Broadband plasmonic absorber for photonic integrated circuits
aa r X i v : . [ phy s i c s . op ti c s ] N ov Broadband plasmonic absorber for photonic integrated circuits
Xiao Xiong, Chang-Ling Zou, a) Xi-Feng Ren, b) and Guang-Can Guo Key Lab of Quantum Information, University of Science and Technology of China, Hefei 230026,P. R. China (Dated: 10 October 2018)
The loss of surface plasmon polaritons has long been considered as a fatal shortcoming in information trans-port. Here we propose a plasmonic absorber utilizing this “shortcoming” to absorb the stray light in photonicintegrated circuits (PICs). Based on adiabatic mode evolution, its performance is insensitive to incidentwavelength with bandwidth larger than 300 nm, and robust against surrounding environment and tempera-ture. Besides, the use of metal enables it to be very compact and beneficial to thermal dissipation. With this40 µ m-long absorber, the absorption efficiency can be over 99 .
8% at 1550 nm, with both the reflectivity andtransmittance of incident light reduced to less than 0 . , and actuating and controlling the micro-and nano-mechanical oscillators . On the other hand,in photonic integrated circuits (PICs), weak signal lightor single photon are used for classical and quantum in-formation processing. Therefore, stray light from strongpump/control light will induce errors in information pro-cessing and high noise background. That is to say, anoptical “dump”, which can perfectly absorb the strongpump/control light with no reflection, is quite neces-sary in PICs. During past decades, a variety of spa-tial two-dimensional (2D) or three-dimensional (3D) ab-sorbers composed of array of plasmonic nano-resonatorshave been proposed . Surprisingly, however, integratedabsorber compatible with dielectric waveguide has beenomitted.One may borrow the idea from the spatial absorbers toPICs by using critically coupled resonators to absorb theincoming light with neither reflection nor transmission.However, there exists several limitations in resonator-based absorber. Firstly, the cavity has to work underthe critical coupling condition, which is highly depen-dent on the geometric parameters of cavity. Secondly,the absorption spectrum is a Lorentz-shaped profile witha relatively narrow bandwidth. Thirdly, the resonancewavelength is sensitive to temperature, thus the absorp-tion spectrum will shift due to light heating, and leadto instability. Fourthly, finite cavity resonance also cor-responds to limited response speed, which means laserpulse can not be absorbed effectively before stable fieldis established in the cavity. In addition, the resonancesare polarized in PICs, hence the two orthogonal polar-izations usually cannot be absorbed simultaneously.In this Letter, we propose a broadband plasmonic ab-sorber for PICs. Since surface plasmon polaritons (SPPs) a) Electronic mail: [email protected] b) Electronic mail: [email protected] enable extreme confinement and have big inherent lossesin propagation , they are of course the best candidateto fulfill the task for absorption in PICs. However, theimpedance mismatch between dielectric and plasmonicmodes will inevitably lead to reflection. Therefore, weutilize the adiabatic mode evolution to efficiently convertthe dielectric waveguide mode to plasmonic mode . As aresult, the absorption can be achieved over a wide rangeof wavelength, and remains robust against surroundingenvironment and temperature . By a simple circulararc structure of dozens of microns long, we realized awaveguide-integrated adiabatic absorber, whose absorp-tion efficiency can reach more than 99 .
8% at 1550 nm,with both the reflectance and transmittance reduced toless than 0 . .
5% from 1400 nm to 1700 nm for both horizontal ( H )and vertical ( V ) polarizations. Additional to the ex-cellent optical performance, the absorber has very goodthermal conductivity considering that laser heating canbe conducted by metal wires or thermal antenna. Webelieve this compact, broadband, robust and thermal-conductive absorber may find applications in practicalPICs.The schematic illustration of our proposal is shownin Fig. 1(a). A silicon waveguide is fabricated on sil-ica substrate, with the waveguide cross-section being300 nm ×
400 nm. And gold (Au) of height h covers theend of the waveguide and consists of two parts: the tan-gent circular arc with radius of curvature being r , and therectangle with width w and length l . The working wave-length is focused on the telecommunication band around λ = 1550 nm. The refractive indices of silicon and sil-ica are n Si = 3 . n SiO = 1 . . Then weperformed numerical simulations with COMSOL Multi-physics 4.3 to test the performance of this absorber. It’sobvious that the performance of an absorber should beestimated with two parameters: transmittance T and re-flectivity R . Here, T is defined as the ratio of total out-going energy flux to total incident energy flux , and R isthe ratio of backward-propagating intensity to forward- Wavelength (nm) (c) n e ff (b) (a) H mode V mode
H mode V mode L ( µ m ) Wavelength (nm)
FIG. 1. (a) Schematic of the adiabatic absorber, which con-sists of the adiabatic circular arc (radius r ) and the absorp-tion rectangle (size l × w × h ). Incident light includes twoorthogonal polarizations ( H and V modes) and propagatesalong the z -axis. (b) Dependence of effective refractive in-dex n eff on incident wavelength λ for dielectric H/V modes(dashed red/blue curves) and plasmon
