An efficient and compact coupler—a device that matches a microwaveguide and a nanowaveguide—is an essential component for practical applications of nanophotonic systems. The number of coupling approaches has been rapidly increasing in the past ten years with the help of plasmonic structures and metamaterials. In this paper we overview recent as well as common solutions for nanocoupling. More specifically we consider the physical principles of operation of the devices based on a tapered waveguide section, a direct coupler, a lens, and a scatterer and support them with a number of examples.
Photonic components have advantages comparing to the electronic ones. Infrared and optical frequencies 1014-1015 Hz provide much broader operational bandwidth than the fastest electronic circuits. The losses in optical waveguides are smaller than in metallic wires. This is why, as D. Miller wrote, “the optical interconnects are progressively replacing wires” [
Nevertheless, the problem is not only to create efficient waveguides that provide subwavelength mode confinement, but also to make an efficient interface between free space or an optical fiber and a subwavelength nanowaveguide, that is, to focus light and launch it efficiently into the waveguide. The artistic view of the situation is depicted in Figure
An artistic view of the problem of coupling light from a wide microscopic fiber to a nanoscopic waveguide. Employment of a coupler, which is represented by a funnel on the figure, minimizes the losses and simplifies optical alignment.
The problem of optical coupling originates from the pronounced modal mismatch between an optical fiber (a conventional single-mode telecommunication fiber has the core of 8
We are witnessing a real explosion of various metamaterial and plasmonic solutions for focusing and nanocoupling in recent years. The reasons for that are first of all the extraordinary optical properties the artificial metal-dielectric structures offer. Not only the proposed device geometries are different, but also the very physical principles they are based on vary significantly.
The goal of this paper is to give an overview of existing nanocoupling solutions for the visible and near-infrared (telecom) range and to reveal the most efficient ones. We wish to focus mostly on the physical effects employed for nanocoupling rather than on technical details of the devices. We are not going to provide the complete set of references on nanocouplers, since with heaps of articles already published and being published every month it is almost impossible. The cited papers should be considered rather as valuable examples of each physical effect employment.
The paper is organized as follows. In Section
We define a nanowaveguide as an electromagnetic waveguide that has lateral sizes in the “nano” range, that is, 1–1000 nm. Depending on the waveguide material and the wavelength of the light nanowaveguide can be subwavelength or not. The modal size of the subwavelength waveguide is smaller than the size of a focused light beam can be. The nanowaveguides can be divided in two groups: dielectric and plasmonic waveguides. Their combinations, the so-called hybrid waveguides, are also possible.
The most common material for dielectric waveguides is silicon due to its high refractive index, transparency at the telecom wavelengths, and CMOS compatibility. Typically, silicon waveguides are rib, ridge, and photonic crystal waveguides. The high refractive index of the silicon waveguide makes it possible to reduce the cross-section down to
Miniaturization of optoelectronic components requires decreasing the size of optical waveguides. However, the natural limitation comes into play. Due to diffraction the smallest size of an optical beam in a medium is on the order of the wavelength. If we consider a wave of the frequency
Plasmonic waveguides are by default metal-dielectric waveguides. They attract a lot of attention since in some configurations they can show the absence of the cut-off wavelength at any waveguide size. Therefore, the mode size can be reduced to extremely small values but at the cost of increased optical losses. Another advantage of the plasmonic waveguides is the presence of metal that can be used not only as a waveguiding element but also as an electric contact that allows using it for tuning the dielectric surrounding (e.g., due to the electrooptical or thermooptical effects). Plasmonic waveguides are currently considered for the potential replacement of the electronic interconnects in the future generation integrated circuits.
Surface plasmon polaritons (SPPs) are the eigenmodes of a metal-dielectric interface. SPPs are combined light-electrons density waves. On a flat metal (permittivity
Several types of plasmonic waveguiding structures were proposed, for example, metal-insulator-metal and insulator-metal-insulator multilayered structures [
A nanocoupler is a device that facilitates coupling of light from free space or a macroscopic optical fiber to a nanowaveguide. It can be understood as a focusing device, a sort of an optical funnel (see Figure
Nanocoupler concept: a focusing device or a mode convertor. As an example the mode of the dielectric waveguide (left) is gradually transformed into the mode of the plasmonic waveguide (right).
