di-rectly in the bus-waveguide. According to the Fano-Andersonmodel, this 2 π phase-difference would result in a Fano line-shape with an infinite asymmetric factor q , which evolves intoa symmetric Lorentzian lineshapes [18]. This explains theLorentzian resonance lineshapes presented in the transmissionspectrum of a conventional waveguide-MRR structure. (b) (d) (a) EE tt i te i eaEiE Ei tE Ete i (c) EitEE out E EE t i eaEiE Ei EiEteE i out E T r a n s m i ss i on ( a . u . ) Wavelength (nm) T r a n s m i ss i on ( a . u . ) Wavelength (nm)
FIG. 1. (a) Propagation of optical filed in a conventional waveguide-MRR structure. (b) Propagation of optical filed in the proposedwaveguide-MRR structure with an air-hole inserted in the bus-waveguide. (c) Transmission spectrum calculated by Eq. 2 with pa-rameter of t = a = 0 . . (d) Transmission spectrum calculated byEq. 4 with parameter of t = a = 0 . and ∆ φ = π/ . According to above analysis, to modify the Lorentzian res-onance lineshapes of the MRR into asymmetric Fano line-shapes, it is essential to change the phase-difference betweenthe discrete state and the continuum state from the integermultiple of 2 π . To do that, we propose to add an air-holein the bus-waveguide around the waveguide-MRR couplingregion, as shown in Figs. 1(b). The inserted air-hole would in-duce a phase-shift for the continuum propagating mode in thebus-waveguide. On the other hand, since the air-hole does notmodify the MRR structure, the condition of constructive inter-ference in the MRR is unperturbed and the discrete resonantmodes experience no extra phase-shift. Consequently, thephase difference between the discrete mode and the contin-uum mode is not equal to the integer multiple of 2 π any more,and asymmetric Fano resonance lineshapes are expected [18].The output optical field of the waveguide-MRR with an air-hole could be calculated by modifying Eq. 1, E out = te − i ∆ φ E (cid:124) (cid:123)(cid:122) (cid:125) continuum state + iκE + iκE + · · · (cid:124) (cid:123)(cid:122) (cid:125) discrete state = ( te − i ∆ φ − κ ae iδ − tae iδ ) E (3)Here, an extra phase-shift ∆ φ induced by the air-hole isadded into the direct transmission part propagating in the bus-waveguide, which is considered as the continuum state. Forthe discrete state of the resonant modes, there is no differencefrom that in Eq. 1. The corresponding power transmissionspectrum is calculated as T ( λ ) = (cid:12)(cid:12)(cid:12)(cid:12) E out E in (cid:12)(cid:12)(cid:12)(cid:12) = (cid:12)(cid:12)(cid:12)(cid:12) te − i ∆ φ − κ ae i πnL R /λ − tae i πnL R /λ (cid:12)(cid:12)(cid:12)(cid:12) (4)With the same parameters used to calculate Fig. 1(c) andby assuming ∆ φ = π/ , the transmission spectrum of thewaveguide-MRR with an air-hole is plotted in Fig. 1(d). Pe-riodic Lorentzian lineshapes at the resonant wavelengths aremodified into asymmetric Fano lineshapes successfully. Tofurther illustrate the role of phase-shift ∆ φ played in theformation of Fano lineshapes, we calculate the transmissionspectra of Eq. 4 with different ∆ φ , and fit them using Fanoformula T = 1 − ( q + Ω) / (1 + Ω ) [19, 20]. Here, Ω is thereduced frequency and q is the asymmetric parameter, whichindicating the strengths of the discrete state and the continuumstate during their coupling. In Fig. 2, the q factors extractedfrom the Fano fittings are plotted with respect to the phase-shift ∆ φ , presenting a cotangent-type function [21]. If thephase-shift equals to integer multiple of 2 π , Eq. 4 degener-ates into Eq. 2, and the extracted q factor tends to be infinity.In this case, because the constructive interference phenom-ena exists in the MRR, the discrete resonant modes couplewith the continuum propagating mode very weakly or neg-ligibly. Therefore, the coupled Fano profile becomes sym-metric Lorentzian function, as observed in the conventionalwaveguide-MRR. When ∆ φ = nπ ( n is odd numbers), theFano lineshape evolves into an electromagnetically inducedtransparency (EIT)-like peak, and q = 0 . Because of de-structive interference between the discrete resonant mode andcontinuum propagating mode, it could be considered there isno coupling to the discrete state ( q = 0 ) and it describes theresonant suppression of the transmission [12]. If the phase-shift has other values, both constructive and destructive in-terference coexists between the discrete mode and the con-tinuum mode, asymmetric Fano lineshapes are generated andthe asymmetric parameters q have non-zero values. Also, asshown in Fig. 2, the sign of q alternates when ∆ φ changeswith a step of π . III. EXPERIMENT RESULTS
