Optical bistability in core-shell magnetoplasmonic nanoparticles with magnetocontrollability

W. J. Yu; H. Sun; L. Gao

doi:10.1364/OE.24.022272

1. Introduction

Optical bistability provides us by controlling light with light, and it just refers to an optical effect where a system exhibits two different values of the local field for a single value of the input field [1–3]. Hence, it can give the optical structures the function to control two distinguishing stable states with the history of the input light. The phenomenon of optical bistability has attracted considerable attention due to its promising applications in nonlinear optical technologies such as all optical switching [4,5], low power lasing [6] and low-threshold optical bistability [7]. In this context, a variational approach [8] and self-consistent mean-field approximation [9,10] were, respectively, proposed to examine the optical bistable behavior of nonlinear plasmonic composites near the surface plasmon resonant wavelengths. Recently, optical bistability and modulational instability in nonlinear plasmonic nanoparticles (NPs) arrays were investigated. And plasmonic kinks, oscillons, solitons, and domain wall due to modulational instability were demonstrated [11]. More recently, a two dimension dielectric/metal composite of coated cylinders has been proposed to demonstrate the nonlocality would lead to the tunable Fano resonances and can significant reduce the switching threshold of the optical bistability in the near field and far field, suggesting a nonlocality enhanced nonlinear optical devices [12].

On the other hand, controlling the surface plasmons with a magnetic field provides further opportunities for designing active plasmonic components. At first, in the presence of an external static magnetic field, the MO materials have different propagation constants for circularly polarized waves with right and left-handedness (RCP and LCP, respectively). This is the reason that MO materials can be utilized to design one-way photonic states [13]. Then, combining MO materials with plasmonic materials such as gold and silver opens new routes in the development of efficient and versatile magneto-plasmonic architectures [14]. For instance, a dielectric/plasmonic cylinders coated with a MO shell can be designed to realize the tunable plasmonic cloaks with an external magnetic field [15,16]. And spherical gain NPs coated with metallic MO shell can operate as a MO spaser amplifying the circularly polarized surface plasmons [17]. More recently, Varytis et al. adopted a rigorous full electrodynamic calculation to investigate strong circular dichroism [18], the plasmon-driven Hall photon currents [19] as well as enhanced Faraday rotation by core-shell magnetoplasmonic NPs [20].

In this paper, we would like to investigate the optical bistable behavior in coated NPs containing a nonlinear plasmonic metallic core and a linear MO shell in the quasistatic limit. We aim at the influence of the MO effect on the bistable hysteresis of the nanostructures. Since the optical features of MO material are purely induced by an external magnetic field, we shall show that can easily control the bistable threshold fields, the bistable region, and the critical volume fraction needed to achieve optical bistability for both CP waves via adjusting the external static magnetic field.

2. Theoretical development

Let us first consider a linear coated magnetoplasmonic nanoparticle consisting of a linear metallic core with the permittivity and radius coated by a MO (Bi:YIG) spherical shell with the permittivity tensor and radius , as shown in Fig. 1. Actually, there are some theoretical discussions on the magnetic-optical enhancement and magnetic spaser based on the present model [17,21], and some works on the experimental synthesis of metallic-MO composite nanostructures in the laboratory [22,23]. For simplicity, we assume that the MO medium magnetization vector (the direction of the external uniform magnetic field B) is parallel to the z-axis. Thus, the permittivity tensor of the shell has the form [24]

{\overset{\leftrightarrow}{ε}}_{s} = (\begin{matrix} ε & i g & 0 \\ - i g & ε & 0 \\ 0 & 0 & ε \end{matrix}),

where the off-diagonal component

g

is responsible for the “strength” of MO activity of the media. It has a dispersive character and depends upon B, vanishing in its absence. As a consequence, the optical anisotropy and the MO effect of such a material is purely induced by the external magnetic field.

Fig. 1 Geometry of the scattering system: an isotropic sphere with permittivity $ε_{c}$ and radius r coated by a MO shell with permittivity tensor ${\overset{\leftrightarrow}{ε}}_{s}$ and outer radius R>r under an external static magnetic field B. The incident plane wave propagating in vacuum with its electric field in the x-y plane impinges on the system parallel to the z-axis.

