Optics Communications 285 (2012) 5122–5127

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Optics Communications

0030-40

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journal homepage: www.elsevier.com/locate/optcom

Plasmonic Bragg reflectors based on metal-embedded MIM structure

Ming Tian a, Ping Lu a,n, Li Chen a, Deming Liu a, Nasser Peyghambarian b

a Wuhan National Laboratory for Optoelectronics, School of Optoelectronic Science and Engineering, National Engineering Laboratory for Next Generation Internet Access System,

Huazhong University of Science and Technology, Wuhan, Hubei 430074, Chinab College of Optical Sciences, The University of Arizona, Tucson, Arizona 85721, USA

a r t i c l e i n f o

Article history:

Received 19 April 2012

Received in revised form

25 July 2012

Accepted 26 July 2012Available online 9 August 2012

Keywords:

Plasmonics

Surface plasmons

Guided waves

Bragg reflectors

18/$ - see front matter & 2012 Elsevier B.V. A

x.doi.org/10.1016/j.optcom.2012.07.072

esponding author.

ail addresses: pluriver@163.com, pluriver@ma

a b s t r a c t

We propose and investigate a metalembedded metal–insulator–metal (MIM) structure plasmonic Bragg

reflector (PBR) using the finite-difference time-domain (FDTD) method with PMLs (perfectly matched

layers) boundary conditions. It improves the performance of conventional step profile MIM PBRs to

some extent. Our numerical study reveals that the metal-embedded PBRs exhibit lower insertion loss,

narrower bandgap, and reduced rippling in the transmission spectrum when compared with the step

PBRs at the same normalized index contrast and transmission levels. The defect mode of the metal-

embedded PBRs also exhibits higher transmission. To suppress the sidelobes in the transmission

spectrum, we further smooth the end of the embedded metal, which demonstrates a better

performance. Then, we find with respect to the Bragg wavelength, the longer wavelengths have a

tendency to spread in the wider regions of the insulator layer; however, the shorter wavelengths have a

tendency to spread in the embedded metal regions. The apodized PBRs with the embedded metal

length decreasing (increasing) efficaciously suppress the ripples at the right (left) band edges. Then, we

use the impedance theoretical model to explain this phenomenon. Finally, we realize a flat-top

transmission band filter by connecting two apodized PBRs, and the band and center wavelength can be

adjusted.

& 2012 Elsevier B.V. All rights reserved.

1. Introduction

Surface plasmons polaritons (SPPs) have been considered asenergy and information carriers to significantly overcome theclassical diffraction limit for their ability of confining and propa-gating the electromagnetic energy in a subwavelength limit [1,2].This could lead to miniaturized photonic circuits with lengthscales much smaller than those currently achieved [3]. Waveguidesconsisting of an insulator sandwiched between two metals to serveas MIM supports propagating surface plasmon modes that arestrongly confined in the insulator region with an acceptablepropagation length. Several MIM waveguides based on SPPs, forexample, bends and splitters, Mach–Zehnder interferometers,couplers and resonator have been designed theoretically anddemonstrated experimentally [4–9]. Meanwhile, there also havebeen many efforts in examining the PBR on the MIM waveguides[10–21].

Since the insulator width modulation results in higher reflec-tion within the PBR bandgap than the refractive index-modulatedschemes, it is preferred for PBR applications [20]. A unit cell of atypical MIM-based step PBR is shown in Fig. 1(b), and the

ll rights reserved.

il.hust.edu.cn (P. Lu).

effective index of a MIM section can be modified by changingthe insulator layer’s width. For an efficient PBR, the concatenatedMIM structure must exhibit not only high reflection within thebandgap but also high transmission outside the bandgap, and isalso expected to exhibit well-defined band edges, and beyond theedges, flat transmission spectra with minimal ripples. Owing tothe abrupt change in index of refraction between the wider andnarrower regions of the insulator layer, the modes in the differentinsulator layer’s widths are mismatched, which induces high lossfor propagating of SPPs regardless of their wavelengths anddecreases the transmission level outside the bandgap [16]. Thewidth of the stop-band is approximated to be [21]

Dog ¼oc4

p sin�1 neff2�neff1

neff2þneff1ð1Þ

where oc is the central frequency of the stop-band. From Eq. (1) itcan be inferred that the width of the stop-band is dependent onthe difference between the two mode indices and hence a largerstop-band width is observed for an acute change of width. But theabrupt change of width also excites higher order modes whoseinterference causes ripples in the transmission spectrum, result-ing in severely obscuring the band edges, widening the bandgap,and leading to an increase in the insertion loss. However, anarrow bandwidth is advantageous for plasmonic applicationsrequiring spectral sensitivity [15].

