The unique physical properties of carbon nanotubes and the flexibility they provide in selecting their characteristics offers great potential for nanotechnology. Carbon nanotubes can be either semi-conducting or metallic, depending on their diameter and helical configuration. They typically have nanometer sized diameters and a length of a few microns, although centimetre long nanotubes have been produced recently. This makes them ideal 1 D systems that possess a ballistic conducting channel, no backward scattering, and energy levels that can be adjusted with external fields. Superconductivity has also been observed in multi-walled carbon nanotubes and single carbon nanotubes have exhibited a superconducting proximity effect. Their current applications range from extremely strong fibres and organic electronics to electrochemical sensors and photon detectors. Carbon nanotubes are formed by rolling up a sheet of graphene into a cylindrical tube. A zigzag nanotube can be a direct semiconductor. The optical properties of such carbon nanotubes have been extensively studied for a straight nanotube inside a weak uniform classical plane wave field. Their quasi one-dimensionality means that their density of states exhibit Van Hove singularities and these contribute to strong optical absorption peaks. However, these results apply the dipole approximation, where it is assumed that the field does not vary along the nanotube's length. It is yet to be investigated how the optical absorption by carbon nanotubes depends on their length and orientation relative to an optical field. It is an object of the present invention to improve the optical excitation and photon absorption properties of carbon nanotubes, leading to a range of applications including highly sensitive photodetectors.

In accordance with the present invention there is provided a photon detection device comprising one or more carbon nanotubes arranged in an evanescent field at or near the outer surface of a subwavelength-diameter optical waveguide when the waveguide transmits light in use, such that the nanotube can absorb photons to excite electrons and thereby detect light guided within the waveguide. The invention is based on a recognition that the electrical field of an optical waveguide that has a diameter smaller than the wavelength of light being guided is tightly confined and primarily exists outside of the fibre in an evanescent field that is large enough to be accessible. Due to the presence of a strong field in a relativity small volume, such waveguides (typically taking the form of small optical fibres, e.g. a so-called "nanofibre") are ideal candidates to achieve a high optical absorption in atomic systems. While the interaction of nanofibres with atom-arrays has been studied, it has not previously been proposed to exploit the extremely strong evanescent fields near the surface of an optical waveguide to convert photons into electronic excitations in a carbon nanotube. It has been found that when a carbon nanotube is positioned near to a subwavelength-diameter optical waveguide such as a nanofibre, optical interaction with electrons in the carbon atoms is enhanced due to the waveguide's transverse confinement of the field. The present invention brings together the unique optical and electrical properties of carbon nanotubes with the ability of optical waveguides e.g. nanofibres to guide light almost entirely in vacuum as an evanescent field in an extremely small volume. Altering the nanofibre properties also make it possible to tailor the electric field.

The invention takes advantage that carbon nanotubes have excellent conductivity and extremely low capacitance, which means that they have highly mobile electrons and little noise, making them ideal for integration into electronic photon detectors. The easily accessible evanescent field of the optical waveguide is coupled with the highly available electrons in the carbon nanotube(s) to result in high absorption probabilities. With current technologies, it has been calculated that room

temperature optical and near infrared photodetectors could be realised with efficiencies that may exceed 90%. Photon detection devices in accordance with the invention can also benefit from fast operation with very short dead times.

Since the evanescent field strength drops off exponentially with radial distance from the optical waveguide, the highest value for the energy coupling will be achieved by having the nanotube as close as possible to the waveguide. This may be achieved by encasing the optical waveguide e.g. fibre within a nanotube. However, the band gap of carbon nanotubes decreases with the nanotube size, so for the device to detect optical and near infrared wavelengths, relatively small diameter nanotubes are required and this generally rules out the possibility of encasing an optical fibre or other waveguide within a nanotube. Instead, the one or more carbon nanotubes are preferably arranged to at least partially overlap with the evanescent field at or near the outer surface of the optical waveguide. Preferably the distance between the centre of each nanotube and the surface of the optical waveguide is around 1 nm. Given that nano-sized structures, whether carbon tubes and/or optical waveguides e.g. fibres, tend to be delicate, there is preferably no physical contact between the at least one carbon nanotube and the optical fibre. In one example, the nanotubes have a radius of 1 nm or less and the distance between a

nanotube's centre and the surface of the optical waveguide is chosen to be 1 .25 nm, so as to avoid any contact.

