ARTICLES PUBLISHED ONLINE: 30 MARCH 2014 | DOI: 10.1038/NNANO.2014.53
Electronic control of optical Anderson localization modes Shayan Mookherjea1 *, Jun Rong Ong1, Xianshu Luo2 and Lo Guo-Qiang2 Anderson localization of light has been demonstrated in a few different dielectric materials and lithographically fabricated structures. However, such localization is difficult to control, and requires strong magnetic fields or nonlinear optical effects, and electronic control has not been demonstrated. Here, we show control of optical Anderson localization using charge carriers injected into more than 100 submicrometre-scale p–n diodes. The diodes are embedded into the crosssection of the optical waveguide and are fabricated with a technology compatible with the current electronics industry. Large variations in the output signal, exceeding a factor of 100, were measured with 1 V and a control current of 1 mA. The transverse footprint of our device is only 0.125 mm2, about five orders of magnitude smaller than optical two-dimensional lattices. Whereas all-electronic localization has a narrow usable bandwidth, electronically controlled optical localization can access more than a gigahertz of bandwidth and creates new possibilities for controlling localization at radiofrequencies, which can benefit applications such as random lasers, optical limiters, imagers, quantum optics and measurement devices.
S
ince the 1960s it has been realized that the right level of disorder can enable very interesting (and also useful) systemwide behaviour; for example, a ‘control knob’ over the energy of excitations in an electronic system can transition a collective ensemble between two very different regimes, which may correspond, for example, to the ‘on’ and ‘off’ states of a switch. Such a device not only remains functional in the presence of disorder, it actually utilizes disorder for its operation, thereby achieving a high degree of robustness in the real world. Such robustness would be highly desirable in nanophotonics, because individual components are sensitive to fabrication disorder. Recent developments in random lasers, imaging and spectral measurement indeed suggest that device functionality can be achieved in the presence of disorder1. Therefore, electronic control over optical localization, if possible, can lead to new applications, among which are modulation of random lasers, tunable spectrometers, imagers, quantum optics, and so on2–4. Anderson localization of light has been studied in dielectric materials such as ground powders5,6, optically induced two-dimensional lattices in photorefractive crystals7 and lithographically fabricated structures2,3,8–10. Controlling optical localization is difficult, so far requiring strong magnetic fields11 or nonlinear optical effects7,10,12. In fact, electronic control over optical localization has not yet been demonstrated. Our work, combining optical Anderson localization in waveguides with the same submicrometre diode technology that forms the basis of the microelectronic industry, is intended for devices that attempt to control disorder for applications. There are also fundamental reasons why electronic control over optical localization is interesting. One such reason is that all-electronic localization is impacted by thermally activated low-frequency noise13–16 and has a narrow usable bandwidth. Optical localized states have an energy (0.8 eV) far above the thermal noise level, so thermally excited population/depopulation is not significant, even at room temperature. The bandwidth of the exponentially localized optical mode exceeds 2 GHz, many orders of magnitude
higher than that of electronically localized modes. Moreover, the localized mode here is optical but the control signal is electronic; in fact, a diode structure is used so as to benefit from the exponential increase in the number of controlling carriers with applied voltage, which is not possible with magnetic fields or nonlinear optical control signals.
Localization in the coupled-resonator chain The paradigmatic model for Anderson localization is a tightbinding chain of N coupled harmonic oscillators, as shown in Fig. 1a, in which the individual resonance frequencies v0 are coupled by a nearest-neighbour coupling coefficient k (normalized to v0 and assumed here to be a real number, for simplicity; see Supplementary Section 1.A for additional information). Despite being composed of essentially reactive (that is, dissipationless) elements, a chain of resonators can efficiently draw energy of a certain range of frequencies from a signal generator located at the input end, and propagate it down the line. The transmission spectrum shows N peaks at radian frequencies vn ≈ v0[1 þ 2kcos(pn/(N þ 1)], n ¼ 1, 2, . . ., N, which represent the normal modes17 (shown as blue-shaded peaks in Fig. 1b), spanning a passband of width 4k. When a swept-wavelength source is used to measure the overall transmission spectrum, the peaks and valleys coalesce to form a spectrum such as that shown in Fig. 1c. When the number of elements increases, the transmission spectrum becomes non-smooth and the channel modes fall into only two categories: those that are transmitting with nearly unity ‘conductance’ (including extended and multimode states) and those that are localized14. Nanoscale fabrication disorder is manifest in small site-to-site variations in v0 and k (ref. 18). Based on the argument of Thouless19, Anderson localization can occur at the band-edges, because the intermode frequency separation, dvi,iþ1 ; |viþ1 2 vi| for i [ {1, 2, . . ., N 2 1}, is smallest at the band-edges and is inversely proportional to N 2 (dvN21,N/v0 ≈ 3kp2/N 2), and can become √ less than the renormalized average disorder strength dkdisorder / N , if N
1 University of California, San Diego, Department of Electrical and Computer Engineering, La Jolla, California 92093-0407, USA, 2 Institute of Microelectronics, A*STAR (Agency for Science, Technology and Research), 11 Science Park Road, Science Park II, 117685 Singapore. * e-mail: [email protected]
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Figure 1 | Coupled oscillators. a, Coupled harmonic oscillators, with resonance frequency v0 and nearest-neighbour coupling coefficient k (normalized to v0; Supplementary Section I.A), can transmit energy from one end of the chain to the other. b, The transmission spectrum comprises the normal mode resonances, which cumulatively span a frequency range 4k, with the band-centre frequency v′0 slightly shifted from v0 by the self-coupling effect. c, Experimental measurement of the transmission spectrum of the coupled microring resonator device studied here, showing coalescence of the individual peaks and valleys into a passband around a centre wavelength of 1,553.6 nm. d, For an ensemble of 6 × 105 band-edge wavelengths where localization is expected to occur, measured over 100 transmission bands on six chips, the variance of the ensemble-averaged normalized intensity, ˜I ; I/kIl was 20 var(˜I) = 9.8 (exceeding the value 2.3 expected for localization ) and the tail of the distribution P(˜I) was distributed according to a stretched-exponential function22,23 shown by the solid line, P(˜I) exp(−2 g˜I) over several orders of magnitude, with an effective conductance parameter g ¼ 0.26+0.03 ≪ 1. These observations suggest that the band-edge transmission of a coupled resonator waveguide was in the localization regime37 (Supplementary Figs 1 and 2). e, For conventional ridge waveguides, a very different kind of distribution is obtained, suggesting a non-localized regime, as shown by the Rayleigh distribution (dashed line), P(˜I) = exp(−˜I).