To verify the above theoretical predictions, we fabricatea side-coupled waveguide-MRR with an air-hole in the bus-waveguide, as displayed in the optical microscope image ofFigure 3(a). The device is fabricated on a silicon-on-insulatorchip, which has an 220 nm thick top silicon layer and a 2 µ m thick buried dioxide layer. Electron beam lithographyand inductively coupled plasma etching are employed to de-fine the devices. The coupling region of the waveguide-MRRis zoomed in a scanning electron microscope (SEM) imageshown in Fig. 3(b). The waveguide and MRR have the samestripe width of 500 nm, and their coupling gap is 120 nm. TheMRR radius is 30 µ m. The inserted air-hole has a diameter ( d )of 300 nm and locates at the middle of the coupling region. -20020 q →∞ q ≈1 q =0 q →-∞ F a no p a r a m e t e r q Phase shift Df q ≈-1 FIG. 2. Fano parameter q is cotangent of the phase-shift ∆ φ with aperiod of 2 π . The insets show the normalized Fano profiles at differ-ent ∆ φ as well as the extracted q factors. We characterize this device by coupling a telecom-bandnarrowband tunable laser into the bus-waveguide via a ver-tical grating coupler. The transmitted optical power of the de-vice is collected from an output vertical grating coupler, andmeasured by a photodiode. Figure 3(c) shows a measuredtransmission spectrum over a range from 1540 nm to 1600nm. Fano resonance lineshapes are observed over a nearly flattransmission background with a spectral period determined byMRR’s free spectral range (FSR ≈ nm). These Fano line-shapes show the largest extinction retios (ER) over 20 dB witha slope rate (SR) of 404.9 dB/nm (at 1599.03 nm). By fittingthe lines to the Fano formula, the asymmetric factor and qual-ity ( Q ) factor are extracted as q ≈ − and Q ≈ , ,respectively. Analyzed from Eq. 4, the ER and SR could beimproved by optimizing the waveguide-MRR structures [22].For example, similar as the ER in a conventional waveguide-MRR, by improving the fabrication process to match the criti-cal coupling conditions, the ER could be maximized. The SRcould be improved by increasing the Q factor, correspond-ing to narrow linewidth of the resonant mode. Also, whileonly the wavelength range of 60 nm is shown in the transmis-sion spectrum, which is limited by the operation spectral rangeof the grating coupler, Fano lineshapes over an even broaderspectral range should be observed by using butt-coupling ge-ometry [23]. We also implement a control experiment byfabricating a waveguide-MRR without air-hole in the bus-waveguide. The other parameters of the waveguide-MRR arenot changed. The measured transmission spectrum is shownin Fig. 3(d). The resonant wavelengths and FSR are the sameas those in the waveguide-MRR with air-hole. Differently,the resonant lineshapes are symmetric Lorentzian type. Whilethe Q factors of the resonant modes are evaluated exceeding35,000, the SRs (around 100 dB/nm) are much lower thanthose obtained in the asymmetric Fano lineshapes. It couldfacilitate the Fano lineshapes for improving the performancesof MRR-based switchings and sensors.As analysed for Eq. 3, the asymmetric Fano lineshapes
30 μm (a) T r a n s m i ss i on ( d B ) T r a n s m i ss i on ( d B ) Wavelength (nm) (c) (b) (d)
500 nm 1 μm300 nm120 nm
FIG. 3. (a) Optical microscope image and (b) the zoomed SEMimage of the fabricated device. (c, d) (c) Transmission spectra ofthe device shown in (a). (d) Tranmission spectrum of conventionalwaveguide-MRR without an air-hole for the control experiment.