Download Full Size | PDF

In the quasistatic approximation, the size of NP is very small compared with the incident wavelength, the local electric field inside the core can be expressed through the incident field $E_{i}$ as [25]

E_{c o r e} = \hat{A} E_{i},

the field inside the MO shell may be sought as

E_{s h e l l} = \hat{B} E_{i} - \frac{\hat{C} E_{i}}{ρ^{3}} + \frac{3 (\hat{C} E_{i} \cdot n) n}{ρ^{3}},

and the field outside the core-shell NP is written as

E_{o u t} = - \frac{\hat{D} E_{i}}{ρ^{3}} + \frac{3 (\hat{D} E_{i} \cdot n) n}{ρ^{3}} + E_{i},

where

\hat{A}

,

\hat{B}

,

\hat{C}

and

\hat{D}

are some unknown antisymmetric tensors, and

ρ

is the distance from the center of the system. Employing the Maxwell’s boundary conditions at the inner and outer surfaces, i.e.,

\begin{array}{l} {D_{c o r e} \cdot n |}_{r} = {D_{s h e l l} \cdot n |}_{r}, {E_{c o r e} \times n |}_{r} = {E_{s h e l l} \times n |}_{r} \\ {D_{s h e l l} \cdot n |}_{R} = {D_{o u t} \cdot n |}_{R}, {E_{s h e l l} \times n |}_{R} = {E_{o u t} \times n |}_{R} \end{array}

we arrive at the following system of equations,

\begin{array}{l} ε_{c} \hat{A} = ε (\hat{B} + \frac{2 \hat{C}}{r^{3}}) + \hat{G} (\hat{B} - \frac{\hat{C}}{r^{3}}) \\ ε (\hat{B} + \frac{2 \hat{C}}{R^{3}}) + \hat{G} (\hat{B} - \frac{\hat{C}}{R^{3}}) = 2 \frac{\hat{D}}{R^{3}} + \hat{I} \\ \hat{A} = \hat{B} - \frac{\hat{C}}{r^{3}} \\ \hat{B} - \frac{\hat{C}}{R^{3}} = - \frac{\hat{D}}{R^{3}} + \hat{I} \end{array}

where

\hat{G}

is the nondiagonal part of the permittivity tensor

{\overset{\leftrightarrow}{ε}}_{s}

. These equations allow us to determine the tensors

\hat{A}

, _and

\hat{D}

_{with the form,}

\hat{A} = (\begin{matrix} a_{11} & i a_{12} & 0 \\ - i a_{12} & a_{11} & 0 \\ 0 & 0 & a_{33} \end{matrix}),

with

a_{11} = \frac{9 R^{3} ε [g^{2} (r^{3} - R^{3}) - 2 r^{3} (ε - 1) (ε - ε_{c}) + R^{3} (ε + 2) (2 ε + ε_{c})]}{P_{+} P_{-}},

a_{12} = \frac{9 g R^{3} ε (r^{3} - R^{3}) (ε + ε_{c} - 2)}{P_{+} P_{-}},

a_{33} = \frac{9 R^{3} ε}{- 2 r^{3} (ε - 1) (ε - ε_{c}) + R^{3} (ε + 2) (2 ε + ε_{c})},

where

P_{\pm} = g^{2} (r^{3} - R^{3}) - 2 r^{3} (ε - 1) (ε - ε_{c}) \pm g (r^{3} - R^{3}) (ε + ε_{c} - 2) + R^{3} (ε + 2) (2 ε + ε_{c})