H/V modes (solidred/blue curves), respectively. Here, l = 20 µ m, w = 1 . µ m, h = 0 . µ m. (c) Dependence of propagation length L on λ for plasmon H (red curve) and V (blue curve) modes, with w = 1 . µ m and h = 0 . µ m. propagating intensity.Firstly, we calculated the effective refractive index n eff of dielectric eigenmode (in pure silicon waveguide with-out metal) and plasmon eigenmode (in metal-coveredsilicon waveguide) as a function of wavelength λ , asshown in Fig. 1(b). We observed that the differencebetween dielectric and plasmon modes is rather big forboth polarizations, especially for H polarization. Thisbig difference, which indicates the mode mismatching be-tween dielectric and plasmon modes, will induce largereflectivity on the interface between pure silicon waveg-uide and metal-covered silicon waveguide. In order toreduce the reflectivity, a designed taper can be usedto convert dielectric guided modes to plasmon modesadiabatically . Here, we just adopted a circular arcwhich is quite simple but works well.Then, we calculated the propagation length of plas-mon modes L depending on λ for H and V modes, re-spectively, as displayed in Fig. 1(c). As the incidentwavelength increases, the propagation length L increasesfor both polarizations. And the propagation length L of H mode keeps larger than that of V mode. Nev-ertheless, for a wide bandwidth of 300 nm, the prop-agation length L of both H and V modes are below4 µ m. According to I ( l ) = I e − l/L , we get to knowthat longer l will bring better absorption performance.Especially, at λ = 1550 nm, the propagation length of H mode is larger, being L = 3 µ m. Thus, we fixed l to be l = 20 µ m, expecting an absorption efficiency of I ( l ) /I = e − / ≈ . L on w and h for H and V modes. It increases with increasing w and h firstly, and get saturated over certain value ( w > . µ m, -4 -2 0 2 40.00.20.40.60.81.0 r=20 r=15 r=10 r=5 r=0 C x ( n ) n i (a) -2.2 -2.1 -2.0 -1.90.000.040.080.12 -4 -3 -2 R r ( m) H mode V mode (b)
FIG. 2. (a) Fourier-transformed spectrum of electric fieldcomponent E m ( z ) in the adiabatic part, with r = 0, 5, 10,15, 20, respectively. Here, the incident field is H mode, with l = 20, w = 1 . h = 0 . µ m). Inset: en-larged view of the peak which stands for the reflected field.(b) Dependence of reflectivity R on r for H and V modes,respectively. h > . µ m). This is because energy is mostly confined inthe metal when the Au coating is ultra-thin, rather thanin the waveguide. When w > . µ m and h > . µ m,the energy of propagating mode is mostly confined in thedielectric waveguide, then the absorption of this devicewon’t be sensitive to the size of metal coating. So wefixed w = 1 . µ m and h = 0 . µ m in the saturated re-gion in our studies.It is conceivable that if the conversion from dielectricmode to plasmon mode in the first half of this absorberis more adiabatic, the reflectivity due to momentum mis-matching will be smaller . Similarly, if the plasmonmode propagates farther, the loss of incident light dueto metallic absorption is larger. That is to say, larger r brings smaller R while longer l brings smaller T . Next,we’ll confirm our predictions with 3D numerical simula-tions. Matched fundamental modes with two orthogo-nal polarizations ( H and V modes) are incident at thewaveguide facet, respectively, and propagate along z di-rection, with the coordinate origin located at the waveg-uide center of incident plane. Note that, benefiting fromthe propagation losses in metal, T can always be reducedas small as possible, as long as l is large enough. As aresult, we focus on the influence of adiabatic radius r onreflectivity R in the following.Denote the electric field component along m direction( m = x ( y ) for H ( V ) polarization) as E m ( z ), which is dis-tributed along the center line of waveguide as a functionof z . In the adiabatic part, E m ( z ) should be a sum offorward- and backward-propagating dielectric modes as E m ( z ) = X n i C m ( n i ) e − jn i kz , (1)where n i is the effective refractive index of different eigen-modes, C m ( n i ) is the corresponding mode amplitude,and k = πλ is the wave number. By applying Dis-crete Fourier Transform (DFT) to E m ( z ), the coefficient C m ( n i ) can be expressed as C m ( n i ) = k π X z E m ( z ) e jn i kz . (2)And the sign before n i represents exactly the energypropagation direction. As shown in Fig. 2(a), theFourier-transformed spectrum consists of two main peaksthat are symmetric distributed. The right main peakstands for the forward-propagating incident mode with n = + n i , while the left one is the backward-propagatingreflected mode with n = − n i . Here, the priminent peakfor n < R is obtained as R = (cid:12)(cid:12)(cid:12)(cid:12) C m ( − n i ) C m (+ n i ) (cid:12)(cid:12)(cid:12)(cid:12) . (3)Here, the incident field has been normalized to be unit forsimplicity. Besides, it’s worth noting that there are manyside lobes around the main peaks, which originates fromthe finite sampling interval. Furthermore, the depen-dences of R on the arc radius r for different polarizationare plotted in Fig. 2(b). As we can see, for r >
15 : µ m,the reflectivity R are reduced to be less than 0 .