Df=0.0p, q →-∞ Df=0.24p, q =-1.3 Df=0.28p, q =-1.1 Df=0.30p, q =-1.0 T r a n s m i ss i on ( a . u . ) Wavelength (nm)
Mid-plane of the coupling region D l =0.0 μm(a) (b) D l =0.5 μm D l =1.5 μm D l =2.5 μm FIG. 4. (a) SEM images and (b) transmission spectra of waveguide-MRR with the air-hole shifted from the mid-plane of the couplingregion by ∆ l =0.0 µ m, 0.5 µ m, 1.5 µ m and 2.5 µ m. The scale barcorresponds to 1 µ m. result from the air-hole-induced phase-difference betweenMRR’s discrete resonant mode and bus-waveguide’s contin-uum propagating mode. To further discuss this point, weexperimentally fabricate more waveguide-MRR devices byvarying the parameters of the inserted air-hole. First, basedon the device design shown in Fig. 3(a), we move the air-hole away from the mid-plane of the waveguide-MRR cou-pling region gradually. SEM images of the fabricated devicesare displayed in Fig. 4(a), which have air-hole location off-sets ( ∆ l ) apart from the mid-plane of 0.0 µ m, 0.5 µ m, 1.5 µ m, 2.5 µ m. Transmission spectra of the devices are shown (a)(b)
160 200 240 280 320 360 400 440 4800.00.20.40.6 q =-0.34 q =-0.52 q =-0.79 q =-1.3 q =-2.7 q =-33 0.63π0.50π0.37π0.24π0.12π P h a s e s h i f t ( p ) Diameter (nm)0.01π T r a n s m i ss i on ( a . u . ) d =180 nm d =240 nm d =300 nm d =360 nm d =420 nm Wavelength(nm) d =480 nm
160 200 240 280 320 360 400 440 480-10-8-6-4-20 I n s e r ti on l o ss ( d B ) Diameter (nm) (c)
FIG. 5. (a) Measured (blue dots) and fitted (red solid, by Eq. 4)transmission spectra of devices with varied air-hole diameters. (b)Phase-shift and q derived from the fitting in (a). (c) The measuredinsertion losses caused by different air-holes. in Fig. 4(b) correspondingly. While the Fano lineshapes ineach device are similar for all of the resonant modes, the res-onant lineshapes vary obviously among different devices dueto the varied ∆ l . By fitting these resonant lineshapes withEq. 4, the phase shift ∆ φ and asymmetric factors q are eval-uated for each device, as shown in Fig. 4(b). The depen-dences of lineshapes on the air-hole locations prove the es-sential of phase-shift induced by the air-hole. For instance,for the device with ∆ l = 2 . µ m, the air-hole moves out ofthe waveguide-MRR coupling region, i.e., there is no air-holein the coupling region. Hence, the discrete resonant modes inMRR coupling back to the bus-waveguide would interferencewith the unperturbed continuum propagating mode in the bus-waveguide, which maintains their phase-difference of integermultiple of 2 π . After the coupling region, while there is anair-hole in the bus-waveguide, the interfering modes propa-gate together and would experience the same phase-shift. Thetransmitted resonant lineshapes have no difference from thatobtained in the conventional waveguide-MRR, showing sym-metric Lorentzian lineshapes.Next, devices with different air-hole diameters are fabri-cated and characterized, as shown in Fig. 5(a). The mea-sured transmission spectra are fitted by Eq. 4 and the q fac-tor and phase-shift ∆ φ induced by the air-holes are evalu-ated as well, as shown in Fig. 5(b). As the sizes of air-holeincrease, phase-shifts and the asymmetric factor q becomelarger. This is consistent with that effective refractive index ofthe propagating mode in the bus-waveguide is changed greaterby the larger air-hole, resulting in larger phase-shift as well.Note, while the inserted air-hole induces a phase-shift of thebus-waveguide successfully, it is also a scattering point forthe propagating mode. To facilitate potential applications ofthe air-hole-enabled Fano lineshapes, it is valuable to evalu-ate the inserting loss induced by the air-hole scattering. Bycomparing to the waveguide-MRR without air-holes, the in-sertion losses caused by the air-holes with different diametersare measured, as plotted in Fig. 5(c). For the air-hole with adiameter of 360 nm, which