III. MODE PROPAGATION AND SKIN DEPTH Surface plasmon dispersion and propagation are governed
9.1 Incoupling into Metal/Insulator/Metal Structures
In recent experimental studies [29, 30, 72] of metal/insulator/metal (MIM) or “plasmonic slot” waveguides, our laboratory has developed a method of coupling light into MIM stacks through subwavelength slits. These slits consist simply of narrow channels milled with a focused ion beam (FIB) through the top metal waveguide cladding and perhaps partway through the waveguide core (illustrated in cross section in the 2D schematic, Figure 9.1(a)). When illuminated by a lamp or laser, the slit is found to be effective at scattering light into waveguided modes of the MIM. These waveguided modes are launched with propagation direction transverse to the slit axis. Another, parallel slit can be milled some distancedaway which scatters light from the guided modes back into free space. If this output slit is milled through only the bottom surface, the result is a dual- sided coupling geometry which allows investigation of waveguide propagation in a dark-field configuration with both far-field illumination and detection [30].
Such a double-slit scheme is an excellent geometry for laboratory investigation; since there is no direct path from the optical source to detector, the dark-field measurement has good signal-to-noise performance in general. However the absolute quantity of power coupled in through the subwavelength aperture may be small (in other words, the insertion loss is large). The incoupled power is highly sensitive to the exact geometry (e.g., width and depth) of the slit. The slit shape influences both the scattering power of the slit itself, and the spatial overlap of the scattered power with the guided modes of the MIM.
Recently we have demonstrated the operation of a micron-scale electrooptic modulator, in a device which combines plasmonic slot waveguiding with the electrical characteristics of a metal-oxide-silicon capacitor, or “plasmostor.” Near-infrared transmission between an optical source and drain is controlled by an applied electric field that modulates the complex refractive index of the Si. In the dark-field configuration, ampli- tude modulation depths as large as 11.2 dB are achieved. Modulation is observed in devices with channel areas (length x thickness) as small as 0.01λ2, with sub-nanosecond switching speeds and minimal power requirements [29].
However, in order to consider integration of plasmostors or other subwavelength active devices as con- stituents of dense subwavelength photonic networks, we must also address strategies for coupling light in from in-plane, and develop design strategies to achieve low overall loss. From semianalytic mode calculation (see Ch. 8) we determine that the losses intrinsic to the waveguided modes of the plasmostor are around 1 dB. Theoretical results from the group of Fan et al. [137] have indicated insertion losses as low as 0.3 dB for an optimized, impedance matching coupler between a dielectric slab waveguide and a plasmonic MIM.
In this section, we employ FDTD simulation, first to characterize the loss of the actual slit coupler which has been employed in the actual plasmostors fabricated to date in Figure 9.1(a), and then to survey alternative coupling schemes which are achievable with minimal incremental changes to the fabricated device structure in Figure 9.1(c,e,g). The simulated MIM stack consists of a core of 160 nm of Si, with 10 nm layer of oxide on one side, and clad on both sides by 400 nm Ag. The simulation is 2D with PML boundaries. Material data are from the Palik handbook, using the Lorentz-Drude model for the dispersive dielectric of Ag, and are given in Appendix B. In all simulations the incident light is TM polarized, monochromatic, continuous wave excitation at the operating frequency of the plasmostor,λ0=1550 nm. In the chosen coordinate system the MIM propagation axis is ˆz. In all cases the input port, whether slit or waveguide end facet, is centered at the center of the simulation volume, with coords[z,x] = [2,0]µm. The power which is considered “incoupled”
is that which passes is steady state through a monitor port consisting of a line segment which intersects the waveguide axis at[z,x] = [2.5,−0.4 : 0.4]µm.
The following incoupling conditions are considered:
1. Slit Incoupling. Source plane is a Gaussian beam with waist (1/e radius) ofw0=1.5µm in the plane
x=1µm, about a half micron above the surface. The slit is an air-filled opening transverse the the waveguide, 400nm wide, 490nm deep through the metal cladding and halfway into the Si core. Note that the assumption that the focal radius≈λis somewhat arbitrary but intended as a “best case” esti- mate; practically the spot would almost certainly be much larger. The reported incoupling coefficient represents the energy coupled into the MIM guide in the+ˆzdirection; due to the symmetry of this coupling scheme, the same amount also couples into the−ˆzdirection.