is larger than a critical length. In the fabricated device k ≈ 1.5 × 1023, which is a fairly typical value in such devices9, and measurements suggest an effective level of disorder of 5% in v and k. The critical length is calculated to be about 44 resonators, and longer chains should exhibit band-edge Anderson localization, as was indeed observed here. To examine the characteristic statistical properties of Anderson localization20, an ensemble of data was acquired, based on measurements made over about 60,000 wavelength points over 100 transmission bands and across six chips, within the spectral range where Anderson localization occurs. Because the coupling coefficients and refractive indices vary over the range of wavelengths used (1,530–1,610 nm), measurements at different wavelengths yield an ensemble of data with different disorder-to-coupling strength ratios. The statistics of the normalized intensity transmission I˜ ; I/kIl, where kIl is the ensemble-averaged intensity, can be a useful indicator of Anderson localization20. We find that ˜ = 9.8 exceeds the threshold value (7/3) expected the variance var(I) for localization in the presence of some absorption. For the quantity defined as the logarithm of the transmission, the magnitude of the ˜ = 7.1 was comparable to its variance var(ln I) ˜ = 9.9, mean −kln Il indicating the likelihood of Anderson localization, rather than tunnelling21. As shown in Fig. 1d, the probability density function of the ˜ has a long-tailed distribution, normalized intensity, P(I), fitted by a ˜ exp(−2 g I˜), where the stretched-exponential function22,23, P(I) effective conductance parameter g ¼ 0.26+0.03 was significantly less than 1 and indicated strong localization (Supplementary Section I.C). This sort of distribution, characteristic of the localized ˜ = exp(−I) ˜ regime, is different from the Rayleigh distribution P(I) ˜ shown in Fig. 1e, which was obtained from measurements of P(I) on long conventional waveguides (without resonators or periodic patterning) located on the same chips. (See Methods for a discussion of the number of modes supported by the waveguide cross-section.) Light transmission through a coupled-microring resonator chain can be simulated using transfer matrices24–26, as described in Supplementary Section I. Because it was not feasible to study a very large number of fabricated samples experimentally, we performed Monte-Carlo simulations of disordered transport and obtained ensemble-averaged results, shown in Supplementary Figs 1–3, which are very similar to those based on experimental measurements27. 2
Optical and electronic aspects of device design As shown in Fig. 2, the device consists of 51 nearest-neighbour coupled resonators (see Methods). Each resonator is a racetrack, with the north and south halves of a ring of radius 10 mm connected with two straight waveguide sections of length 10 mm. Light propagates in the structure from left to right, as indicated in the figure, initially input in the feeder waveguides and coupling between adjacent resonators via waveguide directional couplers. The direction of light circulation in the resonators is shown in Fig. 2b and alternates between clockwise and anticlockwise in adjacent unit cells. The waveguides have a cross-section as shown schematically in Fig. 2c. A 70-nm-thick slab of silicon, doped with p and n implants at a distance of 900 nm from the rib edge, creates a diode in the plane transverse to that of light propagation. Electrons and holes were injected into the waveguide core, where the optical mode resided, when a forward-bias voltage was applied across the diode using the metal contacts. As shown in Fig. 2b, each microring was designed with two p–n junctions at the north and south portions of the racetrack. All junctions were driven by the voltage source in parallel. The injected carrier density can exceed 1 × 1019 cm23, sufficient to significantly alter the optical refractive index, as studied earlier by Soref and Bennett28 and used in data modulation29. Figure 2d shows the calculated phase and absorption change as a function of applied voltage (Supplementary Section III). A large phase shift (reduction of 25 rad) is predicted as the voltage increases above 0.5 V, but the accompanying attenuation (increase) is relatively small, only 0.1 dB over the entire length of the 51-ring structure. Similar to the lowest-order cosine-shaped vibrational mode of a clamped string, the band-edge mode of the coupled-resonator chain is defined by the in-phase oscillation of all the resonators (with only p/51 radians of relative phase difference between adjacent resonators), so a change of tens of radians in phase is a very large effect. On the other hand, the steady-state insertion loss, caused by the exponential absorption of light with propagation length in all dielectric materials, is 5 dB in the chain, so the addition of 0.1 dB loss is a minor effect. Thus, carrier injection into electrically active planar resonators is an effective way to introduce significant phase perturbations on localized modes without the large attenuation increases that could impact extended modes (Supplementary Fig. 3). This is in
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DOI: 10.1038/NNANO.2014.53 Optical waveguides
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Figure 2 | Optical device and electronic control. a, Microscope image of an optical coupled-resonator chain with 51 racetrack resonators, with the waveguides highlighted in light green for clarity. The direction of light input and output is shown along the feeder waveguides with solid arrows, while the dashed arrow shows the fraction of input light not coupled into the device. Electrical contact pads (50 mm squares) are shown at the bottom left for positive (P) and negative (N) voltages, connecting to the p and n contacts, respectively, in each resonator in parallel. b, Each resonator has two regions, at the ‘north’ and ‘south’ curved sections of the racetrack, where a p–n junction is formed by ion implantation and contact metallization (see Methods). The p and n contacts are coloured blue and cyan, respectively. Dotted white lines show the direction of light propagation in adjacent rings (alternating between clockwise and anticlockwise). c, Schematic of the cross-section of the lateral p–n junction (not to scale), perpendicular to the direction of light propagation, such that injected electron and hole carriers interact with the optical mode confined mostly to the central intrinsic-silicon (i-Si) rib section. d, Calculation of the optical phase shift (reduction) and attenuation (increase) when a forward bias voltage is applied across each diode. A total of 102 diodes are used in the 51-resonator chain. The calculation is based on Soref and Bennett’s theory of free-carrier effects in silicon28 and includes the slow-light effects of this waveguide structure (Supplementary Section III).
contrast to electrically pumped random lasers30–32, which can control the degree of optical gain experienced by a localized mode, but not localization itself. Based on these arguments, carrier injection should be a good ‘switch’ for phase-sensitive phenomena such as Anderson localization, which relies on multiple-scattering interference. In this context, localization is defined as a disorder-confined mode with an exponentially decaying envelope in real (coordinate) space along the length of the waveguide. Confinement in the transverse plane is provided by the index contrast between the core and the cladding of the waveguide cross-section. In the following discussion, we select one localized mode (out of more than 50 that could be measured in a typical device between the wavelengths of 1,530 nm and 1,610 nm) with a particularly ‘clean’ contrast from the bandedge to show unambiguous evidence of electronic switching control over that mode. Other localized modes in several different chips, as well as extended modes at nearby wavelengths, are presented in Supplementary Fig. 4.
Infrared imaging/electronic control of optical localization Wavelength-resolved infrared imaging of band-edge localization in this device is shown in Fig. 3. In a measurement of transmission through the device (Fig. 3a), a resonance was observed just beyond the band-edge, where localization is expected to occur10. By imaging the modes at each wavelength, we obtained a detailed map of the optical modes shown in Fig. 3b. The vertical axes of Fig. 3a,b are aligned, so the transmission peaks can be seen to correspond to spatially extended excitations that span from the first to the last ring. Input coupling effects died out by about the ninth ring. However, the transmission of light through the device was finite, even for a localized mode, because the structure was coupled by
the input and output waveguides to the external ‘bath’ of optical modes. Similar behaviour applies in localized electronic systems33. Figure 3c presents a three-dimensional representation of the localized mode region shown in the inset to Fig. 3b, from which we measured a spatial full-width at half-maximum of about three resonator sites, L* ¼ 3 × 20 mm. The mode spanned a spectral width Dl ¼ 0.02 nm (2.5 GHz), that is, an effective quality factor Qeff of 4 × 104. Because the band-edge state was in the vicinity of KBloch ¼ 0, where KBloch is the Bloch wavenumber, the product (KBloch þ DKBloch) × L* was 1.4 × 1022, that is, well within the range of strong localization of excitations at the band-edge of this resonator chain. Figure 3d shows that the envelope of the localized mode has a slowly decaying exponential background (characteristic of camera-imaged optical propagation in dielectric materials, which also collects light from the background and any substrate-guided weakly diffracting modes), on top of which is superimposed the localized mode envelope. The inset to Fig. 3d shows that the localized mode has an exponentially localized envelope, exp(2|j2j0|) where j is a normalized coordinate enumerating the lattice sites and j0 identifies the centre of the mode. The normalizing constant of j and j0 is 3.1+0.5 unit cells, and the full-width at halfmaximum is 2.6 unit cells (see Supplementary Fig. 3 for the corresponding information from simulations). These measurements confirm the presence of an exponentially localized mode in the microring resonator chain near the band-edge2,8,9. Figure 4a presents an infrared camera image of the central portion of the resonator chain for an extended mode, when all the rings are lit up by the propagating light, with a small ring-to-ring intensity variation that shows the typically small effect that disorder has on mid-band transmission. In contrast, the localized mode is confined to only a few resonators, as shown in Fig. 4b. Figure 4c
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Figure 3 | Spectrally resolved infrared imaging of modes. a, The transmission spectrum shows extended mode resonances within the passband and a localized mode at the band-edge. Transmission through the localized mode is non-zero, because the finite-length structure was coupled to input and output waveguides, which support a continuum of modes33. b, At the wavelengths in a, an infrared camera image (12-bit resolution, that is, values between 0 and 4,095) was recorded of light propagating along the chain of resonators, labelled by ring numbers between 1 (input) and 51 (output). Extended mode resonances span the structure, whereas the band-edge localized mode, shown more clearly in the inset, is confined to a few resonators inside the waveguide. c, The localized mode is seen more clearly in this three-dimensional representation. d, Taking a cross-section through c along the resonance wavelength (1,582.45 nm) shows a gradual exponential decay of light along the direction of propagation (dashed line, mainly due to partial imaging of the slab modes under the guided structure), on top of which is super-imposed the localized envelope. Inset: After subtracting out the slow exponential decay from input to output, the localized mode has an exponentially fitted envelope, with unit cells of width 3.1+0.5.
