Ultafast effects in 3D Metamateials Nkoni Katte,2 and Philip G.Evans 3 Electical Engineeing Wilbefoce Univesity, 2 Sensos Laboatoy Wight State Univesity and 3 Oak idge National Laboatoy *Coesponding autho: Nkoni Katte 55 N Bickett oad Wilbefoce Ohio 45384, nkatte@wilbefoce.edu Abstact: he nonlinea optical popeties of metamateials have attacted lots of attention in the last decade, paticulaly because it povides novel ways of tailoing optical functions which will be useful in achieving highe speeds fo optoelectonics and othe photonics cicuits. In most of these metamateials, the nonlineaity of significance lies within it metallic constituents. In this pape we show how extaodinay optical chaacteistics and ultafast esponse can be achieved with use of a chial gold based metamateial. hese nonlinea functions is ealized when plasmonic excitations ae geneated by electomagnetics inteactions, which ae stongly enhanced within the metamateial leading to situation whee effective nonlineaity can be engineeed significantly by changes in the geometical stuctue of the components of the metamateial, and not only by tansitions in the electonic band levels of the mateial [] Keywods: Metamateial, hid ode nonlineaity. Intoduction he ultafast modulation of light with light has been a long sought goal fo eseaches and emains a difficult task, especially in the I and eahetz fequency egion. his is essentially so because the optical nonlineaities in conventional nonlinea mateials ae geneally too weak to alte the intensity of light significantly on a subwavelength scale. [2] With the emegence of metamateials eseach, which have significant metallic content in the ealy 2s, a significant appoach to tackle this poblem is to design nanostuctue which will have highe optical nonlineaities which will be povided by its metallic constituents. he typical nonlineaities in these case ae usually highe than those of common semiconducto such as Si and GaAs that ae popula in the optoelectonics industy. At the inteface of between metals and dielectics it often possible at paticula angles of incident of light to excite a suface wave which consist of electon oscillations, known as plasmons which could be vey significant in enhancing nonlinea effects. he geat challenge in ecent yeas has been to enginee new mateials that will be able enhance shot pulses of light geneated by moden lase systems, without suffeing significant loss, such that these new effects can be pobed. hese new mateials with nonlinea optical chaacteistics, could be used fo optical limiting and switching, sum-fequency geneation, diffeence fequency geneation, fou-wave mixing, and coss-phase modulation, and will lead to faste and moe efficient optical devices [3]. he focus of ou eseach has been to examine designs of metamateials composed of cylindical hollow gold/silve nanoods within an alumina dielectic matix. We have consideed two kinds nanoods aangement, fo a unit cell stuctue; a ectangula lattice and a hexagonal lattice. With the availability of high powe lases systems, one can actually investigate these metamateials with well chaacteized lase beams. It is possible to measue the effective optical nonlineaity of these mateials. Nevetheless befoe fabicating, measuing and chaacteizing should be done, it is vey needful to cay on a holistic computational modeling of the poblem which will guide both the fabication and chaacteization pocesses, and this computational task has been the focus of my poject thus fa. hese Metamateials povide a unique way to enhance the electic fields poduced by these lase beams, since the enhancement is citically dependent on the geomety of metamateial [4]. his is why liteatue is filled with many kinds of geomety which could enhance electic fields Except fom the Poceedings of the 25 COMSOL Confeence in Boston
in a diffeent ways. In this wok we have extended ou calculations beyond a two dimensional (2D) geomety less computationally intensive poblem, to analyze a potentially ealizable thee dimensional (3D) geomety metamateial (MM) with gold (Au) as the plasmonic metal of choice. effect and its coesponding thid ode susceptibility[4]. o make the stuctue chial we intoduced a gold hemispheical hump within anothe alumina matix, nomal to the axis of popagation which is the z-axis. 2. Use of COMSOL Multiphysics o addess this poblem we typically solve Maxwell s equation in the fequency domain to calculate the spectal chaacteistics of the metamateial, using equation () below. We also solve the poblem in the tansient time dependent case to analyze the ultafast effects of the metamateial, using equation (2) below. 2 j ( E) k ( ) E () A A ( A) ( P) 2 Figue : Shows the basic stuctue of the chial metamateial. We also notice vey stong electic field couplings aound the cental nanoods. his esult was obtained afte a popagation time of 7[fs]. he polaization tem is given by () P E (3) E 2 E. We ignoe the second ode tem because metals ae centosymmetic, theefoe the second ode tem is small. his polaization tem is vey citical fo the tansient nonlinea case. We have also used Comsol to solve fo heat geneated in these mateials, but this was not ou pimay goal. 3 esults and Discussion,.8.6.4.2 fo chial fo chial fo achial fo achial Based on some pevious studies, the main task of in this cuent wok is to examine popeties in the linea egime, of poposed designs of Metamateials (MM) which would guaantee high field enhancements needed fo the excitation of nonlinea optical activity [5]. A novelty in ou study this time was to intoduce chiality in ou design. A chial stuctue is a stuctue whose mio image cannot be supeimposed on it. It has been epoted in liteatue that chiality enhances nonlinea optical activity, and paticulaly polaization otation which is well known, and these kind of nonlinea activity is stongly linked to the Ke 2 3 4 5 6 7 8 9 Angle (degees) Figue 2: his figue shows the ansmission and eflection vesus angle of incidence fo both achial ectangula MM and the chial ectangula MM at a wavelength of 8nm Except fom the Poceedings of the 25 COMSOL Confeence in Boston
