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1924 J. Opt. Soc. Am. B/Vol. 26, No. 10 /October 2009 Binfeng et al.

Characteristics analysis of a hybrid surfaceplasmonic waveguide with nanometricconfinement and high optical intensity

Yun Binfeng, Hu Guohua, Ji Yang, and Cui Yiping*

Advanced Photonics Center, Southeast University, Nanjing 210096, China*Corresponding author: cyp@seu.edu.cn

Received April 6, 2009; revised July 26, 2009; accepted August 31, 2009;posted September 1, 2009 (Doc. ID 109696); published September 16, 2009

A hybrid surface plasmonic waveguide with nanometric confinement is proposed. With interactions betweenhigh-index-contrast dielectric waveguide modes and surface plasmon modes of a very thin metal film, nano-metric hybrid surface plasmon modes with high optical intensities can be formed. Characteristics of the sym-metric and asymmetric hybrid surface plasmon modes, including the effective mode indices, propagationlengths, mode sizes, and power intensities at telecom wavelength (1550 nm), are investigated in detail. Simu-lation results show that nanometric mode confinement and a long propagation length can be realized simul-taneously. The high optical power intensity and long propagation length of the nanometric hybrid surface plas-mon modes are very promising for high-density photonic integration and nonlinear waveguide applications.© 2009 Optical Society of America

OCIS codes: 130.0130, 130.2790, 130.3120.

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. INTRODUCTIONurface plasmon polaritons (SPPs) are electromagneticaves coherently coupled to electron oscillations; theyropagate at the interface between a dielectric and a con-uctor and are evanescently confined in the perpendicularirection [1]. Recently, surface plasmonic waveguidesave received considerable attention for their ability to si-ultaneously guide and control light [2]. A variety of sur-

ace plasmonic waveguide structures, such as metal stripeaveguides [3–5], channel plasmon polariton (CPP)aveguides [6–11], metal wedge plasmon polariton (WPP)aveguides [12,13], and dielectric-loaded surface plasmonolariton (DLSPP) waveguides [14–16], have been demon-trated.

It is well known that the optical mode size in a tradi-ional dielectric waveguide suffers from the diffractionimit, which is about half of the wavelength. With the de-elopment of integrated circuits, integrated optical com-onents with much more compact sizes than those of tra-itional dielectric waveguides are badly needed atelecom wavelength (1550 nm). The optical waveguideased on SPP is one kind of promising solution. Due to theurface bounding characteristics of the SPP wave, thePP waveguides have the ability to confine light to sizeshat are much smaller than the diffraction limit. Al-hough lots of SPP waveguide structures have been pro-osed, not all of them can realize the nanometric modeizes. The metal stripe SPP waveguides can support longange surface plasmon polariton (LRSPP) modes withwo-dimensional confinements and very low propagationosses, but their mode sizes are a few micrometers, whichs unsuitable for high photonic integration [4,5]. Also,arious types of CPP geometry have been investigatedheoretically and experimentally, including metal grooves

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6,7], metal gaps [8,9], and meal holes [10,11]. Generally,he losses of these CPP waveguides are high because ma-or optic fields reside in the metal. The optimized metalroove waveguide were realized with a well-confinedode size of about 1.1 µm and a propagation length of

bout 100 µm [7]; the WPP waveguide can support auch more compact SPP mode about a few tens of nanom-

ters, but the propagation length is on the order of a fewicrometers. The DLSPP waveguide can realize sub-avelength confinement (about 915 nm) and moderateropagation length (a few tens of micrometers) [14]. Weave proposed a symmetric DLSPP waveguide composedf two identical dielectric waveguides located on the twoides of a thin metal film [17], whereas the DLSPP wave-uide is realized by locating one dielectric waveguide on ahick metal film. Because of the symmetric structure ofhe symmetric DLSPP waveguide, the LRSPP mode with

