Towards a Realistic Modelling of Ultra-Compact Racetrack Resonators

JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 28, NO. 22, NOVEMBER 15, 2010 3233

Towards a Realistic Modelling of Ultra-CompactRacetrack Resonators

Marco Masi, Régis Orobtchouk, Guofang Fan, Jean-Marc Fedeli, and Lorenzo Pavesi, Member, IEEE

Abstract—We discuss all the necessary parameters to describeoptical racetrack micro resonators fabricated with silicon on in-sulator (SOI) technology. We focus on some fundamental aspectscrucial for a comprehensive and realistic modelling of racetrackresonators as building blocks of complex add-drop filters, likeSCISSOR (Side-Coupled Integrated Spaced-Sequences of Res-onators) or CROW (Coupled Resonator Optical Waveguides).When the radius of curvature is lower than 5 m, and/or theseparation gaps between waveguide and resonator is small, disper-sion law, effective index mismatch, and mode mismatch betweenbend and straight waveguides are relevant for modelling. A newmode solver, specifically suited for high index contrast small modearea waveguides, is used whose results are compared with themeasurement of the optical response of some resonant devices.

Index Terms—Micro-resonators, optical waveguide theory, op-tical propagation.

I. INTRODUCTION

M ICRORING resonators, and to some less extent microracetrack- or stadium- resonators, are at the basis of a

large number of devices for Wavelength Division Multiplexing(WDM), sensing, filtering, switching, routing, or optical inter-connects (e.g., [1]–[5]). Most of their modelings relied on ap-proximations and simplified assumptions which depart from thereal physical properties of the resonator. Within certain limitsthis idealization is justified since it leads to the qualitative un-derstanding of the device behavior. But with increasing integra-tion densities, resonators have smaller bend radiuses and smallcoupling gaps. This implies that one cannot neglect in the mod-elling effects such as coupling losses, effective index differencesand modal mismatches between the straight and bend waveg-uides. For a radius of curvature smaller than m in a SOIsystem, the traditional algorithms furnish very rough estimatesof the optical response of microresonators, especially for somehigh-order filtering applications. Moreover, the situation getsworse for devices based on sequences of microresonator like inSCISSOR or CROW devices. The aim of this paper is to setup ascheme to describe accurately small microresonator or multiple

Manuscript received May 24, 2010; revised July 28, 2010; acceptedSeptember 11, 2010. Date of publication September 27, 2010; date of currentversion November 10, 2010. This paper was supported in part by the EUthrough the FP7 ICT-(216405) project Wavelength Division MultiplexedPhotonic Layer on CMOS.

M. Masi and L. Pavesi are with the Nanoscience Laboratory, Department ofPhysics, University of Trento, I-38123 Povo (Trento), Italy (e-mail: [email protected]).

R. Orobtchouk and G. Fan are with the Institut des Nanotechnologies de Lyon,Université de Lyon, INL-UMR5270, CNRS, INSA de Lyon, 69621 Villeur-banne, France.

J.-M. Fedeli is with CEA-LETI Minatec, 38054 Grenoble Cedex 9, France.Digital Object Identifier 10.1109/JLT.2010.2078797

Fig. 1. Racetrack structure.

cascaded microresonators in order to enhance design methodsof complex optical systems which can tackle, at least partially,fabrication tolerances, narrowing the gap between models andreal devices.

A full description of the single racetrack needs an improvedunderstanding of the behavior of its constituent parts. In thefollowing sections, after a brief theoretical introduction on op-tical coupling and the behavior of add-drop filter, we will dis-cuss the dispersion law of the straight waveguide. The followingsubsection focuses on the characterization of curved waveg-uides and on the influence of the bending on the effective index.Subsection II.D describes experimental results on losses and itscharacterization on some devices and the determination throughcoupled mode theory (CMT) of the odd and even modes arisingfrom the mutual interaction of waveguides. Also the determi-nation of bending losses, the calculation of the coupling coef-ficients and length, and a comparison between the obtained pa-rameters with experimental results will follow. In the last sec-tion we will insert these data into a model of the single race-track resonator. A final comparison among the proposed model,an idealized one, and experimental measurements will close thepaper.

