A B Y Transmission(%)
0 0 0 0.002%
0 1 1 97.3%
1 0 1 96.8%
1 1 0 0.002%
Chapter 4
The Design of Communication Components Based On Plasmonic Double-triangle Resonators with Kerr-type
Nonlinear Medium
4.1 Introduction
In recent years, use of surface plasmon polariton (SPP) and metal - insulator - metal (MIM) structure to design the all-optical ultrafast photonic devices for applications to optical communications and optical signal processing systems have been interested popularly[71-72]. One of the important SPP characteristics is that electromagnetic wave can couple with propagating free electron oscillation at the metal-dielectric interfaces.
SPPs have promising application on the devices of highly integrated optical circuits because they overcome the conventional diffraction limit and can manipulate light on sub-wavelength scales [73-75]. The metal - insulator - metal (MIM) structure consists of two metallic claddings and a dielectric waveguide, which strongly confined the incident light in the insulator region [76]. Many of plasmonic components based on the MIM waveguides have been demonstrated by numerical simulations and/or experiments, such as couplers [77], Bragg grating reflectors [78-81], Mach-Zehnder interferometers, ring resonators [82-83], tooth-shaped waveguide filters [20], all-optical logic gate[84-86], CDF wavelength-division-multiplexer (WDM) [87-96]. The channels-drop-filter (CDF) is a communication component which the optical signal can be fed into one of the input
ports and then the signal passes through the wavelength multiplexer of the channels-drop-filter (CDF) and finally emits at output ports with almost no disturbance [97-99]. The channels-drop-filter (CDF) is consists of three parts: drop waveguide, bus waveguide and resonator system. The incident electromagnetic wave spread along the certain frequencies and bus waveguide will be dropped by resonator systems to drop waveguide. Most common resonator system usually has a rectangle [100], disk and ring resonator. MIM waveguides are prospective for the design of nano-scale all-optical devices for strong localization, as well as relatively simple fabrication. In the other hand, the nonlinear optical waveguide device as an optical signals processing and optical communications systems wavelength-division-multiplexer (WDM) also have great interest. However, use the optical nonlinearity to design WDM devices is not common.
Therefore, a new design of all-optical triplexer based on of the metal-insulator-metal (MIM) plasmonic waveguide structures and the nano-disk resonators filled with the Kerr-type nonlinear medium was proposed. The proposed plasmonic all-optical triplexer can used in the FTTH communication systems.
4.2 Analysis and Numerical Results
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 metal insulator metal (MIM) plasmonic waveguide is much smaller than the wavelength, just the fundamental transverse magnetic (TM) waveguide mode can spread. In TM mode, the dispersion equation in the waveguide is given by [101]：
0
where
ε
∞stands for the dielectric constant at infinite angular frequency with the value of 3.7, ωp =1.38×1016Hz is the bulk plasma frequency, which represents the naturalfrequency of the oscillations of free conduction electrons,
γ
=2.73×1013Hz is the damping frequency of the oscillations, andωis the angular frequency of the incident electromagnetic radiation. And the dielectric in the bus waveguide is assumed to be air withε
d =1. The SPPs are pleased with inputting a TM - polarized plane wave. In the following FDTD simulations, the grid size in the x and z directions are chosen to be ∆x=∆z = 5nm and ∆t = ∆x/2c, which are sufficient for the numerical convergence. The transmission of the structure is defined as T =Ptr/Pin [102]. Pin presents the total
incident power, and Ptr is transmission power.