much longer propagation length and only a bit largerode area than that of DLSPP waveguide can be realized.ll of the above SPP waveguide structures show that thePP confinement is achieved primarily by decreasing thePP field into the dielectric, thereby increasing the SPPower absorbed by metal. So there is a trade-off betweenPP loss and SPP mode confinement. Recently, a hybridPP gap waveguide with nanometric confinement and aelative long propagation length was proposed [18]. Theybrid SPP mode supported by the structure is formed byoupling between the dielectric mode and the surfacelasmon wave, which is at the dielectric/metal interface.n the hybrid SPP waveguide, optical loss is relativelyarge, because the optical field is penetrated into the lossy

etal film. In this article, a hybrid SPP waveguide withery thin metal film is presented. Along with the LRSPPode (with much lower loss) interacting with the dielec-

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ric mode, the hybrid SPP modes with nanometric con-nements and long propagation lengths are analyzed inetail by the finite element method (FEM).In the following, we focus on the hybrid modes formed

y the fundamental dielectric waveguide mode and theoupled SPP modes at telecom wavelength (1550 nm), bute note that higher-order hybrid modes might also exist,epending on the dimensions of the dielectric waveguide.

. MODE CHARACTERISTICS OF THEYBRID SURFACE PLASMONICAVEGUIDE

. Hybrid SPP Waveguide Geometryschematic of the hybrid surface plasmonic waveguide

tructure proposed by us is presented in Fig. 1. Two iden-ical square dielectric waveguides are located separatelyt each side of a thin metal film with a gap distance of h.he refractive indices of dielectric core, cladding, andetal are nH, nL, and nm, respectively. The metal film

hickness is d, and the size of the dielectric waveguideore is w. Also the coordinate axis is given where x, y, andare the transverse, lateral, and propagation direction,

espectively. It is well known that the symmetric SPPode (LRSPP) and asymmetric SPP mode exist when a

ery thin metal film is embedded in the dielectric media3]. The LRSPP mode has been widely used as a low-lossptical waveguide mode [4,5], because the optical field inhe lossy metal region is reduced by the coupling of thePP wave on the two sides of the metal/dielectric inter-

ace. But the optical fields outward the two interfaces ex-end much deeper into the dielectric regions in compari-on with the SPP mode on the single metal/dielectricnterface. So the low loss brings the large mode size (a few

icrometers typically), which is not suitable for high-ensity integration. Recently, Almeida et al. show that aigh optical energy density can be formed in a low-indexap between two high-index dielectric waveguides [19].his is because the electric field must undergo a large dis-ontinuity with much higher amplitude in the low-indexegion for a high-index-contrast interface. In the simula-ion results presented hereafter, an excitation wavelengthf � � 1550 nm, the GaAs core with refractive index ofH=3.5, the SiO2 cladding with refractive index of nL1.5, and the Ag (with a permittivity of �m=−129+3.3i)

ig. 1. (Color online) Cross-sectional view of the hybrid surfacelasmonic waveguide.

lm thickness of d=20 mm are used when simulating theharacteristics of the hybrid SPP modes unless noted oth-rwise [18].

. Metal Thicknessecause the thickness of the metal film has a great effectn the LRSPP mode loss, the effective mode indices andhe propagation lengths with different metal film thick-ess d are analyzed. For comparison, the traditional

nsulator/metal/insulator (IMI) SPP waveguide structuresith insulator’s indices of nI=3.5 and nI=1.5, which cor-

espond to the nH and nL of the hybrid SPP waveguide,re analyzed too. Here the dielectric core size and gap sizere w=200 nm and h=5 nm, respectively. As shown inig. 2, both the real parts of effective mode indices andhe propagation lengths share the same trends as the IMIPP structures when the metal films’ thickness are var-

ed. The propagation length is related to the imaginaryart of effective mode index �Im�neff�� according to the Eq.1) [14]:

Lprop = �/�4� · Im�neff��. �1�

ig. 2. (Color online) (a) Real parts of effective mode indicesRe�neff�� of the hybrid SPP waveguide and the IMI waveguide.b) Propagation lengths of the hybrid SPP waveguide and theMI structure.