II. MODELLING BASICS

A. Some Theoretical Aspects on Phase Mismatch, CouplingCoefficients and the Add-Drop Optical Response

Racetracks resonators (see Fig. 1) have several advantageswith respect to ring resonators. For instance, it is easier todetermine the coupling strength since it is controlled by twoparameters: the length of the two straight coupling guidesand their separation gap. The coupled mode theory betweentwo straight waveguides is more straightforward than betweena straight and a bent waveguide. Spacing tolerances are lesscritical for the coupling gaps in racetracks compared to rings,because if stronger couplings are needed only the couplinglength has to be increased without decreasing the spacingbetween the input guide and the resonator, which is instead

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3234 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 28, NO. 22, NOVEMBER 15, 2010

more difficult to calibrate precisely. In addition, the TE-po-larization is frequently taken as a default for many theoreticalinvestigations and practical applications. But ring resonatorswork better in TM-polarization since the coupling efficiencyis higher for TM than TE-polarization due to its lower fieldconfinement. Therefore, racetracks are more suitable to obtainthe desired couplings in TE. The disadvantage of racetracksversus ring geometries is about losses, since the effective lengthof racetracks is longer than that of rings and due to the phasemismatch between the straight and bend component. For thisreason we will also address the issue of loss optimization.However, if very high quality factors are not needed, this isusually not a real stumbling block.

Let us discuss firstly what happens when the bus waveguidestarts to interact with the racetrack resonator, i.e., when the twowaveguides of the bus waveguide and of the resonator begin tointeract with each other. Coupled mode theory (CMT) worksin a weak coupling regime where it makes first order predic-tions ([6]). For strong couplings other higher order theoriesor direct calculations of Maxwell’s equations are necessary.This happens when the coupling waveguide to the racetrackresonator separation becomes very small (say about 200 nmfor SOI wavguides) and/or the racetrack length is close to thecoupling length. In this case one has two strongly coupledphotonic waveguides where the splitting into symmetric andantisymmetric modes occurs. The propagation constant of theantisymmetric mode of the same order is lower than the sym-metric one because it is pushed into the outer low index region.Now, the degree of synchronism between the two modes, i.e.,the mismatching, is expressed by the difference

where and are the propagation constants of the two waveg-uides. When the two modes are said to be in phase-matching condition. But when strong coupling occurs phase-matching is no longer preserved and it can be shown (see forexample [7] and [8]) that the modal fields in the two coupledwaveguides are determined by an even and odd prop-agation constants given respectively by

with , and the mode coupling coefficientfor the co-directional coupler (that obtained from perturbationtheory with the amplitudes cross-sectional integral over thesection of the two waveguides and with dimension of an inverselength). Therefore, the effective index of the guided modechanges as a result of the waveguide coupling. The optical

modes of the two waveguides can be expressed as a linear com-bination of two modes with propagation constants and .The deviation from the mean is negligible forlarge separations, but can become relevant for small gaps andinduces spectral shifts of the racetrack resonances. These arecalled coupling-induced resonance frequency shifts (CIFS) andcan have deleterious effects on high-order resonant filters [9].

Once the effective indexes of the even and odd modes areknown they can be used to obtain the coupling coefficients andlengths. According to CMT, the cross- and transmission- cou-pling coefficients, and (those derived considering mode in-terference, dimensionless and such that their modulus squarerepresents the fraction of the coupled power), are given by

(1)

where

is the coupling length, while and the even and oddmode effective indexes respectively. In absence of losses,

with and the coupling loss parameter. Butin general since there can be coupling losses due toroughness at the bend-straight interfaces, due to the small powertransfer asymmetry between the odd and even modes and alsodue to the mode conversion losses which however become rel-evant only for very small gaps (smaller than 120 nm). [10]

Given the two coupling coefficients , the upper andlower coupling losses and , the bend and straight propa-gation constants and , the roughness and radiation losses

, and the racetrack’s perimeter (see Fig. 1), thenone can analytically model the spectral response of the racetrackusing the well known relations which connect the In, Through,Add and Drop ports, or resort to the more general transfer matrixanalysis (e.g., [1]–[4], [11]–[13], and [14]), obtaining (2) and (3)shown at the bottom of the page, where T and D are the opticalmode intensity at the Through and Drop ports respectively.