First, we use one straight waveguide and a triangle-teeth-shaped resonator filled
with the Kerr-type nonlinear medium to design a optical filter based on the MIM plasmonic waveguide structure, as shown in Fig. 4.1(a). The parameters of the structure are set to be w = 50nm, h=180nm. When the optical signal is incident at the input port, we investigate the output transmission spectra as shown in Fig. 4.1(b). The refractive index of the Kerr-type nonlinear material can be expressed as
n = n0 + n2 I (4.3) where the value of linear refractive index n0 is set as 1.47, n2 is the nonlinear refractive index coefficient, and I is the pumping beam intensity. The Kerr-type nonlinear material is assumed to be Au-SiO2 and its nonlinear coefficient is n2 = 2.07 × 10-9 m2/V2 [70]. By using the proposed triangle-teeth-shaped resonator filled with the Kerr-type nonlinear medium MIM plasmonic waveguide structure could filter out certain wavelengths. Fig 4.2(a) shows the transmission response of SPPs corresponding to different height. When the height of triangle resonators increase wavelengths shift to longer wavelengths. In Fig. 4.2(b), it shows a linear relationship between the height of triangle resonators and the wavelength dropping range. According to the transmission spectra, we find that this structure have band-pass and band-stop effect. Then, we increase the triangle resonator and add a distance d between the two cavities. We found the band-pass and band-stop
Figures 4.5(a)-(f) show the transmission spectra with different number of the cavity, the
number of cavity are two to seven. The height of the cavity h1 and h2 are 180nm.
According to the above results, when the number of the triangle cavity is more than two, we can see the effects are not very well. So we choose the number of the triangle cavity as two. Because the effect of the band-pass and band-stop of the two cavities are better than the other. Next, we use the plasmonic waveguide structure and double-triangle cavity filled with a Kerr nonlinear material to design the filter as shown in Fig. 4.6.
Finally, we change the height of h2. Figures 4.7(a)-(f) show the transmission spectra with different height h2 of the cavity, the height h2 is varying from 130nm to 170nm.
When h2 =160nm, we can be filter out a narrow band-pass. Next, we will realize triplexer by using the two double- triangle cavity filled with a Kerr nonlinear material.
4.3. Simulation and Results
4.3.1 Triplexer
We use four straight waveguides and six nonlinear double-triangles resonators to construct a novel all-optical triplexer based on MIM waveguide structure, as shown in Fig. 4.8(b). Before designing the triplexer, we must first investigate the influence between two straight waveguides and reflector. In Fig. 4.8(a), we use two straight waveguides and two different nonlinear double-triangles of height resonators to find out the reflector influence. In Fig 4.9, we adjust reflective length from 50nm to 300nm with d = 200nm, h1 = 227nm, h2 = 190nm and w = 50nm. The numerical simulation results show that the best transmission efficiencies at L = 50nm, the peak wavelength at 1310nm and the maximum transmittance is 97.4%. The transmission spectra are shown
in Fig. 4.10. With the same parameters, we find that transmission efficiency of the case with reflector is higher than that of the case without reflector. Next, we use three straight waveguides and four different nonlinear double-triangles of height resonators to find out the influence as shown In Fig. 4.8(b). The parameter L1 is designated as the length between the first and the second straight waveguides, and the parameter L2 is designated as the length between the second and the third straight waveguides. The parameters of the structure are set to be h1 = 227nm, h2 = 190nm, h3 = 257nm, h4 = 218nm, w = 50nm, L = 50nm, and d = 200nm. In Figs. 4.11 (a)-(f), the distance L1 is varying from 400nm to 900nm. When L1 = 700nm, as can be seen that both of the first and second straight waveguides have the optimal transmittances. According to the results, we see that the best distance is L1 = 700nm. Next, we use the same method to investigate the second and the third straight waveguides distance L2. In Figs. 4.12 (a)-(f), the distance L2 is varying from 800nm to 1300nm. When L2 = 1100nm, as can be seen that both of the second and third straight waveguides have the optimal transmittances.
