AU2019100664A4 - Design of a compact device for implementing tunable multiple plasmon-induced transparencies - Google Patents

Abstract

Many potential applications can be implemented based on the Plasmon-induced transparency (PIT) effect. In this patent, tunable multi-PIT phenomena are achieved in a compact plasmonic structure. The proposed structure mainly consists of dual stub cavities coupled with Fabry-perot resonators, respectively, as shown in Fig. 1. According to the temporal coupled-mode theory, the formation mechanism of different transparent windows is explained detailedly. In addition, we found that the structural parameters have an important influence on the transmission characteristics. Ultimately, According to the formation mechanism of different PIT windows, we can individually manipulate transmission characteristics at different PIT windows including the wavelength and transmission of transparency-peak, which are investigated numerically by using the FDTD method. This invention have many potential applications in the area of highly integrated optical data storage. Fig. 1 S+o A i a r2 t2 st S. Silver 2 Air Fig. 2

Description

DESIGN OF A COMPACT DEVICE FOR IMPLEMENTING

TUNABLE MULTIPLE PLASMON-INDUCED TRANSPARENCIES

1. Technical Field

The present invention relates to the field of plasma photonics and nanoscale optical device.

2. Background and Purpose

Electromagnetically induced transparency (EIT) is a consistently quantum destructive interference phenomenon between two different excitation pathways in a three-level atomic system, which generate a narrow transparency window. This wizardly phenomenon has various potential applications in the areas of nonlinear optical processes, ultrafast optical switching, slowing light and optical data storage. However, its practical applications are limited by strict conditions such as macroscopic apparatus, low-temperature environments and stable gas lasers. Fortunately, various analogous EIT effects have been proposed and demonstrated including coupledresonator-induced transparency, metamaterial-induced transparency and plasmoninduced transparency (PIT). Among these methods of implementing EIT-like effect, PIT effect has been studied by a large number of scholars since it can be realized with a small footprint due to the capabilities provided by the surface plasmon polaritons (SPPs) to overcome the diffraction limit and manipulate light in subwavelength domain.

Correspondingly, various structures in metal-insulator-metal (MIM) waveguides systems, which have the fascinating characteristics of strong confinement of light, acceptable propagation length and easy manufacturing, have been proposed for achieving PIT phenomenon. However, most of the devices can only implement a single PIT peak. As we all know, the device that can realize multiple PIT windows simultaneously are urgently needed for many plasmonic circuits. Recently, in order to achieve PIT effect simultaneously in the multi-wavelengths, many types of configurations are presented. However, how to manipulate the transmission characteristics at one of them without affecting other characteristics of PIT effects, which is urgently needed for practical applications, was not illuminated detailedly in these devices.

In order to meet these demands, a device which mainly consists of dual easily fabricated stub cavities coupled with Fabry-Perot (FP) resonators is proposed in this invention. Triple PIT windows was achieved in the proposed device. Formation mechanisms of different PIT responses are elaborated using the temporal coupled-mode theory. The finite-difference time-domain (FDTD) method reveals that structural parameters have important influence on transmission characteristics. Ultimately, according to the reasons for the formation of different PIT windows, the manipulation of the PIT effect at different wavelengths without affecting each other can be realized by adjusting structural parameters. The proposed plasmonic device is of great significance for highly integrated optical systems.

2019100664 18 Jun 2019

3. Brief Description of the Drawings

Fig. 1: Three-dimensional schematic diagram of the proposed device.

Fig. 2: Two-dimensional schematic diagram of the proposed device.

Fig. 3: (a) Transmission spectrum at output port. Field distributions of Hz with the incident light wavelength of (b) 819.1 nm, (c) 855.9 nm, (d) 897.6 nm, (e) 1114.5 nm, (f) 1260.6 nm, (g) 1314.3 nm, and (h) 1364.9 nm.

Fig. 4: (a) Variation tendency of the transparency-peak wavelengths for PITi and PIT2 as length l_s\ increases, (b) Variation tendency of the transparency-peak wavelengths for PITi and PIT2 as length l_S2 increases, (c) Transmission at transparencypeak in different coupling distances d\ for PITI and PIT2. (d) Transmission at transparency-peak in different coupling distances di for PITi and PIT2.

4. Detailed Implementation Description

The two-dimensional schematic diagram of the present invention is showed in the Fig. 2. As marked in the figure, the parameters of the structure l_s\, Ip, Isi and Z/2 are the lengths of the stubi, FPi, stub2 and FP2 resonators, respectively. The widths of waveguide, stub cavities and FP resonators are expressed as w. di represents the coupling distance between stub/ and FP₍ resonators (z = 1, 2). D stand for the separation between stubi and stub2 cavities. S’+in, S^l-in, S‘+y and S‘-y respectively represent the amplitudes of the waves of different propagating directions in the bus waveguide and FPi resonator. In the stucture, the dielectric in waveguide and resonators is set as air whose refractive index is n = 1. Besides, the background material is supposed to be silver whose frequency-dependent relative permittivity can be characterized by the Drude model:£_m(a>) = — (όρΙ\ω{ω + i/)]. Here &»= 3.7, ωρ = 9.1 eV and /=0.018 eV are the dielectric constant of the infinite frequency, the bulk plasma frequency and the electron collision frequency, respectively, ω means the angular frequency of the incident wave. Then, in this model, SPPs waves are exerted from the fundamental TM mode whose dispersion relation in the MIM waveguide can be obtained by the following equations:

(1) (2) where Sd, s_m, kd and km respectively represent the permittivities and propagation constants of the dielectric and metal, ko and β stand for the wave vector in the vacuum and waveguide.