2. Endfire Incoupling. Source plane is a Gaussian beam with waistw0=1.5µm, incident normal to the end facet of a truncated MIM.
3. Thin Waveguide Incoupling. Source is the lowest-order TM mode of an air-clad Si-core waveguide with a 160 nm core, the same thickness as the Si core of the MIM.
4. Tapered Waveguide Incoupling.Source is the lowest-order TM mode of an air-clad Si-core waveguide with a 970 nm core, the same thickness as the entire MIM stack. This waveguide is joined to the 170 nm Si core of the MIM by a 1µm segment of concave parabolic taper. The tapered segment is clad in air.
5. Metal-Clad Tapered Incoupling.Source is the lowest-order TM mode of an air-clad Si-core waveguide with a 970 nm core, same thickness as the entire MIM stack. This waveguide is joined to the 170 nm Si core of the MIM by a 1µm segment of concave parabolic taper. The tapered segment is clad in Ag.
Table 9.1: Power incoupled to Ag/Si/Ag plasmonic waveguide from free space Gaus- sian beams in endfire or slit configuration, or from Si core dielectric waveguide.
Geometry Incoupled Power (%) Incoupled Power (dB)
Slit, Tightly focused beam 5.2% -12.8dB
Endfire, Tightly focused beam 14.8% -8.3dB
Thin 160 nm waveguide, endfire 35.9% -4.4dB
970 nm guide, Air clad taper 20.4% -6.9dB
970 nm guide, Ag clad taper 24.0% -6.2dB
We find that the insertion loss for the waveguide end-fire scheme, see Table 9.1, is only -4.4 dB, an improve- ment of about 8 dB over the currently employed slit-coupling geometry. This type of analysis allows us to trade off the demand for increased performance with the desire to minimize added design complexity. Most
Z Position [um]
X Position [um]
Layout (Real Index)
0 0.5 1 1.5 2 2.5 3 3.5 4
-1.5 -1 -0.5 0 0.5 1 1.5
0.5 1 1.5 2 2.5 3
(a) Slit layout
Z Position [um]
X Position [um]
Hy field
0 0.5 1 1.5 2 2.5 3 3.5 4
-1.5 -1 -0.5 0 0.5 1 1.5
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
(b) Slit incoupled Hy field
Z Position [um]
X Position [um]
Layout (Real Index)
0 0.5 1 1.5 2 2.5 3 3.5 4
-1.5 -1 -0.5 0 0.5 1 1.5
0.5 1 1.5 2 2.5 3
(c) Endfire layout
Z Position [um]
X Position [um]
Hy field
0 0.5 1 1.5 2 2.5 3 3.5 4
-1.5 -1 -0.5 0 0.5 1 1.5
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
(d) Endfire incoupled Hy field
Z Position [um]
X Position [um]
Layout (Real Index)
0 0.5 1 1.5 2 2.5 3 3.5 4
-1.5 -1 -0.5 0 0.5 1 1.5
0.5 1 1.5 2 2.5 3
(e) Thin (160nm) waveguide layout
Z Position [um]
X Position [um]
Hy field
0 0.5 1 1.5 2 2.5 3 3.5 4
-1.5 -1 -0.5 0 0.5 1 1.5
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
(f) Thin waveguide incoupled Hy field
Z Position [um]
X Position [um]
Layout (Real Index)
0 0.5 1 1.5 2 2.5 3 3.5 4
-1.5 -1 -0.5 0 0.5 1 1.5
0.5 1 1.5 2 2.5 3
(g) Metal clad taper layout
Z Position [um]
X Position [um]
Hy field
0 0.5 1 1.5 2 2.5 3 3.5 4
-1.5 -1 -0.5 0 0.5 1 1.5
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
(h) Metal clad taper incoupled Hy field
Figure 9.1: Illustrated survey of simulated geometries for coupling into Ag/Si/Ag plas- monic waveguide from free space Gaussian beams or from Si core dielectric waveguide.
Left column: Color scale represents the materials’ real optical index in all space, ma- terials Ag (black), air (white), Si (purple), and oxide (blue) are visible. Right column:
importantly, the substantial improvement reported here can be achieved without varying the width of the Si core in the dielectric waveguide region relative to that of the core in the MIM active region.