Optical bistability in subwavelength compound metallic grating H. Lu and X. M. Liu* State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China *
[email protected]
Abstract: We have investigated the optical bistability behavior based on an electromagnetically induced reflection (EIR) effect in a compound metallic grating consisting of subwavelength slits and Kerr nonlinear nanocavities embedded in a metallic film. The theoretical and simulation results show that a narrow peak in the broad reflection dip possesses a red-shift with increasing the refractive index of coupled nanocavities. Importantly, we have obtained an obvious optical bistability with threshold intensity about ten times lower than that of metallic grating coated by nonlinear material. The results indicate that our structure may find excellent applications for nonlinear plasmonic devices, especially optical switches and modulators. ©2013 Optical Society of America OCIS codes: (240.6680) Surface plasmons; (230.4555) Coupled resonators; (310.6628) Subwavelength structures, nanostructures.
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#188562 - $15.00 USD (C) 2013 OSA
Received 9 Apr 2013; revised 14 May 2013; accepted 20 May 2013; published 31 May 2013 3 June 2013 | Vol. 21, No. 11 | DOI:10.1364/OE.21.013794 | OPTICS EXPRESS 13794
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1. Introduction Plasmonics in nanostructures are widely regarded as an exciting and promising technology for efficient manipulation of photons and realization of highly-integrated optical components [1,2]. So far, a large number of plasmonic devices have been proposed and investigated, such as waveguides [3–5], filters [6], couplers [7], mirrors [8], Bragg reflectors [9], sensors [10], transducer [11], optical buffers [12], modulators [13], solar cells [14], logic gates [15], and optical switches [16,17]. Optical bistability has attracted much attention owing to its widely potential applications in optical devices such as optical logical gates, switches, transistors, memories, and so on [18]. Recently, plasmonic nanostructures were found to be capable of paving another pathway to realize strong nonlinear optical effects and minimize optical components, attributing to the significant field enhancement and light manipulation on deeply subwavelength scale [19]. For example, optical bistability behavior was found in the periodically nanostructured metal films [20]. The specific optical nonlinear property has also been found in one-dimensional metallic slit arrays [17, 19, 21]. For instance, Min et al. investigated the excellent optical bistability and switching behaviors in the subwavelength metallic grating coated by Kerr nonlinear materials [17, 21]. As one of important factors for the nonlinear effect, the threshold intensity can be improved by using nonlinear material with larger third-order nonlinear susceptibility [17, 22]. Due to the limitation of optical materials, it is significant to explore other effective accesses to the decrease of threshold intensity. As a fascinating phenomenon, electromagnetically induced transparency (EIT) occurs in the atomic systems due to the quantum interference generated by driving the atom with an
#188562 - $15.00 USD (C) 2013 OSA
Received 9 Apr 2013; revised 14 May 2013; accepted 20 May 2013; published 31 May 2013 3 June 2013 | Vol. 21, No. 11 | DOI:10.1364/OE.21.013794 | OPTICS EXPRESS 13795
external laser [23]. The EIT effect has promising applications in enhanced nonlinear optical processes, optical switching, and optical storage due to the strong dispersion [24]. However, chip-scale applications of the atomic EIT are unsuitable owing to the rigorous conditions [24]. Fortunately, optical behaviors analogous to EIT were found in the optical resonator systems [25, 26]. The EIT-like effect is also observed in plasmonic structures [24, 27–29]. Recently, the EIT-like effect was utilized to investigate optical bistability in plasmonic waveguidecoupled resonators [30] and coupled quantum-well nanostructure [31]. However, the investigation of EIT-like effect is still rare for the nonlinear optical enhancement in plasmonic systems such as metallic grating. In this paper, we have investigated the optical bistability effect an EIT-like response in a novel plasmonic configuration, which consists of a metallic grating with subwavelength slits and nanocavities embedded in a metallic film. It is found that the narrow reflection peak is determined by the coupling strength and detuning between metallic slits and nanocavities. The theoretical results are verified by numerical simulations. The induced reflection peak exhibits a red-shift with the increase of the refractive index in coupled nanocavities. By inserting the Kerr nonlinear material into the nanocavities, an obvious optical bistability are obtained in the compound metallic grating. Especially, the threshold intensity of the bistability is remarkable compared with that of metallic grating coated by nonlinear material.
Fig. 1. Schematic of the metallic grating with geometrical parameters: the period of grating P, thickness of metallic film h, slit width a, coupling distance between silts and nanocavities g, as well as length and width of cavities L and w.
2. Model and theories In Fig. 1, we show the schematic of the plasmonic system, which consists of a compound metallic grating with periodic subwavelength dielectric slits and rectangular nanocavities. The dynamic transmission through the simple metallic grating can be attributed to two types of transmission resonances, which are identified as horizontal and vertical surface-plasmon resonances [32]. The first one is due to the coupled surface plasmon polaritons (SPPs) excited on the interfaces of the metallic grating, and the other is a Fabry-Perot (F-P) like waveguide resonance formed in the narrow slits. The slits work as “cavities” with regions II/I and II/III acting as two mirrors. Different from coupled SPPs, the waveguide resonance is mainly dependent on geometrical features of slits, not the period of the grating. The F-P like resonance is considered in the grating structure. Here, the metal is assumed as silver, whose permittivity can be determined by the Drude model: εm(ω) = ε∞-ω2p/(ω2 + jωγ). Here ε∞ is the dielectric constant at the infinite frequency. ωp and γ represent the bulk plasma and electron collision frequencies, respectively. These parameters for silver can be set as ε∞ = 3.7, ωp = 9.1 eV, and γ = 0.018 eV [7, 33, 34]. The regions III and I are assumed as air for simplicity. The permittivity of dielectric material in slits and nanocavities is assumed as 2.25. The p-polarized (magnetic field parallel to the z direction) plane wave is incident normally on the metallic grating. To analyze the optical response, a simple two-oscillator system is described in Fig. 2(a). The lower cavity is represented by oscillator 1, which is driven by the incident light only launched from the left port. The upper cavity is represented by oscillator 2, which is excited only by the coupling between two cavities. By the temporal coupled-mode theory [35, 36], the
#188562 - $15.00 USD (C) 2013 OSA
Received 9 Apr 2013; revised 14 May 2013; accepted 20 May 2013; published 31 May 2013 3 June 2013 | Vol. 21, No. 11 | DOI:10.1364/OE.21.013794 | OPTICS EXPRESS 13796
equations for the temporal evolution of the cavity modes a and b in oscillators 1 and 2 can be respectively described as, da / dt = ( − jω1 − γ 11 − γ 12 )a + Si γ 11 − jκ b,
(1)
db / dt = ( − jω2 − γ 2 )b − jκ a.
(2)
Here ω1 and ω2 represent the resonance frequencies of oscillators 1 and 2. γ11 and γ12 are the decay rates due to the radiative and internal loss in oscillator 1, respectively. γ2 stands for the decay rate due to the internal loss in oscillator 2. κ is the coupling coefficient between the two oscillators. Si, Sr, and St depict the incident, reflection, and transmission waves, respectively. The input and reflection waves satisfy a relationship: Sr = −Si + a. We assume that the decay rates of the two resonators have the relationship: γ12, γ2