M. Tian et al. / Optics Communications 285 (2012) 5122–5127 5123

In this work, we first propose a metal-embedded MIM struc-ture PBR design to improve the performance associated withconventional step PBRs. A unit cell of the metal-embedded PBR isshown in Fig. 1(c). In Section 2, we present the metal-embeddedPBR, which can be realized in a two-dimensional (2D) plasmonpolaritons metal using a FDTD method with perfectly matchedlayers boundary conditions. In Section 3, we discuss the width ofbandgap, the transmission characteristics outside the bandgapand mode propagation patterns of the metal-embedded PBR, andthen compare with step PBR. In order to decrease the rippleseffect, we smooth each end of the embedded metal. Then, weconstruct a cavity by introducing a defect into the PBR. In Section4, we realize a flat-top transmission band filter by connecting twoapodized metal-embedded PBRs. Last, the results show that themetal-embedded profile has potential to ease fabrication and canmitigate the problems caused by the abrupt change of width.

2. Model and computational details

Fig. 1 shows a schematic diagram of the plasmonic2D-structure and the device parameters, defined in Fig. 1, arechosen mainly to facilitate the comparison between the step andmetal-embedded PBRs. The dielectric in the metal slit is air withrefractive index n¼1. The metal is chosen to be silver, whosefrequency-dependent relative permittivity is characterized by theDrude model [22]

emðoÞ ¼ e1�o2

p

o2þ iogð2Þ

here eN is the dielectric constant at infinite angular frequency, op

is the bulk plasma frequency, which represents the naturalfrequency of the oscillations of free conduction electrons, and grepresents the damping frequency of the oscillations. The valuesof these parameters can be set to be 3.7, 9.1 eV,and 0.018 eV,correspondingly. o is the angular frequency of the incident light.

We fix the slit width m¼150 nm and n¼50 nm and we can getthe effective refractive indices of two sections as Re(neff1)¼1.1391and Re(neff2)¼1.3742 at the telecom wavelength lb¼1.55 mm,respectively. According to the Bragg condition [21]

Reðneff1ÞL1þReðneff2ÞL2 ¼ lb=2 ð3Þ

Fig. 1. Schematic diagram of (a) a metal-embedded PBRs structure, an

where lb is the Bragg wavelength; we can realize Bragg scatteringby choosing the corresponding length as L1¼270 nm andL2¼340 nm. When (m,n)¼(150 nm,100 nm), we set L1¼280 nmand L2¼360 nm. For other slit widths, the length can be obtainedby a similar way [23,24]. The total length of the PBR unit cell is setto be L¼L1þL2 to match the Bragg wavelength. We utilize theFDTD method to investigate the transmission response of thisstructure. In the simulations, TM waves with magnetic fieldsoriented in the z-direction are used, the grid sizes are set to beDx¼Dy¼5 nm and the temporal step is Dt¼Dx/(2c), which arefound to be sufficient for the convergence of numerical results[25]. Here, c is the velocity of light in vacuum. Perfectly matchedlayers are used in the x and y directions.

3. Simulation results and discussion

To be fair and meaningful for the comparisons on the trans-mission characteristics, we should let the metal-embedded andstep PBRs’ transmission levels as close to each other as possible atthe Bragg wavelength l¼1.55 mm and the same for the normal-ized index contrast [15]. Fig. 2 shows calculated transmissionspectra of the step and metal-embedded PRBs consisting of 4 and12 periods of Bragg cells with (m,n)¼(150 nm,50 nm). The stepPRBs with (m,n)¼(150 nm,100 nm) have 8 periods of Bragg cells.So, their transmission values are 0.01523, 0.01681 and 0.01616 atthe telecom wavelength. The transmission levels come within0.17% difference; thus, we can think that their transmission levelsare equal.

First, we compare the step with metal-embedded PRBs of(m,n)¼(150 nm,50 nm). The 3 dB bandwidth of the metal-embedded PBRs bandgap is 291 nm which is 75.7% narrowerthan the 1197 nm bandwidth of the step PBRs. In order to betterillustrate the profile of the ripples beyond the band edges, weintroduce the ripple factor [26]

R¼ ðImax�IminÞ=ðImaxþ IminÞ ð4Þ

where Imax is the maximum transmission and Imin is the minimumtransmission outside the bandgap. In the case of the metal-embedded PBRs, ripple factor beyond the band edges is 0.1645which is 55.3% smaller than 0.3679 of the step PBRs. Fig. 2 showsthe reduction in rippling in the transmission spectrum leading tohighly enhanced transmission levels outside the bandgap.

d the unit cells of (b) a step PBR and (c) a metal-embedded PBR.