On the other hand,

\hat{D} = (\begin{matrix} d_{11} & d_{12} & 0 \\ - d_{12} & d_{11} & 0 \\ 0 & 0 & d_{33} \end{matrix}),

where the element

d_{i j}

is also related to

ε_{c}

,

{\overset{\leftrightarrow}{ε}}_{s}

,

r

and

R

, and here we don't show the formula of

d_{i j}

due to its complex form. In the subspace

E_{i z} = 0

, there are two eigenvalues of the tensor

\hat{D}

_,

α_{\pm} = d_{11} \pm i d_{12} = \frac{R^{3} [g^{2} (r^{3} - R^{3}) - r^{3} (2 ε + 1) (ε - ε_{c}) \pm g (r^{3} - R^{3}) (ε + ε_{c} + 1) + R^{3} (ε - 1) (2 ε + ε_{c})]}{P_{\pm}}

Actually,

α_{\pm}

is nothing but the polarizabilities corresponding to the left and right circularly polarized (LCP and RCP, respectively) incident light [25].

According to Eqs. (2) and (7), the field in the core can be written as

E_{c o r e} = (\begin{matrix} a_{11} & i a_{12} & 0 \\ - i a_{12} & a_{11} & 0 \\ 0 & 0 & a_{33} \end{matrix}) (\begin{matrix} E_{i x} \\ E_{i y} \\ 0 \end{matrix}) = (\begin{matrix} a_{11} E_{i x} + i a_{12} E_{i y} \\ - i a_{12} E_{i x} + a_{11} E_{i y} \\ 0 \end{matrix})

Then,

{| E_{c} |}^{2} = E_{c o r e} \cdot E_{c o r e}^{*} = ({| a_{11} |}^{2} + {| a_{12} |}^{2}) {| E_{i} |}^{2} + (a_{11} a_{12}^{*} + a_{12} a_{11}^{*}) (E_{i x} E_{i y}^{*} - E_{i y} E_{i x}^{*})

When the incident light is LCP or RCP

E_{i} = E_{0} e^{i k z} {(\begin{matrix} 1 & \pm i & 0 \end{matrix})}^{T}

(here we omit the harmonic time dependence of the electric field

e^{- i ω t}

), the relation between the field in the core and the external applied field can be simplified as

{| E_{c} |}^{2} = 2 E_{0}^{2} [{| a_{11} |}^{2} + {| a_{12} |}^{2} \mp (a_{11} a_{12}^{*} + a_{12} a_{11}^{*})]

where

a_{i j}

is the element of the tensor

\hat{A}

_.

Next, we would like to learn nonlinear coated NPs in which spherical metallic core is nonlinear with the field-dependent permittivity ${\tilde{ε}}_{c} = ε_{c} + χ {| E_{c} |}^{2}$ . In general, in the weakly nonlinear limit, the contribution from the nonlinear part is much less than the linear one. However, in the strong field case, the nonlinear part may be comparable to or even larger than the linear one. In this connection, we should adopt the self-consistent field theory to evaluate the local filed in the nonlinear core [10,26,27]. Similar as Eq. (16), the relation between the local field in the nonlinear core and the applied filed can be written as

{| E_{c, n o n} |}^{2} = 2 E_{0}^{2} {{| a_{11} ({\tilde{ε}}_{c}) |}^{2} + {| a_{12} ({\tilde{ε}}_{c}) |}^{2} \mp [a_{11} ({\tilde{ε}}_{c}) a_{12} {({\tilde{ε}}_{c})}^{*} + a_{12} ({\tilde{ε}}_{c}) a_{11} {({\tilde{ε}}_{c})}^{*}]}

Not that

a_{1 j} (j = 1, 2)

are dependent on

{\tilde{ε}}_{c}

, or

{| E_{c, n o n} |}^{2}

. As a consequence, Eq. (16) can readily be solved in a self-consistent manner for

{| E_{c} |}^{2}

, and hence the desired optical bistability may be obtained. Here we mention that since both

a_{11}

and

a_{12}

contain the off-diagonal term

g

in the MO shell, which can be tuned with an external magnetic field. Therefore, in our present nonlinear coated nanodevices, the tunable optical bistability with an external magnetic field can be realized.

