Bimetallic Fe-Ag arrays with extraordinary nonlinear refraction and nonlinear Faraday rotation at telecommunication wavelength (1550 nm)


 There is a pressing need to discover magneto-optical materials and devices with better performance and lower cost that operate at telecommunication wavelengths. Here we report the discovery of giant negative nonlinear refraction and nonlinear Faraday rotation at 1550 nm using an array of bimetallic Fe-Ag nanopyramids. This system exhibited a very large third order nonlinear refractive index (n2 = -2.32 cm2/GW) and nonlinear figure of merit (F = 2.3). The same system also exhibited an extraordinarily large magneto-optical susceptibility (χi4 = 6.5 × 10-12 esu) and photoinduced nonlinear Faraday rotation up to 2.5 radian/μm at a magnetic field of 0.5 T. The nonlinear response was dependent on the degree of overlap of the Fe nanopyramid on the Ag nanopyramid which influences the strength of plasmon induced dipoles on the Ag nanopyramid. This nanoscale system opens up a rich new set of possibilities in utilizing magneto-plasmonic materials to miniaturize future multifunctional devices at telecommunication wavelengths.

stability arising from synergetic effects. In the past, metals like Fe, Co, Ni, Pt, Pd and Al have been combined with the noble metals Ag, Au and Cu to enhance the plasmonic and magneto-plasmonic properties. For example, ferroplasmons have been discovered in Ag-Co bimetallic nanoparticles, in which strong surface plasmons have been observed in the Co side of the metallic system while preserving its ferromagnetism [32,33]. Additionally, the Ag-Co and Ag-Fe system have also demonstrated reduced degradation rate of plasmonic signals due to oxidation of silver thus leading to very stable plasmonic behavior over long periods of time [33,34]. Fe 2 O 3 -Au core shell nanoparticles have been reported to have a high Faraday rotation at resonant frequency ascribed to spectral overlap of magneto-optical transition to plasmonic resonance [35].
In this article, we report the discovery of giant third order nonlinear refractive index and photo-induced nonlinear Faraday rotation at 1550 nm from a hexagonal array of partially overlapped Fe-Ag truncated nanopyramids. This nanopyramidal system exhibited a very large third order nonlinear refractive index (n 2 = -2.32 cm 2 /GW) and nonlinear figure of merit (F = 2.3). The same system also exhibited a photoinduced nonlinear Faraday rotation of magnitude of 2.5 radian/µm at a magnetic field of 0.5 T. We found that these effects are strongly dependent on the plasmon induced dipole strength from Ag nanopyramids across the Fe nanopyramids and which in turn depends on the overlapping extent of Fe nanopyramids on Ag nanopyramids.

Nonlinear optical properties
We studied nonlinear optical properties of nanopyramidal systems viz. pure Ag, pure Fe and Fe-Ag (with 30% and 90% overlap) at 1550 nm whose surface plasmons induced resonant absorption was at 750 nm (except for pure Fe pyramidal system). The third order optical nonlinearities were studied by f-scan methods, particularly transmission f-scan and reflection f-scan, which are modifications of the conventional z-scan method [36][37][38]. These methods allow us to measure the nonlinear index of refraction (n 2 ) in reflection and the nonlinear absorption or two photon absorption coefficient (β ) in transmission modes. The electric field (E) dependent polarization (P) of a nonlinear system can be expressed as where, χ (i) (i=1,2,3...) is the i th order nonlinear susceptibility of the nonlinear system. The real part of the EEE is related to n 2 while imaginary part is related to β . A schematic of experimental set up to calculate the value of n 2 and β is shown in Fig. 1 (a). First, for the open aperture configuration, we used a 1550 nm fiber laser with a pulse duration of 64 fs, and an average power of 20 mW which was incident on an electrically focused tunable lens (EFTL). The samples were placed at distance f s from the EFTL. The output of the lens impinged in the sample and the intensity in the sample was controlled by changing the focal length of the EFTL with applied current. The transmitted laser beam was detected with a Ge-photodetector, and the normalized transmittance was used to calculate the value of β using the relation as, with Here, L e f f is the effective sample thickness given by L e f f = (1−e −αL ) α , L being sample thickness and α being linear absorption coefficient. Also, R is reflection coefficient and I o is peak intensity of the beam which is function of focal length. Also, ρ is expressed as ρ = 2ln(1+ √ τ) τ with τ being full width at half maximum pulse duration.
Second, the samples were tilted at an angle of θ with respect to the laser beam direction and the light reflected by the sample surface was analyzed to measure the n 2 . The normalized reflected beam intensity can be expressed as Here, f , Z 0 ( f ), θ , n o and k 2 are the focal length of EFTL, Rayleigh range, angle between normal to the incident beam and sample surface, linear refractive index and extinction coefficient respectively.

