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Nonlinear magneto-plasmonics (NMP) describes systems where nonlinear optics, magnetics and plasmonics are all involved. In such systems, nonlinear magneto-optical Kerr effect (nonlinear MOKE) plays an important role as a characterization method, and Surface Plasmons (SPs) work as catalyst to induce many new effects. Magnetization-induced second-harmonic generation (MSHG) is the major nonlinear magneto-optical process involved. The new effects include enhanced MSHG, controlled and enhanced magnetic contrast, etc. Nanostructures such as thin films, nanoparticles, nanogratings, and nanoarrays are critical for the excitation of SPs, which makes NMP an interdisciplinary research field in nanoscience and nanotechnology. In this review article, we organize recent work in this field into two categories: surface plasmon polaritons (SPPs) representing propagating surface plasmons, and localized surface plasmons (LSPs), also called particle plasmons. We review the structures, experiments, findings, and the applications of NMP from various groups.
© 2015 Optical Society of America
1. Introduction
Surface plasmons (SPs) consist of coherent delocalized electrons that exist at the interface between a metal and a dielectric [1–3]. Two types of SPs are commonly studied. One consists of propagating plasmons, or surface plasmon polariton (SPP), which can be excited by photons with a prism or a grating as a coupler to match the wave vectors of photon and surface plasmon. The other is a localized surface plasmon (LSP) which can be excited by photons absorbed by nanoparticles with sizes comparable or smaller than the wavelength of the photons. Both types of SPs have the same significant effect: the electromagnetic (EM) field is greatly enhanced at the surface where SPs are excited [3–5].
The field enhancement effect of SPs is very favorable to nonlinear optical (NLO) processes, which are inherently very weak. SPs can boost parametric nonlinearity processes mainly in two ways. The first one is that the plasmon-enhanced electric field E(ω) boosts the polarization P, described in the electric-dipole approximation by Eq. (1):
where is the linear optical susceptibility tensor and is the second-order nonlinear susceptibility tensor, which gives rise to second-harmonic generation (SHG), taking into account that the 4th-rank susceptibility tensor representing the quadrupolar contributions is much smaller. SHG is only allowed in media without inversion symmetry because it is an even-order () NLO effect. Therefore, SHG can be generated only in noncentrosymmetric media or at surfaces or interfaces between centrosymmetric media where the inversion symmetry is broken [6,7]. This is the second way that SPs can boost parametric nonlinearites: SHG is generated at surfaces or interfaces, the same region where SPs are excited and the enhanced field is strongest. Plasmon-enhanced SHG has been reported first by Simon et al. on silver films [8]. Later studies have shown SPs-enhanced SHG in other materials [9–11], SPs-enhanced THG [12,13], and four wave mixing [14,15] in various structures.Plasmon-induced effects on the nonlinear index, which is another branch of NLO processes, are also being studied. The interesting applications include: all optical switching and modulation in plasmonic wave-guides, controlling light with light in plasmonic nanostructures, etc [16–18]. The terminology “nonlinear plasmonics” is adopted to describe systems where SPs and NLO processes co-exist as mentioned above [18].
Another topic, where SPs are highly involved, is magneto-plasmonics (MP), which describes systems where SPs and magnetic features coexist [19]. The studies in MP fall into two main categories: SPs’ effect on magneto-optical (MO) activities [20], and magnetic field tuning of SPs. MO activities, especially magneto-optical Kerr effect (MOKE) [21], play important role in both categories. For the former one, Eq. (2) briefly describes how SPs affect the MO activities through the enhanced field:
where rps is the MO polarization conversion, which determines the Kerr rotation, Ɛmo is MO constant of the material, d is the thickness of the thin layer MO material. Ep and Es are the component of p and s polarization field in the MO material [19,22]. The MOKE response is boosted by the SPs-enhanced field. The first experimental study of this effect has been reported by Safarov et al. on metallic multilayer films [23]. Later on, the studies have been expanded to ferromagnetic metal nanoparticles (including nanowires, nanodiscs, etc.), noble metal-ferromagnetic nanoparticles, noble metal nanoparticles and ferromagnetic dielectric layers, perforated continuous layers, etc [19]. with applications for bio-chemical sensors [24–26] and optical isolators and modulators [27,28]. For the second category of studies in MP, the magnetic field exerts an influence on the SPs by modulating SPs’ wave vector through MO constant Ɛmo, which is a function of the applied magnetic field [19]. The major application of this effect is active plasmon wavevector modulation [29].In this paper, we review the interdisciplinary studies at the intersection of Nonlinear Plasmonics (NP) and Magneto-Plasmonics (MP), referred to as Nonlinear Magneto-Plasmonics (NMP). NMP adopts nonlinear MOKE, especially magnetization-induced second-harmonic generation (MSHG) [30] as a research tool. MSHG is more surface sensitive than the linear optical MOKE, because it is sensitive to the interface or surface magnetization where the symmetry is broken [6,7,30,31]. On the other hand, compared to metal surface second-harmonic generation (SHG) in NP, MSHG contains nonzero magnetic components of the second-order nonlinear susceptibility tensor which makes MSHG extremely sensitive to subtle modifications of the spin-polarized electronic structure of transition metal surfaces [32,33], the same region where SPs are present. Hence, NMP combines the strength and unique features of NP and MP. The studies are classified according to the types of SPs into two categories: SPP and LSP.