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Figure 4 | On and off states of the localized mode. a, An infrared camera image of a part of an extended mode, for comparison. The 12-bit camera readout values range from 0 to 4,095. b, Using the same camera settings, the localized mode at 1,582.45 nm was imaged, showing light localization over about three microring resonators. c, When a voltage exceeding 1 V was applied across the p–n junction, the mode was turned off, with the camera image showing residual speckle. b and c were acquired under dynamic conditions, that is, by synchronizing the camera to an on–off voltage pulse train. d, Transmission spectrum versus applied voltage, showing a blueshift (to shorter wavelengths) of the localized mode resonance, as well as a large (factor of 75) attenuation of the peak. (See Supplementary Fig. 5 for a comparison of the effect of voltage on extended and localized modes.). 4
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Figure 5 | Switching waveform of localization. a, While a voltage pulse train (0 V ‘off’, 10 V ‘on’) was applied across the diode, the voltage detected by a photodetector proportional to transmission (T) through the device and the camera-imaged optical mode intensity (IRC) were recorded simultaneously (see Methods). The time axis is shaded yellow when the voltage is ‘on’. The speed of switching is limited to a few tens of hertz by the imaging time of the infrared camera (20 ms per frame) and because several frames were imaged and averaged for each on and off state in order to reliably generate the IRC graph from relatively weak optical images. b, The contrast was quantified by the ratio of transmission for the cases when the voltage was off (localization established) and on (localization de-established), with a value of 1 representing ‘no change’. The contrast was measured versus the applied voltage, and the measured data were fit using a sigmoidal function (shown by the dashed line), demonstrating a slope of 20.3 dB V21 in the range between 1 and 2 V; that is, less than 1 V swing was sufficient to change the optical contrast by a factor of 100.
shows the same region of the resonator chain when electronic carriers are injected into the waveguide using the p–n junction under forward bias (1.5 V): the localized mode is de-established. To understand this switching, recall that an Anderson localized mode is characterized by a phase resonance among the multiply scattering resonators (in this case, the nanoscale roughness within the optical pathway of each racetrack). This phase relationship is strongly perturbed by the injected carriers by up to tens of radians of added phase. This change is completely reversible— turning off the voltage allows carrier drift and recombination away from the junction. Removal of the added phase re-establishes the localized mode at the original wavelength shown in Fig. 4b. The amplitude of the localization resonance is related to the spatial position of the localized mode within the structure, with stronger resonances if the mode is localized near the centre rather than towards one of the two edges14. This range of voltages has a much stronger effect on localized modes than on extended modes, as shown in Supplementary Fig. 5. Figure 4d shows that the injected carriers cause a blueshift of the localized mode resonance, as well as strong attenuation of the peak (by nearly 20 dB, which is significantly greater than the increase in absorption, Da ¼ 20.1 dB, calculated in Fig. 2d). Note that thermal heating would have caused a redshift (to longer wavelengths) of the resonance34. Accordingly, the observed blueshift effects can be dominantly attributed to electronic carriers.
On–off switching of a localized mode While an on–off control voltage pulse train was applied across the p–n junction, the optical transmission light through the device (at the wavelength of the localized mode, 1,582.45 nm) and the infrared camera image were recorded simultaneously. In Fig. 5a, yellow shaded regions indicate the periods when a forward-bias voltage (þ10 V) is applied across the junction and unshaded regions indicate when no voltage is applied (0 V). The upper graph, labelled T (transmission) was proportional to the voltage measured using a photodetector at the output of the chip, with contrast exceeding 20 dB (a factor of 100). Note that, in this device, the control signal and measured readout were both electronic signals and the intermediate localization mode was optical. To confirm that the switching was due to optical localization itself being established and de-established, the lower graph was recorded at the same time using infrared camera images of the localized mode (shown
in Fig. 4b). The image readout along the outline of the microrings was integrated numerically, yielding the quantity IRC (integrated readout of camera) shown in the lower panel of Fig. 5a, demonstrating that the localized mode was turned on and off by the injected electronic carriers. The contrast in IRC is a little bit lower than that of T because of the lower dynamic range and higher noise floor of the infrared camera compared to the photodetector. Figure 5b shows the on–off contrast as a function of the magnitude of the applied voltage. Here, contrast was defined as a ratio between the transmission T in the voltage-on and voltage-off states, with a contrast of 1 indicating no change. Contrast values greater than 1 indicate that the voltage-on transmission was suppressed relative to the voltage-off transmission value. The measured data points are fit well by a sigmoidal function, g(j ) ¼ a þ b/[1 þ exp(2|j|/c)], where a, b and c are fitted constants, using the Levenberg–Marquardt nonlinear least-squares algorithm. Most significant changes were observed when the voltage just exceeded 1 V; for example, the contrast increased by a factor of b/a 2 1 ¼ 106 (20.3 dB) between 1 V and 2 V. This voltage range agrees closely with the voltage range over which the change in optical phase (Df ) and absorption (Da) is most significant, as shown in Fig. 2d, and is in a convenient range for electronic driver circuits. The current through each diode at a forward-bias voltage of 2 V is only 10 mA, that is, representing a total current of 1 mA through the 102 diodes on the chip (see Supplementary Section III), yielding a total power consumption of 2 mW distributed throughout the device of length 1 mm via the electrical wiring network. This power density is vastly smaller than required for all-optical control over localization, for example, nine orders of magnitude smaller than the power levels required for the proposal of alloptical control of localization in photonic crystals12, where because of the fundamentally weak optical nonlinearity, a power density of 5 × 103 W mm21 is required. Note that, in both cases, optical localization over about three to four unit cells of the periodic lattice structure may be achieved. When imaging the weak levels of scattered light collected from the localized mode, the infrared camera requires a fairly long integration time of 20 ms per frame. To generate the data shown in Fig. 5a, several frames were recorded for each stage of the ‘on’ and ‘off’ pulse sequence, so the applied pulse frequency was limited to a few tens of hertz. We stress that the limitation on switching speed here was only because of in situ dynamic imaging and
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real-time image processing (see Methods). Although injectionbased modulators suffer from an intrinsic diode bandwidth of 250 MHz due to minority carrier dynamics, the nonlinear transfer function of microring resonators29 as well as the use of pre-emphasis on the electrical drive waveform35 have allowed the optical modulation bandwidth to exceed 40 times the diode bandwidth, enabling data communication speeds greater than 10 Gb s21. Because the intrinsic bandwidth of the localized mode is more than 2.5 GHz, there is nothing fundamental that prevents electronic control of optical localization at nanosecond speeds. The length of the structure (1.05 mm) is only 3% of the electromagnetic wavelength at 10 GHz, so the electrical contacts can be viewed as a lumped element for the radiofrequency wave. However, some aspects of the device, for example, the long wires from the contact pads to the rings, should be redesigned for lower resistance, and the p–n junctions should surround a greater fraction of the ring circumference so that injected carriers do not diffuse along the racetrack away from the contact regions, thus increasing the carrier-extraction time.