The present inventors have recognised that the dipole approximation can not be applied in the case of nanotubes since the optical field typically changes rapidly along a nanotube's length. The inventors have calculated the (internal) quantum efficiency, i.e. the probability that a nanotube, placed inside the evanescent field of an optical waveguide, absorbs a photon and found that the absorption is extremely dependent on a nanotube's orientation relative to the waveguide. However a straight nanotube, e.g. of length L, may be oriented at any angle ^ relative to the optical waveguide, where 0 < ψ≤ 90° includes both parallel and perpendicular orientations.

In general, average photon absorption has been found to increase with the length of the nanotube, but the absorption tends to converge to a maximum value if the nanotube is oriented at a non-zero angle to the optical waveguide rather than being arranged in parallel. Thus, the longer the nanotube(s), the more preferable it is for them to be arranged substantially parallel to the optical waveguide with an angle φ close or equal to zero. For a substantially parallel orientation the absorption has been found to increase with the length of the nanotube without reaching a peak. Absorption may approach 100% for extremely long nanotubes, for example nanotubes of length 1 mm arranged in parallel with an optical waveguide. Thus, in one set of embodiments, the one or more nanotubes are arranged substantially parallel to the longitudinal axis of the optical waveguide.

For shorter nanotubes, it is preferable for them to be arranged substantially perpendicular to the optical waveguide. In another set of embodiments, the one or more nanotubes are oriented at an angle 0 < ψ≤ 90° relative to the longitudinal axis of the optical waveguide. It will be understood that each nanotube may be oriented at a given angle ^ without every nanotube necessarily being at the same angle φ. For example, different nanotubes may be oriented at different non-parallel angles.

In at least some embodiments it is preferable that the one or more nanotubes are oriented at an angle of about 90° relative to the longitudinal axis of the optical waveguide. For substantially orthogonal nanotubes, at first the absorption increases rapidly with length, which is due to the linear increase in electron number. But as the length increases further this effect is counterbalanced by the fact that the field strength decreases exponentially away from the optical waveguide. For a perpendicular nanotube having a radius < 1 nm and arranged with its centre at a distance of 1.25 nm from the surface of the optical waveguide, the absorption was found to hardly increase at all after the nanotube length exceeded approximately 2 μηη. However, orthogonally arranged nanotubes have been found to perform much better than parallel nanotubes when the nanotubes are relatively short. In such embodiments the one or more nanotubes preferably have a length L in the range of 1 μπΊ < L < 2 μηη. The length L may be chosen from one or more of: (i) 0.2-0.4 μηη; (ii) 0.4-0.6 μηι; (iii) 0.6-0.8 μηι; (iv) 0.8-1.0 μηι; (v) 1.0-1 .2 μηι; (vi) 1 .2-1 .4 μηι; (vii) 1.4-1.6 μηη; (viii) 1 .6-1 .8 μηη; and (ix) 1 .8-2.0 μηη. Of course different nanotubes may have different lengths within any given range.

In one preferred embodiment the device comprises an array of N aligned nanotubes with the optical waveguide arranged with its longitudinal axis substantially orthogonal to the direction of alignment of the array. The optical waveguide may, for example, pass through, or be placed in or on top of, an array of substantially parallel nanotubes. The density of the nanotubes in a 1 D array may be 10-100 nanotubes per μηη of orthogonal optical waveguide. In at least some preferred embodiments there is provided a 2D array of aligned nanotubes. Techniques for generating such semiconducting nanotube "forests" have already been described, for example by P. Li and J. Zhang, J. Mater. Chem. 21 , 1 1815 (201 1 ) and L. Qu, F. Du and L. Dai, Nano Letters 8, 2682 (2008).