Plasmonics and microstructure
In order to understand the origin of giant optical nonlinearity observed in the Fe-Ag nanopyramidal system, we investigated the plasmon induced linear optical behavior and electron energy-loss behavior. The plasmon induced linear optical absorption properties of the nanopyramidal system [pure Ag, pure Fe, Fe-Ag (30 % and 90 % overlap)] were measured using normally incident broadband light. We saw that the pure Ag has a sharper dipole resonance curve followed by Fe-Ag (∼30 % overlap) and Fe-Ag (∼90 % overlap) at 750 nm (near the energy of two photons at 1550 nm) as shown in Fig. 2(a). The dipole resonance peak at 750 nm was achieved in each pyramidal system by controlling the thickness of the Ag pyramids which was ∼17 nm while the height of the Fe pyramids in each case was ∼9 nm. The representative SEM image of pure Ag and 30 % overlapped Fe-Ag nanopyramidal system is shown in Fig. 2(b) and (c). The pure Fe nanopyramidal system didn't show any significant absorption features in the wavelength region studied here. Moreover, we didn't see any linear absorption feature in the 1550 nm in all nanopyramidal systems as evident from the inset of Fig. 2(a). The enhancement in optical nonlinearity observed in the pure Ag or the Fe-Ag system compared to that of the pure Fe system was attributed to matching of the two photon resonance conditions.
The plasmonic systems (Ag and Fe-Ag) had plasmon induced resonance peak wavelengths at 750 nm which is near the fundamental frequency for two photons at 1550 nm. However, the giant enhancement in the Fe-Ag system over the Ag system was completely unexpected since the plasmon induced dipole resonance is more damped in the Fe-Ag system compared to the Ag system, as evident from Fig. 2(a). Nevertheless, this analysis firmly established that the matching of two photon resonance conditions partially contributed to the observed optical nonlinearity, as pure Ag, and Fe-Ag nanopyramidal system had significantly higher optical nonlinearity than pure Fe.
One of the reasons for the very large nonlinear optical responses from Fe-Ag nanopyramidal array could be a synergistic effect between Fe metal and Ag metal nanopyramids. To explore the system further, we investigated the electron energy-loss spectra from those nanostructures as shown in Fig. 3(a), (b) an (c). The dipole induced electron energy-loss peaks were observed at 1.60 ± 0.02 eV in each case, slightly shifted from the observed optical absorbance at 1.65 ± 0.01 eV (750 nm). This difference in observed electron energy-loss and optical absorbance peak comes from their observed part of the dielectric function. In case of EELS, we observe Im( ε−1 ε+1 ), while in optical absorption we observe Im(ε), ε being the complex dielectric function of the system [42]. To analyze the energy-loss behavior from the corner of Ag nanopyramids, the features in electron energy-loss peak from Ag corners [marked as A, B, C in Fig. 3] of each Ag, Fe-Ag (30 % overlap) and Fe-Ag (90 % overlap) were quantified in terms of peak intensity and area [in parts per million (ppm)]. We found that the peak intensity of pure Ag nanopyramids were higher than that of Fe-Ag, and the Fe-Ag (30 % overlap) had higher peak intensity than Fe-Ag (90 % overlap). Further, peak intensity and peak area of Ag corners (B and C) adjacent to the Fe overlap were smaller than free corner (A). Moreover, 30 % overlapped Fe-Ag nanopyramids had significantly larger intensity and area (at B and C corners) than 90 % overlapped Fe-Ag nanopyramids as summarized in Table I.
What was apparant from the optical and EELS analysis of nanopyramidal system was that the surface plasmon dipoles are stronger for the 30 % overlapped as compared to the 90 % overlapped case. The plas-  Fig. 2(d).  and M are plasmon dipole induced electric polarization and magnetization of ferro-electrons in Fe nanopyramids. This moment is expected to control the third order optical nonlinearity in nanomaterials [43,44].
So, the plasmon induced effect in ferromagnetic material like M-E effect could be an important factor, apart from matching of the two photon resonance conditions, for enhancement of the nonlinear optical behavior in Fe-Ag nanopyramidal system.

