In- and out-coupling devices for subwavelength waveguides. Part 2
Efficient technologies for coupling light into certain types of wide non-subwavelength waveguides (for example, optical fiber or silicon waveguide) are developed quite well. It is therefore possible to launch optical radiation first into a wide waveguide and then to a subwavelength waveguide. This can be realized in various ways (Fig.1), namely as:
1. End-fire coupling,
2. Resonant waveguide section,
3. Gradually tapered section,
4. Directional coupler.
1. End-fire coupling
In case of the end-fire connection (Fig. 1a) the waveguides are brought into a physical contact. This type of the waveguides connection is widely used in optical communication equipment for connecting optical fibers with connectors and adaptors. However, upon propagation the radiation is not only transmitted from the first into the second waveguide, but is also reflected and scattered due to different waveguides impedances and mode field spatial profiles (Fig. 2). The closer the electromagnetic modes field profiles resemble each other, the larger is the coupling efficiency (CE). Theoretically calculated CE for coupling a silicon waveguide into a plasmonic waveguide of a similar size is around 50% , but for a certain combinations of the waveguides CE can reach 90% . In practice, however, experimentally measured values are sufficiently smaller. For example, in the work  CE = 30% at the wavelength 1.55 µm was demonstrated.
The concept of using a resonant waveguide section (Fig. 1b) is similar to the ideas of using antireflection coatings with the refractive index n and thickness λ/4n (λ is the wavelength in vacuum) in optics and quarter-wavelength transformers in microwaves. Physically, a large transmission is reached by using a resonator for matching the waveguide impedances. The drawback of using a resonator is the working wavelength range narrowing and losses increase due to a lossy material employment inside the resonator. The resonant section may be used for matching plasmonic waveguides of different cross-sections  as well as for matching a dielectric waveguide with a plasmonic waveguide. For example, numerical modelling demonstrated matching of a wide (500 nm) and narrow (50 nm) plasmonic waveguides with CE = 86% .
3. Gradually tapered waveguide section
Gradually tapered waveguide section (Fig. 1c) between the waveguides of different cross-sections resembles the previous type of IOD, however, the main difference is that the gradually tapered waveguide section is non-resonant. The physical principle of its operation is minimization of the back – and side – scattering upon a gradual adiabatic mode transformation. For a tapered section without losses the largest CE would be reached for an infinite length of the section. In practice, however, the optimal length is determined by the balance  between absorption and scattering.
Gradually tapered section can be made from the same material than the waveguide itself (dielectric, metal), but can also be made of a structured material (metamaterial). The dielectric tapered waveguides can be fabricated by pulling a heated optical fiber . Nevertheless, even narrowing down the fiber to a subwavelength size it is not possible to reach the subwavelength size of the mode due to the natural diffraction limit. Short inverse tapers have found their application for light coupling to the photonic crystal waveguides . Their application allows for reducing reflection down to 1%.
It has been shown theoretically the possibility for light transmission with the CE around 70% at the wavelength 1.5 µm . Experimentally measured CE from a waveguide of the width 1500 nm to a metallic nanowire of the width 30 nm was 56%  at the wavelength 1.425 µm.
Employment of the structured metamaterials in the tapered section creates additional difficulties in the devices fabrication as well as additional losses related to metamaterials due to the resonant consisting elements. For example, in the work  it was demonstrated theoretically light concentration down to the size of λ/30, however, transmittance was only about 13%.
Employment of the gradually tapered waveguide section also allows for reaching enormously large electric field strength in optical  as well as terahertz  ranges.
4. In- and out-coupling devices on the basis of a directional coupler
The action of the directional coupler (Fig.3) is based on different waveguides modes hybridization under a sufficiently strong interaction between them. The propagating mode of the input waveguide hybridize in the interaction region and is converted into a linear combination of the hybrid eigenmodes. Upon the modes propagation the spatial beatings occur and the power maximum is observed consequently in the first and then the second waveguide. Appropriate selection of the hybrid section length allows for maximal power transfer from the first waveguide into the second one. Similar devices are applied in microwave engineering as well as optical communication (for example, fused multiplexor in fiber optics).
Similar devices for light coupling from dielectric to plasmonic waveguides were demonstrated theoretically, as well as experimentally [11–13]. The length of the interaction region in various systems varied from a few micrometers  to tens and even hundreds of micrometers , depending on the types of the interacting waveguides. Numerically computed and experimentally measured coupling efficiency at the wavelength 1.55 µm for coupling from a silicon waveguide to a plasmonic slot waveguide was 60% .
In certain cases, it is possible to employ not only a traditional placement of the waveguides "one next to another", but also the situation when one waveguide penetrates into another. For example, it is possible to insert a silicon waveguide into a plasmonic slot waveguide. The theoretical CE=88% was much more modest in experiment (35%) .