Conclusions In summary, we have demonstrated electronic switching of optical Anderson localization modes, showing carrier injection-based control using p–n junction diodes that infiltrate the optical waveguide structure. The same idea can be applied to other periodically patterned nanophotonic structures, such as photonic crystals8, as well as quasicrystals36 and aperiodic structures such as random lasers. The basic underlying principle is drawn from the large phase change that can be created (with relatively insignificant absorption increase), the degradation-free reversibility of the effect, and the low energy of the control signals, which are attractive features both for physics studies and for the development of device technology using controlled localization.
Methods Device design and fabrication. The devices were fabricated on silicon-on-insulator wafers at the Institute of Microelectronics in Singapore. Two etch steps were used for the rib waveguide cross-section (Fig. 2c). The waveguides, of width 0.55 mm, height 0.22 mm and slab thickness 70 nm, were designed for low-loss (1 dB cm21) transmission in the lowest-order mode of the transverse electric (TE) polarization defined relative to the device plane. Finite-element calculations showed three modes (two TE- and one transverse magnetic (TM)-polarized) that can be guided in straight waveguides, but the TM mode and the high-order TE mode suffer higher bending loss in the microrings and do not propagate in the coupled-microring device25. The slab waveguide regions were doped with boron (33 keV) and phosphorous (90 keV) to an area density of 1 × 1015 cm22 at a distance of 900 nm from the edge of the rib waveguide. A further implantation was performed at lower energy to provide a shallower implant near the contact regions. Implants were activated by a rapid thermal anneal process, followed by additional processing steps to form contact vias and aluminium interconnects. Although 102 diodes were driven in parallel, the metal traces and vias provided enough resistance (172+12 V) to prevent thermal and current runaway (Supplementary Fig. 7). The microring resonators were arranged in a racetrack configuration with a radius of R ¼ 10 mm and directional coupler length Lc ¼ 10 mm. The rings were nominally identical, with apodized waveguide–resonator coupling coefficients formed by varying the inter-waveguide gap in the directional couplers from 210 nm for the first and last couplers to 320 nm in the middle. The propagation loss coefficient is defined as a ¼ awgpReff/|k|, in terms of the propagation loss of a silicon nanophotonic waveguide (awg ≈ 1 dB cm21), the effective bending radius (Reff ¼ R þ lc/p) and the magnitude of the inter-ring coupling coefficient (|k| ≈ 0.4). The measured band-centre propagation loss was 0.1 dB/ring, including slow-light effects. A measurement of the group delay versus wavelength (using a Luna OVA 5000) was used to infer that band-edge propagation loss was a factor of about two greater than at band-centre wavelengths. Experimental set-up. Optical waveforms were generated by a narrow-linewidth single-mode tunable diode laser. The narrow linewidth of the laser (100 kHz) corresponds to a coherence length exceeding all characteristic optical lengths in the device and experimental system. Optical signals were detected using an InGaAs photodetector module. Electrical signals were generated using a function generator and applied to the contact pads on the chip using tungsten probes controlled by micropositioners. The chip was mounted on a temperature-controlled stage, using a thermo-electric controller in feedback to maintain a stable temperature. 6
DOI: 10.1038/NNANO.2014.53
Polarization-maintaining fibres, fibre-loop paddles and lensed tapered fibres with antireflection coating were used to couple light to and from the silicon chip, and nanopositioning stages with piezoelectric actuators were used for accurate positioning of the fibre tips to the waveguide facets. The insertion loss of each fibreto-waveguide coupler was estimated as 4.5 dB, averaged over the wavelengths of interest, based on calibration measurements on separate test sites. Infrared imaging. In generating the data shown in Fig. 3, a 320 × 256 pixel cooled infrared InGaAs camera (Xenics XEVA) with 30 mm pitch in the image plane was used with a ×20 microscope objective lens. The camera used 12-bit analog-to-digital conversion for electronic readout, resulting in quantization levels between 0 and 4,095 arbitrary digital units (ADU). A typical 0.25% noise in the 12-bit ADU scale translates, in the logarithmic scale, to 10 dB noise within the 36 dB full range. A typical infrared camera image of light propagating in a silicon photonic chip, with analog-to-digital converter settings that avoid saturation as well as readout noise at the lower levels, resulted in only 20 dB of usable information. In generating spectroscopic imaging data, the wavelength of the tunable laser was scanned in steps of 0.002 nm and a sequence of infrared camera images (320 × 256 pixels) was acquired at each wavelength. A portion of a representative image is shown in Fig. 4a. Corresponding to the imaged field-of-view, a binaryvalued computational image mask of each racetrack was constructed in Matlab, consisting of a two-dimensional array of either 1 or 0 for each entry, with 1 indicating the presence of a ring at the particular coordinate location. The mask for each ring was multiplied, in turn, with the infrared image acquired at a particular wavelength, and the camera readout values along the racetrack perimeter were averaged, yielding a single number that represented the amplitude of the optical excitation of an individual resonator at that wavelength. This spectrally and spatially resolved measurement is shown in Fig. 3b.