M. Tian et al. / Optics Communications 285 (2012) 5122–51275124

Two nice features contribute to the decrease in the insertion lossof the metal-embedded PBRs. Outside the bandgap, even after 12periods, the metal-embedded PBRs retain 480% of the originalinput power except for the one close to the band edge.

From the numerical simulations of the PBRs, we obtain thesnapshots of the propagating mode’s field patterns and plot themin Fig. 3. The operation wavelengths are marked in Fig. 2 as A–D.Fig. 3(a), (c) and (d) contrast the metal-embedded PBR’s modefield patterns within (A at l¼1.55 mm) and outside (C atl¼1.769 mm and D at l¼1.344 mm) the bandgap. It is clear thatthe wavelength which is outside the bandgap is transmitted andthe wavelength which is inside is not, giving a straightforwardillustration of the filtering characteristic. At l¼1.769 mm, the stepPBR is still in the bandgap and the propagation is inhibited, asshown in Fig. 3(b).

The S-shaped PBR in Ref. [12] was implemented by roundingthe sharp corners of the wider half of a step PBR, which renderedthe flat-topped profile. By introducing a gradual change of theeffective index of refraction the sidelobes can be reduced. Incontrast, refractive index distribution in a unit cell of the metal-embedded PBR is step, so the improvement may be due to thedifference of electric field distribution for metal-embedded andstep PBRs (see Fig. 3(b)–(d)). First, at the interface between thetwo MIM sections, some light energy is reflected or absorbed at

Fig. 2. Transmission spectra for the step with (m,n)¼(150 nm,50 nm)(blue curve)

and (m,n)¼(150 nm,100 nm) (olive dotted curve), and metal-embedded (red

curve) PBRs with (m,n)¼(150 nm,50 nm). The mode patterns for points A–D are

shown in Fig. 3. (For interpretation of the references to color in this figure, the

reader is referred to the web version of this article.)

Fig. 3. Field profiles 9Hz92 at different wavelengths for the metal-embedded PBRs at

l¼1.769 mm.

the 50 nm width metal surface without bias (for the step PBRs,more energy is reflected or absorbed at the 100 nm width metalsurface). Then, the other part of light energy is split into twobeams, causing inflow into the narrower regions, and thenthrough the 50 nm thickness metal leading to weak couplingand interference in the wider regions, which reduce the patternmiss-matching of the two sections [17] for the metal-embeddedPBRs. It decreases the reflection at other wavelengths where theBragg condition is not satisfied thus narrowing the bandgap. Fig. 2also shows transmission spectra of the step PRBs with(m,n)¼(150 nm,100 nm); the 3 dB bandwidth and ripple factorof the PBRs are 442 nm and 0.172,respectively, both of which arenot better than those of metal-embedded PBRs, and furtherconfirms the above analysis.

Because scattering of causes the abrupt change in index ofrefraction between the wider and narrower regions of theinsulator layer, we introduce a gradual change of the effectiveindex of refraction so that the sidelobes can be reduced. In theinset of Fig. 4, we smooth each end of the embedded metal byadding a semicircle with radius R¼n/2, while other parametersremain unchanged. Thus, as the width changes gradually, so doesthe effective index. Fig. 4 shows transmission spectra for therectangle and smooth metal-embedded PBRs. We see that thesidelobes are slightly suppressed, albeit at the expense of a

(a) l¼1.55 mm, (c)l¼1.769 mm and (d) l¼1.344 mm, and for the step PBRs at(b)

Fig. 4. Transmission spectra for the rectangle (black curve) and smooth (red

curve) metal-embedded PBRs. Inset: smooth each end of the embedded metal by

adding a semicircle with radius R¼n/2, while other parameters are the same as in

Fig. 2.(For interpretation of the references to color in this figure, the reader is

referred to the web version of this article.)

M. Tian et al. / Optics Communications 285 (2012) 5122–5127 5125

somewhat reduced transmission minima around the centerwavelength. The 3 dB bandwidth and ripple factor of the PBRsare 279 nm and 0.154 respectively.