We understand the nanocoupler as a focusing device or a mode convertor that gives a high coupling efficiency (CE) which is the ratio of the power loaded into the waveguide
High coupling efficiency automatically means low losses, including absorption Small size on the order of several micrometers. This is an important requirement for the integration of the nanocoupler within an optical integrated circuit. Simplicity and small price of fabrication. This requirement is important for the mass production but not so important on the stage of the scientific development. Spectral selectivity. The importance of this property depends on the application. In many cases a broad bandwidth is desirable. However, there are some applications, where a narrow bandwidth is preferable, for example, if the coupler is used at the same time for the wavelength demultiplexing. Polarization sensitivity. The importance of this requirement depends on the application and on the selected nanowaveguide. If the nanowaveguide is polarization sensitive, the nanocoupler’s working polarization should be matched with the polarization of the waveguide or it should be polarization insensitive.
We have to emphasize that the nanocoupler differs from a nanofocusing or a nanoimaging device. The goal of nanoimaging or nanofocusing is only to image a tiny light source or focus light into a small spot, respectively, no matter how large is the fraction of the transmitted power with respect to the incident power, while for the nanocoupler the coupling efficiency is the most crucial parameter. For example, the stimulated emission depletion technique [
The role of the nanocoupler is to match the impedances (or wavevectors) and field profiles of an incident wave and a mode of the accepting nanowaveguide. Depending on the employed physical mechanisms several types of nanocouplers can be singled out. Tapered waveguides (Figure Light can be coupled first to a wide waveguide (e.g., a silicon or long-range surface plasmon-polariton waveguide) and then with the help of a directional coupler or a resonant stub coupled into a smaller nanowaveguide (Figure Light can be tightly focused with a lens (Figure A single or multiple scatterers can be used for coupling (Figure There are some other ideas that do not fall into the previously mentioned categories. We will refer to them under a unified shield as
Types of the possible nanocouplers realizations: (a) tapered waveguide coupler, (b) direct coupler transferring the power from a wide waveguide to a narrow waveguide, (c) lens coupler, (d) scatterer coupler.
The nanocoupler can be arranged as a separate device (Figure
Possible geometrical configurations of the coupler: (a) a separate device, (b) integrated with a nanowaveguide (WG) on the same chip, (c) integrated with an excitation fiber.
Two main excitation configurations are important in the practical applications: lateral coupling (Figure
Two practically important coupling configurations: (a) lateral and (b) vertical. Black arrows show the direction of light propagation.
As we already mentioned the tapered waveguide coupler is nothing else but a waveguide with the gradually decreasing core. A mode of the waveguide is subjected to adiabatic compression, when propagating to the tip. Thus it reaches more favorable conditions for coupling to the nanowaveguide. The tapering angle and the rate of compression determine the coupling efficiency and depend on the properties of materials. Therefore, further classification of the tapered waveguides follows the material properties: fully dielectric tapers having the dielectric core and the dielectric cladding (Figure hybrid tapers having the metallic core and dielectric cladding or the dielectric core and metallic cladding (Figure metamaterial tapers having the structured metal-dielectric composite core (Figure
The types of taper couplers: (a) fully dielectric taper, (b) hybrid taper with metal core or cladding, (c) metamaterial taper.
