Coherent metamaterial absorption in a fibre network

As illustrated in Fig. 1a, the functionality of the network is based on controlling absorption of light with light on an ultrathin metamaterial absorber. It has two bidirectional ports, i.e. two inputs, α and β, and two outputs, γ and δ. The input waves propagate in opposite directions and, provided that they are mutually coherent, co-polarized and of equal intensity, they will form a standing wave with electric field nodes and anti-nodes (Fig. 1b). A sufficiently thin film may thus be placed at a node, where the electric field is zero due to destructive interference, or at an anti-node where the electric field amplitude is enhanced by constructive interference. Since truly planar structures interact with normally incident waves only via the electric field23, this implies that a planar thin film placed at a node will be perfectly transparent, while the same thin film will be strongly excited if placed at an anti-node. With respect to absorption, which is limited to 50% in planar materials illuminated by a travelling plane wave24, standing wave illumination allows absorption to be controlled from 0 to 100% in the ideal case7. Such performance in the optical part of the spectrum, as is relevant to optical fibre technology, may be approximated with materials that are thin compared to the optical wavelength and exhibit equal levels of transmission and reflection in addition to around 50% travelling wave absorption. This combination of parameters may be achieved for example in nanostructured plasmonic metamaterials8 and 30-layer graphene11,25.

Fig. 1 Coherent interaction of light with light on a metasurface. a Coherent optical input signals α and β interact on a metasurface absorber, generating output signals γ and δ. The metasurface has been fabricated by nanostructuring the central 25 × 25 μm2 of a 70-nm-thick gold layer covering the cleaved end-face of a polarization-maintaining single-mode silica fibre (inset scanning electron microscope images, black scale bar 100 μm, grey scale bar 1 μm). b The counterpropagating coherent input signals form a standing wave wherein the metasurface can be located at a position of destructive interference of electric fields (node) where absorption is suppressed or at a position of constructive interference (anti-node) where absorption is increased. In the ideal case, absorption can correspondingly be controlled from 0 to 100% Full size image

The planar absorber used here is a plasmonic metamaterial consisting of a 70-nm-thick gold film perforated with an array of asymmetrically split ring apertures, as previously deployed in free-space demonstrations of coherent light absorption and transparency8. The dependence of this structure’s transmission, reflection and absorption characteristics on aperture size and geometry26 is well understood, allowing for easy optimization throughout the optical telecommunications bands. Our switch operates at wavelengths around λ = 1550 nm, where its 70 nm thickness corresponds to λ/22. The metamaterial structure was fabricated by thermal evaporation of gold and subsequent focused ion beam milling on a 25 × 25 μm2 area covering the core of a cleaved polarization-maintaining single-mode silica fibre (see inset to Fig. 1a), with the symmetry axis of the metamaterial aligned to the slow axis of the fibre (see Methods section for details). The fibre output was coupled to a second cleaved polarization-maintaining optical fibre using two microcollimator lenses to realize an in-line fibre metadevice (Fig. 2a).

Fig. 2 The packaged metadevice and its properties. a Schematic representation of the fully fiberized experimental setup with a photograph of the packaged metadevice (without lid, black scale bar 5 mm) consisting of the metasurface-covered fibre (Fig. 1a) coupled to a bare fibre end using a pair of microcollimator lenses. The inset shows eye diagrams of the intensity of output channel δ recorded for intensity modulation of input channel β at 40 Gbit s−1, where colour indicates counts and the white scale bar indicates 10 ps. b Measured output intensities I γ and I δ (relative to I α ) as well as the total output power and metadevice losses (relative to the total input power) as a function of the phase difference between the input signals at the metasurface at a wavelength of 1550 nm. c Measured output intensity I δ (data points) relative to the fixed input intensity I α as a function of input intensity I β for various phase differences between the input beams, with fits (lines), again at 1550 nm Full size image

The metadevice is terminated with standard FC/APC fibre connectors and it was characterized in a fibre interferometer assembled from standard polarization-maintaining fibre components (Fig. 2a). The output of a fibre-coupled CW laser was split along two paths of similar length, with one path containing an electro-optical phase or intensity modulator and the other containing a variable attenuator to allow balancing of the power propagating along the two paths. The paths were then recombined within the metadevice and the output signals were detected via circulators using an oscilloscope (see Methods section for a more detailed description). We note that practical applications would require some means of active stabilization of the optical path lengths, however the system shown here is sufficient to characterize the principle of operation of the fiberized switch. This is illustrated by the eye diagrams in Fig. 2a, which show that the eye closes on a timescale of seconds due to phase drift in the interferometer.