Nonlinear Faraday rotation
Given the above hypothesis, we explored the possibility of external magnetic effects on the nonlinear behavior of this system by employing both the f-scan and polarization rotation measurements simultaneously, as suggested by Frey et al [45]. The Fe-Ag system, which showed the large value of n 2 (i.e. 30 % overlap Fe-Ag), the nonlinear Faraday rotation at 1550 nm was studied. In the presence of external static magnetic field, the polarization of the system can be expressed as Here, χ EH is the second-order nonlinear susceptibility which is related to linear Faraday rotation/magnetic circular dichroism (MCD) while χ (4) EEEH is the fourth-order nonlinear susceptibility which describes nonlinear Faraday (polarization) rotation.
The schematic diagram for the experimental set up to measure nonlinear Faraday rotation is shown in Fig. 4(a). The laser with linear polarized light was focused on the sample by the EFTL and a regular f-scan was taken as a function of the applied magnetic field in the Faraday configuration where the static magnetic field varied from 0 up to 0.5 T in steps of 0.1 T. We recorded the transmission of the laser beam as a function of current in the EFTL at some fixed value of the magnetic field, after the beam was passed through a Thomson polarizer oriented at a 45 • angle with respect to the incoming polarization when there was no magnetic field applied. The transmitted intensity of the beam can be expressed as (6) and the polarization angle of rotation (ΔΘ) can be expressed as Where, H is the applied magnetic field and V is the Verdet constant, and χ 4 i and χ 3 i are the imaginary components of the fourth-order nonlinear and third-order nonlinear susceptibilities. The first term in equation 7 corresponds to the linear Faraday effect, while the second term is the photo-induced contribution to the nonlinear rotation. The transmittance of the beam passing through the analyzer can be calculated using Malus's law in the small angle approximation and optimizing for sensitivity as, At low intensity, we observed that all the scans showed the same value indicating that the linear Faraday rotation is negligible for the sample at 1550 nm (zero offset in the wings as a function of the B-field). This linear rotation behavior is expected due to the off-resonance condition (away from the plasmon resonance energy). The equation 8 contains information about the linear and nonlinear Faraday effects. As we didn't observe any linear Faraday rotation behavior, the observed rotation at higher intensities is due to pure photo-induced Faraday effect. In this case the above expression can be written as For fit, first, we calculated the third-order nonlinear susceptibility in terms of the two photon absorption coefficient (β ) which was obtained to be χ 3 i = β n 2 cλ 8π 3 = 9.4 × 10 −8 esu. Then, χ 4 i was obtained by fitting equation 9 at 0.5 T. We found the value for the nonlinear fourth order susceptibility to be χ 4 i = 6.5 × 10 −12 esu. The value obtained for χ 4 i is six orders of magnitude larger than in dilute semiconductors [25].