2. Nonlinear magneto-plasmonics with surface plasmon polaritons
The first NMP experimental study was carried out by Tessier et al. in 1999 [34,35]. The measurements were done using the attenuated total reflection (ATR) technique in the Kretschmann geometry [1] [Fig. 1(a)]. For light incident in the x-z plane [Fig. 1(b)], the longitudinal, transverse, and polar MSHG are classified according to the direction of magnetization component parallel to the x, y, and z-axis, respectively [30]. Both transverse (T) and longitudinal (L) MSHG were studied on an Au (25 μm thick) / Co (3 μm thick) / Au (3 μm thick) / air system.
Fig. 1 (a) Kretschmann geometry for SPP excitation in NMP, and (b) coordinate system for MSHG. Red lines represent the fundamental beam, which is normally generated by a Titanium doped Sapphire laser, with a wavelength of around 800 nm. Blue lines represent the double frequency beam with a wavelength of about 400 nm. (adapted from ref. 38)
In the coordinate system depicted by Fig. 1(b), the nonlinear susceptibility tensors for L- and T-MSHG are derived with proper simplification by symmetry as [30]
andwhere odd terms change signs with magnetization reversal and thus exhibit the switching process, while the even terms are not sensitive to magnetization and are considered as crystal contribution. Knowing the polarization of the incident beam, the second-order nonlinear optical polarization can be calculated by the tensors.In Tessier’s study, a second-harmonic signal (includes MSHG and SHG) enhanced by a factor of four was observed. The most interesting result of this study is the sign reversal effect of the magnetic contrast near the SP resonance [Fig. 2] . The magnetic contrast can be defined as
where I( + M) and I(-M) are intensities for the two magnetization states. The reversal effect refers to the change of the signs of magnetic contrast C. That means the value of I( + M) and I(-M) has a drastic change at about 44° incident angle, where the SHG signal has a strong minimum.Fig. 2 Longitudinal and transverse magnetic contrasts of MSHG as a function of the incident angle, the signs of magnetic contrast change drastically at about 44°, the open dots are measured values, the curves represent best fits. (adapted from ref. 35)
A model on the basis of a nonlocal field theory [36] was developed to explain the sign reversal effect. The nonlinear susceptibility is assumed to be nonlocal in z direction. Following this approach, as a result of self-consistent solutions of the wave equations the fundamental electric fields of the light are continuous functions, which can be calculated on the basis of the Green’s functions for the interfaces of trilayer films. Taking into account multiple interference of different contributions, the total nonlinear electric field was calculated numerically. This model allows to distinguish the contributions of the various interfaces to SHG, and agrees with the experimental data very well.
Historically, one dilemma for MP systems is that the noble metal layer supports high quality SP, but a very large magnetic field (several Tesla) is needed to achieve MO activity. On the other hand, the ferromagnetic (FM) layer exhibits large MO activity, which makes it possible to make real MO devices. However, the huge losses in the FM layer causes an overdamping of plasmon resonance, and thus impairs the strength of SP. The prevailing configuration, noble metal/FM/noble metal heterostructures [23–26,29,34,35,37], combines the strength of good quality SP and large MO effect, but makes the structure complex and separates the source of SP and magnetization which compromises the coupling between them.
Taking the advantage of the spatial overlap of SPP and MSHG source, a simpler structure, 10-nm thick single-crystal Fe film (grown on an MgO (001) substrate with axis [110] along the x-direction), was adopted by Zheng et al. [38]. Large enhancement of the MSHG signal intensity was observed under ATR [Fig. 3(a)]. A comparison between the contrast ratio of SPP-enhanced MOKE and MSHG signal shows NMP has much more pronounced effect over MP [Fig. 3(b)]. Figure 3(b) shows a continuously enhanced contrast ratio for T-MSHG over a large range of incident angle. The results suggest that as an inherent surface sensitivity technique, MSHG would be ideally paired with SPs for sensing applications.
