All-optical logic operation of polarized light signals in highly nonlinear silicon hybrid plasmonic microring resonators
J ING D AI,1,2M INMING Z HANG,1,2,*F EIYA Z HOU,1,2Y UANWU W ANG,1,2L ULUZI L U,1,2AND D EMING L IU1,2
1School of Optical and Electronic Information,Huazhong University of Science&Technology,Wuhan430074China
2National Engineering Laboratory for Next Generation Internet Access Systems,Wuhan430074,China
3Huazhong University of Science&Technology,Wuhan430074,China
*Corresponding author:mmz@https://www.doczj.com/doc/a54813327.html,
Received16December2014;revised12February2015;accepted13April2015;posted14April2015(Doc.ID230870);published7May2015 All-optical logic operation is theoretically demonstrated by means of polarization-dependent four-wave mixing (FWM)processes in a highly nonlinear silicon hybrid plasmonic waveguide(HPWG)microring resonator.We design an ultra-compact(radii 1μm)microring resonator(MRR)that is realized by using a silicon HPWG with the capacity for subwavelength-bending.The HPWG exhibits very high confinement(A eff～0.045μm2)that
can result in a remarkably high nonlinear parameter(γ～3000W?1m?1),given a highly nonlinear gap material.
By manipulating the polarization properties of the pump and signals with a very low electric field (j E j～108Vm?1),all-optical NOT,NOR,and NAND logical operations are obtained through the FWM process.
These compact all-optical nanoplasmonic devices are stable,fabrication simplified,and silicon on insulator(SOI) compatible.?2015Optical Society of America
OCIS codes:(190.4360)Nonlinear optics,devices;(240.6680)Surface plasmons;(190.4380)Nonlinear optics,four-wave mixing;
(230.5750)Resonators;(130.3750)Optical logic devices.
https://www.doczj.com/doc/a54813327.html,/10.1364/AO.54.004471
1.INTRODUCTION
Optical waveguides that enable light confinement at the nano-scale have been researched for a long time.Among various nanophotonic waveguides[1–4],the nanoplasmonic wave-guide is a very attractive and promising candidate to achieve future photonic circuits with ultrahigh integration and large on-chip circuit capacity[4].Plasmonics is an emerging field of nanophotonics in which light is controlled and guided be-yond the diffraction limit by exploiting the unique optical properties of metal-dielectric interfaces.Several years ago,some nanoplasmonic waveguiding configurations were proposed and demonstrated,including dielectric loaded surface plasmon polariton waveguides[5],long range surface plasmon polariton waveguides[6],metal-dielectric slab waveguides[7],metal–insulator–metal(MIM)waveguides[8],and metal V-groove waveguides[9].However,for these previous proposed nano-plasmonic waveguides,the propagation loss is proportional to their mode confinement,i.e.,low propagation loss is always accompanied by a weak mode confinement and a strong mode confinement usually results in a large propagation loss.
To overcome this drawback,hybrid plasmonic waveguides (HPWGs)combined of a dielectric and a plasmonic waveguide [10](including a high-index region,a metal region,and a low-index nano-slot between them)is proposed;it has the ability to offer a better compromise between the losses and confinement than the pure surface plasmon(SP)mode.Many applications [11]based on HPWGs have been implemented including polarizers,polarization splitters,polarization rotators,direc-tional couplers,power splitters,microring(microdisk)resona-tors,modulators,switches,optical tweezers,nanolasers,and so on.One particular advantage of their application lies in the production of remarkably high optical nonlinear effects by the hybrid integration of highly nonlinear materials[12,13]. The nanoscale optical mode confinement and subwave-length-bending radii of HPWGs give rise to high integration densities that enable an overall reduction of the device dimen-sions and result in a remarkably high nonlinear parameter.For instance,by combining the optical nonlinearities and surface plasmons[14],all-optical switching[15–18]and all-logic gate devices[19,20]have been proposed and realized.They have attracted considerable interest for optical computing and ultra-high speed information processing.However,these works that utilize Kerr effects[15],photogenerated free carrier effects (FCE)[16],two-photon absorption(TPA)processes[17
], 1559-128X/15/144471-07$15/0$15.00?2015Optical Society of America
and four-wave mixing(FWM)effects[18],merely focus on the intensity variation of the pump light in optical nonlinear proc-esses;the role of polarization is usually neglected.In addition, another drawback is that these previous proposed devices usu-ally have no good integration compatibility,which could limit the application of all-optic circuits.