Figure 2b shows the phase-dependent output intensities I γ and I δ relative to the input intensity I α = I β as a function of the phase difference between the inputs at a wavelength of 1550 nm. The overall output power can be controlled from about 9% to about 57% of the total input power, where a low output level corresponds to constructive interference of the incident waves on the metasurface and thus coherent absorption, while a high output level corresponds to coherent transparency. Both output signals display a similar phase-dependence; however, the phase-dependent output intensity I δ offers somewhat higher contrast and therefore we focus on this output. It should be noted that, for an ideal metadevice containing a perfectly symmetric ultrathin absorber showing 50% single-beam absorption (with no other loss mechanisms) and equal reflection and transmission for both directions of propagation, both output intensities would be identical and modulated from complete absorption to perfect transmission. Differences between the measured output channels arise in the present case from the asymmetric construction of our metadevice that contains a metasurface fabricated on the glass/air interface of one of the optical fibres. The whole metadevice exhibits about 24% single-beam transmission, 18% (8%) reflection and 58% (68%) losses for a single input signal α (β). However, only part of these losses correspond to metasurface absorption that can be coherently controlled, while other sources of loss include the fibre connections of the metadevice, scattering and unwanted reflections within the microcollimator and fabrication imperfections such as imperfect alignment of the metasurface orientation with the slow axis of the fibres.

The nonlinear functionality of the switch is illustrated by Fig. 2c, which shows how the output intensity I δ depends on the input intensity I β while I α remains constant for various phase differences between the input beams. The measured output intensity I δ as a function of input I β is nonlinear and generally follows the behaviour predicted by Fang et al.7. For input phase differences of less than π/2 it is also nonmonotonic—counterintuitively the output intensity decreases with increasing input intensity and reaches a minimum before increasing when I β becomes large. For an input phase difference of π/2, changes in the measured output intensity I δ are approximately proportional to changes in the input intensity I β . For larger input phase differences, I δ flattens with increasing I β , but is steep for small I β suggesting possible applications in small signal amplification. Thus, the results presented in Fig. 2b, c show that large changes of the metadevice output result from modulation of phase or intensity of one of the metadevice inputs.

All-optical signal processing

All-optical signal processing operations with input/output relations analogous to logical functions may now be realized in the network by exploiting coherent transparency and/or coherent absorption in the metadevice. In what follows, binary logical states encoded in beams of equal intensity but opposite phase in the metasurface plane are denoted '+' and '−', while opposing states encoded as low/high intensity are denoted '0'/'1'. Consider, in the first instance, the case of mutually coherent, binary, phase-modulated input signals + and −: constructive interference of identical bits α and β will lead to coherent absorption on the metasurface, while destructive interference of opposing bits will lead to coherent transparency, producing an intensity-modulated (0/1) output α XOR β. The behaviour of an ideal switch is summarized in Table 1 and the measured behaviour of the experimental metadevice is shown in Fig. 3a, for a modulation frequency of 10 kHz. The switch clearly presents XOR functionality with high contrast (>10×) between the output states. The intensity of the output logical 1 is about 30% lower than in the ideal case due to losses within the metadevice. Note that the XOR function can be inverted to α XNOR β by providing an additional external phase-shift θ ext = π to one of the input signals. Furthermore, a fixed input signal β of + or − could be used to map the phase-modulated signal α to an intensity-modulated signal with (NOT α) or without (IDENTITY α) inversion.

Table 1 Logical functions between mutually coherent, equal intensity, phase-modulated input bits α and β (I α = I β = 1) Full size table

Fig. 3 All-optical signal processing at 10 kHz at a wavelength of 1550 nm. a XOR function between phase-modulated input signals α and β producing an intensity-modulated output based on coherent absorption of identical bits and coherent transparency for opposing bits. b NOT function on a single intensity-modulated signal α. The inversion of signal α in the presence of beam β (which is always on) results from coherent absorption of incoming signal pulses when the metasurface is located at a standing wave anti-node. c AND function between intensity-modulated signals α and β resulting from coherent transparency of the metasurface for simultaneous illumination from both sides when the metasurface is located at a standing wave node. The logical states are indicated on the right-hand side of each graph. Minor signal distortions are due to the limited bandwidth of the waveform generator Full size image

The network can also perform signal processing operations analogous to logical functions on intensity-modulated input data. The simplest example is a NOT function. Such inversion of an intensity-modulated signal α is achieved by leaving input beam β always on with its phase adjusted such that coherent absorption will occur for simultaneous illumination of the metasurface from both sides (θ ext = 0). Input pulses α (logical 1) will be coherently absorbed resulting in low output (logical 0). On the other hand, low input signals α (logical 0) will allow light from input β to reach the outputs (logical 1). For an ideal metadevice, the expected output intensities are 0 and 25% of the input intensity, respectively; our experimental device achieves about 5 and 23% at a modulation frequency of 10 kHz, which is more than sufficient to distinguish the logical states (Fig. 3b).