Fig. 3 (a) Enhanced signal strength of transverse MSHG as a function of the incident angle on 10-nm thick Fe thin film sample, and (b) comparison of SPP-enhanced magnetic contrast of MSHG and MOKE. The ATR curve (green) is shown as reference. (adapted from ref. 38)
Note that the ATR curve for this pure Fe film is not as sharp as that of noble metals as it is stretched out due to absorption, i.e. strong damping. The simple structure makes the analysis easier. The experimental ATR curve agrees with the calculated one very well. The trend of MSHG values as a function of incident angle in Fig. 3(a) is very similar to a calculated curve, if one of the nonlinear susceptibility tensors dominates over others. This indicates that there exists a great anisotropy in the second-order susceptibility tensor of T-MSHG and its expression can be simplified.
A further study on the same system reveals a strong control effect of SPs on the magnetic contrast [39]. Due to the cubic magnetic anisotropy, single-crystalline iron film has four magnetization states [40–42]. The magnetic contrast between these states can be varied over a wide range with the presence of SPs [Fig. 4]. The magnetic contrast of transverse and longitudinal MSHG display opposite trends, which originates from the change of relative phase between MSHG components caused by SPs. Such a system enables simultaneous investigation of both longitudinal and transverse magnetization components regardless of the external magnetic field. This study has potential usage in quaternary magnetic storage systems because it enables the read-out of all four magnetization states from crystalline iron with high contrast ratio.
Fig. 4 As a magnetically anisotropic material, crystalline Fe has four magnetization states. With the help of SPs, MSHG technique can read out all four magnetization states with good magnetic contrast, the longitudinal and transverse MSHG can be studied simultaneously. The hysteresis loops on the right reveal the control effect of magnetic contrast with NMP. (adapted from ref. 39)
Newman et al. studied enhancement of MSHG by grating-excited SPs [43,44], in which the sharp drop of reflectance from gratings indicates the optical energy being converted from the incident beam to plasmon generation. An enhanced SHG and fractional intensity change (similar concept to magnetic contrast) are observed on a nickel grating used in optical disk manufacture with a period of 1200 nm and a profile depth of 70 nm.
The group of Kirilyuk and Rasing adopted a more complex grating structure, 100 × 100 μm array of 120 nm thick Au stripes deposited on 4 μm thick (Bi, Tm) iron garnet (BTIG) grown on gallium gadolinium garnet (GGG) substrate [45]. Through systematic measurements as a function of SPs excitation wavelength and angle of incidence, it is demonstrated that at an optimized condition SPs can be excited at both Au/air and Au/(Bi, Tm) interface, which is buried beneath Au stripes. Furthermore, the MSHG is enhanced at Au/(Bi, Tm) interface despite the very thick 120 nm Au layer [Fig. 5]. This finding is appealing for MP device manufacture. This study also pointed out the future direction and application could reside in an optical control of the MP properties and ultrafast nonlinear plasmonics.
Fig. 5 (a) Au/BTIG/GGG grating structures, (b) at 31° incidence, wavelength dependence of reflectivity and SHG intensity. Vertical dashed lines indicate the spectral positions of SPs at two interfaces, and (c) SHG intensity as a function of wavelength and angle of incidence, point 1 and 2 indicate the conditions where SPs at each interface are excited, respectively, point 3 indicates the condition that SPs are excited at both interfaces. (adapted from ref. 45)
The same group also conducted NMP research on an Au(2 nm)/Co(60 nm)/Ti(2 nm)/Si(111) plasmonic crystal [46]. In this system, the Au and Co layers were decorated with a hexagonal array of circular holes of average diameter of 250 nm and average pitch size of 470 nm. The authors provided profound discussion on the effect of SPs on MSHG. The enhanced MSHG strength and magnetic contrast is observed in the vicinity of the SPs. Direct phase measurements using the nonlinear interferometry method [47,48] show that the change of magnetic contrast originates from the change of phase between magnetic and nonmagnetic MSHG contributions [Fig. 6]. The activation of a nonlocal quadrupole mechanism [18,49] of the MSHG by SPs was attributed to such phase change.
Fig. 6 (a) SHG magnetic contrast as a function of incident angle for the reference (empty dots) and perforated (green full dots) films. Black diamonds represent the phase difference between even and odd (refer to Eq. (3) and (4)) magnetic SHG contributions, (b) relative phases of the even (red empty dots) and odd (blue full dots) SHG components. The dashed area represents phase shift introduced by the SPPs. Dotted lines are the result of an interpolation. The vertical line refers to the SP resonant angle. (adapted from ref. 46)
In earlier time, the group of Kirilyuk and Rasing also reported strong magnetization induced changes of the infrared-visible sum-frequency generation (SFG) intensity from thin magnetic films using a free electron laser. The reported effect occurs with the help of the SPs excited by magnetic grating made from Pt/CoNi/Pt sandwich [50].