provides a remarkable Fano line-shape, the resulted insertion loss is about 5 dB.As predicted in Fig. 2, more plentiful lineshapes couldbe obtained if the phase-shifts are large enough, such as anEIT-like lineshape ( ∆ φ = π ), Fano lineshapes with differentasymmetric directions ( ∆ φ > π ). However, from the abovefabricated devices, the obtained maximal phase shift is about0.63 π with the air-hole diameter of 480 nm. This air-hole sizeapproaches to the full width of the waveguide. Hence, it is im-possible to achieve a phase shift of π by inserting the circularair-hole. Also, as shown in Fig. 5(c), this air-hole with a diam-eter of 480 nm induces an insertion loss larger than 10 dB. Torealize more lineshapes, the structure of the inserted air-holecould be optimized. For example, an elliptical air-hole or anarray of small circular air-holes could be involved around the waveguide-MRR coupling region, which would induce largerphase shift in the bus-waveguide and reduce the insertion losssimultaneously. IV. CONCLUSION
In conclusion, we have demonstrated that Fano resonancelineshapes could be realized reliably in a waveguide-MRRstructure by simply inserting an air-hole in the side-coupledwaveguide. By analysing the light propagation in the cou-pled structure, the air-hole-induced phase-shift is revealedto account for the formation of Fano resonance lineshapes.The theoretical predictions are verified experimentally wellby fabricating devices with different parameters of the in-serted air-holes. Fano resonance lineshapes are obtained overa broad spectral range with high ERs (¿ 20 dB) and SRs (¿400 dB/nm). Because the proposed design only requires tomodify the bus-waveguide with an air-hole, eliminating thecomplex integration of other photonic structures, it reservesthe compactness of the conventional waveguide-MRR struc-ture. In addition, as discussed in the devices with different pa-rameters of the air-hole, the generated Fano lineshapes havelarge tolerances of the structure designs and fabrications. Weexpect the air-hole-enabled Fano resonance lineshapes in thewaveguide-MRR could be employed to improve the perfor-mances of MRR-based optical switchings, sensors and filters.
FUNDINGS
National Natural Science Foundations of China (61775183,11634010, 61522507); the Key Research and DevelopmentProgram (2017YFA0303800, 2018YFA0307200); the KeyResearch and Development Program in Shaanxi Province ofChina (2017KJXX-12, 2018JM1058); the Fundamental Re-search Funds for the Central Universities (3102018jcc034,3102017jc01001).
ACKNOWLEDGMENT
The authors would thank the Analytical & Testing Centerof NPU for the assistances of device fabrication. [1] P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R.Holzwarth, and T. J. Kippenberg, Optical frequency comb gen-eration from a monolithic microresonator, Nature 450, 1214(2007).[2] X. Guo, C.-l. Zou, C. Schuck, H. Jung, R. Cheng, and H.X. Tang, Parametric down-conversion photon-pair source on a nanophotonic chip, Light. Sci. & Appl. 6, e16249 (2017).[3] Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Micrometre-scale silicon electro-optic modulator, nature. 435, 325 (2005).[4] T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Microres-onatorbased optical frequency combs, science. 332, 555559(2011).[1] P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R.Holzwarth, and T. J. Kippenberg, Optical frequency comb gen-eration from a monolithic microresonator, Nature 450, 1214(2007).[2] X. Guo, C.-l. Zou, C. Schuck, H. Jung, R. Cheng, and H.X. Tang, Parametric down-conversion photon-pair source on a nanophotonic chip, Light. Sci. & Appl. 6, e16249 (2017).[3] Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, Micrometre-scale silicon electro-optic modulator, nature. 435, 325 (2005).[4] T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, Microres-onatorbased optical frequency combs, science. 332, 555559(2011).