Notice the fourth power of in (3), which means that, contraryto the idealized model, especially in the Drop the real resonatorhas a high sensitivity to coupling losses.

B. Modelling of the Straight Waveguide

The dispersions of the refractive indexes of silicon and silicahave been obtained at room temperature (20 C) by fitting thedata from [15]

(4)

(5)

which at m give and .

(2)

(3)

MASI et al.: TOWARDS A REALISTIC MODELLING OF ULTRA-COMPACT RACETRACK RESONATORS 3235

Fig. 2. Effective index variation versus wavelength in TE polarization for stripstraight waveguides of different width and core dimensions.

TABLE I� ��

The stripe waveguides have been modelled with a full vecto-rial finite difference (FVFD) mode solver which was developedat INL. For straight waveguides transparent boundaries condi-tions (TBC) were used. TBC implement a realistic boundary thatallows the wave to leave the computational region without nu-merical appreciable reflections. These properties make a FVFDwith TBC most appropriate for high refractive index contrastand a small core SOI rib-waveguides. For bend waveguides uni-axial perfectly matched layers (UPML) were used as absorbingboundary conditions. The mode solver developed at INL useseither cartesian or cylindrical coordinates.

Fig. 2 reports the effective indexes for waveguide width(wgw) of 400, 450 and 500 nm and for two core thicknesses of200 nm and 220 nm in TE polarization. Larger widths wouldlead to multimode guides. For m and 220 nmcore, already the second mode appears, but it is fortunatelyvery lossy. The effective mode dispersions can be fitted by apolynomial regression of the second order.

The polynomial coefficients, the width and the height of thecore of a stripe straight waveguides for a wavelength range be-tween 1250–1650 nm are reported in Table I.

C. Modelling of the Bend Waveguide

We used FVFD in cylindrical coordinates with UPMLboundary conditions to model curved waveguides. The electricand magnetic components are governed by wave equationsthat are a linear system of two differential equations wherethe r and z components of the electric and magnetic fields arecoupled [16]

(6)

(7)

where is the permeability, thevacuum wave number, the complex propagationconstant with the radiation loss parameter, and

(8)

the real part which gives the effective index for the bend.Since losses due to bending are negligible in high refractiveindex contrast bending with respect to scattering losses dueto roughnesses, we focus our attention on the real part of thepropagation constant. Note that in cylindrical coordinates thepropagation constant is dimensionless and proportional to ,and that it expresses also the azimutal mode number for aresonant mode of a ring resonatorat .

An open question is the value of the curvature radius ,i.e., in the equation is the outer, middle or inner radius of thewaveguide, or the position of maximal field intensity whichshould be used? The specific choice leads to contradicting re-sults because the radius determines not only different magni-tudes for the propagation constant, but also a different signaturein the change of the effective index be-tween the same bend and straight waveguide. Does bendingcause an increase or a decrease of the effective index? Wechoose the outer core radius as as in [17]. The shift of themode profile away from the center towards the edge of a bentwaveguide can be seen readily by conformal transformationwhere the constant index profile of a curved waveguide is trans-formed to an exponentially decreasing profile with increasingbend curvature of a leaky straight waveguide. A graphical ex-ample of this effect is shown in Fig. 3. Therefore, the light


Fig. 3. Magnetic field and zoom onto its shifted field center (�� m,� � � �m, � � �� m). The white straight line indicates the geometricalcenter of the waveguide, the cross the position of maximal optical field intensity.

traveling on a radius has a smaller optical path lengthdespite the larger physical path, due to a smaller effectiveindex for the bend than for the straight waveguide of similarcross-section. This implies

(9)

And in (9) equality must hold because we are considering themode with the same azimutal number (i.e.,

). Once (6) and (7) are solved the shift of the maximum op-tical field intensity from the waveguide center can be found, .This is then used to scale the propagation constant accordinglyto .

Fig. 4 shows some electric field maps for the componentof the fundamental mode for the almost straight ( m)and bend waveguides with different curvature radii of

m, m and m.The so-obtained values for the variation of the effective index

due to bending are shown in Fig. 5 for different radii, wave-guide widths and core thicknesses. For – m the fithas been truncated because the mode becomes radiative. The

m waveguide becomes radiative for a larger curva-ture radius than the m and m waveg-uides. In addition, the m waveguide is multimode.Therefore, in the following we have chosen a mwaveguide. For future reference Table II gives the parameters ofa fit to .