1% forboth H and V modes.Similarly, by applying DFT to E m ( z ) in the absorp-tion part, we obtained the Fourier-transformed spectraof H and V modes, which contain the information aboutplasmon eigenmodes. As illustrated in Fig. 3(a), the nor-malized spectrum for H -polarized incident field consistsof two peaks. While no peak appears in the region n i < H -polarized plasmon eigenmodes cal-culated under 2D simulations (shown in the inset in Fig.3(a)), with the major (minor) peaks being plasmon fun-damental (high-order) eigenmode. Unlike the situationin Fig. 3(a), the normalized spectrum for V -polarizedincident field (Fig. 3(b)) includes four peaks, and theystand for the four V -polarized plasmon eigenmodes of dif-ferent order (inset of Fig. 3(b)), respectively. Here, many V -polarized plasmon eigenmodes of higher-order are ex-cited, due to the discontinuity of metal in the interfacebetween the arc and rectangle at the top of waveguidefor V polarization. This sudden change of refractive in-dex also results in the special trend of the blue curveshown in Fig. 2(b), where R of V mode does not de-crease monotonously with the increase of r . While for H -4 -2 0 2 40.00.20.40.60.81.0 C x ( n ) n i (a) -4 -2 0 2 40.00.20.40.60.81.0 C y ( n ) n i (b) I IIIII IV I II III IV
FIG. 3. Normalized Fourier-transformed spectra of electricfield component E m ( z ) in the absorption part for (a) H modeand (b) V mode, respectively, with r = 20 µ m. Inset: the fielddistributions of plasmon eigenmodes, which correspond to thepeaks in Fourier-transformed spectra, respectively. Scale barin the insets I-IV: 300 nm. -5 -4 -3 -2 (b)(a) R Wavelength (nm)
H mode V mode -4 -3 -2 -1 T Wavelength (nm)
H mode V mode
FIG. 4. Dependence of (a) R and (b) T on λ for H and V modes. Here, l = 20, w = 1 . h = 0 . r = 17 . µ m). polarization, the fundamental dielectric mode is adiabat-ically converted into fundamental plasmon mode (withthe high-order plasmon mode being negligible), and thereflectivity R drops monotonously as r increases, sincethe metal is getting close to the waveguide slowly enough.Therefore, the performance of V mode can be improvedby etching or evaporating a metal slope in the interfacebetween the arc and rectangle at the top of waveguide.Finally, we calculated the dependence of R and T onincident wavelength λ for both H and V polarizations.As shown in Fig. 4(a), the reflectivity R is kept lessthan 0 .
1% for both polarizations over a bandwidth aswide as 300 nm. As for the transmission T shown in Fig.4(b), it increases with increasing incident wavelength for H polarization, while maintains well below 0 .
3% over abandwidth of 300 nm for V polarization. In order tofurther increase the absorption efficiency, the absorptionpart can be engineered to be longer, which is quite con-venient. Or, the waveguide in the absorption part canbe tapered to adiabatically transfer more energy into themetal and improve the absorption loss.There are still several points that we want to discuss.For instance, to further improve the absorber’s perfor-mance with less reflectivity as well as less transmission,the process of mode conversion can be engineered to bemore adiabatic (larger r ), and the distance for absorp-tion needs to be longer (larger l ). And considering theadoption of metal, which is a good thermal conductor,heat dissipation can be easily improved by adding moremetal, etching nanostructures at the top of the metalrectangle like heat sink, and guiding the thermal energywith a metallic wire or thermal emitter . Since inci-dent optical energy is totally converted to thermal en-ergy, it fundamentally eliminates the negative effect ofstray light. While for resonance-based absorber, a por-tion of the incident light will be transformed to scatteringlight. Additionally, since the imaginary part of the refrac-tive index of Au increases with higher temperature, theincrease of temperature in metal caused by energy ab-sorption will further improve the absorption efficiency ofthis absorber, rather than wrecking it. Finally, since thisabsorber works based on adiabatic mode conversion, itsperformance is insensitive to geometric parameters andimposes little requirement on processing technology. Ourcalculation proves that, even if the lateral displacementbetween dielectric waveguide and plasmonic absorber isas large as 100 nm, the absorption efficiency for both H and V modes can still be maintained around 99%.In conclusion, we propose a plasmonic absorber forguided waves in PICs, which is based on adiabatic modeconversion and can achieve an absorption efficiency morethan 99 .
8% (with both reflectivity and transmission lessthan 0 . µ m × µ m × µ m) and con-ducive to heat dissipation. Besides, since the absorptionis realized adiabatically with a circular arc, this absorberhas a bandwidth as wide as 300 nm for both H and V polarizations, and its performance is also robust againstsurrounding environment and temperature. It is essentialfor integrated photonic chips, and will find applicationsin PICs-based optics. ACKNOWLEDGMENTS
This work was funded by NBRP (grant nos.2011CBA00200 and 2011CB921200), the InnovationFunds from the Chinese Academy of Sciences (grant no.60921091), NNSF (grant nos. 10904137, 10934006 and11374289), the Fundamental Research Funds for the Cen-tral Universities (grant no. WK2470000005), and NCET. R. W. Boyd,
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