While the NOT function was based on coherent absorption, an AND function between binary intensity-modulated signals can be realized by exploiting coherent transparency. In this case, a phase shift is applied to one input signal, such that simultaneous illumination of the metasurface from both sides leads to coherent transparency (θ ext = π). For an ideal device, this would lead to 100% output intensity for interaction of two pulses on the metasurface and at least 4× lower output intensity for any other combination of input bits (Table 2). Experimentally we observe the AND function with more than 3× contrast between the logical output states at a modulation frequency of 10 kHz. In principle, other logical functions including XOR and OR for intensity-modulated signals can be realized for suitable choices of θ ext 22.

Table 2 Logical function α AND β between mutually coherent, intensity-modulated input bits α and β Full size table

Gigabits per second and beyond

In practical systems, optical signals transmitted by optical fibres are modulated at GHz frequencies rather than kHz, and also make use of a range of optical wavelengths. We therefore tested the metadevice at modulation frequencies 5–6 orders of magnitude higher than presented in Fig. 3 and at wavelengths ranging from 1530 to 1565 nm (telecommunications C-band), as illustrated in Figs. 4 and 5. To this end, the output of the fibre interferometer was amplified with an erbium-doped fibre amplifier (EDFA) which provided an average output power of 1 mW. This conveniently ensures that the threshold power between logical 0 and logical 1 will always be close to 1 mW. Figure 4a shows the XOR function on phase-modulated signals (as described above) now at a modulation frequency of 1.2 GHz, while Fig. 4b shows the NOT function on an intensity-modulated signal also at 1.2 GHz. An AND function was realized by intensity modulation of the laser light entering the interferometer (i.e. modulation before the 50:50 splitter shown in Fig. 2a) and the introduction of a path difference in the interferometer arms to delay the modulated signals α and β relative to one another as illustrated by Fig. 4c. This is equivalent to an intensity-modulated bit sequence 0011 in channel α and 1001 in channel β, resulting in an output 0001, i.e. α AND β, in the detected output channel.

Fig. 4 All-optical signal processing at 1.2 GHz at a wavelength of 1550 nm. a XOR function between phase-modulated input signals α and β producing an intensity-modulated output based on coherent absorption of identical bits and coherent transparency for opposing bits. b NOT function on a single intensity-modulated signal α in the presence of a constant beam β, resulting from coherent absorption of incoming signal pulses when the metasurface is located at a standing wave anti-node. c AND function on two intensity-modulated signals α and β resulting from coherent transparency of the metasurface for simultaneous illumination from both sides when the metasurface is located at a standing wave node. The elevated noise level in c, as compared to a, b, is due to a change in the experimental configuration (described in Methods). The logical states are indicated on the right-hand side of each graph Full size image

Fig. 5 Broadband inversion NOT α of a 40 Gbit s−1 input signal α at wavelengths from 1530 to 1565 nm. The input signal corresponds to an intensity-modulated bit pattern 1011 repeating at 10 GHz (top); corresponding output traces for different wavelengths (below) show that the metadevice inverts the bit pattern in all cases. Beam β is continuously in the on state (logical 1). The logical states 1 and 0 are indicated on the right-hand side and separated by a horizontal dotted line on each graph Full size image

Figure 5 shows the NOT function of the switching network at a frequency of 10 GHz. The periodic input signal α was generated with a bit pattern generator and is equivalent to a bit sequence of 1011, which is inverted to become 0100 at a rate of 40 Gbit s−1. Measurements at wavelengths from 1530 to 1565 nm show successful signal inversion, thereby illustrating the broadband nature of the underlying coherent absorption effect across the full wavelength range of the tuneable laser used in the experiment. With 50 μW peak power in each input channel and a 25 ps pulse duration per bit, the modulator’s energy consumption is 2.5 fJ per bit, which corresponds to about 20,000 photons per bit. Given that coherent absorption of single photons has been demonstrated11, we expect that energy consumption in the attojoule per bit regime should be possible with a sufficiently sensitive detection system.

The modulation results obtained at GHz frequencies are similar to those obtained at kHz frequencies. At GHz frequencies, some distortion is apparent in both the signals used to drive the phase and intensity modulators as well as the measured output signal, where contrast is slightly reduced. These distortions arise from the frequency response and background noise of the modulators and amplifiers used in the experiments. While our experimental equipment does not allow us to test the performance of the modulator in the fibre environment beyond 40 Gbit s−1, we expect that the switching network with metamaterial absorber can in principle operate at much higher frequencies. Indeed, the underlying phenomena of coherent absorption and coherent transparency in plasmonic metamaterials occur on timescales as short as 10 fs, implying a potential bandwidth on the order of 100 THz10. Based upon the spectral width of its plasmonic absorption peak, the metamaterial used in the present study may be expected to efficiently absorb pulses as short as 40 fs, corresponding to a potential bandwidth of tens of THz (Supplementary Note 1). However, such bandwidth will be difficult to realize in a fiberized switch due to dispersion limitations of the fibres.