In this paper,a polarization-dependent,FWM-based,all-optical logic operation in a highly nonlinear silicon hybrid plasmonic microring resonator(Si-HPMRR)is theoretically demonstrated by using the finite-difference time-domain (FDTD)method.The structure is like those in Refs.[19,20]. Silicon photonics have become very popular because of CMOS (complementary metal oxide semiconductor)compatibility and SOI(silicon on insulator)compatibility,and they also offer the possibility of integrating electronics and plasmonics on the same chip conveniently.Therefore,the SOI-compatibility of a silicon hybrid nanoplasmonic waveguide[21]makes the fab-rication simplified.At the same time,a polarization FWM tech-nique[22]is adopted by switching the polarization states of incident lights with a very low electric field(j E j～108Vm?1); thus,we can effectively manipulate the FWM process and obtain specific logic relationships between incident signals and output lights(i.e.,NOT,NOR,and NAND).Compared with other intensity-dependent all-optical logic gates,these ones are more compact(ultra-compact radii 1μm),simply constructed(Si-HPMRR),flexible(SOI-compatibility),and exhibit potential for the integration of all-optic circuits.
2.DEVICE STRUCTURE AND OPERATING PRINCIPLES
A.Highly Nonlinear Silicon Hybrid Plasmonic Microring Resonator
Figure1(a)shows the schematic configuration of the present highly nonlinear Si-HPMRR.The Si-HPMRR studied in this work has a similar structure to that described in[19].The FWM processes can occur in this device,and these are inves-tigated in detail in the following parts:the pump light P and the signal lights S i(i 1;2)are the input lights,which are con-sidered to be Gaussian pulses,and S out is the emitted light.
Figure1(b)illustrates the cross section of the silicon HPWG.It is consist of silicon(Si),highly nonlinear material [DDMEBT(2-[4-dimethylamino)phenyl]-3-{[4-(dimethyla-mino)phenyl]ethynyl}buta-1,3-diene-1,1,4,4-tetracarbonitrile) polymer,which fills the nano-sized gap],metal,and silicon di-oxide(SiO2).The structure with a nanometer-sized DDMEBT polymer layer sandwiched between the Ag top layer and Si layer is formed on a SiO2substrate.All these metallic and dielectric
parts on the silica substrate have the same width as the HPWG, and w represents the width of the waveguide.The height of
each Si layer and DDMBET layer is denoted by h Si and h D, respectively.Metal is defined as silver(Ag)with a height of h m.
The DDMEBT[23]is described by a linear and nonlinear in-dex of n0～1.8and n2～1.7×10?17m2∕W,with a third-order susceptibility ofχ3?3×10?19m2V?2in the wavelength range from1.3to1.7μm.For silicon and silicon dioxide,the
refractive index of one dielectric is usually given by the Sellmeier formula[19]in the wavelength range from1.3to 1.7μm.The cladding considered here is air.The TPA param-eter of silicon isβTPA 5×10?12m∕W[24].Furthermore, we stress that DDMEBT is free from TPA and FCE.The silver metal is described by a relative Drude permittivity dispersion [25]as follows:
ε ω ε∞?
f2p
f2 ifγ
;(1)
whereε∞ 5,f p 2175THz,andγ 4.35THz.