3. Numerical results

We are now in a position to present the numerical results. The linear permittivity of the metallic core is assumed to be given by the Drude formula $ε_{c} = ε_{\infty} - ω_{p}^{2} / (ω^{2} + i ν ω)$ , where $ε_{\infty} = 4.96$ , $ℏ ω_{p} = 9.54 e v$ and $ℏ ν = 0.055 e v$ [28]. The parameters for the anisotropic shell with Bi:YIG are $ε = 5.5 + 0.0025 i$ , $g = (- 1 + 0.15 i) \times 10^{- 2}$ [29].

In Fig. 2, we show the scattering efficiency of the linear coated NP, defined as with the factor given by for LCP, as a function of the incident wavelength . It is evident that the linear scattering efficiency exhibits significant enhancement around the surface plasmon resonant wavelength of the present coated nanosphere. For a given size , as the volume fraction of the core [] increases, the scattering peak is increased, accompanied with the blue-shift of the resonant wavelength, as shown in Fig. 2(a). Actually, for pure metallic NPs (), the surface plasmon resonant wavelength is given by = 343nm. In Fig. 2(b), the resonant wavelengths are almost unchanged as the shell size increases when is fixed. Qualitively, in the quasistatic limit, the equivalent permittivity of the core-shell NPs are only dependent on the volume fraction , not the single size or . Hence, for the fixed , the surface plasmon resonant wavelength keeps invariant with increasing . Here, we would like to mention that the scattering efficiency for RCP (not shown here) is quite similar as those in Fig. 1 for LCP but with a minor difference in the surface resonant wavelength. In this regard, one may adopt , the difference between the scattering efficiency for LCP and RCP incident light to measure the circular dichroism quantitatively, and strong circular dichroism may be observed [18].

Fig. 2 The scattering efficiency versus $λ$ for LCP when (a) R is fixed at 10nm and (b) $η$ is fixed at 0.4.

Download Full Size | PDF

The far-field scattering spectra can also be reflected from the near-field properties. In Fig. 3, we show the corresponding field distributions of the coated NPs at the surface plasmon resonant wavelength $λ = 430 n m$ , and below (or above) the resonant wavelengths. One observes the local-fields in the metallic core coated with the MO shell are almost uniform in both resonant and nonresonant wavelengths due to the dipolar approximation. At the nonresonant incident wavelengths [see Fig. 3 (b) and Fig. 3(c)], the small local fields in the MO shell and the host medium are almost unperturbed, and hence the scattering efficiency is small. On the contrary, at the surface resonant wavelength [see Fig. 3 (a)], the local field is largely enhanced with the resonant state resulting in large scattering efficiency.

Fig. 3 Distribution of the local fields for (a) $λ = 430 n m$ , (b) $λ = 400 n m$ and (c) $λ = 450 n m$ . The relevant parameters are $R = 10 n m$ and $η = 0.4$ .

Download Full Size | PDF

The enhancement of local fields within the metallic core near the surface plasmon resonant wavelengths represents an ideal condition to boost the nonlinear response of optical materials. Therefore, we consider the optical switching effects in such nonlinear core-shell metal-MO NPs. For this propose, we consider the nonlinear permittivity of the metallic score to be ${\tilde{ε}}_{c} = ε_{c} + χ {| E_{c} |}^{2}$ with the third-order nonlinear susceptibility $χ = 3 \times 10^{- 9} e s u$ [28], which is given in the esu-cgs system. Accordingly, the unit of electric field is chosen as statvolt/cm ( $1 s t a t v o l t /cm = 3 \times 10^{4} V/m$ ). In Fig. 4(a), we plot the electric field amplitude in the nonlinear core $E_{c}$ as a function of the external field $E_{0}$ for various volume fraction $η$ . Bistable responses can be clearly observed. Take $η = 0.5$ as an example, the electric field in the nonlinear core first increases as the incident field increases from zero. When the incident field amplitude reaches the upper threshold field $E_{0 - u p p e r} \approx 1 .497 \times 10^{3} statvolt/cm$ , the electric field amplitude in the core will discontinuously jump to the top stable branch. If the incident field is decreased back from a large value to zero, the electric field in the core will first decrease continuously, and then jump down to the lower stable branch when the incident field amplitude reaches the lower threshold field $E_{0 - l o w e r} \approx 0. 691 \times 10^{3} statvolt/cm$ . We find that the bistable region gets broad, accompanied with the increase in both lower and upper threshold fields as $η$ increases. To one’s interest, one predicts there is a critical volume fraction $η_{c} \approx 0.398$ , below which the optical bistable behavior vanishes, as shown in Fig. 4(b).