Advantageously, such a 2D arrangement of substantially parallel nanotubes can facilitate the attachment of electrodes to collect the excited electrons via an applied voltage, for example with the array of aligned nanotubes sandwiched between two electrodes. The aligned nanotubes may be grown on a conducting substrate that can then serve as an electrode. The free ends of the nanotubes in the array can then be connected to an additional electrode.

A 2D array of carbon nanotubes may typically have a density of 100-10,000 nanotubes per μηη ² . There may be provided an array of N aligned nanotubes with a density chosen from one or more of: (i) 100-500 μηη ^"2 ; (ii) 500-1000 μη"Γ ² ; (iii) 1000- 2000 μπν ² ; (iv) 2000-3000 μπΤ ² ; (v) 3000-4000 μπΤ ² ; (vi) 4000-5000 μπΤ ² ; (vii) 5000- 6000 μηΤ ² ; (viii) 6000-7000 μηΤ ² ; (ix) 7000-8000 μηΤ ² ; (x) 8000-9000 μηΤ ² ; and (xi) 9000-10,000 μπΊ ^"2 . In one example there is provided an array of nanotubes extending a distance of 500 nm away from the surface of the optical waveguide, 15- 50 μπΊ along its length, with a forest density of 900 μηη ^"2 and a density per unit length of the optical waveguide of (2 χ 500 nm χ 900 μηη ^"2 =) 900 nanotubes per μηη. Such a 2D array can be used to absorb light of a wide range of wavelengths, which can be selected by the nanotubes present and choice of optical fibre diameter. This type of array of carbon nanotubes coupled to a 400 nm diameter optical fibre has been seen to absorb light at wavelengths that are typically used for optical communication. Due to a nanotube's bandgap dependence on external fields there is also the possibility of adjusting the absorption frequencies by using an external field.

In another set of embodiments the probability of light absorption is enhanced by wrapping the nanotube(s) around the optical waveguide to combine both parallel and orthogonal absorption effects. As mentioned above, the strong absorption for a perpendicular nanotube is limited by the drop-off in field strength. However, this can be prevented by maintaining a constant distance between the nanotube and the centre of the optical waveguide. The nanotube can locally approximate a perpendicular nanotube by spiralling around the optical waveguide. Thus in one set of embodiments, the one or more nanotubes are arranged helically relative to the longitudinal axis of the optical waveguide. A 'winding number', 1/1/, for a spiral arrangement can be defined as the number of loops per unit length along the longitudinal "z" axis of the optical waveguide. This winding number is equal to 1 1/ = 1/di where d _t is the z-distance for one loop. An angle is also formed between the spiralling nanotube and the axis of the optical waveguide, which is given by φ ₅ = arctan(2nl/l R ₍₁ ), where R _n is the radius of the optical waveguide, e.g. an optical fibre. Since these spiralling nanotubes can interact with the field over an arbitrary length, their absorption approaches 100% given sufficient length and an allowed transition. When a nanotube is coiled around an optical waveguide the average photo absorption probability steadily increase with nanotube length, up to 100% for long nanotubes.

Spiralling nanotubes can have higher absorption probabilities than a parallel configuration. An optimal spiralling rate can be selected to enhance the absorption, for example maximising the winding number W for an optical fibre of a given diameter and a spacing chosen to prevent physical contact between the fibre and the spiralling nanotube, and between adjacent loops of the nanotube. A coiled arrangement also allows for further specification of the absorbed light's polarization or propagation direction with the choice of winding number. The winding also dramatically reduces the length of the system. For example, for a nanotube with a winding number of W = -0.1 nm ^"1 , the average absorption between 1 .5 eV and 2.5 eV exceeds 50% when the nanotube's length is 5 mm. For a 250 nm diameter optical fibre this spiral arrangement only extends 64 μηη along the fibre. Thus highly compact nanoscale photodetectors may be achieved.