If one takes an optical fiber, heats it up, and then pulls, the diameters of the core and shell simultaneously decrease. So it is possible to draw the core down to a nanosize diameter. Low-loss tapered fibers were fabricated and measured [
Nevertheless, the dielectric tapered waveguide coupler finds useful applications. As L. Zimmermann reported at the Silicon Photonics Workshop in 2011 [
Tapered fiber tips covered with metal are the essential part of the scanning near-field optical microscopy. It allows spatial compression of light below the diffraction limit by employment of SPPs [
Another approach was proposed in [
The idea behind this nanocoupler type is to use a metamaterial as the taper core. The advantage of utilization of metamaterials is that their properties are not strictly limited to that we have from natural materials and can be designed to reach amazing diversity and values. An optical funnel containing a metal-dielectric photonic crystal was proposed in [
A dielectric adiabatically tapered fiber is a well-known instrument of field concentration. However, it can provide either small spot size with low transmission or high transmission at the cost of large size of the light beam and the coupler itself. The metal- or metamaterial-based tapers can be of significantly smaller length. They can give field concentration and reasonable transmittivity (e.g., 20%). The difficulties in practical realization of effective design solutions are connected with the technological constrains; for example, fabrication of a regularly packed bundle of metallic cylinders of radius 10 nm separated with 2 nm of dielectric is currently out of reach.
Based on the geometrical position of one waveguide with respect to another, the direct couplers can be divided into the following classes: one waveguide next to or inside another (Figure end-fire direct connection of the waveguides (Figure resonant stub between the waveguides (Figure
Types of the direct couplers: (a) one waveguide next to or inside another, (b) end-fire coupling, (c) resonant stub between waveguides.
Direct couplers as we classified them are either directional couplers or schemes including end-fire coupling. Directional couplers are classical components of photonic integrated circuits. They are typically used for wavelength division or light switching. The principle of their operation is based on the coupling between parallel waveguides due to overlapping of their modes fields. The coupling leads to the hybrid modes (supermodes, compound modes) formation. The strength of the mode coupling can be controlled by the distance between the cores. Therefore, such couplers require preliminary feeding of a large waveguide at an intermediate step. Then disposing the first waveguide in a close proximity with a nanowaveguide we initiate their coupling with a consequent transit of the light energy in the second channel. Directional couplers are characterized by the coupling length, the distance, on which the maximal amount of the energy is transferred in the second channel and vice versa. The coupling length, in turn, is proportional to the wavenumbers mismatch. As a rule, directional couplers have a relatively large coupling length, what results in the total size of such systems about 10–20
The end-fire coupling scheme also exploits the fields overlapping mechanism. Here the coupling appears as a result of the field profiles matching. The scheme does not require a lengthy coupling part; however, short sizes come at a price of lower coupling efficiency. To improve the efficiency a resonant stub is often placed between the input and nanosized waveguides.
A typical scheme for direct coupling is to arrange one waveguide above another such that the eigenmodes of the waveguides hybridize, and the waveguides become coupled. In such case energy from the input mode is transferred from one waveguide to another and back. Making the overlap region equal to the coupling length it is possible to achieve the maximal energy transfer efficiency. Such systems were proposed, simulated, and experimentally realized for dielectric [
The configuration when one waveguide protrudes into another is possible to certain waveguide types only, since the bigger waveguide should contain empty space inside. For example, it is possible to insert a silicon waveguide inside a plasmonic slot waveguide, but not into another silicon waveguide. Several designs for telecom wavelengths were proposed [
The end-fire coupling is the simplest case of the waveguides connections, and it is common in the optical communication systems. Nevertheless, the end-fire coupling from a dielectric to plasmonic slot waveguide or a nanowire is not usually very efficient due to the pronounced impedances mismatch. However, if the optimization of the geometry is conducted the coupling efficiency more than 70% [
The use of resonant stubs (e.g., a
The
While giving high values of the coupling efficiency (in case of a directional coupler up to 60%) and being feasible for fabrication, the direct nanocouplers require additional structures such as an input silicon waveguide and a preliminary coupler to this silicon waveguide. That makes the total CE of up to 40% and extends the nanocoupler dimensions up to several dozens of micrometers. Moreover, additional structures (e.g., a preliminary coupler) may require additional processing steps during fabrication.