Figures2(a)and2(b)show the typical guided-power density distribution P z x;y of the TM fundamental mode(hybrid plasmonic mode)and the TE fundamental mode,respectively. The hybrid plasmonic mode/TM fundamental mode sup-ported by the structure is demonstrated to be capable of simultaneously achieving nano-scale light confinement as well
Fig.1.Schematic diagram of the proposed all-optical logic gates
based on polarization-dependent FWM processes.(a)Silicon hybrid
plasmonic microring resonators.(b)Cross section of the
HPWG.
Fig. 2.Typical guided-power density distribution P z x;y for
(a)the fundamental TM eigenmode(hybrid plasmonic mode)and
(b)the fundamental TE eigenmode in the HPWG atλ0 1.50μm,
with n Si 3.45,n
SiO2
1.44,w 300nm,and h D 40nm.
(c)Effective mode area A eff and nonlinear parameter coefficientγ
of the silicon HPWG with respect to the operation wavelengthλ0
in the range from1.3to1.7μm.
as relatively long propagation distances at the telecom wave-length.The propagation length is L m 1∕ 2Im f k g [10].The calculated L m is 70–100μm in the range from 1.3to 1.7μm.
In addition,the TE fundamental mode is not a hybrid plasmonic mode,but a conventional dielectric mode.The light still is confined mainly in the high-index silicon part.
The effective mode size A eff and nonlinear parameter γcan be rewritten [26]as
A eff R
?E ×?H ·?z d A
2R j ?E ×?H ·?z j 2d A ;(2)γ 2πλˉn 2A eff ˉn 2 k ε0
μ0 R n 2
x;y n 2 x;y 2j ?E j 4 j ?E j 2 d A 3R j ?E ×H ! ·?z
j d A ;(3)
where ?E
and ?H are the electric field vector and magnetic field vector,respectively.ˉn 2can be viewed as the nonlinear refractive index averaged over an inhomogeneous cross section weighted with respect the field distribution.There is a factor that produces an ～2times higher value for γfor the HPWG.Figure 2(c)shows the effective mode area A eff and nonlinear parameter coefficient γof the silicon HPWG with respect to the operation wavelength λ0in the range from 1.3to 1.7μm.The HPWG exhibits very high confinement (A eff ～0.045μm 2)that can result in a remarkably high non-linear parameter (γ～3000W ?1m ?1).
Utilizing this kind of HPWG,we design an ultra-compact silicon hybrid plasmonic microring resonator,and the radius is set as R 1μm .The other geometrical parameters are set as follows:w 300nm ,h Si 300nm ,h D 40nm ,h m 200nm ,and w gap 120nm .For the light transmission of the fundamental hybrid plasmonic mode/TM fundamental mode for a Si-HPMRR,Fig.3shows the calculated broadband response within the 1.3–1.7μm wavelength range when the gap width w g is chosen as 120nm and R 1μm .The reso-nance wavelengths are listed as 1.30864,1.38420,1.46823,1.56136,and 1.6661μm.
However,for the light transmission of the TE fundamental mode for a Si-HPMRR,the microring resonator (MRR)
showed no effect because of the sharp bends (R 1μm ),thus no similar spectral response exists.In other words,the Si-HPMRR in this work is only a TM-mode MRR;a TE-mode MRR does not exist.
However,for the light transmission of the TE fundamental mode for a Si-HPMRR,the microring resonator (MRR)showed no effect because of the sharp bends (R 1μm ),thus no similar spectral response exists.In other words,the Si-HPMRR in my work is only a TM-mode MRR;a TE-mode MRR does not exist.