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1926 J. Opt. Soc. Am. B/Vol. 26, No. 10 /October 2009 Binfeng et al.

So with the specially designed hybrid waveguide pa-ameters (w=200 nm, h=5 nm), the hybrid SPP mode isery similar to a SPP mode. However, as the hybrid SPPaveguide mode is actually a hybrid of the dielectricode and the SPP mode, it can also transform to a

ielectric-like waveguide mode by varying the dielectricore size and gap size. As shown in Figs. 3(a)–3(d), by in-reasing the dielectric core sizes and gap sizes, the hybridPP modes are changing from SPP-like modes toielectric-like modes.

. Hybridization of the SPP Mode and the Dielectricode

n order to explain the hybridization principle of the hy-rid SPP waveguide, the real parts of the effective indicesRe�neff�� of the hybrid SPP waveguides with different di-lectric core size w and gap size h are analyzed and theesults are shown in Fig. 4. The top and bottom dashedines are the Re�neff� of the IMI SPP waveguides with nI3.5 and nI=1.5, respectively. In Figs. 4(a) and 4(b), theffective mode indices of the pure dielectric waveguidesith different sizes are also plotted for comparison. It is

lear that all the Re�neff� of the hybrid SPP modes areigher than the effective mode indices of the dielectricaveguide modes, because the SPP modes are coupledith them. It is also reasonable that the Re�neff� of the hy-rid SPP modes are approaching those of the IMI SPPaveguides �nI=1.5� and of the pure dielectricaveguides when the sizes of the dielectric waveguidesre decreasing or increasing, respectively. And with theecreasing of the gap size h, the differences between theybrid SPP modes and the pure dielectric waveguideodes are increased, because the SPP modes can interactith the dielectric modes more effectively.In order to demonstrate the hybridization characteris-

ics of the hybrid SPP modes, a parameter �a+�w ,h��2,hich represents the characters of the hybrid mode basedn the couple mode theory is introduced [18]:

ig. 3. Optical power density of the symmetric hybrid SPPodes with different dielectric size w and gap size h (with metal

lm thickness of d=20 nm). All the units of the axis in the figurere �10−7 m. (a) w=200 nm, h=5 nm (b) w=300 nm, h=20 nmc) w=400 nm, h=50 nm (d) w=600 nm, h=100 nm.

�a+�w,h��2 =nhyb�w,h� − nIMI

�nhyb�w,h� − nd�w�� + �nhyb�w,h� − nIMI�,

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here the nhyb�w ,h�,nIMI are the real parts of the effectiveode indices of the hybrid SPP mode and IMI SPP mode

nI=1.5�, respectively. And nd is the effective mode indexf the pure dielectric waveguide mode. The �a+�w ,h��2 is aeasure of the character of the hybrid SPP mode. The hy-

rid SPP mode is quite like the SPP mode whena+�w ,h��2�0.5, and it is much like the dielectric wave-uide mode when �a+�w ,h��2�0.5. The condition of

a+�w ,h��2=0.5 is the critical coupling point. From Eq. (2),t is clear that the critical coupling occurs only when theondition of nIMI=nd is satisfied, which is the critical cou-ling condition of the mode coupling theory. The modeharacter parameters �a+�w ,h��2 of the hybrid SPP modesith different dielectric core size w and gap size h are alsolotted in Fig. 4(c) and Fig. 4(d). According to Fig. 4, therere three conclusions that can be made. First, the differ-nces between the hybrid SPP modes and the pure dielec-ric waveguides are increasing when the gap sizes are re-uced; it is reasonable because the SPP modes cannteract with the pure dielectric waveguide modes moreffectively with smaller gaps between them. Second, allhe curves of �a+�w ,h��2 with different gap sizes intersectust at the point of �a+�w ,h��2=0.5, where the critical cou-ling occurs. Third, the dielectric core size (about w170 nm), which corresponds to the critical coupling of

he symmetric hybrid SPP mode is smaller than that ofhe asymmetric hybrid SPP mode (about w=220 nm).his is because, in order to satisfy the critical couplingondition �nIMI=nd�, the dielectric core size for the asym-etric hybrid SPP mode must be larger than that of the

ymmetric hybrid SPP mode to realize a larger nd, whichan cope with the larger nIMI of the asymmetric IMI SPPode.