According to the results, we see that the best distance is L2 = 1100nm. As the results shown above, we proposed all-optical triplexer as shown in Fig. 4.8(b). The parameters of the proposed are h1 = 227nm, h2 = 190nm, h3 = 257nm, h4 = 218nm, h5 = 270nm, h6
= 230nm, w = 50nm, L = 50nm, L1 = 700nm, L2 = 1100nm, and d = 200nm. The transmission spectra of the all-optical triplexer are shown in Fig. 4.13(a). The dropped peak-wavelengths of the MIM plasmonic all-optical triplexer are λ1 = 1550nm, λ2 = 1490nm, and λ3 = 1310nm, respectively, and the transmission efficiencies are 95.7%, 88.4%, and 98.1%, respectively. The field distributions of the proposed all-optical triplex for wavelengths of 1310nm, 1490nm, and 1550nm are shown in Figs. 4.13(b)-(d).
As the numerical results shown above, the proposed MIM plasmonic optical filter could really function as an all-optical triplexer.
4.4. Summary
In this chapter, we have successfully proposed a novel triplexer filter structure based on nonlinear triangle resonators in metal-insulator-metal waveguides. At first, we investigate the height of the triangle resonators. We find that the longer height we set, the longer wavelength trough wavelength shifts. According to this result, we can simply filter out the desired wavelength by adjusting the height of the triangle. We also discuss the coupling length, we find that the coupling length increases, the quality factor is also increases. By simulation result, the quality factor of the filter can be controlled by changing the coupling length. We add a reflector and find out the best reflective length to improve transmission efficiency. By applying above methods, our proposed triplexer filter is designed. The triplexer that we proposed can accurately wavelength at 1310nm, 1490nm and 1550nm with transmission efficiency about 90%. The triplexer filter shows good promising for the FTTH applications. The total size of the proposed optical triplexer is only 3.2μm×1.5μm.
Fig. 4.1 (a) The proposed optical filter based on the triangle-tooth-shaped resonator filled with the Kerr-type nonlinear medium. (b) The normalized transmission spectrum of the proposed optical filter.
(a)
(b)
Fig. 4.2 (a) The transmission spectrum for the different height of the proposed triangle-tooth-shaped resonator with h = 160-280 nm and w = 50nm, (b) The relationship between the resonant-wavelengths and the height of the proposed triangle-tooth-shaped resonator.
(a)
(b)
Fig. 4.3 (a) The proposed optical filter based on the triangle-teeth-shaped resonator filled with the Kerr-type nonlinear medium. (b) The normalized transmission
spectrum of the proposed optical filter.
(b)
(a)
Fig. 4.4 Transmission spectra for fixed h1 = h2 = 180nm with different coupling distances d (a) 0nm, (b) 50nm, (c) 100nm, (d) 150nm, (e) 200nm, (f) 250nm.
(a) (b)
(c) (d)
(e) (f)
Fig. 4.5 The normalized transmission spectra for fixed h1 = 180nm, h2 = 180nm and d=200nm with different number of the teeth-shaped-cavities (a) two-cavity, (b) three-cavity, (c) four-cavity, (d) five-cavity, (e) six-cavity, and (f) seven-cavity.
(a) (b)
(c) (d)
(e) (f)
Fig. 4.6 The proposed optical filter based on the double-triangle-teeth-shaped resonators filled with the Kerr-type nonlinear medium, with different height h1 and h2.
Fig. 4.7 Transmission spectra for fixed w = 50nm, d = 200nm and h1 = 180nm with different h2 (a) 130nm, (b) 140nm, (c) 150nm, (d) 160nm, (e) 170nm.
(a) (b)
(c) (d)
(e)
Fig. 4.8 (a) The proposed optical filter based on the nonlinear double-triangle-teeth-shaped resonators with a reflector at the end of the MIM plasmonic waveguide structure. (b) The proposed MIM plasmonic all-optical triplexer.
(a)
(b)
Fig. 4.9 Transmission spectra for the different reflective length L with h1 = 227nm, h2 = 190nm, d = 200nm, w = 50nm.
Fig. 4.10 Transmission spectra with reflector and without reflector.
Fig. 4.11 Transmission spectra for fixed L = 50nm and h1 = 227nm, h2 = 190nm, h3
= 257nm, h4 = 218nm, w = 50nm, d = 200nm with different L1 (a) 400nm, (b) 500nm, (c) 600nm, (d) 700nm, (e) 800nm, (f) 900nm.