Lens is a well-known focusing device. However, we should emphasize that the requirements for a nanocoupler are stricter than to a focusing device, since nanocoupler should provide, apart from focusing, the high coupling efficiency. To be implemented as a nanocoupler a lens must have high transmission and execute matching of the focused beam to the nanowaveguide mode.
Based on the lens material and their functionality we divide lenses into the following categories: dielectric lens (Figure plasmonic lens (Figure negative refractive index lens (Figure photonic crystal lens (Figure hyperlens (Figure
Types of lens couplers: (a) dielectric lens, (b) plasmonic lens, (c) negative index lens, (d) photonic crystal lens, (e) hyperlens.
A dielectric lens is a focusing device known for several centuries. It is well described in classical optical textbooks (see, e.g., [
Except a standard dielectric lens we should mention also two other focusing devices, namely, a Fresnel lens and a graded index (GRIN) lens. The Fresnel lens and zone plate are well described in optical textbooks [
The GRIN lens was developed for photonics packaging [
Very useful for practical purposes is a focusing optical fiber that combines mechanical flexibility of a fiber with the focusing effect of a lens. Commercial focusing fibers can provide a focal spot down to 2
Using plasmonic effects in metal-dielectric zone plates is quite new since fabrication of fine metallic structures has become possible only recently. The plasmons, excited in the concentric grating by an incident light wave, contribute to the energy transfer to the central ring. The wave constructive interference condition should be satisfied not only for the diffracted light waves but also for the plasmons. A comprehensive review of the plasmonic lenses can be found in [
The focusing effect of a plasmonic lens was experimentally shown in 2002 by Lezec et al. [
As can be seen from the previously mentioned results the plasmonic lens can provide the subwavelength focusing, but practically the focal spot is not much smaller comparing to a dielectric lens, while the transmittivity is lower due to the presence of metal elements.
The seminal idea that a plane slab of a negative index material may focus light was mentioned byVeselago in 1968 [
The negative refractive index occurs as a rule in materials that simultaneously possess negative dielectric permittivity and magnetic permeability. Acomprehensive overview of the negative index metamaterials can be found in [
A negative index slab lens can be used not only for focusing and imaging but also as a coupler. The idea to use a flat negative index slab for coupling between two identical nanowaveguides was proposed by Degiron et al. [
In the most cases proposed metamaterials consist of planar layers, since their fabrication is based on the planar technology. That results in the optical anisotropy. To overcome such drawback several isotropic NIMs designs were proposed [
The losses in a negative index metamaterial coupler are an important issue, since they reduce the coupling efficiency and decrease the spatial resolution. This is why a lot of efforts are applied at the moment to compensate the losses with gain material [
The negative refraction phenomenon may occur not only in negative index materials but also in photonic crystals typically at frequencies close to the bandgap edge [
Another solution for the subwavelength focusing involves a material with the hyperbolic dispersion, a so-called indefinite medium [
A medium with the hyperbolic dispersion is anisotropic by definition. To reach positive and negative permittivity for different directions one may use either metallic wires or a metal-dielectric multilayer stack. In case of wires the effective permittivity can be negative for electric field polarization along the wires, while for the polarization perpendicular to the wires the relevant principle value of the permittivity tensor is positive. In case of the metal-dielectric stack, the electric field polarized parallel to the metallic plates experiences negative dielectric response, while the permittivity associated with the perpendicular polarization is positive. A detailed theory of the multilayer and wire-medium hyperlens can be found in the works [
The first theoretical work on a wire medium hyperlens [
Arranging metal wires in the tapering-up-like manner, not only the 1 : 1 image transfer but also the image magnification can be achieved. An analysis of the homogeneous medium approximation eligibility for the wire medium superlens was conducted in work [
A flat metal-dielectric stack can transfer the subdiffraction image as a near-field lens. Using cylindrical or spherical multilayer system the image may be magnified up to above the diffraction limit. Such magnified image may be registered with an optical microscope afterwards. So the hyperlens can serve as an addition to the standard optical microscope or photolithographic system improving the resolution below the diffraction limit. The first theoretical work [
Despite the fantastic resolution, the hyperlens typically has low transmission. Using the Fabry-Perot effect it is possible to increase the transmittivity values. For example, in the work [
An imaging device such as lens does not necessarily provide high coupling efficiency since the primary goal of imaging is focusing of light, regardless of the transmittivity. The dielectric lens can give high transmittivity (close to 100%) but the focal spot size is diffraction limited. A photonic crystal lens can indeed provide focusing at a specific frequency. However, the resolution of such lens is not much better than the diffraction limit allows. The plasmonic lens can provide a better spatial resolution with the cost of lower transmittivity. The negative index metamaterial lens is still far from the practical realization. From the resolution point of view, the hyperlens is the best. Theoretically it can provide the resolution as small as
The main idea behind the scatterer coupler is that there are single or multiple particles that first capture the radiation from the free space and then launch it into the waveguide. Based on the geometrical placement and material we singled out the following types: antenna coupler (Figure grating coupler (Figure random scatterers (Figure
Types of scatterer couplers: (a) antenna, (b) grating, (c) random scatterers.