When resonance condition is satisfied, the SPPs waves can be coupled directly to the stub cavities from bus waveguide and indirectly coupled into the FP resonators via the stub cavities. Transmission characteristics of the system can be investigated according to the temporal coupled-mode theory. The temporal evolution of the normalized mode amplitude cu of the stub/ can be described as:

= (/> - k_oi - k_wi - kf^ai + ej^i4k~(S^l+in + S^l_in) + e^,<pfijk^S^l _+fi (3)

2019100664 18 Jun 2019

The parameter of an means the resonance frequency of stub/ resonator, koi, kwi and kfi are decay rates due to internal loss in the stub/, the decay rates induced by the energy escape into the bus waveguide and FP/ resonators, respectively, φ™ and φβ are the phase of the coupling coefficients. In addition, the waves in the FPz resonator should satisfy a steady-state relation:

= -Sl +fi + e	(4a)
S)fl =	(4b)
'i~ c +θί	(4c)

where δί means the amplitude attenuation between the incoming and outgoing waves of the FPz resonator. «<and θι stand for effective refractive index and the additional phase shift in the FP/ resonator. Moreover, based on energy conservation, the amplitudes Shout and S-out of the outgoing waves can be written as:

°-out °-ιη ^c (5a)

S^l+out = S^l+in - e ^j,Pwi/k^i^ai (5b)

In the linear system, the field everywhere oscillates as e~^J0}t and dcf/dt = —ja>t. When the light is only inputted from the left port of the bus waveguide, based on the above analysis, we can deduce the transmission and reflection coefficients of the single stub/ coulped with FP_; as follows:

(6a) (6b) j(a>i a)+k_oi+k_wi+kyi l+Sie^i

Consequently, feedback and transmitted waves of the zth stub cavity satisfy the following matrix:

ct

L^a+outJ

h .

^a+tn ci

L^a-outJ (7)

According to the above equation, the transmission characteristics of the entire device can be derived as:

Γ S’ 1 °-in

S+out.

r₂

t₂ rz ^t2.

^ri

ti tl

A in c

L'-’-outJ (8) where a is the phase difference between the 1th and 2th stub cavities. When the interval D is equal to 0, the size of device is minimized. And the maximum transmission transmission efficiency T can be obtained at the output port, which can be expressed as: r=|^|² = |^|² (9) ^ύ+ιη ^i_ri^r2

2019100664 18 Jun 2019

Based on above analysis, it is known that transmission characteristics of proposed device is not only related to interference between radiative resonator and subradiant resonator but also included phase coupling mechanisms. Moreover, transmission T can be manipulated by adjusting the coupling distance di since the coupling distance di is related to the transmission coefficients ti and reflection coefficients n.

The FDTD method is introduced to investigate the transmission characteristics of the device. Firstly, the structural parameters are set as La = 120 nm, Ip = 260 nm, La = 200 nm, Ip = 420 nm, d\ = 25 nm, and ¢/2 = 20 nm. And the wide w = 50 nm is a constant in this invention. The transmission spectrum of the proposed device is drawn in Fig. 3(a). As depicted in the Fig. 3(a), triple PIT windows with transmission of transparencypeaks are 50%, 90% and 42% can be observed and central wavelength respectively located at 2b = 855.9 nm (PITi), 2d = 1114.5 nm (PIT3) and 2f = 1314.3 nm (PIT2) between the four dips at 2a =819.1 nm, 2c = 897.6 nm, 2e = 1260.6 nm and 2g = 1364.9 nm. The field distributions of Hz at the transmission peaks and dips marked by A, B, C, D, E, F and G are sketched in Figs. 3(b)-3(h). It can be seen from field distributions that the formation of PITi and PIT2 originate from the interaction between stub; cavity and FP, resonator, and the reason for the formation of PIT3 is due to phase interference between the two stub cavities. Besides, according to previous theoretical analysis and field distributions, PITi (PIT2) is mainly formed by the interaction of stubi (stub2) cavity and FPi (FP2) resonator. Therefore, we can solely manipulate the transmission characteristics of PITi or PIT2 by adjusting the parameters of structure.

