Plasmonic Luneburg lens and plasmonic nano-coupler Download: 688次
With the development of the photonic integrated circuit, it is respected to integrate optical devices and electronic devices in a single chip[1,2]. The most challenging problem is the different length scales between photonics and electronics. The diameter of standard single-mode fibers in the telecom industry is 9 μm. The electronic elements in the integrated circuit are with nanoscale (). Surface plasmon polaritons (SPPs) are considered to be the most possible solutions[3]. SPPs are electromagnetic surface waves associated with a collective oscillation of electrons that propagate along the interface between a metal and a dielectric[4]. Plasmonic devices, which can confine light in regions with dimensions that are smaller than the wavelength of the photons in free space, have the potential to match the different length scales associated with photonics and electronics in a single nanoscale device[5]. However, the abrupt discontinuities in the material properties or geometries of conventional plasmonic elements lead to increased scattering of SPPs, which significantly reduces the efficiency of these nanoscale plasmonic devices[6–
It has been proposed that transformation optics can be applied to plasmonic systems[1012" target="_self" style="display: inline;">–
In this Letter, we present a more accurate design of a plasmonic metasurface Luneburg lens (PMLL), which is based on average permittivity approximation. The dielectric with air holes can be considered as a new material, which has an equivalent permittivity ; the effective mode index is calculated according to and plasmonic dispersion equations. To assess the mismatch caused by manufacturing errors, perturbations were added to the input parameters in the simulations. Simulations indicated the full width at half-maximum (FWHM) and the location of the focus point have robustness to manufacturing errors. More importantly, we show a PMLL coupler model, which can solve the problem of the scale mismatch. This coupler coupled the 10 μm width input SPPs to the 40 nm width output waveguide. Finite difference time domain (FDTD) solutions were used to demonstrate the design. Simulations show perfect focusing ability of a PMLL and low coupling loss of the compact coupler model. The proposed design is compatible with standard lithographic technology. We believe that this design could lead to more feasible and convenient strategies for the production of other GRIN (lens based on GRIN) plasmonic devices.
The PMLL consists of a 220 nm dielectric film with a nanostructure on an Au substrate as shown in Fig.
Fig. 1. (a) Schematic diagram for a PMLL. (b) Quarter enlarged view of the top of the dielectric film with air holes. (c) Transverse cross section of the intensity profile at the point in the direction. (d) Intensity distribution of SPPs [three-dimensional (3D) simulation] propagating along direction and passing through a PMLL. The red circle indicates the radius R of the PMLL. The red dotted circle indicates the real area of the designed lens. The white dotted line indicates the position .
The index distribution of a traditional Luneburg lens satisfies the expression where characterizes the distance to the center of the PMLL. is the radius of the PMLL. The red circle in Fig.
Here, is the height of the dielectric film. represents the SPP wave vector along the direction. is the frequency of the SPPs. is the speed of light in vacuum. stands for the permittivity of the air. stands for the permittivity of the dielectric. stands for the permittivity of the Au. The effective mode index of the SPPs can be defined as Eq. (
Furthermore, according to Eqs. (
Here, is the volume fraction of the air hole. The radius of air holes is calculated from the equation . Considering that it is hard for the diameter to be larger than in the manufacturing process, the diameter is set to be 8.7 μm. The red dotted circle in Fig.
The Lumerical FDTD Solutions ® software is used to confirm the design. SPPs propagate along direction and pass through a PMLL [Figs.
The height of the dielectric film is changed to be 170 nm, 200 nm, 250 nm, and 290 nm, while the distribution of air holes has not been changed. The height of air holes is equal to the height of the dielectric film. The simulations shown in Fig.
Fig. 2. (a), (c), (e), and (g) Transverse cross sections of the intensity profile at the point in the direction. (b), (d), (f), and (h) Intensity distributions of SPPs (3D simulation) propagating along direction and passing through the PMLL with different heights. The red circles indicate the radius R of the PMLL. The red dotted circles indicate the real area of the designed lens. The white dotted lines indicate the position .
The radius of the air holes is set to be 90 % or 110 % of the designed values, as shown in Figs.
Fig. 3. (a) and (e) Schematic diagram for a PMLL. (b) and (f) Quarter enlarged view of the top of the PMMA film with air holes. (c) and (g) Transverse cross section of the intensity profile at the point in the direction. (d) and (h) Intensity distributions of SPPs (3D simulation) propagating along direction and passing through a PMLL. The red circles indicate the radius R of the PMLL. The red dotted circles indicate the real area of the designed lens. The white dotted lines indicate the position .
The different length scales limit the integrated optical and electronic devices in a single chip[24]. To associate with photonics and electronics in a single nanoscale device, SPPs should be coupled to a nanoscale waveguide. In view of the excellent focusing ability and the robustness to manufacturing errors, the PMLL can be utilized to design a compact high-performance coupler in photonic and electric integrated circuits, as shown in Fig.
Fig. 4. (a) Schematic diagram for a taper. (b) Schematic diagram for a PMLL coupler. (c) Transverse cross section of the electric field profile at the position . (d) Electric field profile of SPPs propagating along direction, passing through a taper coupler, and coupled to the 40 nm wide waveguide. (e) Transverse cross section of the electric field profile at the position . (f) Electric field profile of SPPs propagating along direction, passing through a PMLL, and coupled to the 40 nm wide waveguide. The red circle indicates the position of the PMLL, and the white dotted line indicates the position of the monitor.
As shown in Fig.
The calculated coupling loss of the PMLL coupler was 8 dB for the designed wavelength . The calculated coupling loss of the taper coupler was 12.2 dB. In addition, the designed PMLL coupler showed a higher coupling efficiency in a broad bandwidth of , as shown in Fig.
Fig. 5. The performance of the PMLL coupler and taper coupler based on 3D simulations in a broad bandwidth.
In conclusion, we demonstrated that a PMLL designed by average permittivity approximation and plasmonic dispersion equations performed well. The characteristics of a PMLL have robustness to manufacturing errors. We also demonstrated that a PMLL can work as a compact coupler in plasmonic integrated circuits; the performance of this kind coupler is far better than the traditional inverse width tapers. Such an element can be manufactured in a single lithographic patterning step, which means such elements have great potential to be widely used in plasmonic integrated circuits. Furthermore, this method can be used to design plasmonic elements working in the telecom wavelength of 1550 nm. Silicon can be an option of the material of dielectric layer. It shows the potential to integrate electronic, photonic, and SPPs in a single chip. We believe that this design could lead to more feasible and convenient strategies for the production of other GRIN (lens based on GRIN) plasmonic devices.
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Lei Zhang, Lin Wang, Yanqing Wu, Renzhong Tai. Plasmonic Luneburg lens and plasmonic nano-coupler[J]. Chinese Optics Letters, 2020, 18(9): 092401.