Fig. 4 (a) The local field in nonlinear core $E_{c}$ as a function of the incident field $E_{0}$ for various volume fraction $η$ . The incident wavelength $λ = 430 n m$ . (b) the upper and lower threshold fields as a function of $η$ .

Download Full Size | PDF

Since for the MO shell, the off-diagonal term of the permittivity tensor $g$ can be adjusted through the magnetic field B, we shows the optical bistability for various values of $g$ in both cases of LCP and RCP incident waves in Fig. 5. In the absence of B, we have $g = 0$ , and the optical anisotropy and the MO effect of the shell material is absent. In this case, both incident LCP and RCP yield the same optical bistable curve [see the black dashed line in Fig. 5(a)]. For incident RCP, one can see that both the upper and lower threshold fields increases with increasing $g$ or the external magnetic fields, as shown in Fig. 5(a) or Fig. 5(b). In addition, broad hysteresis loop for large B is found. On the other hand, for incident LCP, the increase in the external magnetic field (or g) results in the decrease of the upper and lower threshold fields [see Fig. 5(a) or Fig. 5(b)]. Moreover, from Fig. 5(b), the upper threshold fields are dependent on the value of $g$ significantly compared with the lower threshold field. And the LCP wave possesses the lower threshold field than the RCP wave. Here, we would like to give some physical explanations about the effect of the external magnetic field on the bistable threshold fields. In essence, the large enhancement of optical nonlinearity results from the enhancement of the spatial local field in the nonlinear metallic core, which will lead to the lower threshold field. The corresponding linear field distributions in such coated nanostructures for LCP incidence for different B are plotted in Fig. 5(c). We note that the magnitude of the electric field in the core for LCP incident wave is indeed enhanced with increasing $g$ , and hence the threshold fields become small. Here we conclude that the bistability behavior of the structure depends on the incidence polarization as well as the “strength” of MO effect. This magnetic-controllable optical bistability can directly lead to the design of nonlinear optical nanocircuit components and new-generation tunable sensors [5].

Fig. 5 (a) The field in nonlinear core $E_{c}$ as a function of the incident field $E_{0}$ for various $g$ for both LCP and RCP incidence. (b) the thresholds fields $E_{0 - u p p e r}$ and $E_{0 - l o w e r}$ as a function of $g$ . (c) the distribution of the local electric fields in the corresponding linear system for LCP incidence. The other parameters are: $λ = 430 n m$ , $R = 10 n m$ and $η = 0.5$ .

Download Full Size | PDF

We have mentioned above that the bistability will disappear below the critical value $η_{c}$ . Here, we shall show the effect of the gyration parameter $g$ on the critical volume fraction in Fig. 6. As $g$ increases, $η_{c}$ for incident LCP wave increases while the one for RCP wave decreases. Therefore, the presence of B can also modify the operational volume fraction range of the optical bistability.

Fig. 6 (a) The upper and lower threshold fields as a function of $η$ for various $g$ . (b) The critical fractional volume $η_{c}$ as a function of $g$ when $λ = 430 n m$ and $R = 10 n m$ .

Download Full Size | PDF

4. Conclusion

In this paper, we propose a new nonlinear nanostructure—a plasmonic metallic core coated with MO shell to realize the tunable optical bistable behavior with the external static magnetic field B. In the quasistatic limit, we show that for LCP and RCP incident waves, such nanostructures exhibits different hysteresis loops. Both upper and lower threshold fields decrease (or increase) and the bistable region becomes narrow (or broad) for LCP (or RCP) wave by increasing the strength of external magnetic field B. Moreover, as the strength of MO effect increases, the critical volume fraction $η_{c}$ for LCP (or RCP) wave increases (or decreases). Since the optical properties of the shell (such as the strength of the MO activity) depend on the external static magnetic field, one can tune the threshold fields and the bistable region for both CP waves by tuning the magnitude of the external magnetic field. In other words, the optical bistability of this kind of nanostructures can be easily controlled by adjusting the static magnetic field. Our study may pave some ways for us to realize tunable nonlinear optical nanodevices such as optical nanoswitches, optical isolators and so on.