It will be understood that what is meant by a "carbon nanotube" is a molecule formed from the element carbon and having a tubular structure with a diameter < 1 μηη, preferably < 500 nm, further preferably < 100 nm and even more preferably < 10 nm. The diameter of the nanotube may be chosen from one or more of: (i) 0.1 - 0.5 nm; (ii) 0.5-1 .0 nm; (iii) 1 .0-1 .5 nm; (iv) 1 .5-2.0 nm; (v) 2.0-3.0 nm; (vi) 3.0-4.0 nm; (vii) 4.0-5.0 nm; (viii) 5.0-6.0 nm; (ix) 6.0-7.0 nm; (x) 7.0-8.0 nm; (xi) 8.0-9.0 nm; and (xii) 9.0-10 nm. The tubular structure may have a hollow cylindrical or toroidal configuration. The nanotube may be single-walled or multi-walled.

As is explained above, where a carbon nanotube is arranged substantially parallel to an optical waveguide its light absorption can increase in proportion to the length of the parallel arrangement. In such arrangements the one or more carbon nanotubes may have a length up to 1 mm. The length of the carbon nanotubes can be chosen depending on their orientation relative to the optical waveguide. In preferred embodiments the carbon nanotubes are zigzag nanotubes because they can be direct semiconductors. However, the invention can also use other semiconducting nanotube types such as chiral nanotubes.

It will be understood that what is meant by an "optical waveguide" is a waveguide for electromagnetic waves of any suitable wavelength, in particular for waves in the visible and near-infrared spectrum. Whereas silica waveguides with diameters larger than the wavelength of transmitted light are widely used in optical communications, sensors and other applications, only in more recent times have subwavelength-diameter optical fibres or wires been proposed for photonic device applications as low-loss optical waveguides, especially in the visible to near-infrared spectral range. Some techniques for fabricating optical fibres with diameters down to 50 nm are discussed in Nature 426, 816 (2003) and reviewed in Optics Express 12, 1025 (2004). The subwavelength-diameter optical waveguide is preferably a single mode optical waveguide, i.e. the only mode present is the HE fundamental mode. The optical waveguide is preferably a subwavelength-diameter optical fibre. The optical fibre may comprise an air-clad core of a dielectric material such as fused silica (Si0 ₂ ) or single crystal silicon. In preferred embodiments the optical fibre comprises a cylindrical vacuum-clad silica fibre. Preferably the optical fibre is a nanofibre, i.e. a fibre having a diameter < 1 μηη, making it suitable for electromagnetic waves having optical and near-infrared wavelengths. The optical fibre may have a diameter as small as 50 nm, but preferably it is larger than 100 nm in diameter, further preferably around 250 - 400 nm in diameter. The smaller the fibre diameter relative to the wavelength, the larger the evanescent field but this reduces the field intensity and absorption. Altering the properties of the fibre such as diameter therefore makes it possible to tailor the electric field. Fibres with a smaller diameter have a larger evanescent field but also suffer from higher losses. The diameter of the optical fibre may be chosen from one or more of: (i) 50-100 nm; (ii) 100-200 nm; (iii) 200-300 nm; (iv) 300-400 nm; (v) 400-500 nm; (vi) 500-600 nm; (vii) 600-700 nm; (viii) 700-800 nm; and (ix) 800-900 nm.