B.FWM Theory Applied to the Microring Resonator
In degenerate FWM processes,the nonlinear interaction of two waves at the frequency “signal ”and “pump ”leads to the for-mation of a third wave at the frequency “idler.”Assuming neg-ligible depletion of the pump or signal due to the generation of the idler,the FWM conversion efficiency in an optical MRR [27–30]is given by
ηFWM FE 4P FE 2s FE 2i γ2P 2P j L eff j
2
L 2eff L 2exp ?αL 1?exp ?αL j ΔkL αL ?j ΔkL 2
FE p;s;i σ1?τexp ?αL ∕2 jk p;s;i
;
(4)
where ηFWM is the conversion efficiency that represents the ratio of the incoming signal power divided by the outgoing idler power,γis the effective nonlinearity,P p is the input pump power,L eff is the effective length,and FE p ,FE s ,and FE i are the resonant intensity enhancement factors for the pump,sig-nal,and idler,respectively.L is the circumference of the ring,and σand τare the coupling and transmission coefficients,re-spectively,with σ2 τ2 1.k p;s;i are the wavenumbers of the pump,signal,and idler fields with the phase mismatch Δk 2k p ?k s ?k i .Although the non-zero value of the group velocity dispersion (GVD)causes the resonances to be un-equally spaced in frequency (or energy)[29],the modes of the MRR are inherently phase-matched [31].In this paper,we neglect the effect of the GVD in that the effect of GVD is not analyzed in detail.
The field inside the ring is enhanced by a factor of FE with respect to the exciting wave in the bus waveguide.If the input exciting wave deviates from the resonance frequency,the field enhancement factor FE can be approximated as [27]
FE FE res 1
????????????????????????????????1
2Δ
ω
ΔωFWHM 2r ;(5)where FE res is the resonant intensity field enhancement that was discussed in the previous paragraph,Δωdenotes the de-tuning from the nearest resonance line,and ΔωFWHM is the corresponding full width at half-maximum (FWHM).
3.SIMULATION RESULTS
In the simulation model,the FDTD method [27]is used to analyze the polarization-dependent FWM processes in the Si-HPMRR.We could then describe the logic relationship between the polarization of the input pump or signals light
1.3
1.4
1.5
1.6 1.7
0.00.20.40.60.81.0
N o r m a l i z e d o u t p u t
Wavelength (μ
m)
Fig.3.Broadband spectral response in the range from 1.3to 1.7μm for the silicon hybrid plasmonic resonator with R 1μm when the gap width between the bus waveguide and ring was w gap 120nm
.
and the corresponding output light by utilizing the FWM process.
We mark the TE polarization state as symbol “1”and the TM polarization state as symbol “0,”where the polarization state of the light source at selected wavelengths could be ma-nipulated by a polarization modulator.For the corresponding output idle light,assuming the threshold of optical intensity as ?50dB ,if the normalized intensity is greater than the thresh-old,S out is marked as “1,”otherwise,it is marked as “0.”The output idler waves are optically filtered out and the photode-tectors are used to confirm the logic by simple electronic threshold judgments.
In the following simulation parts,the normalized intensity spectra detected for TM mode waves at the output port are calculated by the FDTD method for various optical logical operations such as NOT,NOR,and NAND.
The Si-HPMRR,where the gap width w g is chosen as 120nm and R 1μm ,is indicated by Fig.1(a).The wave-length ranges from 1.3to 1.7μm for the TM-polarized lights/hybrid plasmonic mode,where the resonance wavelengths are listed as 1.30864, 1.38420, 1.46823, 1.56136,and 1.6661μm.There only exists light transmission in the MRR for the TM-polarized lights/hybrid plasmonic mode,and here,the FWM process could occur.
A.NOT Logic Operation
In this case,a pump P and a signal light S 1are both launched into the Si-HPMRRs,with the wavelengths of ～1468.23nm and ～1561.36nm ,and electric fields j E j of 8×108Vm ?1and 2×108Vm ?1,respectively.The corresponding wavelength for S out is ～1384.20nm .