Funding

National Natural Science Foundation of China (NSFC) (Grant No. 11374223); National Basic Research Program (Grant No. 2012CB921501); Qing Lan Project; Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

References and links

1. Y. R. Shen, “Recent advances in optical bistability,” Nature 299(5886), 779–780 (1982). [CrossRef]

2. K. M. Leung, “Optical bistability in the scattering and absorption of light from nonlinear microparticles,” Phys. Rev. A Gen. Phys. 33(4), 2461–2464 (1986). [CrossRef] [PubMed]

3. R. Neuendorf, M. Quinten, and U. Kreibig, “Optical bistability of small heterogeneous clusters,” J. Chem. Phys. 104(16), 6348–6354 (1996). [CrossRef]

4. D. A. Mazurenko, R. Kerst, J. I. Dijkhuis, A. V. Akimov, V. G. Golubev, D. A. Kurdyukov, A. B. Pevtsov, and A. V. Sel’kin, “Ultrafast optical switching in three-dimensional photonic crystals,” Phys. Rev. Lett. 91(21), 213903 (2003). [CrossRef] [PubMed]

5. C. Argyropoulos, P. Y. Chen, F. Monticone, G. D’Aguanno, and A. Alù, “Nonlinear plasmonic cloaks to realize giant all-optical scattering switching,” Phys. Rev. Lett. 108(26), 263905 (2012). [CrossRef] [PubMed]

6. V. R. Almeida and M. Lipson, “Optical bistability on a silicon chip,” Opt. Lett. 29(20), 2387–2389 (2004). [CrossRef] [PubMed]

7. Y. Huang, A. E. Miroshnichenko, and L. Gao, “Low-threshold optical bistability of graphene-wrapped dielectric composite,” Sci. Rep. 6, 23354 (2016). [CrossRef] [PubMed]

8. D. J. Bergman, O. Levy, and D. Stroud, “Theory of optical bistability in a weakly nonlinear composite medium,” Phys. Rev. B Condens. Matter 49(1), 129–134 (1994). [CrossRef] [PubMed]

9. L. Gao, L. Gu, and Z. Li, “Optical bistability and tristability in nonlinear metal/dielectric composite media of nonspherical particles,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 68(6 Pt 2), 066601 (2003). [CrossRef] [PubMed]

10. L. Gao, “Optical bistability in composite media with nonlinear coated inclusions,” Phys. Lett. A 318(1–2), 119–125 (2003). [CrossRef]

11. R. E. Noskov, P. A. Belov, and Y. S. Kivshar, “Subwavelength modulational instability and plasmon oscillons in nanoparticle arrays,” Phys. Rev. Lett. 108(9), 093901 (2012). [CrossRef] [PubMed]

12. Y. Huang and L. Gao, “Tunable Fano resonances and enhanced optical bistability in composites of coated cylinders due to nonlocality,” Phys. Rev. B 93(23), 235439 (2016). [CrossRef]

13. A. R. Davoyan and N. Engheta, “Theory of wave propagation in magnetized near-zero-epsilon metamaterials: evidence for one-way photonic states and magnetically switched transparency and opacity,” Phys. Rev. Lett. 111(25), 257401 (2013). [CrossRef] [PubMed]

14. G. Armelles, A. Cebollada, A. García-Martín, and M. U. González, “Magneto-plasmonics: combining magnetic and plasmonic functionalities,” Adv. Opt. Mater. 1(1), 10–35 (2013). [CrossRef]

15. W. J. M. Kort-Kamp, F. S. S. Rosa, F. A. Pinheiro, and C. Farina, “Tuning plasmonic cloaks with an external magnetic field,” Phys. Rev. Lett. 111(21), 215504 (2013). [CrossRef] [PubMed]