Embodiments of the present invention may be used to detect light (that is, electromagnetic radiation) at any wavelength being guided by the subwavelength- diameter optical waveguide. In practice, optical waveguides having a diameter less than 50 nm have yet to be made and this limits the wavelength of photons that may be detected by the device. Currently proposed embodiments of the device can provide for highly efficient conversion of photons into electronic excitations over a wide range of optical wavelengths (e.g. 100-1000 nm), including the visible range of 380-740 nm, and near infrared wavelengths (e.g. 740 nm - 300 μηη). Photon detection devices according to embodiments of the present invention may be useful not only as light-harvesting devices, e.g. nanoscale photonic devices, but also (if operation is fully coherent) as quantum memories where the photonic state is coherently mapped into electronic degrees of freedom. This would potentially open up applications in light switching and for the creation of slow light (i.e. the propagation of an optical pulse at a very low group velocity).

When viewed from a further broad aspect, the present invention provides a method for coupling photons to the electronic states of a carbon nanotube in which electromagnetic energy is guided by a subwavelength-diameter optical waveguide and the carbon nanotube is arranged to interact with the evanescent field of the optical waveguide. Such a method may find a variety of uses, including (but not limited to) photon detection as well as quantum memories. Any of the preferred features described above may be provided, either alone or in combination, in accordance with embodiments of such a method.

It will be understood that, in at least some preferred embodiments, the method comprises coupling photons to the electronic states of more than one carbon nanotube. ln some embodiments the method may comprise orienting the nanotube(s) at an angle ^ relative to a longitudinal axis of the optical waveguide, where 0 < ψ≤ 90°, and preferably arranging the nanotube(s) substantially perpendicular to a longitudinal axis of the optical waveguide. In some embodiments the method may comprise arranging an array of N substantially aligned nanotubes with the axis of the optical waveguide substantially orthogonal to the direction of alignment of the array. The method may further comprise connecting electrodes at either side of the array. In some embodiments the method may comprise orienting the nanotube(s) at an angle ^ relative to a longitudinal axis of the optical waveguide, where 0 < ψ≤ 90°, and preferably arranging the nanotube(s) substantially parallel to the longitudinal axis of the optical waveguide. In some embodiments the method may comprise arranging the nanotube(s) helically relative to the longitudinal axis of the optical waveguide.

Some preferred embodiments of the present invention will now be described, by way of example only, and with reference to the accompanying drawings, in which: Fig. 1 a is a representation of a graphene lattice and Fig. 1 b is a perspective view of a section from a zigzag carbon nanotube;

Fig. 2 is a schematic representation of a straight nanotube oriented at an angle φ relative to an optical nanofibre;

Fig. 3 shows photon absorption probabilities for a 2 μηη long nanotube, oriented perpendicular to the nanofibre, at different photon energies;

Fig. 4 shows the average photon absorption probability for a straight nanotube of length L for different angles between the nanotube and the nanofibre;

Fig. 5 is a schematic representation of a nanotube spiralling around an optical nanofibre;

Fig. 6 shows the average photon absorption probability for a nanotube of length L coiled around the nanofibre;

Fig. 7 shows the average photon absorption probability for nanotubes coiled around the nanofibre for different winding parameters;

Fig. 8 is an illustration of a possible photodetector device; and Fig. 9 shows the absorption probability for a circularly polarized photon in a nanofibre laid inside a "forest" of nanotubes in a device as illustrated by Fig. 8.

As is illustrated by Fig. 1 , carbon nanotubes are formed by rolling up a sheet of graphene 100 into a cylindrical tube 102. A single walled carbon nanotube

(SWCNT) 102 can be thought of as a sheet of graphene 100 wrapped into a tube. Graphene is a regular 2D hexagonal Bravais lattice of carbon atoms 104 and its structure is shown in Fig. 1 a with the unit cells vectors labelled a and a ₂ . These vectors have a length a which is related to the distance a _c between neighbouring atoms 104 by a = V3a _c « 0.246 nm. The unwrapped unit cell 106 for a zigzag (3,0) nanotube 102 is shown shaded and the C vector defines the nanotube's

circumference. In Fig. 1 b a section from a zigzag (7,0) nanotube 102 is shown with its unit cell 108 shaded. T is the tangential unit vector of the nanotube's unit cell 108.