A very recent NMP study on grating structures has been reported by the group of Murzina [51]. A grating with a period of d = 730 nm is formed by 40-nm thick gold film stripes covering a 2-μm thick bismuth iron garnet (BIG) layer on a gadolinium gallium garnet (GGG) substrate. Such structure is called a magneto-plasmonic crystal (MPC). In this study, both the SPPs at metal/dielectric interfaces and the waveguide modes [52,53] in the dielectric slab contribute to the field enhancement. Besides the phase modulation by the SPP, a strong modulation of the SHG intensity by both SPPs and the waveguide modes is observed. The field enhancement contributed by multi-sources shows an unique feature of properly designed MPCs [Fig. 7]. This study is very attractive for potential applications of the MPC structures as magnetic field active modulator.
Fig. 7 (a) The grating structure is also called magneto -plasmonic crystal, a transmission geometry is used to excite SPP and generate SHG. A dc magnetic field is applied parallel to the stripes to control the light flow, (b) Wavelength dependent transmission and SHG intensity indicate both SPPs and waveguide modes contribute to the SHG. IIa, IIb and IIc indicate the waveguide modes, and III indicate the SPP. (adapted from ref. 51)
3. Nonlinear magneto-plasmonics with localized surface plasmons
The first localized surface plasmons (LSPs)’ effect on MSHG has been reported by the group of Murzina in 2001 [54]. Wavelength-dependent MSHG measurements of CoxAg1-x and (CoFe)x(Al2O3)1-x nano-granular film show pronounced LSP resonances in the vicinity of 620 to 640 nm, where the second-harmonic signal is strongest. The effect of component weight x on LSP-enhanced MSHG and magnetic contrast for the above two materials is also studied [Fig. 8]. A later paper reported magnetic induced third-harmonic generation (THG) in the same system [55]. Good agreement between the observed LSPs resonances and numerical calculations confirmed the LSPs’ effect on magnetization-induced SHG and THG. The authors suggest the excitation of LSPs play an important role in the correlation between giant magnetroresistance (GMR) and MSHG.
Fig. 8 (a)(b) MSHG intensity as a function of x. x is the weight of element for CoxAg1-x and (CoFe)x(Al2O3)1-x nano-granular films at the fundamental wavelengths of 1064 nm and 800 nm, (c) MSHG magnetic contrast and magnetoresistance as a function of x for CoxAg1-x. (adapted from ref. 54)
The same group also reported studies of NMP on Fe2O3(Au) nanoparticles, Au/Co/Au nanosandwiches, magnetophotonic microcavities (MMCs) and magnetophotonic crystals. Plasmon-assisted modifications of magneto-optical response and magnetization-induced SHG and THG were studied [56,57].
Valev et al. studied MSHG on G-shape nickel nanostructure with a four-fold in plane symmetry [58]. MSHG signals are also expected to have four-fold symmetry [59] because it is a symmetry sensitive technique. Surprisingly, besides the four-fold symmetry main peaks of MSHG signal enhanced by LSPs, there appear secondary peaks, which make the whole response asymmetric [Fig. 9]. By excluding the magnetic field, surface anisotropy, diffraction induced wavelength independence, the sides of the G-shape nanostructures, or a shift of the plasmon resonance caused by angle-of-incidence structure, the authors suggest a magneto-chiral effect [60–63] as the reason for the asymmetry. The plasmonic and nonlinear optical response are tuned by such effect. This study shows a novel way in NMP to combine nanophotonics, nanoelectronics and nanomagnetics. Since chirality can lead to negative refractive index, a device that can switch the sign of refractive index with magnetic field is proposed.
Fig. 9 (a)(b)MSHG intensities as a function of azimuthal sample rotation angle show asymmetric secondary peaks, (c)(d) the position of secondary peaks changes with wavelength, while the structure remain same, which excludes the structure anisotropy as the origin of the asymmetry, (e) the position of the secondary peaks remains unaffected with different magnetic field applied, which excludes the magnetic field as the origin, (f) the four-fold symmetric sample and experimental setup. (adapted from ref. 58)
4. Conclusion and perspectives
We have reviewed the studies in nonlinear magneto-plasmonics (NMP), from the experiments, structures, scientific findings to possible applications. Many interesting effects are revealed (Table 1).
Table 1. Comparison of different NMP structures
We propose the future studies of NMP will reside in the following three major directions: 1) development of NMP devices with real applications; 2) effects of other techniques on NMP, for example, the temporal study by pump-probe technique; 3) active control of one element by the other, for example, MSHG surveys the control of magnetization by SPs at the interface.
Acknowledgments
The optical experiments performed at the College of William and Mary are supported by the Department of Energy (DOE) through Grant No. DE-FG02-04ER46127. The sample growth at NRL is supported by core programs at NRL and the NRL Nanoscience Institute.
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