16. W. J. M. Kort-Kamp, F. S. S. Rosa, F. A. Pinheiro, and C. Farina, “Molding the flow of light with a magnetic field: plasmonic cloaking and directional scattering,” J. Opt. Soc. Am. A 31(9), 1969–1976 (2014). [CrossRef] [PubMed]

17. D. G. Baranov, A. P. Vinogradov, A. A. Lisyansky, Y. M. Strelniker, and D. J. Bergman, “Magneto-optical spaser,” Opt. Lett. 38(12), 2002–2004 (2013). [CrossRef] [PubMed]

18. P. Varytis, N. Stefanou, A. Christofi, and N. Papanikolaou, “Strong circular dichroism of core-shell magnetoplasmonic nanoparticles,” J. Opt. Soc. Am. B 32(6), 1063–1069 (2015). [CrossRef]

19. P. Varytis and N. Stefanou, “Plasmon-driven large Hall photon currents in light scattering by a core–shell magnetoplasmonic nanosphere,” J. Opt. Soc. Am. B 33(6), 1286–1290 (2016). [CrossRef]

20. P. Varytis, P. A. Pantazopoulos, and N. Stefanou, “Enhanced Faraday rotation by crystals of core-shell magnetoplasmonic nanoparticles,” Phys. Rev. B 93(21), 214423 (2016). [CrossRef]

21. M. Abe and T. Suwa, “Surface plasmon resonance and magneto-optical enhancement in composites containing multicore-shell structured nanoparticles,” Phys. Rev. B 70(23), 235103 (2004). [CrossRef]

22. H. Uchida, Y. Masuda, R. Fujikawa, A. V. Baryshev, and M. Inoue, “Large enhancement of Faraday rotation by localized surface plasmon resonance in Au nanoparticles embedded in Bi:YIG film,” J. Magn. Magn. Mater. 321(7), 843–845 (2009). [CrossRef]

23. L. Wang, C. Clavero, Z. Huba, K. J. Carroll, E. E. Carpenter, D. Gu, and R. A. Lukaszew, “Plasmonics and enhanced magneto-optics in core-shell co-ag nanoparticles,” Nano Lett. 11(3), 1237–1240 (2011). [CrossRef] [PubMed]

24. L. D. Landau, L. P. Pitaevskii, and E. M. Lifshitz, in Electrodynamics of Continuous Media, Course of Theoretical Physics Vol. 8 (Butterworth-Heinemann, 1984), 2nd ed.

25. D. G. Baranov, A. P. Vinogradov, and A. A. Lisyansky, “Magneto-optics enhancement with gain-assisted plasmonic subdifraction chains,” J. Opt. Soc. Am. B 32(2), 281–289 (2015). [CrossRef]

26. H. L. Chen, D. L. Gao, and L. Gao, “Effective nonlinear optical properties and optical bistability in composite media containing spherical particles with different sizes,” Opt. Express 24(5), 5334–5345 (2016). [CrossRef]

27. H. Chen, Y. Zhang, B. Zhang, and L. Gao, “Optical bistability in a nonlinear-shell-coated metallic nanoparticle,” Sci. Rep. 6, 21741 (2016). [CrossRef] [PubMed]

28. N. Lapshina, R. Noskov, and Y. Kivshar, “Nanoradar based on nonlinear dimer nanoantenna,” Opt. Lett. 37(18), 3921–3923 (2012). [CrossRef] [PubMed]

29. V. I. Belotelov, L. L. Doskolovich, and A. K. Zvezdin, “Extraordinary magneto-optical effects and transmission through metal-dielectric plasmonic systems,” Phys. Rev. Lett. 98(7), 077401 (2007). [CrossRef] [PubMed]

Optical bistability in core-shell magnetoplasmonic nanoparticles with magnetocontrollability

Abstract

1. Introduction

2. Theoretical development

3. Numerical results

4. Conclusion

Funding

References and links

Cited By

Figures (6)

Equations (17)

Optics Express