One can see that for bending radius larger than about mthe effect of the curvature is substantially negligible. For smallerradii , which corresponds to a resonance

Fig. 4. Mode profiles of the first mode ( field, �� m, � �� m, 220 nm core) for bend waveguides of different curvature radii (fromthe top to the bottom: � � �� m, � � �� m, � � � �m, � �� m).

wavelength shift in a micro-disk of up to a dozen nm, i.e., anentire free spectra range (FSR).


TABLE II�� ; (� � �� M)

Fig. 5. Effective index variations due to bending compared to the straightwaveguide.

Fig. 6. Optical microscope image of the test device used for the losses mea-surements of the curved waveguides (� � �� m).

D. Evaluating Bend Losses, Coupling Coefficients and PhaseMismatching

Bends and resonators were fabricated on SOI wafers by DUVlithography, within the WADIMOS project. [18] The test de-vices used for loss measurements of the curved waveguides arecomposed by 100 90 bends as shown in Fig. 6. An offset con-figuration has been tested where the width of the straight wave-guide varies between 0.38 to 0.5 and that of the curved oneaccording to its radius as given in Fig. 7, in order to evaluate theradiation and reflection effects on the losses of the bend. A se-lection of the bend losses measurements (TE-mode, m)versus the wavelength is shown in Fig. 8.

Fig. 7. Type of offsets used.

Fig. 8. Bend losses versus the wavelength for different widths of the straightwaveguide (bend wgw= m, � � � m, TE-mode).

The measurements, carried out at the INL laboratory, have anaccuracy of about 0.01 dB/90 . The 500 nm wide waveguide hasbeen used as reference with respect to the 450 nm wide wave-guide where the bends have offset. The offset is aimed to makenegligible the mode mismatch losses at the bends. Offset bendsin the 450 nm wide waveguide yields the smaller losses despitethe smaller waveguide width: about 0.024 dB/90 throughout allthe 1.5–1.6 m spectrum. Similar values have been found alsofor 0.5 m widths at m, but for larger wavelengths theloss increases up to 0.06 dB/90 at 1.61 m. This shows the rele-vance of the modal matching at the bends via waveguide offset.

The mode solver is then used to calculate the even and oddmodes of a system formed by two straight coupled waveguides(waveguide coupler) and its effective indexes. From this oneobtains the difference between the effective index and the meanof the even and odd modes in a straight waveguide for variouswavelengths and coupling spacings


Fig. 9. Difference between the effective index and the mean of the even and oddmodes in a straight waveguide for various coupling spacings (TE-polarization).

TABLE IIIEVEN-ODD MODE EFFECTIVE INDEX MISMATCH

Fig. 10. Coupling length spectral variation of twin waveguide couplers for dif-ferent spacing.

An illustration of such calculation is given in Fig. 9 for TE po-larization. The variation is very small but sufficient for allowinga shift of the resonant wavelength of several tenths of nm fora coupling length of 10 m. Table III furnishes the appropriatefitting parameters.

From the even and odd effective indexes, the couplinglength and coefficients can be calculated with (1). A compar-ison with experiments can be done by fitting the measuredthroughput signal out of a racetrack resonator. Knowingthe propagation constant, the losses involved, setting the

dB (see the next section) and consid-ering symmetric coupling , from (2) we have thecoupling coefficient and then, from (1), the coupling length

is finally obtained. A comparison between the modelledand experimental measured coupling lengths of a waveguidecoupler versus the wavelength for a spacing of 200 nm and220 nm is given in Fig. 10.

Despite a general agreement, we observe a tendency of themodel to overestimate the coupling length. This can be due toa difference between the nominal and the actual values of the

TABLE IVCOUPLING LENGTH COEFFICIENTS

waveguide width. Indeed the model results are extremely sen-sitive to the waveguide width. The coupling length dependenceon the wavelength can be approximated by a polynomial regres-sion of the second order. The coefficients of the regression aresummarized in Table IV.