. Confinement and Losshe two most important parameters of SPP waveguidesre mode confinement and loss. Because the metal filmsnd high-index contrast dielectric waveguides are at theop and bottom interfaces of the hybrid SPP waveguides,here must be great discontinuity of the optical fields atoth interfaces. The symmetric hybrid SPP mode, whichhould be termed as the hybrid long-range surface plas-on polariton (HLRSPP) mode, can be formed in the gap

egion [as shown in Fig. 1] for these two reasons: First,ith the symmetric dielectric waveguide structures onach side of a thin metal film, the familiar low-loss LR-PP mode can be introduced into the gap region; second,he very extended optical field of the LRSPP mode isblocked” by the high-index-contrast dielectric top inter-ace of the gap region. This is because, for a high-index-ontrast interface, the electric field must undergo a largeiscontinuity with much higher amplitude in the low-ndex side in order to satisfy the continuity of the normalomponent of the electric flux density, which is an inter-ace condition of Maxwell’s equations [19]. Here, the highnd low indices at the top interface of the gap region are

=3.5 and n =1.5, respectively. With this physical real-

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Binfeng et al. Vol. 26, No. 10 /October 2009 /J. Opt. Soc. Am. B 1927

zable high-index contrast, the optical power at the low-ndex side is almost 30 times that of the high-index side.o with the proposed hybrid SPP waveguide structure,he HLRSPP with both very good confinement and rela-ively low loss can be realized.

In order to examine the confinement capabilities andoss properties of the hybrid SPP waveguides, we analyzend show in Fig. 5 the normalized powers, intensities inhe gap regions, the normalized mode areas �Am /A0�, andhe Im�neff� of the hybrid SPP modes with different dielec-ric core size w and gap size h. The mode area Am and theiffraction-limited area A0=�2 /4 are defined the same asn [18]. The optical power Pgap and the average optical in-ensity Igap=Pgap/ �wh� inside the gap region as functionsf dielectric core size w and gap size h are shown in Figs.(a)–5(d). Both Pgap and Igap are normalized with respecto the total waveguide power. The results show that therere obvious peaks both for Pgap and Igap, which are com-letely different from that of the pure dielectric gap wave-uide [19]. A much higher normalized optical intensity inhe gap region can be realized in comparison with theure dielectric gap waveguide, because the SPP modeith good surface bounding capability is introduced. Also,

ig. 4. (Color online) Real parts of effective indices and the moielectric core size w and gap size h. (a, c) Symmetric SPP hybri

n order to study the losses of the hybrid SPP modes, themaginary parts of the effective mode indices �Im�neff�� ofhe hybrid SPP modes are analyzed and shown in Figs.(e) and 5(f). Three obvious phenomena are observed:irst, all Im�neff� of the hybrid SPP modes (symmetric andsymmetric) have maxima with dielectric core sizes al-ost the same as those where the maximum optical in-

ensities occur. It is very reasonable because the high op-ical intensity, which interacts with the metal, results inigh loss. Second, the maximum of Im�neff� is increasedhen the gap size is reduced. This is also very reasonableecause the normalized optical intensity is increased dueo the reduction of the gap size, which is obvious as shownn Figs. 5(c) and 5(d). Third, with the same dielectric coreize and gap size, both the normalized optical power andptical intensity of the asymmetric SPP mode are largerhan those of the symmetric SPP mode. In order to de-cribe the mode confinements relative to diffraction limit,he normalized mode areas of the hybrid modes are plot-ed in Fig. 5(g). From Fig. 5(g), the minimum normalizedode areas of the symmetric (at w=200 nm) and asym-etric SPP modes (at w=150 nm) are 0.0207 and 0.0103,

espectively. This means that the mode sizes about 1/50

racter parameters of the hybrid SPP waveguides with differentes. (b, d) Asymmetric hybrid SPP modes.