According to the definition [
In principle, according to the definition, some nanocouplers of other types, for example, a lens coupler, can also be called antennas. In this section, however, we limit ourselves to the traditional geometrical antenna configurations, which consist of a single of multiple metallic particles, specially tuned for accepting electromagnetic radiation.
Optical nanoantennas drew the attention of many research groups [
Despite a lot of similarities, there are essential differences between radio and plasmonic antennas [ Metals are not such good conductors in the optical range as on the radio frequencies. Their permittivity is dispersive. It can be approximated by the Drude or more accurate Drude-Lorentz formulas [ A typical penetrations depth is several dozens of nanometers [ The usual condition for the resonance of radiofrequency antennas is that the length of the antenna must be equal to the integer of a half of the wavelength. This condition is not satisfied for the optical antennas and should be corrected [
Plasmonic nanoantennas have attracted huge attention in the recent years because of their ability to concentrate light in the tiny gaps and significantly enhance light intensity [
Despite the fact that from the very beginning antennas served for coupling to a waveguide (transmission line), the application of an antenna for optical nanocoupling was proposed only recently [
The advantage of the nanoantenna is that it is very compact. Moreover, the directivity of the antenna coupler can be tuned by design, thus enabling the maximal coupling efficiency at any desired angle of incidence. The first nanoantenna couplers analysis showed theoretically the coupling efficiency of 10% [
An array of nanoantennas is closely related to the diffraction grating employment as a coupler. However, the difference is that each nanoantenna has a specific length designed to be in resonance with an incident electromagnetic wave, while in the diffraction grating each line can be very long. The lines of the diffraction grating lie on top of the waveguide and scatter light into the waveguide. It is of outmost importance that the scattered radiation from each line contributes constructively to the wave propagating in the waveguide. In other words, the role of the grating is to match the tangential wavevector component
A diffraction grating is typically employed for coupling to a silicon waveguide in the vertical coupling configuration. The spot size from a single mode fiber is usually about 10
A grating coupler can also be used for the surface plasmon polaritons waveguide excitation. The coupling efficiency up to 68% was theoretically shown [
As we mentioned before the nanocoupler can be understood as a mode transforming device. In principle we can designate two extreme cases for mode conversion: evolution, that is, a careful adiabatic compression towards mode profile matching—this is realized by long tapered fibers—and revolution, that is, complete mode structure destruction and then construction of another mode in the same way as a new building can be built from the bricks of a ruined house. This analogy would mean introduction of a set of random scatterers. The photons coming from the first waveguide experience multiple scattering, and statistically some of them can couple to a mode of the second waveguide.
It is clear that the coupling efficiency of such random material coupler cannot be high due to the random nature of the photon scattering process. However, there was recently shown that under certain circumstances adisordered medium can work for light focusing [
The antenna nanocoupler is a natural transition of a standard microwave approach for coupling an electromagnetic wave to an optical (plasmonic) waveguide. There is a theoretical 50% limit of the coupling efficiency of the antenna systems [
In this section we included all other ideas that do not fall into the previously mentioned categories. Such coupling ideas are: transformation optics coupler, topology optimization designed coupler.