To further investigate the property of step and metal-embedded PBRs, we introduce defects by inserting air insulatorsections with 50 nm width and 540 nm length in the middle ofstep PBRs. For metal-embedded PBRs, we introduce defects byinserting metal rectangular sections with 50 nm width and600 nm length in the middle. The spectrum displays a sharp peakinside the PBRs band gap in Fig. 5, suggesting the existence of adefect mode. At this point, the defect mode of the step PBRsexhibits 38.9% transmission and 33.0 nm linewidth, resulting in aQ factor of 47.0. For the defect mode of metal-embedded PBRs, theresults are 71.3%, 48.4 nm, and 32.0 correspondingly. Fig. 6 showsthe defect mode pattern 9Hz92 for (a) the metal-embedded and(b) the step PBRs at l¼1.55 mm. The defect mode represents thehigh-level transmission occurring within a PBR’s bandgap due to adefect in the PBR’s periodicity. Optical power will be concentratedaround the defect due to the formation of resonance modes.

4. A wide flat-top transmission band filter

In Fig. 3(c) and (d), with respect to the Bragg wavelength, thelonger wavelengths have a tendency to spread in wider regions ofthe insulator layer; however, the shorter wavelengths have atendency to spread in the inset metal regions. So, we can adjustthe length of the metal embedded to control the transmission ofsideband wavelength, and then decrease the ripple factor, thus,smoothing the transmission spectra. Fig. 7 shows the transmis-sion spectra for the uniform and apodized PBRs with (a) theembedded metal length decreasing and (b) increasing. The setperiod for 610 nm and (m,n)¼(150 nm,50 nm) remain

Fig. 5. Transmission spectra of the metal-embedded and step PBRs including a

defect with length 600 nm and 540 nm, and 50 nm width; other parameters are

the same as in Fig. 2.

Fig. 6. Defect mode pattern 9Hz92 for (a) the metal-embedded and (b) th

unchanged. L2 length of the uniform PBRs is 340 nm, and thedetailed parameters of L2 are shown in Table 1 for apodized PBRs.In Fig. 7(a), we decrease the embedded metal length, to reducethe ripples at the right band edges; the ripple factor is 0.0059 andthe transmission as high as 95.3%. In the meantime, it increasesthe ripples beyond the left band edges, and the results areconsistent with our previous analysis. From the same principles,when we increase the embedded metal length, the ripples at theleft band edges (1–1.4 mm) will be suppressed, and the ripplefactor and the transmission are 0.011 and 89.9%, respectively.When the wavelength is shorter than 1 mm, the ripples will besevere, owing to appearance of high order plasmonic Braggreflection [15].

e step PBRs at l¼1.55 mm with the defect length 600 and 540 nm.

Fig. 7. Transmission spectra for the uniform and apodized PBRs with the

embedded metal length (a) decreasing and (b) increasing.

Fig. 8. Transmission spectrum of the filter whose Bragg wavelength is 1.55 mm,

connected with (a) 1.1 mm and (b) 1 mm Bragg wavelength metal-embedded

apodized PBRs filter and their intervals are both 500 nm.

Table 1L2 parameters for apodized PBRs. (unit: nm).

L2 (1) L2 (2) L2 (3) L2 (4) L2 (5)–L2 (8) L2 (9) L2 (10) L2 (11) L2 (12)

(a) 100 160 220 280 340 280 220 160 100

(b) 420 400 380 360 340 360 380 400 420

M. Tian et al. / Optics Communications 285 (2012) 5122–51275126

Now, we use the impedance theoretical model to explain theabove phenomenon. The characteristic impedance of the funda-mental TM mode in a silver parallel-plate waveguide is uniquelydefined as the ratio of voltage V to surface current density I and isequal to [27]

ZTM ¼ V=I¼ Exd=Hz ð5Þ

where Ex and Hz are the transverse components of the electricand magnetic field, respectively, and we assume a unitlengthwaveguide in the z direction.

Silver satisfies the condition 9emetal9c9edielectric9 at the opticalcommunication wavelength 1550 nm. Thus, 9Exmetal9{9Exdielectric9so that the integral of the electric field in the transverse directioncan be approximated by Exdielectric, and we may therefore definethe characteristic impedance of the fundamental MIM mode as

ZTM ¼ Exd=Hz¼ Exdielectricd=Hzdielectric ¼ bd=n02oe0 ð6Þ

The dielectric in the metal slit is air with refractive index n0¼1and the slit width is d. So the impedance of MIM waveguide isequal to

ZTM ¼

ffiffiffiffiffiffim0

e0

rReðneff Þd ð7Þ

Propagation constant b is usually presented by a dimension-less effective index neff¼b/k0 for the guided modes, where k0 isthe vacuum wave-vector. o is angular frequency of input light.When the slit widths are 50, 100 and 150 nm, the impedances are25.88, 45.27 and 64.35 O mm, respectively. For the thickness-modulated PBR, the impedance is different from those of the twosections; if the impedance difference is too big, it will lead to highreflection at other wavelengths where the Bragg condition is notsatisfied [15]. In this case, the PBRs exhibit higher transmissionloss outside the bandgap, and hence wider bandgap.