III. SPECTRAL RESPONSE MODELLING OF THE

RACETRACK RESONATOR

By using all the parameterizations reported in the previoussections and tables, we can model the optical path in a racetrackresonator as

(10)

where and are the variation between the effectiveindex of the straight waveguide from the mean value of the oddand even modes in the two coupling regions of the racetracks(Fig. 1). There is no loss of generality if the optical path is ex-pressed as a weighted mean of the effective indexes as

with

and the resonators’s physical perimeter. Themean propagation constant is , and the still exactphase delay induced by the racetrack as a whole .

In the following we will work with these averaged quantitiesand represent them with the parametrization of the previous sec-tions. With the results of Table I, the group index becomes

(11)

which does not depend from parameter , while the group ve-locity dispersion (GVD) parameter D is

(12)

with the speed of light.Given the propagation constant at resonance

we can write

where the right-hand side is obtained as a first order Taylor seriesexpansion of at the -th resonance wavelength and is the


difference between the wavelengths of two resonances, i.e., theFSR. Since

(13)

where (11) has been applied, then the FSR is

(14)

(15)

Therefore, (14) is an implicit function in through (10).Table I and (12) show that the dispersion changes sign for the

200 nm versus 220 nm wide strip waveguide. Fine engineeringof the core thickness might be a mean to obtain a nearly zeroGVD waveguide, but this is usually not an easy task from thepractical point of view and SOI waveguides with small cores andhigh refractive index contrast may suffer of highly dispersiveeffects. Errors on the FSR depend both on the effective indexand the dispersion law as

(16)

In other words, in order to obtain reasonable evaluations ofthe FSR and resonant mode frequencies, one must match boththe effective index and the effective index dispersion, especiallywhen dispersive effects become consistent.

In order to assess the mode solver’s accuracy we obtained thenecessary parameters experimentally measuring the response ofa set of racetrack resonators. In particular, to establish from themeasurement data the dispersion law of Table I we proceededas follows. First we took two resonant modes and andmeasured the FSR between and .Trough (11) and (14) a system of two equations and two un-knowns follows:

(17)

which yields the experimental values of parameters and to becompared with those of Table I. Then, in order to obtain the thirdparameter, one measures a resonant mode at some other wave-length , inserts and into the optical path of (15) through(10) and solves for

(18)

Here and are still obtained by the parametersof Tables II and IV, but the relative error on these can be con-sidered negligible compared to that on the effective index of thestraight waveguide. The last free parameter left is the resonant

Fig. 11. The racetrack’s measured spectrum.

Fig. 12. The racetrack’s spectrum obtained from the experimentally deduceddisersion law.

mode number , which can be only an integer number and isfound by matching the effective index dispersions obtained bythe experimental values and by the and values re-ported in Table I. It is assumed that it is the integer which bestmatches the theoretical curve of Table I through 18. An assump-tion that can be verified by comparing the spectral response as-sociated to the so obtained dispersion law. And from this the ac-curacy of the mode solver effective index functions versus theexperimental curve can be assessed.

Fig. 11 shows an example of a measured through and dropport signals of a racetrack resonator with m,

m, m, m, and nm.Fig. 12 shows the analytical spectrum calculated from the exper-imentally obtained dispersion law (we obtain:

m m ). We note that the exper-imental effective index function applied to the analytical modelreproduces the racetrack spectrum.

It must be noted that, while the precise knowledge of dis-persion law determines the FSR and the mode resonance fre-quencies, it still does not determine the extinction rates of theThrough and Drop ports, which depend also on the couplingloss. The latter is a quite difficult parameter to be directly mea-sured. In principle it could be inferred from (2) and (3) by mea-suring the slight shift it produces in the maximal transmissionof the Drop signal. In practice this implies a precise normal-ization of the drop signal intensity which is usually affected by


Fig. 13. Racetrack’s spectrum obtained from the mode solver parameters.