Inspired by the metamaterials possibilities of obtaining whatever permittivity and permeability values the field of transformation optics has recently emerged [
A problem of coupling can be expressed in the language of the transformation optics. To design a nanocoupler is to determine such spatial distribution of permittivity and permeability that provides impedance matching and squeezing of the light from a thick waveguide to a thin one. In some sense the GRIN lens is also an example of the transformation optics application. Some designs for squeezing light [
Very often, however, the transformation optics designs require unusual values of permittivity and permeability that are not realistic even with the help of metamaterials (e.g., diverging permittivity and permeability values without losses or extremely large anisotropy).
Another approach to the coupler design is to select from the very beginning the realistic material properties (in the simplest case, of two materials) and to determine the spatial distribution (topology) of the materials that gives the largest coupling efficiency. With the efficient numerical algorithms one has no need to go deep into physical consideration when designing the nanocoupler. Such approach is called
The transformation optics devices very often require unrealistic material properties. In contrary to the transformation optics the topology optimization starts from the realistic material properties and then finds the necessary geometry. We should admit that both of these approaches can be applied to almost any coupler in the Sections 4–7. Therefore we should better say that these are not independent physical approaches, but rather useful design methodologies.
In this paper we have analyzed various physical principles that can be used for coupling light from an optical fiber or free space to nanosized waveguides. The range of approaches is very broad, so we divided the subject into four classes (tapered waveguide coupler, direct coupler, lens coupler, and scatterer coupler). The most important features of each approach are summarized in Table
Comparison of various nanocoupling approaches.
Approach | Coupling efficiency: low ( |
Size: compact ( |
Subwavelength coupling or focusing | Lateral or vertical coupling | References |
---|---|---|---|---|---|
4.1. Tapered dielectric | High | Both | No | Lateral | [ |
4.2. Tapered metal | Medium and large | Compact | Yes | Lateral | [ |
4.3. Tapered metamaterial | Low and medium | Compact | Yes | Lateral | [ |
5.1. Next to another | High | Both | Yes | Lateral | [ |
5.2. End-fire | High | Compact | No | Lateral | [ |
5.3. Resonant stub | High | Compact | Yes | Lateral | [ |
6.1. Dielectric lens | High | Large | No | Lateral | [ |
6.2. Plasmonic lens | Medium | Compact | Yes | Lateral | [ |
6.3. Negative index lens | N/a | N/a | Yes | Lateral | [ |
6.4. Photonic crystal lens | N/a | Compact | Yes | Lateral | [ |
6.5. Hyperlens | Low or medium | Compact | Yes | Lateral | [ |
7.1. Antenna | Medium | Compact | Yes | Both | [ |
7.2. Grating | High | Large | No | Vertical | [ |
7.3. Random scatterers | Low | N/a | Yes | Both | [ |
The most compact solution for the nanocoupling is the antenna coupler. The most efficient are the tapered waveguide and the grating coupler combined with the directional coupler. The hyperlens gives a good trade-off between subdiffraction imaging and transmission. The designs that use negative index materials are lossy and therefore can hardly be used for the nanocoupler at the moment. A discovery of new plasmonic materials with smaller losses or optical losses compensation with gain can probably make the latter approaches useful for light coupling.
We see the future of the nanocouplers mostly in their technical improvement. This includes a search for better materials, optimization of the designs, and fabrication technologies. The previously mentioned coupling approaches can also be the building blocks of more advanced photonic devices. For example, tapering the directional slot waveguides coupler and filling the slots with a nonlinear material [
The authors acknowledge the members of the Metamaterials group at DTU Fotonik for useful discussions and the financial support from the Danish Council for Technical and Production Sciences through the projects GraTer (11-116991), NIMbus and THzCOW.