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1928 J. Opt. Soc. Am. B/Vol. 26, No. 10 /October 2009 Binfeng et al.

nd 1/100 of the diffraction limit can be achieved by theymmetric and asymmetric SPP modes. Also the asym-etric SPP mode has better confinement and higher loss

han those of the symmetric one, which are just like thosef the pure IMI SPP waveguide.

ig. 5. (Color online) Normalized powers, intensities, normalizeetric hybrid SPP modes. (b, d, f) Asymmetric hybrid SPP modePP modes (d=20 nm, h=5 nm).

Finally, for the gap size of h=5 nm, the symmetric andsymmetric hybrid SPP modes with the largest normal-zed optical intensities are shown in Figs. 6(a) and 6(b).he corresponding dielectric core sizes are w=200 nmnd w=150 nm for the symmetric and asymmetric hybrid

e areas and the Im�neff� of the hybrid SPP modes. (a, c, e) Sym-ormalized mode areas of the symmetric and asymmetric hybrid

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PP mode, respectively, and the normalized optical inten-ities are about 130 �m−2 and 250 �m−2, respectively,hich are much higher than the 9 �m−2 of the optimizedielectric silicon-on-insulator (SOI) waveguide with 360m � 200 nm cross section. They also are higher thanhat of the pure dielectric waveguide gap [19]. As shownn Figs. 5(e) and 5(f), with these geometry parameters themaginary parts of the symmetric and asymmetric hybridPP modes are about 0.00041 and 0.0238, which give theropagation lengths of 301 µm and 5.19 µm, respectively.rom Fig. 5(g), the corresponding normalized mode areasre 0.0207 (about �2 /200) and 0.0103 (about �2 /400). Theode areas of the proposed hybrid SPP waveguide are

omparable to those in [18], and at optimized mode areaondition, the propagation length of the symmetric hybridPP mode is longer than the 40 � 150 µm in [18],hereas the propagation length of the asymmetric hybridPP mode is shorter than that in [18]. In comparison withhe DLSPP waveguide (mode size about 915 nm andropagation length about a few micrometers), a muchmaller (far beyond the diffraction limit) mode area and aonger propagation length can be obtained by the sym-

etric hybrid SPP mode. The mode areas of the proposedybrid SPP waveguide are also much smaller than thosef the LRSPP waveguides (about a few micrometers), buthe LRSPP waveguides have much longer propagationengths (a few millimeters). Also, in comparison with thether SPP waveguides (such as the CPP and WPP), auch smaller nanometric mode area (far beyond the dif-

raction limit) can be realized by the proposed hybrid SPPaveguide with only a little loss cost. It can be concluded

hat nanometric mode confinement and relatively largeropagation length can be realized simultaneously by theymmetric hybrid SPP mode, and by decreasing the gapize the hybrid SPP mode can be much more compressedn the gap region, and a higher normalized optical inten-ity can be achieved with a higher loss cost.

. CONCLUSIONn this paper, the detailed characteristics of the symmet-ic and asymmetric hybrid SPP modes with nanometricizes in the low-index gap region between the dielectricaveguide core and the thin metal film are analyzed. The

imulation results show that the hybrid SPP modes areormed by the interactions between the dielectric wave-

ig. 6. (a) Optical power density of the symmetric mode of theybrid SPP waveguide (w=200 nm, h=5 nm). (b) Optical powerensity of the asymmetric mode of the hybrid SPP waveguidew=150 nm, h=5 nm). All the units of the axis in the figure are10−7 m.

uide modes and the SPP modes supported by the thin

etal film. By altering the dielectric waveguide core sizesnd the gap sizes, the hybrid SPP modes can be trans-ormed from the SPP-like modes to the dielectric-likeodes. And by optimizing the waveguide geometry pa-

ameters, a long-range hybrid SPP mode with a nanomet-ic size and a high normalized optical intensity can be re-lized.

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