Received 19 September 2013; accepted 17 February 2014; published online 30 March 2014
References 1. Wiersma, D. S. Disordered photonics. Nature Photon. 7, 188–196 (2013). 2. Sapienza, L. et al. Cavity quantum electrodynamics with Anderson-localized modes. Science 327, 1352–1355 (2010). 3. Crespi, A. et al. Anderson localization of entangled photons in an integrated quantum walk. Nature Photon. 7, 322–328 (2013). 4. Redding, B., Liew, S. F., Sarma, R. & Cao, H. Compact spectrometer based on a disordered photonic chip. Nature Photon. 7, 746–751 (2013). 5. Wiersma, D. S., Bartolini, P., Lagendijk, A. & Righini, R. Localization of light in a disordered medium. Nature 390, 671–673 (1997). 6. Sto¨rzer, M., Gross, P., Aegerter, C. M. & Maret, G. Observation of the critical regime near Anderson localization of light. Phys. Rev. Lett. 96, 063904 (2006). 7. Schwartz, T., Bartal, G., Fishman, S. & Segev, M. Transport and Anderson localization in disordered two-dimensional photonic lattices. Nature 446, 52–55 (2007). 8. Topolancik, J., Ilic, B. & Vollmer, F. Experimental observation of strong photon localization in disordered photonic crystal waveguides. Phys. Rev. Lett. 99, 253901 (2007). 9. Mookherjea, S., Park, J. S., Yang, S. H. & Bandaru, P. R. Localization in silicon nanophotonic slow-light waveguides. Nature Photon. 2, 90–93 (2008). 10. Lahini, Y. et al. Anderson localization and nonlinearity in one-dimensional disordered photonic lattices. Phys. Rev. Lett. 100, 013906 (2008). 11. Kenke, R. & Maret, G. Affecting weak light localization by strong magnetic fields. Physica Scripta T49, 605–609 (1993). 12. Liu, H-Y. et al. Self-induced Anderson localization and optical limiting in photonic crystal coupled cavity waveguides with Kerr nonlinearity. Appl. Phys. Lett. 90, 213507 (2007). 13. Giamarchi, T. & Schulz, H. J. Anderson localization and interactions in one dimensional metals. Phys. Rev. B 37, 325–340 (1998). 14. Pendry, J. Symmetry and transport of waves in one-dimensional disordered systems. Adv. Phys. 43, 461–542 (1994). 15. Vandamme, L. K. J. & Hooge, F. N. What do we certainly know about noise in MOSTs? IEEE Electron. Dev. Lett. 55, 3070–3085 (2008). 16. Forbes, L. On the theory of 1/f noise of semi-insulating materials. IEEE Electron. Dev. Lett. 42, 1866–1868 (1995). 17. Fetter, A. L. & Walecka, J. D. Theoretical Mechanics of Particles and Continua (McGraw-Hill, 1980). 18. Cooper, M. L. et al. Statistics of light transport in 235-ring silicon coupledresonator optical waveguides. Opt. Express 18, 26505–26516 (2010). 19. Thouless, D. J. Maximum metallic resistance in thin wires. Phys. Rev. Lett. 39, 1167–1169 (1977). 20. Chabanov, A. A., Stoytchev, M. & Genack, A. Z. Statistical signatures of photon localization. Nature 404, 850–853 (2000). 21. Markos, P. & Soukoulis, C. M. Intensity distribution of scalar waves propagating in random media. Phys. Rev. B 71, 054201 (2005).
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22. Kogan, E. & Kaveh, M. Random-matrix-theory approach to the intensity distributions of waves propagating in a random medium. Phys. Rev. B 52, R3813 (1995). 23. Van Rossum, M. C. W. & Nieuwenhuizen, T. M. Multiple scattering of classical waves: microscopy, mesoscopy, and diffusion. Rev. Mod. Phys. 71, 313–371 (1997). 24. Poon, J. K. S. et al. Matrix analysis of microring coupled-resonator optical waveguides. Opt. Express 12, 90–103 (2004). 25. Xia, F., Rooks, M., Sekaric, L. & Vlasov, Y. Ultra-compact high order ring resonator filters using submicron silicon photonic wires for on-chip optical interconnects. Opt. Express 15, 11934–11941 (2007). 26. Cooper, M. & Mookherjea, S. Modeling of multiband transmission in long silicon coupled-resonator optical waveguides. IEEE Photon. Technol. Lett. 23, 872–874 (2011). 27. Markos, P. Numerical analysis of the Anderson localization. Acta Physica Slovaca 56, 561–685 (2006). 28. Soref, R. A. & Bennett, B. Electrooptical effects in silicon. IEEE J. Quantum Electron. 23, 123–129 (1987). 29. Xu, Q., Schmidt, B., Pradhan, S. & Lipson, M. Micrometre-scale silicon electrooptic modulator. Nature 435, 325–327 (2005). 30. Leong, E. & Yu, S. UV random lasing action in p-SiC(4H)/i-ZnO–SiO2 nanocomposite/n-ZnO:Al heterojunction diodes. Adv. Mater. 18, 1685–1688 (2006). 31. Chu, S., Olmedo, M., Yang, Z., Kong, J. & Liu, J. Electrically pumped ultraviolet ZnO diode lasers on Si. Appl. Phys. Lett. 93, 181106 (2008). 32. Zhu, H. et al. Low-threshold electrically pumped random lasers. Adv. Mater. 22, 1877–1881 (2010). 33. Basko, D., Aleiner, I. & Altshuler, B. Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states. Ann. Phys. 321, 1126–1205 (2006). 34. Vlasov, Y. A., O’Boyle, M., Hamann, H. F. & McNab, S. J. Active control of slow light on a chip with photonic crystal waveguides. Nature 438, 65–69 (2005).
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35. Green, W. M., Rooks, M. J., Sekaric, L. & Vlasov, Y. A. Ultra-compact, low RF power, 10 Gb/s silicon Mach–Zehnder modulator. Opt. Express 15, 17106–17113 (2007). 36. Mahler, L. et al. Quasi-periodic distributed feedback laser. Nature Photon. 4, 165–169 (2010). 37. Deng, C-S., Xu, H. & Deych, L. Effect of size disorder on the optical transport in chains of coupled microspherical resonators. Opt. Express 19, 6923–6937 (2011).
Acknowledgements The authors thank J.B. Pendry, D. Wiersma, P. Lodahl, C. Lopez, Y. Vlasov and H. Cao for discussions. This work was supported by the US National Science Foundation (grants ECCS 092539, 1028553, 1153716 and 1201308) and the Center for Integrated Access Networks—a National Science Foundation Engineering Research Center. J.R.O. acknowledges support from the Agency for Science, Technology and Research (A*STAR), Singapore. All statements of fact, opinion or conclusions contained herein are those of the authors and should not be construed as representing the official views or policies of the US Government.
Author contributions S.M. conceived the study, coordinated the project and wrote the manuscript with input from all authors. J.R.O. designed the lithographic layout for the devices, which were fabricated by X.L. and L.G.Q. Measurements were performed by S.M. and J.R.O. All authors reviewed the manuscript.
Additional information Supplementary information is available in the online version of the paper. Reprints and permissions information is available online at www.nature.com/reprints. Correspondence and requests for materials should be addressed to S.M.
Competing financial interests The authors declare no competing financial interests.
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Electronic control of optical Anderson localization modes Shayan Mookherjea1 *, Jun Rong Ong1, Xianshu Luo2 and Lo Guo-Qiang2 Anderson localization of light has been demonstrated in a few different dielectric materials and lithographically fabricated structures. However, such localization is difficult to control, and requires strong magnetic fields or nonlinear optical effects, and electronic control has not been demonstrated. Here, we show control of optical Anderson localization using charge carriers injected into more than 100 submicrometre-scale p–n diodes. The diodes are embedded into the crosssection of the optical waveguide and are fabricated with a technology compatible with the current electronics industry. Large variations in the output signal, exceeding a factor of 100, were measured with 1 V and a control current of 1 mA. The transverse footprint of our device is only 0.125 mm2, about five orders of magnitude smaller than optical two-dimensional lattices. Whereas all-electronic localization has a narrow usable bandwidth, electronically controlled optical localization can access more than a gigahertz of bandwidth and creates new possibilities for controlling localization at radiofrequencies, which can benefit applications such as random lasers, optical limiters, imagers, quantum optics and measurement devices.