The optical properties of straight carbon nanotubes, inside a weak uniform classical plane wave field, have been extensively studied and reported in the literature. Their quasi one-dimensionality means that their density of states exhibit Van Hove singularities and these contribute to strong optical absorption peaks. These results apply the dipole approximation, where it is assumed that the field does not vary along the nanotube's length. However, in embodiments of the present invention where one or more carbon nanotubes are coupled to a subwavelength-diameter optical fibre (hereinafter referred to as a "nanofibre"), this treatment must be extended by allowing for the spatial dependence of the field. This situation is particularly relevant when the electrons are delocalized in a tightly-confined field, such that the field varies greatly over a few hundred nanometres. The degree to which the electrons are delocalized is a topic of ongoing research and various studies have been done on the coherence length in nanotubes. The results range from 10 nm to several microns, suggesting that the spatial field dependence is certainly important for confined fields and may also be relevant for plane waves.

There is seen in Fig. 2 a straight nanotube 200 oriented at an angle φ relative to an optical nanofibre 202. The probability that a nanotube, placed inside the

evanescent filed of a nanofibre, absorbs a photon is extremely dependent on the nanotube's orientation. For a nanofibre made of a silica core and having a diameter as small as 50 nm, a high proportion of the light field exists outside of the fibre's core. This means the field is easily accessible when the carbon nanotube is positioned near the nanofibre. The use of subwavelength-diameter optical fibres allows the interaction to be enhanced due to the transverse confinement of the field. Altering the nanofibre's properties also allows the field to be tailored. Fibres with a smaller diameter have a larger evanescent field but also suffer from higher losses. There is shown in Fig. 2 a cylindrical nanofibre core 202 with a radius of R and cladding provided by the vacuum, with refractive index n ₂ = 1. The refractive index of the silica core 202 is n-ι = 1.45 and the material absorption of the silica is negligible over the short distances being considered. Silica core fibres with subwavelength-diameter are single mode fibres, i.e. the only mode present is the HE fundamental mode.

For fibres larger than 100 nm in diameter the photon losses are small and can be ignored over short distances. Calculations were performed using nanofibres of diameter 250 nm and focusing on the forward propagation and right polarized guided modes, i.e. f = p = +1. All other modes are related to these results by symmetry. The value of G is then highly dependent on the way the nanotube 200 is orientated relative to the nanofibre 202. Since the field strength drops off exponentially, the highest value for the coupling will be achieved by having the nanotube 200 as close as possible to the fibre 202. In these examples, the distance between the nanotube's centre and the surface of the nanofibre 202 is chosen to be 1 .25 nm. The nanotubes considered have a radius less than 1 nm so this distance avoids any contact. In Fig. 2 the straight nanotube 200, of length L, may be oriented at an angle φ relative to the nanofibre 202 which includes parallel and perpendicular orientations. Two further example orientations of a

nanotube 204, 206 are also shown in Fig. 2.