DISCUSSION
The nonlinear optical processes in metallic nanostructures are generally governed by various excitations like multiphoton absorption, thermal scattering, interband and intraband transitions and geometry [46][47][48] . In our experiment, we ruled out the possibility of thermal scattering, by using a very low energy pulse of 0.4 nJ/pulse, with an average power of 20 mW on the sample, along with a repetition rate of 50 MHz, which put the system in a relatively low intensity regimen. Also the excitation wavelength of 1550 nm was far away from the plasmon resonance and therefore, low linear absorption and consequently low heating of the nanostructures is expected. Additionally, the enhancement of two photon absorption (by four times) of Fe-Ag nanoparticles over that of pure Ag nanoparticles in off-resonant wavelength was attributed to the interband and intraband transition of Fe-metals which subsequently reduced the absorption saturation effect of Fe-Ag system over pure Ag [49]. Surprisingly, we observed that the Fe-Ag nanopyramidal system has an enhancement of about 10 times that of the Ag system at lower photon energy (1550 nm). Another important observation of the optical nonlinearity of the Fe-Ag system over pure Ag was large as well as negative value of n 2 which was not reported in the previous study. It indicates the Fe-Ag system is self-defocusing while the pure Ag system is self-focusing. This is likely due to the difference in local optical response/polarization of Fe and Ag nanopyramids with incident laser fields as discussed above. Of particular interest was the same Fe-Ag system with the extraordinarily large value of nonlinear (photo-induced) Faraday rotation and nonlinear magneto-optical susceptibility at the same wavelength. While the EELS results strongly suggest a contribution from plasmon induced activity in the origin of the giant nonlinear properties of this metallic system, other mechanisms may still be important. For instance, one can expect the enhancement in the optical nonlinearity of the Fe-Ag system due to evanescent wave intensification at the magnetic/nonmagnetic interface through Schoch effect (magnetoelastic origin) and/or Goos-Hänchen effect (electromagnetic origin) [50,51]. The observation of large optical nonlinearity and strong nonlinear (photo-induced) polarization rotation effect on this system at the same wavelength of 1550 nm is very unique and clearly suggests an exciting system for further exploration.

CONCLUSION
To summarize, we investigated the nonlinear optical and magneto-optical properties of bi-metallic nanopyramidal systems in telecommunication wavelength. We found that the giant value of nonlinear optical and magneto-optical coefficients are due to two photon absorption phenomena which is further enhanced due to plasmon induced synergistic effect between two metallic systems. We further found that the partially

Angle-resolved nanosphere lithography
To fabricate the pyramidal metallic nanostructures from the nanosphere lithography, the polystyrene beads of diameter 500 nm were used to mask the quartz substrates by the technique used by Prasad et al [34]. The partial overlapping in nanopyramids was achieved by tilting the masked substrates on the sample holder away to the metallic vapor direction. To achieve 90 % overlapped in between Fe and Ag sample holder was tilted away by 1 • to vapor direction, while to achieve 30 %, the sample holder was tilted away by 5 • .

EELS fit
In order to quantify the plasmon peak position and peak area-Gaussian peaks and Lorentzian peaks were fit to the data. A multiplication of the Lorentzian functions was used to approximate the zero loss peak. A fit of zero loss peak is shown in Fig. 5. Figure 5. Fit spectra of zero-loss spectrum peak (black solid line) taken from red box.
The summation of gaussian peaks were used to produce noise free models of the electron energy-loss spectra. Inelastic scattering in ppm (parts per million) was calculated using the relation: I×10 6 I 0 Where I is the beam current in a pixel from the spectrum and I 0 is the incident beam current. The Gaussian peak corresponding to the dipole plasmon peak position was used to analyze the area and peak intensity (in ppm) of plasmon loss for corresponding position (A, B and C). A representative of fit data is shown in Fig. 6.