S
ince the 1960s it has been realized that the right level of disorder can enable very interesting (and also useful) systemwide behaviour; for example, a ‘control knob’ over the energy of excitations in an electronic system can transition a collective ensemble between two very different regimes, which may correspond, for example, to the ‘on’ and ‘off’ states of a switch. Such a device not only remains functional in the presence of disorder, it actually utilizes disorder for its operation, thereby achieving a high degree of robustness in the real world. Such robustness would be highly desirable in nanophotonics, because individual components are sensitive to fabrication disorder. Recent developments in random lasers, imaging and spectral measurement indeed suggest that device functionality can be achieved in the presence of disorder1. Therefore, electronic control over optical localization, if possible, can lead to new applications, among which are modulation of random lasers, tunable spectrometers, imagers, quantum optics, and so on2–4. Anderson localization of light has been studied in dielectric materials such as ground powders5,6, optically induced two-dimensional lattices in photorefractive crystals7 and lithographically fabricated structures2,3,8–10. Controlling optical localization is difficult, so far requiring strong magnetic fields11 or nonlinear optical effects7,10,12. In fact, electronic control over optical localization has not yet been demonstrated. Our work, combining optical Anderson localization in waveguides with the same submicrometre diode technology that forms the basis of the microelectronic industry, is intended for devices that attempt to control disorder for applications. There are also fundamental reasons why electronic control over optical localization is interesting. One such reason is that all-electronic localization is impacted by thermally activated low-frequency noise13–16 and has a narrow usable bandwidth. Optical localized states have an energy (0.8 eV) far above the thermal noise level, so thermally excited population/depopulation is not significant, even at room temperature. The bandwidth of the exponentially localized optical mode exceeds 2 GHz, many orders of magnitude
higher than that of electronically localized modes. Moreover, the localized mode here is optical but the control signal is electronic; in fact, a diode structure is used so as to benefit from the exponential increase in the number of controlling carriers with applied voltage, which is not possible with magnetic fields or nonlinear optical control signals.
Localization in the coupled-resonator chain The paradigmatic model for Anderson localization is a tightbinding chain of N coupled harmonic oscillators, as shown in Fig. 1a, in which the individual resonance frequencies v0 are coupled by a nearest-neighbour coupling coefficient k (normalized to v0 and assumed here to be a real number, for simplicity; see Supplementary Section 1.A for additional information). Despite being composed of essentially reactive (that is, dissipationless) elements, a chain of resonators can efficiently draw energy of a certain range of frequencies from a signal generator located at the input end, and propagate it down the line. The transmission spectrum shows N peaks at radian frequencies vn ≈ v0[1 þ 2kcos(pn/(N þ 1)], n ¼ 1, 2, . . ., N, which represent the normal modes17 (shown as blue-shaded peaks in Fig. 1b), spanning a passband of width 4k. When a swept-wavelength source is used to measure the overall transmission spectrum, the peaks and valleys coalesce to form a spectrum such as that shown in Fig. 1c. When the number of elements increases, the transmission spectrum becomes non-smooth and the channel modes fall into only two categories: those that are transmitting with nearly unity ‘conductance’ (including extended and multimode states) and those that are localized14. Nanoscale fabrication disorder is manifest in small site-to-site variations in v0 and k (ref. 18). Based on the argument of Thouless19, Anderson localization can occur at the band-edges, because the intermode frequency separation, dvi,iþ1 ; |viþ1 2 vi| for i [ {1, 2, . . ., N 2 1}, is smallest at the band-edges and is inversely proportional to N 2 (dvN21,N/v0 ≈ 3kp2/N 2), and can become √ less than the renormalized average disorder strength dkdisorder / N , if N
1 University of California, San Diego, Department of Electrical and Computer Engineering, La Jolla, California 92093-0407, USA, 2 Institute of Microelectronics, A*STAR (Agency for Science, Technology and Research), 11 Science Park Road, Science Park II, 117685 Singapore. * e-mail: [email protected]
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is larger than a critical length. In the fabricated device k ≈ 1.5 × 1023, which is a fairly typical value in such devices9, and measurements suggest an effective level of disorder of 5% in v and k. The critical length is calculated to be about 44 resonators, and longer chains should exhibit band-edge Anderson localization, as was indeed observed here. To examine the characteristic statistical properties of Anderson localization20, an ensemble of data was acquired, based on measurements made over about 60,000 wavelength points over 100 transmission bands and across six chips, within the spectral range where Anderson localization occurs. Because the coupling coefficients and refractive indices vary over the range of wavelengths used (1,530–1,610 nm), measurements at different wavelengths yield an ensemble of data with different disorder-to-coupling strength ratios. The statistics of the normalized intensity transmission I˜ ; I/kIl, where kIl is the ensemble-averaged intensity, can be a useful indicator of Anderson localization20. We find that ˜ = 9.8 exceeds the threshold value (7/3) expected the variance var(I) for localization in the presence of some absorption. For the quantity defined as the logarithm of the transmission, the magnitude of the ˜ = 7.1 was comparable to its variance var(ln I) ˜ = 9.9, mean −kln Il indicating the likelihood of Anderson localization, rather than tunnelling21. As shown in Fig. 1d, the probability density function of the ˜ has a long-tailed distribution, normalized intensity, P(I), fitted by a ˜ exp(−2 g I˜), where the stretched-exponential function22,23, P(I) effective conductance parameter g ¼ 0.26+0.03 was significantly less than 1 and indicated strong localization (Supplementary Section I.C). This sort of distribution, characteristic of the localized ˜ = exp(−I) ˜ regime, is different from the Rayleigh distribution P(I) ˜ shown in Fig. 1e, which was obtained from measurements of P(I) on long conventional waveguides (without resonators or periodic patterning) located on the same chips. (See Methods for a discussion of the number of modes supported by the waveguide cross-section.) Light transmission through a coupled-microring resonator chain can be simulated using transfer matrices24–26, as described in Supplementary Section I. Because it was not feasible to study a very large number of fabricated samples experimentally, we performed Monte-Carlo simulations of disordered transport and obtained ensemble-averaged results, shown in Supplementary Figs 1–3, which are very similar to those based on experimental measurements27. 2
Optical and electronic aspects of device design As shown in Fig. 2, the device consists of 51 nearest-neighbour coupled resonators (see Methods). Each resonator is a racetrack, with the north and south halves of a ring of radius 10 mm connected with two straight waveguide sections of length 10 mm. Light propagates in the structure from left to right, as indicated in the figure, initially input in the feeder waveguides and coupling between adjacent resonators via waveguide directional couplers. The direction of light circulation in the resonators is shown in Fig. 2b and alternates between clockwise and anticlockwise in adjacent unit cells. The waveguides have a cross-section as shown schematically in Fig. 2c. A 70-nm-thick slab of silicon, doped with p and n implants at a distance of 900 nm from the rib edge, creates a diode in the plane transverse to that of light propagation. Electrons and holes were injected into the waveguide core, where the optical mode resided, when a forward-bias voltage was applied across the diode using the metal contacts. As shown in Fig. 2b, each microring was designed with two p–n junctions at the north and south portions of the racetrack. All junctions were driven by the voltage source in parallel. The injected carrier density can exceed 1 × 1019 cm23, sufficient to significantly alter the optical refractive index, as studied earlier by Soref and Bennett28 and used in data modulation29. Figure 2d shows the calculated phase and absorption change as a function of applied voltage (Supplementary Section III). A large phase shift (reduction of 25 rad) is predicted as the voltage increases above 0.5 V, but the accompanying attenuation (increase) is relatively small, only 0.1 dB over the entire length of the 51-ring structure. Similar to the lowest-order cosine-shaped vibrational mode of a clamped string, the band-edge mode of the coupled-resonator chain is defined by the in-phase oscillation of all the resonators (with only p/51 radians of relative phase difference between adjacent resonators), so a change of tens of radians in phase is a very large effect. On the other hand, the steady-state insertion loss, caused by the exponential absorption of light with propagation length in all dielectric materials, is 5 dB in the chain, so the addition of 0.1 dB loss is a minor effect. Thus, carrier injection into electrically active planar resonators is an effective way to introduce significant phase perturbations on localized modes without the large attenuation increases that could impact extended modes (Supplementary Fig. 3). This is in
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contrast to electrically pumped random lasers30–32, which can control the degree of optical gain experienced by a localized mode, but not localization itself. Based on these arguments, carrier injection should be a good ‘switch’ for phase-sensitive phenomena such as Anderson localization, which relies on multiple-scattering interference. In this context, localization is defined as a disorder-confined mode with an exponentially decaying envelope in real (coordinate) space along the length of the waveguide. Confinement in the transverse plane is provided by the index contrast between the core and the cladding of the waveguide cross-section. In the following discussion, we select one localized mode (out of more than 50 that could be measured in a typical device between the wavelengths of 1,530 nm and 1,610 nm) with a particularly ‘clean’ contrast from the bandedge to show unambiguous evidence of electronic switching control over that mode. Other localized modes in several different chips, as well as extended modes at nearby wavelengths, are presented in Supplementary Fig. 4.