For the step PBR with (m,n)¼(150 nm,50 nm), the impe-dances are 64.35 and 25.88 O mm. For the step PBR with(m,n)¼(150 nm,100 nm), the impedances are 64.35 and45.27 O mm. And the impedances are 64.35 and 51.76 O mm forthe metal-embedded PBR with (m,n)¼(150 nm,50 nm). Theimpedance difference of the metal-embedded PBR is small, sothe metal-embedded PBRs exhibit lower transmission loss outsidethe bandgap, narrower bandgap, and reduced rippling in thetransmission spectrum when compared with the step PBRs atthe same normalized index contrast and transmission levels.

For the same slit width, the real part of the effective refractiveindex decreases when the wavelength increases. When theembedded metal length decreases (increases) the longer (shorter)wavelengths spread in the 150 nm (50 nm) width of the insulatorlayers decreasing (increasing) the impedance to 64.35 (51.76). Inthis case, decreasing the impedance difference, it will lead tomore energy of wavelengths that do not satisfy the Braggcondition and transmitting the grating, which exhibits lowertransmission loss outside the bandgap.

A wide band-pass plasmonic filter is one of the importantdevices in the field of optical integrations. In the transmissionband of the MIM waveguide, there are many plasmonic modesexperiencing multiple interferences. So the transmission spec-trum always has oscillations due to the Fabry–Perot effect whichis a negative impact on plasmonic integrated circuits. Now, we

use the above unique phenomenon to design a wide band-passfilter.

At first, we design two metal-embedded PBRs apodized filterswhich smooth the ripples at the right band edges (the method seeFig. 7(a)), and their Bragg wavelengths are (a) 1.1 mm and (b)1.0 mm. Then, connect (a) or (b) with the apodized filter ofFig. 7(b). Fig. 8 shows their transmission spectra; we can see thata flat-top transmission band appears. In Fig. 8(a), a flat top bandemerges from 1.26 to 1.40 mm, its transmittance is as high as 88%and the ripple factor only 0.01. In Fig. 8(b), a flat top bandemerges from 1.10 to 1.40 mm; its transmittance is as high as86% and the ripple factor is 0.03. However, from 1.17 to 1.35 mm,the ripple factor is only 0.003 and its transmittance is 490%.From Fig. 8, we can obtain that the flat-top transmission band andcenter wavelength can be adjusted by the two connect filters.Owing to existence of high order plasmonic Bragg reflection, theflat-top transmission band is far less than lb/2.

5. Conclusions

In conclusion, we propose to employ metal-embedded profilesin the design of MIM-based PBRs to solve the technical problems

M. Tian et al. / Optics Communications 285 (2012) 5122–5127 5127

associated with the conventional step profile PBRs. Using FDTD,we numerically investigate the performance of the metal-embedded PBRs. For fair performance comparison between thetwo types of PBRs, we assure that the two PBRs exhibit close toequal transmission levels at the Bragg wavelength and thenormalized index contrast, and then compare their performance,and spectral characteristics in the bandgap and outside thebandgap. The metal-embedded PBRs exhibit 75.7% narrower3 dB bandwidth, and significantly reduced rippling in the trans-mission spectrum outside the bandgap when compared withthose for step PBRs. Such features lead directly to higher outputpower levels for the transmitted wavelength components andhence, result in lower insertion loss. We attribute these advan-tages in the metal-embedded PBRs to the good model match.Comparison of the defect modes of the metal-embedded and stepPBRs also shows that the former exhibits high transmission. Then,we find that the apodized PBRs with the embedded metal lengthdecreasing (increasing) efficaciously suppress the ripples at theright (left) band edges, and we realize a wide flat-top transmis-sion band filter by connecting two apodized PBRs; also the flat-top transmission bandgap and center wavelength can be adjustedby the two connected filters. Owing to the existence of high orderplasmonic Bragg reflection, the flat-top transmission bandgap isfar less than half of Bragg wavelength.

Acknowledgment

This work was supported by a grant (Nos. 60937002 and60807017) from Natural Science Foundation of China and a grant(HUST: No.2011TS058) from the Fundamental Research Funds forthe Central Universities. The authors would like to thank engineerHehua Zhang of Dongjun Information Technology Co., Ltd., forthoughtful and engaging discussions related to this work.

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