The absorption probabilities η for different wavelengths of light and different zigzag nanotubes are shown in Fig. 3 for 2 μηη nanotubes arranged perpendicular to the nanofibre. The absorption of photons with energies greater than 6 eV is not considered since these are not visible. Distinct absorption peaks are clearly visible and the largest absorption occurs for a (1 1 ,0) nanotube. In Fig. 3 the solid lines refer to the absorption of circularly polarized light into a nanofibre. The lines correspond to (7,0), (8,0) and (1 1 ,0) nanotubes. The absorption for a nanotube in a linearly polarized coherent plane wave, without a fibre, is also shown in Fig. 3 (dashed lines). This plane wave coherent light beam is linearly polarized along the nanotube, has a cross-sectional area of 4 μηη ² and exhibits the same absorption peaks as the fibre, but varies less with the light's frequency. It can be seen that the (1 1 ,0) nanotube has its smallest energy transition dramatically reduced (no solid line peak visible for the (1 1 ,0) nanotube). This extra effect is caused due to larger evanescent fields, for an increasing wavelength relative to the fibre radius. This reduces the field intensity and absorption. The quantum efficiencies are a similar order of magnitude as those observed experimentally. The different nanotubes show shifted absorption peaks. These can be further adjusted with external fields or choosing other nanotubes. The resonant energy values are unchanged with the orientation and thus a range to average over can be chosen as a general measure of absorption. The mean absorption η was calculated over the (7,0) nanotube's lowest absorption energy, particularly a range of 1 eV from 1.3 eV (953 nm) to 2.3 eV (539 nm) was chosen. The resulting η is approximately independent of Γ in a range of Γ= 0.01 eV to Γ = 0.001 eV deviating only by a few percent. The smallest and second smallest transitions, En and E ₂ 2, are indicated. A broadening parameter of Γ = 0.01 eV was used. The corresponding mean absorption probability, η, against nanotube length L, for the lowest energy transition, is shown in Fig. 4 for various angles between a straight (7,0) nanotube and nanofibre. At L = 4 μηη, from top to bottom, the angles between nanotube and fibre are φ = 0 (parallel; line 400), -π/32 (line 402), -3π/8 (line 404), π/2 (perpendicular; line 406), π/32 (line 408), π/8 (line 410). The mean absorption has taken over a 1 eV region, from 1 .3 eV to 2.3 eV. The results show that the absorption converges to a maximum value as the length is increased, unless the nanotube is parallel to the fibre.

The nanotube perpendicular to the fibre has a very strong absorption for short lengths. In this situation we see the absorption increasing strongly with nanotube length which is due to the linear increase in electron number. As the length increases further this effect is counterbalanced by the fact that the field strength decreases exponentially away from the nanofibre. The absorption hardly increases at all after the nanotube exceeds approximately 2 μηη. Over short distances there are other nanotubes that have a higher absorption probability. These are close to being orthogonal. The parallel orientation increases slowly but does not peak. As is discussed below, the probability can be enhanced by spiralling the nanotube to combine both effects. If linear polarized light was used instead of circular polarized light the absorption could be twice as high depending on the nanotube's position in the nanofibre plane. There is also seen a difference between angles of ±π/32, with the higher absorption being dependent on the light's polarization and propagation.

The strong absorption for a perpendicular nanotube is limited by the drop-off in field strength. However, this can be prevented by maintaining a constant distance between the nanotube and nanofibre centre, R _n . As illustrated in Fig. 5, a nanotube 500 can locally approximate a perpendicular nanotube by spiralling around the nanofibre 502. Although this bending does alter the electronic and optical properties these effects are small and can be safely ignored here. A

'winding number', W, is defined for the spiral as the number of loops per unit length along the z axis. This winding number is equal to W = 1/c/,, where c/, is the length of one loop along the z axis. An angle is also formed between the spiralling nanotube 500 and the optical fibre's axis, which is given by φ ₅ = arctan(2nl liR _/1 ), where R _n is the radius of the optical fibre 502. Since these spiralling nanotubes can interact with the field over an arbitrary length their absorption approaches 100% given sufficient length and an allowed transition. The average absorption probabilities in this case are plotted in Fig. 6 and show a steady increase in the absorption probability with nanotube length. Fig. 6 shows the average absorption probabilities for winding numbers -0.0016 nm ^"1 (line 600), -0.0008 nm ^"1 (line 602); 0 nm ^"1 (parallel; line 604), 0.0016 nm ^"1 (line 606), and 0.0008 nm ^"1 (line 608). This demonstrates that the spiralling nanotubes can have higher absorption probabilities than the parallel configuration. In Fig. 7 there is plotted the average absorption probability rf against Φ ₅ for nanotubes of different lengths. From top to bottom the nanotubes have lengths of 10 μηη (line 700), 5 μηη (line 702) and 1 μηη (line 704). An optimal spiralling rate Φ ₅ can be seen to enhance the absorption.