Infrared imaging/electronic control of optical localization Wavelength-resolved infrared imaging of band-edge localization in this device is shown in Fig. 3. In a measurement of transmission through the device (Fig. 3a), a resonance was observed just beyond the band-edge, where localization is expected to occur10. By imaging the modes at each wavelength, we obtained a detailed map of the optical modes shown in Fig. 3b. The vertical axes of Fig. 3a,b are aligned, so the transmission peaks can be seen to correspond to spatially extended excitations that span from the first to the last ring. Input coupling effects died out by about the ninth ring. However, the transmission of light through the device was finite, even for a localized mode, because the structure was coupled by
the input and output waveguides to the external ‘bath’ of optical modes. Similar behaviour applies in localized electronic systems33. Figure 3c presents a three-dimensional representation of the localized mode region shown in the inset to Fig. 3b, from which we measured a spatial full-width at half-maximum of about three resonator sites, L* ¼ 3 × 20 mm. The mode spanned a spectral width Dl ¼ 0.02 nm (2.5 GHz), that is, an effective quality factor Qeff of 4 × 104. Because the band-edge state was in the vicinity of KBloch ¼ 0, where KBloch is the Bloch wavenumber, the product (KBloch þ DKBloch) × L* was 1.4 × 1022, that is, well within the range of strong localization of excitations at the band-edge of this resonator chain. Figure 3d shows that the envelope of the localized mode has a slowly decaying exponential background (characteristic of camera-imaged optical propagation in dielectric materials, which also collects light from the background and any substrate-guided weakly diffracting modes), on top of which is superimposed the localized mode envelope. The inset to Fig. 3d shows that the localized mode has an exponentially localized envelope, exp(2|j2j0|) where j is a normalized coordinate enumerating the lattice sites and j0 identifies the centre of the mode. The normalizing constant of j and j0 is 3.1+0.5 unit cells, and the full-width at halfmaximum is 2.6 unit cells (see Supplementary Fig. 3 for the corresponding information from simulations). These measurements confirm the presence of an exponentially localized mode in the microring resonator chain near the band-edge2,8,9. Figure 4a presents an infrared camera image of the central portion of the resonator chain for an extended mode, when all the rings are lit up by the propagating light, with a small ring-to-ring intensity variation that shows the typically small effect that disorder has on mid-band transmission. In contrast, the localized mode is confined to only a few resonators, as shown in Fig. 4b. Figure 4c
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Figure 3 | Spectrally resolved infrared imaging of modes. a, The transmission spectrum shows extended mode resonances within the passband and a localized mode at the band-edge. Transmission through the localized mode is non-zero, because the finite-length structure was coupled to input and output waveguides, which support a continuum of modes33. b, At the wavelengths in a, an infrared camera image (12-bit resolution, that is, values between 0 and 4,095) was recorded of light propagating along the chain of resonators, labelled by ring numbers between 1 (input) and 51 (output). Extended mode resonances span the structure, whereas the band-edge localized mode, shown more clearly in the inset, is confined to a few resonators inside the waveguide. c, The localized mode is seen more clearly in this three-dimensional representation. d, Taking a cross-section through c along the resonance wavelength (1,582.45 nm) shows a gradual exponential decay of light along the direction of propagation (dashed line, mainly due to partial imaging of the slab modes under the guided structure), on top of which is super-imposed the localized envelope. Inset: After subtracting out the slow exponential decay from input to output, the localized mode has an exponentially fitted envelope, with unit cells of width 3.1+0.5.
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Figure 4 | On and off states of the localized mode. a, An infrared camera image of a part of an extended mode, for comparison. The 12-bit camera readout values range from 0 to 4,095. b, Using the same camera settings, the localized mode at 1,582.45 nm was imaged, showing light localization over about three microring resonators. c, When a voltage exceeding 1 V was applied across the p–n junction, the mode was turned off, with the camera image showing residual speckle. b and c were acquired under dynamic conditions, that is, by synchronizing the camera to an on–off voltage pulse train. d, Transmission spectrum versus applied voltage, showing a blueshift (to shorter wavelengths) of the localized mode resonance, as well as a large (factor of 75) attenuation of the peak. (See Supplementary Fig. 5 for a comparison of the effect of voltage on extended and localized modes.). 4
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Figure 5 | Switching waveform of localization. a, While a voltage pulse train (0 V ‘off’, 10 V ‘on’) was applied across the diode, the voltage detected by a photodetector proportional to transmission (T) through the device and the camera-imaged optical mode intensity (IRC) were recorded simultaneously (see Methods). The time axis is shaded yellow when the voltage is ‘on’. The speed of switching is limited to a few tens of hertz by the imaging time of the infrared camera (20 ms per frame) and because several frames were imaged and averaged for each on and off state in order to reliably generate the IRC graph from relatively weak optical images. b, The contrast was quantified by the ratio of transmission for the cases when the voltage was off (localization established) and on (localization de-established), with a value of 1 representing ‘no change’. The contrast was measured versus the applied voltage, and the measured data were fit using a sigmoidal function (shown by the dashed line), demonstrating a slope of 20.3 dB V21 in the range between 1 and 2 V; that is, less than 1 V swing was sufficient to change the optical contrast by a factor of 100.
shows the same region of the resonator chain when electronic carriers are injected into the waveguide using the p–n junction under forward bias (1.5 V): the localized mode is de-established. To understand this switching, recall that an Anderson localized mode is characterized by a phase resonance among the multiply scattering resonators (in this case, the nanoscale roughness within the optical pathway of each racetrack). This phase relationship is strongly perturbed by the injected carriers by up to tens of radians of added phase. This change is completely reversible— turning off the voltage allows carrier drift and recombination away from the junction. Removal of the added phase re-establishes the localized mode at the original wavelength shown in Fig. 4b. The amplitude of the localization resonance is related to the spatial position of the localized mode within the structure, with stronger resonances if the mode is localized near the centre rather than towards one of the two edges14. This range of voltages has a much stronger effect on localized modes than on extended modes, as shown in Supplementary Fig. 5. Figure 4d shows that the injected carriers cause a blueshift of the localized mode resonance, as well as strong attenuation of the peak (by nearly 20 dB, which is significantly greater than the increase in absorption, Da ¼ 20.1 dB, calculated in Fig. 2d). Note that thermal heating would have caused a redshift (to longer wavelengths) of the resonance34. Accordingly, the observed blueshift effects can be dominantly attributed to electronic carriers.