unbalance in the Y-splitter or MMI-component used (Fig. 6) In-terestingly however, once the dispersion law is obtained withthe above procedure, the fine tuning of the coupling loss param-eter in the analytical model to reproduce also the experimentallymeasured extinctions, can nevertheless furnish a first estimate.For the specific case here reported we obtain a coupling loss of

dB.Fig. 13 shows the spectrum obtained from the parameters fur-

nished by the mode solver ( mm ). The difference is not negligible, a cer-

tain discrepancy is visible, especially in the FSR which results3 nm smaller than the observed one. On one side this showshow the exact determination of the mode resonances and itsFSR is very sensitive to the evaluation of the precise dispersionlaw. The dispersion law should be determined with a precisionbetter than 1% which is out of reach of the presently availablemode solver softwares. On the other side, Fig. 14 shows that thedifference between the experimentally deduced effective indexlaw and that predicted by computational means alone are quitesimilar and differ in the 1.5–1.6 m in the worst case only by2%. We consider this a fairly good accuracy. We compared ourFVFD mode solver with others (see [19]) and obtained the sameresults when averaging the refractive index at the boundaries ofthe waveguide in order to overcome the strong discontinuity ofthe first derivative of the permittivity at the boundaries. The onlydifference with the other methods is that it is possible to performthe modelling without averaging of the refractive index (the fi-nite difference scheme is applied to the first derivative of thepermittivity times the field, as describe in (6) and (7)), while thedispersion law of the materials is included in the calculation. Itis much more complicate with the 3-D FDTD (besides requiringmuch more computing power). Also with finite element methodmode solvers it is not possible to perform the modelling withoutaveraging. The difference must also be searched in the fabrica-tion tolerances. Especially geometrical properties like small de-viations from the nominal waveguide widths, unperfect sidewallsurface verticality of the waveguides can induce unpredictableeffective index variations which make the precise FSR and res-onant mode wavelength control still a difficult task.

Finally, we would like to illustrate how it is possible to ob-tain experimentally the coupling factors and the total loss of theracetrack only by measuring the contrasts of the Through and

Fig. 14. Effective index difference between the experimental and mode solvermodel.

Drop signals. From (2) and (3) the maximum and minimum ofthe Through and Drop functions are

(19)

(20)

If we assume symmetric coupling, the coupling factor and lossesare equal, i.e., and . Then we candefine the contrast on the Drop signal as

(21)

Inversion of (21) gives

(22)

Proceeding in the same manner with the contrast on theThrough signal and using (21), one obtains

(23)

which implies that

(24)

with a parameter which expresses in pure terms of signalcontrasts the total loss given by the sum of the coupling andradiation losses. And from (22) and (24) the contrasts furnishalso the information on the coupling coefficients as

(25)

To compare the effectiveness of this method to the mode solvingapproach we measured the contrasts of the Through and Drop in


TABLE VTHROUGH COUPLING COEFFICIENTS OBTAINED FROM MODE CONTRASTS

the spectral response of Fig. 11 and obtained the values reportedin Table V.

Within an error of few percent (the fluctuation associ-ated with the measurement error on the contrasts caused byFabry–Perot noise and other uncertainties) there is a substantialagreement between the two methods. This approach whichdetermines quantitatively the coupling coefficients from theextremal values of the resonant modes by applying (22), (24)and (25) is simple and has better physical foundations thanmere parameter adjustments which fit the simulated versus realspectrum, and can be useful as an experimental validation ofmode solving and 3D-FDTD simulations.

IV. CONCLUSION

We analyzed a set of crucial optical and physical propertiesof racetrack resonators and their constituent waveguides. As-sisted by a self developed FVFD mode solver with TBC orUPML boundaries we modelled the straight and curved waveg-uides, the bend losses, the coupling coefficients and, consideringalso small effects like phase mismatch, suggested that bendswith 2–3 m radius with single-mode waveguides of 0.45 mwidths are a good compromise between the reduction of the ra-diation losses in the bend and small footprint of the racetrackresonator. Moreover, through experimental characterization ofactual devices we could compare the quality of our model andestablish accuracies of about 1–2% in the effective index model-ling. And yet this is still not enough to determine optical prop-erties like the FSR and the precise determination of resonantmode wavelengths with a nm precision. We concluded that, atthe present, discrepancies should be ascribed to fabrication tol-erances than to inadequacies of the theoretical models. Finallywe showed that it is possible to determine the coupling coeffi-cients by measuring the spectral contrasts of a resonator. Otheroptimizations can of course be pursued (e.g., the modelling ofthe coupling loss, of the roughness losses or of the asymmetriccoupling [20]). However, we believe that the present paper sum-marize and outlines the main aspects necessary to pave the wayto further understanding, control and realization of ultra-com-pact photonic devices based small resonators.