.7.6,.8.6.4.2 2 4 6 8 Angle (degees) Figue 3: his figue shows the ansmission and eflection vesus angle of incidence fo the chial MM at a wavelength of 2nm. Fom the figues above, we notice that thee is a similaity in the pofile fo the achial case at 8nm and the chial case at 2nm, as in both cases thee is a maximum in ansmission and a minimum in eflection at aound 63 degees. But the value of the ansmission at 2nm in the chial case ises to almost a value of. It is of inteest to study these mateials at longe wavelengths since thee is a citical shotage of modulating devices in the infaed and teahetz egions. Fo the achial MM, when we vaied the inne ai hole adius fom 4nm to nm, while leaving the oute ai hole adius at a constant value of 6nm we obtained the esult shown below fo ansmission and eflection.,.5.4.3.2. 4 5 6 7 8 9 adius of ai hole (nm) Figue 4: Shows the ansmission and eflection vesus the adius of ai, when the incident angle is, degee at an opeating wavelength of 8nm, fo the achial MM. he above esults, gives us the necessay ideas we need, so as to optimize ou designs fo the applications of inteest such as switching, and optical limiting. A study of the chial stuctue, at zeo degee incident angle, fo vaious wavelengths of inteest shows that the size of the hemisphee does not citically impact the ansmission, eflection and Absoption. On the othe hand if we look at the spectum as seen in Figue 5, fo the case whee the adius of the hemisphee is 5nm we notice a maximum in absoption at about 759nm. he absoption late falls quickly to zeo fo longe wavelength. his esult povides us with a good idea of how to futhe investigate the system.,, A.9.8.7.6.5.4.3 A.2. 5 6 7 8 9 2 3 4 5 Wavelength (nm) Figue 5: ansmission, eflection and Absoption vesus wavelength fo a chial MM, with a hemisphee adius of 5nm at zeo degee incident. Except fom the Poceedings of the 25 COMSOL Confeence in Boston
he tue nonlineaities can only be measued expeimentally, with a pump pobe expeiment o a Z-scan expeiment. Yet in ode fo us to do that we need to figue out with these initial calculations ways to incease these nonlinea ultafast effects. It will be vey needful fo these devices to function at low intensities. ypically it takes intensities in the -GW/cm 2 ange to excite significant nonlineaities in MM. hee seveal expeiments lately that show significant excitations with intensities of the ode MW/cm 2 [, 6]. It will be good to be able to ealize these ultafast effects at lowe incident light intensities In ou initial tansient calculations we incident a beam of pulse width 2[fs] which has an intensity at focus of about MW/cm^2. hen we look at exit powe leaving the MM it case whee no nonlineaities ae excited and in the case whee nonlineaities ae excited. In liteatue thee ae some many diffeent values of these nonlineaities. ypically fo Au it is the ode of -8 m 2 /V 2, yet thee ae conditions whee these values can be inceased, because of chiality and ode nano-mechanical foces to values of about -2 m 2 /V 2 [4, 6,7]. We obtained esults of the exit powe as function of time as shown in Figue 6 below. Exit powe in (watts) 3.5 3 2.5 2.5.5 I=MW/cm 2 incident angle=63 degee exit powe @ K3=m 2 /V 2 exit powe @K3=3e-2m 2 /V 2 2 3 4 5 6 time (seconds) 7 8 9 x -4 Figue 6: Shows the exit powes as function of time. he blue line epesents the case when nonlinea effects ae pesent, and the black line epesents the case when, no nonlineaities ae exited. 4. Conclusion We have shown how, nonlinea effects could be designed by changing seveal physical paametes such as cylinde, adius, and designing fo chiality. We also notice, that ou studies povides a significant way to appoach the poblem of design nonlinea devices which will function in the deep into the I. Expeimental esults ae expedient at this point to guide the theoetical fame wok we have developed and to give us the actual ange of values of nonlineaities we can obseve with the mateials we have chosen. his is necessay because we can chose to exploe othe mateials such as cabon nanotubes and gaphene which have been shown to enhanced plasmonic nonlineaities [2]. 5. efeences [] Neia, A.D. et al. Eliminating mateial constaints fo nonlineaity with plasmonic metamateials. Nat. Commun. 6:7757 doi:.38/ncomms8757 (25). [2]A. Nikolaenko, N. Papasimakis, A. Chipouline, F. Angelis, E. Fabizio, and N. Zheludev, Hz bandwidth optical switching with cabon nanotube metamateial. OPICS EXPESS 668, Vol 2 No 6 Mach 22. [3] Matti Kauanen, and Anatoly V. Zayats S. Nonlinea Plasmonics, Natue Photonics 6, 737-748 Novembe 22 [4] en, M. et al. Giant nonlinea optical activity in a plasmonic metamateial. Nat. Commun. 3:833 doi:.38/ncomms85 (22). [5] P. Evans and N. Katte Numeical study of Chemically Synthesized 3D Nonlinea Metamateials, Poposal Submitted to Depatment of Enegy office of Science. Januay 24. [6] Jun-Yu Ou, E. Plum, J. Zhang, and N. I. Zheludev 25 Modulating light with light via giant nano-opto-mechanical nonlineaity of plasmonic metamateial axiv.og/pdf/56.5852 [7] Zhu, Y., Hu, X.Y., Fu, Y.L., Yang, H. & Gong, Q.H. Ultalow-powe and ultafast alloptical tunable plasmon-induced tanspaency in metamateials at optical communication ange. Sci. ep. 3, 2338; DOI: 38/sep2338 (23). Except fom the Poceedings of the 25 COMSOL Confeence in Boston
6. Acknowledgements his wok was suppoted in pat by the U.S. Depatment of Enegy, Office of Science, Office of Wokfoce Development fo eaches and Scientists (WDS) unde the Visiting Faculty Pogam (VFP). Except fom the Poceedings of the 25 COMSOL Confeence in Boston