(a) (b)
(c) (d)
(e) (f)
Fig. 4.12 Transmission spectra for fixed L1 = 700nm and h3 = 257nm, h4 = 218nm, h5 = 270nm, h6 = 230nm, w = 50nm, d = 200nm with different L2 (a) 800nm, (b) 900nm, (c) 1000nm, (d) 1100nm, (e) 1200nm, (f) 1300nm.
(a) (b)
(c) (d)
(e) (f)
Fig. 4.13 (a) Transmission spectra of the proposed MIM plasmonic all-optical triplexer. The magnetic field distributions of the resonant wavelengths (b) 1310nm, (c) 1490nm, and (d) 1550nm.
(a)
(b) (c)
(d)
Chapter 5 Conclusions
5.1 Summary
In this thesis, we investigate the characteristic of metal-insulator-metal waveguides structure and different resonators. By utilized the properties of the resonator waveguides and metal-insulator-metal waveguides structure, we proposed several novel all-optical devices. According to the simulation results, we verified that these devices can be used widely for optical communication systems and optical signal processing.
In chapter 3, we had successfully demonstrated the ultracompact all-optical logic gates. We have numerically investigated the all-optical plasmonic logic gate based on nano-disk cavity structures filled with optical nonlinear Kerr material. At first, we investigate the radius of the disk resonators. We find that the larger radius we set, the longer wavelength trough-wavelength shifts. The relationship between the resonant wavelengths and the coupled-aperture width of the nano-disk resonators is approximately inversely. The active tuning of the pumping light also makes the wavelength shifts. According to the numerical results as shown above, it is seen that the operating wavelength can be easily tuned by changing the radii of the resonators, the coupled-aperture width of the nano-disk resonators, and the pump light. The transmission efficiency of the high logic state is about 94% and low logic state is 0.002%. Next, we added the number of nano-disk resonators to obtain the wider band-stop, and design all logic gates. For the proposed AND gate logic gate, the
normalized transmission efficiency of the high logic state is about 94.5% and the low logic state is 0.002%. For the proposed OR logic gate, the normalized transmission efficiency of the high logic state is about 95.4% and the low logic state is 0.002%. For the proposed NOR logic gate, the normalized transmission efficiency of the high logic state is about 97.4% and the low logic state is 0.003%. For the proposed XNOR logic gate, the normalized transmission efficiency of the high logic state is about 97.4% and the low logic state is 0.004%. For the proposed NAND logic gate, the normalized transmission efficiency of the high logic state is about 97.3% and the low logic state is 0.002%. And for the proposed XOR logic gate, the normalized transmission efficiency of the high logic state is about 97.3% and the low logic state is 0.002%. According to the numerical results, we can implement the proposed devices which can function as logic gates.
In chapter 4, we use the triangle-teeth-shaped resonators filled with the Kerr-type nonlinear medium to design an all-optical triplexer. By properly adjusting the heights of the triangle-teeth-shaped resonators and the coupling distances, proposed metal-insulator-metal (MIM) plasmonic waveguide could filter out certain wavelengths.
It can be used to design a novel all-optical triplexer, which can filter out the optical communication wavelengths 1310nm 、 1490nm, and 1550nm, respectively. The transmission efficiency is higher than 90%. It shows good promising for the FTTH applications.
5.2 Suggestions for Future Researches
In recent years, the use of surface plasmon waveguide structure to design
all-optical devices is rare popular method. However, using the nonlinear material to design structure is the most. We proposed three and eight-channel WDM of the peak wavelength width are only 2~3nm. The intensity of incident light source may be instability. This result in our structure will cause the transmission efficiency dropped significantly. We hope improved the peak wavelength width of devices up to ±5nm. In optical signal processing, we hope to design more different structure of the WDM such as disk or square. By more different structure component combination, we further design more all-optical devices.
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