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Marco Masi was born in April 1965 in Milan, Italy. He received the M.S. degreein astrophysics at the university of Padua, Italy. After authoring several articlesin astronomy, statistical mechanics and mathematical physics he is currentlypursuing the Ph.D. degree at the Nanoscience Laboratory of the University ofTrento, Italy.

His present interests focus on silicon photonics, in particular on the design,modeling and fabrication of photonic integrated circuits of micro-resonant struc-tures, its applications to WDM and interconnect technologies, and possible otherareas of physics.

Regis Orobtchouk received the Ph.D. from the University of Paris XI, France,in 1996.

In 1998, he joined the INL (Institut des Nanotechnologies de Lyon) Labora-tory, INSA de Lyon, as an Assistant Professor. He is the author and coauthor 23papers in international journals, 1 book contribution 5 patents and 56 interna-tional conferences. His major interest is focused on silicon based photonics foroptical interconnect and telecommunication applications. A part of his work isalso related to the fabrication of periodic nanostructure by holographic method.


Guofang Fan was born in Jiangxi, China, in 1978. He received the M.S. degreein optics from Tianjin University, China, in 2001 and the Ph.D. degree in opto-electronics from Tianjin University, China in 2007.

From 2007 to 2008, he worked as a Postdoc researcher at Paul-Drude-Institutfür Festkoerperlektronik, Germany, where he worked on the silicon-on-insu-lator wavguide structrues modulated by surface acoustic waves. From 2008, heworked in silicon photonics as a Postdoc Researcher at the Institut des Nan-otechnologies de Lyon, CNRS, France. His research interests include siliconphotonics, optical resonators, and guided acusto-optical devices.

Jean-Marc Fedeli received the electronics engineer diploma from INPGGrenoble, France, in 1978.

Then he conducted researches at the CEA-LETI on various magnetic mem-ories and magnetic components as project leader, group leader, and programmanager. For two years, he acted as Advanced Program Director in Memscapcompany for the development of RF-MEMS, then he returned to CEA-LETIin 2002 as coordinator of silicon photonic projects. Under a large partnershipwith universities and research laboratories, he works on various technologicalaspects on Photonics on CMOS (Si rib and stripe waveguides, Si3N4 and a-Siwaveguides), Si modulators, Ge photodetectors, SiOx material, InP sources onSi. His main focus is on the integration of a photonic layer at the metallizationlevel of an electronic circuit. He has been participating on different EuropeanFP6 projects (PICMOS, PHOLOGIC, MNTE, ePIXnet). Under the EuropeanFP7, he is involved in the WADIMOS and PhotonFAB (ePIXfab) projects andmanaging the HELIOS project.

Lorenzo Pavesi was born November 21, 1961. He received the Ph.D. degree inphysics in 1990 at the Ecole Polytechnique Federale of Lausanne, Switzerland.

He is Professor of Experimental Physics at the University of Trent, Italy. In1990 he became Assistant Professor, an Associate Professor in 1999 and FullProfessor in 2002 at the University of Trento. He leads the Nanoscience Labora-tory (25 people), teaches several classes at the Science Faculty of the Universityof Trento, and is dean of the Ph.D. School in Physics. He founded the researchactivity in semiconductor optoelectronics at the University of Trento. Duringthe last years, he concentrated on Silicon based photonics where he looks forthe convergence between photonics and electronics by using silicon nanostruc-tures. He is interested in active photonics devices which can be integrated insilicon by using classical waveguides or novel waveguides such as those basedon dynamical photonic crystals. His interests encompass also optical sensors orbiosensors and solar cells. In silicon photonics, he is one of the worldwide rec-ognized experts, he organized several international conferences, workshops andschools and is a frequently invited speaker. He is an author or coauthor of morethan 280 papers, author of several reviews, editor of more than 10 books, authorof 2 books and holds six patents. He holds an H-number of 36 according to theweb of science.

Dr. Pavesi is a distinguished speaker of the IEEE Photonics society for2010–2011. He is the president and founder of the IEEE Italian chapter onNanotechnology.

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Towards a Realistic Modelling of Ultra-Compact Racetrack Resonators

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