Chapter 2: The Basic Theory and Method
3.2 Analysis and Numerical Results
In this chapter, we proposed and numerically investigated all-optical plasmonic logic gates based on the nonlinear nano-disk cavity resonators. We used bus waveguides and filled with optical nonlinear materials nano-disk resonators to construct logic gates based on MIM waveguide structure.
The dielectric constant of the Kerr-type nonlinear medium in the resonator is changed
by varying the pump light and the signal transmission can thus be controlled. The logic gate performance was analyzed and simulated by finite difference time domain (FDTD) method. The performance of the proposed devices has advantages of small size, requirement of low pumping light intensity that have potential applications in ultra compact all-optical integrated photonic circuits.
Under normal circumstances, the interfaces between semi - infinite materials having negative and positive dielectric constants can effectively guide the transverse magnetic (TM) surface waves. Since the width of the MIM plasmonic waveguide is much smaller than the wavelength, just the fundamental TM waveguide modes can spread. For TM modes, the dispersion equation is given by [67]：
0
k is the free-space wave vector. The propagation constant β is represented
as effective index neff = β / k0 of the waveguide for SPP.
In the chapter, the dielectric is assumed to be air with
ε
d =1, and the metal to be silver. The dielectric constantε
mof silver can be calculated by Drude model [68]：( ) ( )
value of 3.7, ωp =1.38×1016Hz is the bulk plasma frequency, which represents the
natural frequency of the oscillation of free conduction electrons.
γ
=2.73×1013Hzis the damping frequency of the oscillation, andω is the angular frequency of the incident electromagnetic radiation. The SPPs are pleased with inputting a TM - polarized plane wave. The transmission of the structures is defined as T =Ptr/Pin [69]. Pin presentsthe total incident power, and Ptr is the transmission power. The refractive index of the Kerr-type nonlinear material can be expressed as
n = n0 + n2 I (4.3) where the value of the linear refractive index n0 is set as 1.47. The Kerr-type nonlinear material is assumed to be Au-SiO2, and its nonlinear refractive index is n2 = 2.07 × 10-9 m2/V2 and I is the pumping beam intensity [70].
The proposed of single aperture-side-coupled dielectric nano-disk resonators is shown in Fig. 3.1, which is consisted of a waveguide coupled to aperture-side-coupled dielectric nano-disk cavity filling with a Kerr-type nonlinear material. The parameters of the structure are set to be w = 50nm, w1 = 20nm, h = 100nm, and R = 290nm. We studied the influence of the radius of the nano-cavity on the resonance wavelengths by the FDTD method. The radius is set as variable while the other parameters are fixed as above. Figures 3.2 (a) and (b) show the transmission spectra with different radius R. The resonant peak-wavelengths have a red-shift with increasing of the radius. Fig. 3.2 (a) shows the different radius R=250nm to 370nm and the Fig. 3.2 (b) shows the relationship between the resonant trough-wavelength and the radius of nano-cavity is
approximately linear. And the coupled-aperture width is set as variable while the other parameters are fixed as above. Fig. 3.3 (a) and (b) show the transmission spectra with different width w1. The resonant trough-wavelengths have a red-shift with reducing of the width. Fig 3.3 (a) shows the different width w1=10nm to 50nm and Fig. 3.3 (b) shows the relationship between the resonant trough-wavelength and the coupled-aperture width w1 of the nano-disk resonators is approximately inversely. Then we use the same method to investigate the channel length h between the nano-disk resonators and the bus waveguide. In Figs. 3.4 (a)-(f), the length h is varying from 40nm to 140nm. As the numerical results shown above, the operating wavelength can be easily tuned by changing the radius and the coupled-aperture width of the nano-disk resonator.
Fig.3.5 (a) shows the proposed two nonlinear aperture-coupled dielectric nano-disk resonators. We use the same radii of the nano-disk resonators and two different coupled-aperture width of cavity to find out the influence. The parameters of the proposed structure are setting to be R = 290nm, h = 100nm, d = 240nm, w1 = 20nm, w2
= 30nm, and w = 50nm. According to the above results, the transmission spectra of the output nano-disks possess band-stop wavelengths of 1310nm and 1300nm, respectively.
As shown in Fig. 3.5 (b) it is found that the resulting band-stop about 10nm, where the transmission waves through two mirrors generate the destructive interference around the transparency wavelength. Next, we investigate the distance d between the nano-disk cavities. In Figs. 3.6 (a)-(h), the distance d is varied from 0nm to 320nm. When d
=240nm, we can get the better band-stop and band-pass results.
Finally, we set the two nano-disk resonators as a unit cell nano-disk resonator and
investigate the influence of the number of the nano-disk resonators. The number and the radii of the are set as variable while the other parameters are fixed as shown in Tab. 3.1.
Figures 3.7(a)-(f) show the transmission spectra with different number of the cavity, the number of cavity are two to twelve. Numerical results of the number of the nano-disk cavity is eight. The best band-pass and the band-stop is eight nano-disk resonators. Next, we analyze AND, OR, NOR, XNOR, NAND and XOR logic gates by using the eight nano-disk resonators filled with a Kerr-type nonlinear material, as shown in Fig. 3.8.
Before designing the logic gates, we suit investigate the parameters of the proposed structure to obtain the optimal values for designing the logic devices.