First of all, we investigate the influence of the length La on the transmission characteristics. The length //1 is expressed as //1 = 2Λι + a and a = 20 nm. The length l_s\ is varied from 110 nm to 130 nm with the step size is 5 nm and the other parameters are fixed. As the length La increases, the variation of transparency-peak wavelengths for PIT 1 and PIT2 are drawn in Fig. 4(a). It is noteworthy that the resonance wavelength of PITi exhibits red-shift with the increase of length La, which is basically a linear relationship. Meanwhile, the resonance wavelength of PIT2 has almost no movement. So the transparency-peak wavelength of PITi can be individually manipulated without affecting PIT2 by changing the length La. Next, we increases the length Λ2 from 190 nm to 210 nm with an interval of 5 nm. The length Ip is set to 2/.s2 + a and the parameter l_s\ is fixed at 120 nm. Fig. 4(b) depicts the variation of central wavelengths for PITi and PIT2 windows. It can be observed from Fig. 4(b) that the resonance wavelength of PIT2 gradually increases as the length La increases, and the resonance wavelengths of PITi are barely changed. Therefore, the manipulation of transparency-peak wavelength for PIT2 is achieved.

Moreover, we explore the relationship between the coupling distance d\ and transmission of PITi and PIT2. The coupling distance d\ is taken from 10 nm to 35 nm in steps of 5 nm whereas other parameters remain unchanged. Fig. 4(c) illustrates the relationship between transmission of transparency-peak and coupling distance d\. As the coupling distance d\ increases, the transmission of transparency-peak gradually decreases at PITi. Meanwhile, the transmission is hardly affected at PIT2. This provide a method of manipulating the transmission of PITi separately. Furthermore, the effects of the coupling distance ¢/2 on the transmission is investigated. The coupling distance ¢/2 is changed from 10 nm to 35 nm with an interval of 5 nm and the other parameters

2019100664 18 Jun 2019 are kept fixed. As the coupling distance ch increases, the variation in the transmission of transparency-peak for PITi and PIT2 are plotted in Fig. 4(d). Contrary to the consequence of adjusting coupling distance d\, when the coupling distance increases, the transmission of transparency-peak at PIT 1 is barely influenced and the transmission at PIT2 presents a decreasing trend. Therefore, we can manipulate the transmission at transparency-peak for PIT2 without affecting the characteristics of PITi.

2019100664 18 Jun 2019

Editorial Note

There is only One page of Claim

2019100664 18 Jun 2019

Claims (4)

1. A compact device for implementing tunable multiple plasmon-induced transparency (PIT) windows is invented. The structure of the device is composed of dual stub cavities, respectively, coupled with Fabry-perot (FP) resonators and a bus waveguide. The material of the background metal is set to silver. The dielectric in the resonators and waveguide is air. Triple PIT responses are implemented based on different formation mechanisms. Moreover, the theoretical model showed that the structural parameters have an important influence on the transmission characteristics. Ultimately, According to the formation mechanism of PITi and PIT2, we can separately manipulate transmission characteristics including the wavelength and transmission of transparency-peak at PITi and PIT2 windows.

2. Triple PIT responses are implemented based on different formation mechanisms (as mentioned in claim 1), which are embodied as:

Triple PIT windows with transmission of transparency-peaks are 50%, 90% and 42% can be observed and central wavelength respectively located at Ab = 855.9 nm (PITi), 2/)=1114.5 nm (PIT3) and Af = 1314.3 nm (PIT2) between the four dips at Aa =819.1 nm, Ac = 897.6 nm, Ae = 1260.6 nm and Ag = 1364.9 nm. Based on theoretical analysis, it is known that the formation of PITi and PIT2 originate from the interaction between radiative resonator and subradiant resonator, and the reason for the formation of PIT3 is due to phase interference.

3. We can separately manipulate transmission characteristics at PITi and PIT2 windows (as mentioned in claim 1), which is as follows:

According to theoretical analysis and field distributions of device, PITi (PIT2) is mainly formed by the interaction of stubi (stub2) cavity and FPi (FP2) resonator. Therefore, we can solely manipulate the transmission characteristics of PITi by adjusting the structural parameters of stubi cavity and FPi resonator. Similarly, transmission characteristics of PIT2 can be manipulated by changing the structural parameters of stub2 cavity and FP2 resonator. Ultimately, we can individually manipulate transmission characteristics at PIT 1 and PIT2 windows.

4. We can manipulate transmission characteristics including the wavelength and transmission of transparency-peak at PITi and PIT2 windows (as mentioned in claim 1), which is as follows:

When the input signal frequency is equal to the resonance frequency of stub cavity, the surface plasmon polaritons (SPPs) waves can be coupled directly to the stub cavities from bus waveguide and indirectly coupled into the FP resonators via the stub cavities. Since effective path of the cavity affects the resonance frequency of the cavity, we can manipulate the wavelength of transparency-peak at PITi (PIT2) window by adjusting the lengths of stubi (sfffe) and FPi (FP2) resonators. In addition, transmission of transparency-peak at PIT 1 (PIT2) can be manipulated by adjusting the coupling distance d\ (di).