The coil geometry shown in Fig. 5 has a high absorption probability of up to 100% for long nanotubes. However, producing such a setup in a laboratory may be rather challenging with current technology. This setup also allows for further specification of the absorbed light's polarization or propagation direction with the choice of winding number. The winding also dramatically reduces the length of the system. For a nanotube with a winding number of W = -0.1 nm ^"1 , the average absorption between 1.5 eV and 2.5 eV exceeds 50% when the nanotube's length is 5 mm. For the 250 nm diameter fibre this only extends 64 μηη along the fibre.

In Fig. 6 the case of a parallel nanotube is also shown. The photon absorption probability of each nanotube is, in case of a (7,0) nanotube, given by the φ = 0 line in Fig. 4 and the overall absorption probability is

Taking 100 nanotubes of length L = 1 mm parallel to the fibre and using η =0.07 (see Fig. 6) we obtain an overall absorption probability of η _ω > 99%, which greatly exceeds that of standard avalanche photodiodes. Fig. 8 illustrates a possible photodetector 800. Here a "forest" 802 of aligned semiconducting nanotubes (thick dark lines 804) are grown between two

electrodes 806, 808. The nanofibre 810 is positioned between these

electrodes 806, 808. Once a light field excites an electron the resistance between the electrodes 806, 808 drops dramatically, which allows the photon to be recorded. A practical setup is given by arranging N horizontal nanotubes in a parallel array and placing the nanofibre orthogonally on top of the array. Based on current nanotube arrays, the density of a 1 D array of nanotubes could be 10-100 nanotubes per μηη while the density of a 2D array of nanotubes could be 100- 10,000 nanotubes per μηι ² . For one nanotube, η is used as a measure of the absorption probability. The photon absorption probability of each nanotube is then, in case of a (7,0) nanotube, given by the π/2 line 406 in Fig. 4 and taking η = 0.00015 (see Fig. 4) this leads to an overall absorption probability η ₍₀ ι > 95% for N > 20000, a value again greatly exceeding those of currently available avalanche photodiodes. For N > 40000 the efficiency exceeds 99% which can currently only be achieved by highly complex superconducting detectors. An advantage of such a device is that it can be operated at room temperature. Each nanotube may have a length of 2 μηη and connected at the ends by electrodes which collect the excited electrons via an applied voltage. As illustrated in Fig. 8, aligned vertical nanotubes 804 can also be grown on a conducting substrate, that can then serve as one electrode 808. The nanofibre 810 can then be placed orthogonally to the nanotubes 804 and the remaining ends of the nanotubes 804 connected to an additional electrode 806. The diameter of the nanotubes 804 in this example is in the range of 1±0.5 nm. These nanotube systems typically have a density of 100-10,000 nanotubes per μηι ² . The nanotubes 804 are distributed uniformly over a selected region and it is assumed that they are a uniform mix of semiconducting zigzag nanotubes. The overall absorption probability has been calculated for a forest that extends a distance of 500 nm from the nanofibre and 15 μηη along its length, with a density of 900 nanotubes per μηη ² . The results with nanofibres that have diameters of 250 nm (black line 900) and 400 nm (dashed line 902) are shown in Fig. 9. A broadening parameter of Γ = 0.01 eV was used. These absorb light of a wide range of wavelengths, that can be selected by the nanotubes present and choice of nanofibre diameter. A typical absorption probability of η ₍₀ ι > 50% can be seen, for 250 nm diameter fibres, and by extending the system's length from 15 μηη to 50 μηη this is increased to r| _to t >95%. Nanotubes arrayed around a 400 nm fibre are also seen to absorb light at wavelengths that are typically used for optical

communication. Due to the nanotube's bandgap dependence on external fields there is also the possibility of adjusting the absorption frequencies by using an external field.