The polarization state of the pump is set as TM-polarized.At the same time,by setting the polarization state of S 1as TM-polarized,the FWM process obviously could occur,as
Table 1.Logic Operation of the NOT Optical Gate P /(Polarization State)S 1/(Polarization
State)
S out /(Intensity)TM 0(TM)1 ≈?27dB TM
1(TE)
0
-120
-90-60
-300
N o r m a l i z e d i n t e n s i t y (d B )
Wavelength (μm)
-120
-90-60-300N o r m a l i z e d i n t e n s i t y (d B )
Wavelength (μm)
Fig. 4.Logic operation of the NOT gate.The polarization-dependent FWM process and simulated results for (a)the logic operation of “NOT 0 1”when S 1is TM polarized and (b)the logic operation of “NOT 1
0”when S 1is TE polarized.
1.3
1.4
1.5
1.6
1.7
-120
-90
-60-300
N o r m a l i z e d i n t e n s i t y (d B )
Wavelength (μm)
1.3 1.4
1.5 1.6 1.7
-120
-90-60-300
N o r m a l i z e d i n t e n s i t y (d B )
Wavelength (μm)
1.3
1.4
1.5
1.6
1.7
-120
-90-60-30
N o r m a l i z e d i n t e n s i t y (d B )
Wavelength (μm)
1.3
1.4
1.5
1.6
1.7
-240
-210-180-150
-120N o r m a l i z e d i n t e n s i t y (d B )
Wavelength (μm)
Fig.5.Logic operation of the NOR gate.The polarization-depen-dent FWM process and simulated results for (a)the logic operation of “0NOR 0 1”when S 1is TM polarized and S 2is TM polarized,(b)the logic operation of “0NOR 1 0”when S 1is TM polarized and S 2is TE polarized,(c)the logic operation of “1NOR 0 0”when S 1is TE polarized and S 2is TM polarized,and (d)the logic operation of “1NOR 1 0”when S 1is TE polarized and S 2is TE polarized.
shown in Fig.4(a).The normalized intensity of S out reaches about ?27dB .If S 1is TE-polarized,the FWM process is not observed,as shown in Fig.4(b).Subsequently,we obtained a NOT logic function as listed in Table 1.
B.NOR Logic Operation
In this case,two signal lights S 1and S 2are both launched into the Si-HPMRRs,with the wavelengths of 1468.23and 1561.36nm,and the same electric field j E j of 4×108Vm ?1.The corresponding wavelength of S out is 1384.20nm.
When both S 1and S 2are TM-polarized,an obvious FWM process is observed,as illustrated in Fig.5(a),and the normal-ized intensity of out S out reaches ?25dB .The FWM processes will not occur under other circumstances,as shown in Figs.5(b)–5(d);therefore,a NOR logic function is achieved with the logic table listed in Table 2.
C.NAND Logic Operation
In this case,a pump P and two signal lights S 1and S 2are all launched into the silicon hybrid plasmonic MRRs,whose wavelengths are 1468.23,1561.36,and 1666.1nm,and the corresponding electric fields j E j are 2×108Vm ?1,1×108Vm ?1,and 1×108Vm ?1,respectively.The corre-sponding wavelength of S out is near 1308.64nm.
As indicated by Fig.6(d),if we set the polarization state of the pump as TM-polarized and both S 1and S 2are TE-polarized,the FWM process will not take place,while an ob-vious FWM process could be observed under other conditions,as shown in Figs.6(a)–6(c).The subsequent NAND logic function is available with the logics listed in Table 3.4.DISCUSSION
Results shown in the previous sections are based on ideal con-ditions such as ideal light sources and ideal Si-HPMRR.In fact,it is more likely that the input light may exhibit certain central frequency (wavelength)shifts,or the Si-HPMRR may exhibit certain resonance wavelength shifts.In other words,the main one for existing experimental deviations lies in the difference between the resonant wavelength of the MRR and the input light wavelength.For simplicity ’s sake when investigating such uncertainty,we added a perturbation on the central wavelength of the input light sources,i.e.,λ0 λ0 Δλ,where λ0is the incident signal or pump and Δλis the wavelength perturbation.As an example,we then simulate the NAND gate under the different wavelength perturbations and the results are shown in https://www.doczj.com/doc/a54813327.html,pared with the case without perturbations [here,Fig.7(a)is the duplicate of Fig.6(b)],we can see that the wave-length shifts may bring about the degradation of target light power S out and induce wavelength shifts of the target light S out in Figs.7(b)and 7(c).As shown in Fig.7(b),when there
exists a relatively small wavelength shift of ～4nm for the light sources,the normalized intensity of S out is about ?35dB ,that is to say,the logic functions could still be valid by power thresh-old detection.However,when there exists a relatively large
Table 2.Logic Operation of the NOR Optical Gate S 1/(Polarization State)S 2/(Polarization
State)
S out /(Intensity)0(TM)0(TM)1 ≈?25dB 0(TM)1(TE)0
1(TE)
0
1.3
1.4
1.5 1.6
1.7
-120
-90-60-300
N o r m a l i z e d i n t e n s i t y (d B )
Wavelength (μm)
1.3
1.4
1.5 1.6
1.7
-120
-90-60-300
N o r m a l i z e d i n t e n s i t y (d B )
Wavelength (μm)
-120
-90-60-300
N o r m a l i z e d i n t e n s i t y (d B )
Wavelength (μm)
-120
-90-60-30
0N o r m a l i z e d i n t e n s i t y (d B )
Wavelength (μm)
Fig.6.Logic operation of the NAND gate.The polarization-dependent FWM process and simulated results for (a)the logic oper-ation of “0NAND 0 1”when S 1is TM polarized and S 2is TM polarized,(b)the logic operation of “0NAND 1 1”when S 1is TM polarized and S 2is TE polarized,(c)the logic operation of “1NAND 0 1”when S 1is TE polarized and S 2is TM polarized,and (d)for the logic operation of “1NAND 1 0”when S 1is TE polarized and S 2is TE polarized.
wavelength shift of ～8nm for the light sources,as shown in Fig.7(c),the normalized intensity of S out is about ?60dB ,that is to say,the logic functions could not be valid.In other words,the difference between the resonant wavelength of the MRR and the input light wavelength has an important impact on the logic functions in this kind of optical logic device.5.CONCLUSION
Utilizing polarization-dependent FWM,all-optical logic oper-ation in a Si-HPMRR is demonstrated by using the FDTD
method.First,we designed an ultra-compact (radii 1μm )MRR operating at the near-infrared wavelength range (1300–1700nm)and realized it by using silicon HPWG with the capacity for subwavelength-bending.The HPWG exhibits very high confinement (A eff ～0.045μm 2)that can result in a remarkably high nonlinear parameter (γ～3000W ?1m ?1),given a highly nonlinear gap material.By manipulating the polarization properties of the pump and signals with a very low electric field (j E j ～108Vm ?1),all-optical NOT,NOR,and NAND logical operations are obtained.These compact all logic devices are stable,robust,fabrication simplified,and SOI-compatible for integrating a nanoplasmonic circuit and a silicon nanophotonic circuit on the same chip,which can be done https://www.doczj.com/doc/a54813327.html,pared with other intensity-dependent all-optical logic gates,the ones proposed here are more compact (radii 1μm ),simply constructed (Si-HPMRR),flexible (SOI-compatibility),and exhibit high potential for the integra-tion of all-optic circuits.
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Table 3.Logic Operation of the NAND Optical Gate P /
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1(TE)
1(TE)
0
-120
-90-60-300
N o r m a l i z e d i n t e n s i t y (d B )
Wavelength (μm)
-120
-90-60-300
N o r m a l i z e d i n t e n s i t y (d B )
Wavelength (μm)
1.3
1.4
1.5
1.6
1.7
1.3
1.4
1.5
1.6
1.7
-120
-90-60-30
0N o r m a l i z e d i n t e n s i t y (d B )
Wavelength (μm)
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