On–off switching of a localized mode While an on–off control voltage pulse train was applied across the p–n junction, the optical transmission light through the device (at the wavelength of the localized mode, 1,582.45 nm) and the infrared camera image were recorded simultaneously. In Fig. 5a, yellow shaded regions indicate the periods when a forward-bias voltage (þ10 V) is applied across the junction and unshaded regions indicate when no voltage is applied (0 V). The upper graph, labelled T (transmission) was proportional to the voltage measured using a photodetector at the output of the chip, with contrast exceeding 20 dB (a factor of 100). Note that, in this device, the control signal and measured readout were both electronic signals and the intermediate localization mode was optical. To confirm that the switching was due to optical localization itself being established and de-established, the lower graph was recorded at the same time using infrared camera images of the localized mode (shown
in Fig. 4b). The image readout along the outline of the microrings was integrated numerically, yielding the quantity IRC (integrated readout of camera) shown in the lower panel of Fig. 5a, demonstrating that the localized mode was turned on and off by the injected electronic carriers. The contrast in IRC is a little bit lower than that of T because of the lower dynamic range and higher noise floor of the infrared camera compared to the photodetector. Figure 5b shows the on–off contrast as a function of the magnitude of the applied voltage. Here, contrast was defined as a ratio between the transmission T in the voltage-on and voltage-off states, with a contrast of 1 indicating no change. Contrast values greater than 1 indicate that the voltage-on transmission was suppressed relative to the voltage-off transmission value. The measured data points are fit well by a sigmoidal function, g(j ) ¼ a þ b/[1 þ exp(2|j|/c)], where a, b and c are fitted constants, using the Levenberg–Marquardt nonlinear least-squares algorithm. Most significant changes were observed when the voltage just exceeded 1 V; for example, the contrast increased by a factor of b/a 2 1 ¼ 106 (20.3 dB) between 1 V and 2 V. This voltage range agrees closely with the voltage range over which the change in optical phase (Df ) and absorption (Da) is most significant, as shown in Fig. 2d, and is in a convenient range for electronic driver circuits. The current through each diode at a forward-bias voltage of 2 V is only 10 mA, that is, representing a total current of 1 mA through the 102 diodes on the chip (see Supplementary Section III), yielding a total power consumption of 2 mW distributed throughout the device of length 1 mm via the electrical wiring network. This power density is vastly smaller than required for all-optical control over localization, for example, nine orders of magnitude smaller than the power levels required for the proposal of alloptical control of localization in photonic crystals12, where because of the fundamentally weak optical nonlinearity, a power density of 5 × 103 W mm21 is required. Note that, in both cases, optical localization over about three to four unit cells of the periodic lattice structure may be achieved. When imaging the weak levels of scattered light collected from the localized mode, the infrared camera requires a fairly long integration time of 20 ms per frame. To generate the data shown in Fig. 5a, several frames were recorded for each stage of the ‘on’ and ‘off’ pulse sequence, so the applied pulse frequency was limited to a few tens of hertz. We stress that the limitation on switching speed here was only because of in situ dynamic imaging and
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real-time image processing (see Methods). Although injectionbased modulators suffer from an intrinsic diode bandwidth of 250 MHz due to minority carrier dynamics, the nonlinear transfer function of microring resonators29 as well as the use of pre-emphasis on the electrical drive waveform35 have allowed the optical modulation bandwidth to exceed 40 times the diode bandwidth, enabling data communication speeds greater than 10 Gb s21. Because the intrinsic bandwidth of the localized mode is more than 2.5 GHz, there is nothing fundamental that prevents electronic control of optical localization at nanosecond speeds. The length of the structure (1.05 mm) is only 3% of the electromagnetic wavelength at 10 GHz, so the electrical contacts can be viewed as a lumped element for the radiofrequency wave. However, some aspects of the device, for example, the long wires from the contact pads to the rings, should be redesigned for lower resistance, and the p–n junctions should surround a greater fraction of the ring circumference so that injected carriers do not diffuse along the racetrack away from the contact regions, thus increasing the carrier-extraction time.
Conclusions In summary, we have demonstrated electronic switching of optical Anderson localization modes, showing carrier injection-based control using p–n junction diodes that infiltrate the optical waveguide structure. The same idea can be applied to other periodically patterned nanophotonic structures, such as photonic crystals8, as well as quasicrystals36 and aperiodic structures such as random lasers. The basic underlying principle is drawn from the large phase change that can be created (with relatively insignificant absorption increase), the degradation-free reversibility of the effect, and the low energy of the control signals, which are attractive features both for physics studies and for the development of device technology using controlled localization.
Methods Device design and fabrication. The devices were fabricated on silicon-on-insulator wafers at the Institute of Microelectronics in Singapore. Two etch steps were used for the rib waveguide cross-section (Fig. 2c). The waveguides, of width 0.55 mm, height 0.22 mm and slab thickness 70 nm, were designed for low-loss (1 dB cm21) transmission in the lowest-order mode of the transverse electric (TE) polarization defined relative to the device plane. Finite-element calculations showed three modes (two TE- and one transverse magnetic (TM)-polarized) that can be guided in straight waveguides, but the TM mode and the high-order TE mode suffer higher bending loss in the microrings and do not propagate in the coupled-microring device25. The slab waveguide regions were doped with boron (33 keV) and phosphorous (90 keV) to an area density of 1 × 1015 cm22 at a distance of 900 nm from the edge of the rib waveguide. A further implantation was performed at lower energy to provide a shallower implant near the contact regions. Implants were activated by a rapid thermal anneal process, followed by additional processing steps to form contact vias and aluminium interconnects. Although 102 diodes were driven in parallel, the metal traces and vias provided enough resistance (172+12 V) to prevent thermal and current runaway (Supplementary Fig. 7). The microring resonators were arranged in a racetrack configuration with a radius of R ¼ 10 mm and directional coupler length Lc ¼ 10 mm. The rings were nominally identical, with apodized waveguide–resonator coupling coefficients formed by varying the inter-waveguide gap in the directional couplers from 210 nm for the first and last couplers to 320 nm in the middle. The propagation loss coefficient is defined as a ¼ awgpReff/|k|, in terms of the propagation loss of a silicon nanophotonic waveguide (awg ≈ 1 dB cm21), the effective bending radius (Reff ¼ R þ lc/p) and the magnitude of the inter-ring coupling coefficient (|k| ≈ 0.4). The measured band-centre propagation loss was 0.1 dB/ring, including slow-light effects. A measurement of the group delay versus wavelength (using a Luna OVA 5000) was used to infer that band-edge propagation loss was a factor of about two greater than at band-centre wavelengths. Experimental set-up. Optical waveforms were generated by a narrow-linewidth single-mode tunable diode laser. The narrow linewidth of the laser (100 kHz) corresponds to a coherence length exceeding all characteristic optical lengths in the device and experimental system. Optical signals were detected using an InGaAs photodetector module. Electrical signals were generated using a function generator and applied to the contact pads on the chip using tungsten probes controlled by micropositioners. The chip was mounted on a temperature-controlled stage, using a thermo-electric controller in feedback to maintain a stable temperature. 6
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Polarization-maintaining fibres, fibre-loop paddles and lensed tapered fibres with antireflection coating were used to couple light to and from the silicon chip, and nanopositioning stages with piezoelectric actuators were used for accurate positioning of the fibre tips to the waveguide facets. The insertion loss of each fibreto-waveguide coupler was estimated as 4.5 dB, averaged over the wavelengths of interest, based on calibration measurements on separate test sites. Infrared imaging. In generating the data shown in Fig. 3, a 320 × 256 pixel cooled infrared InGaAs camera (Xenics XEVA) with 30 mm pitch in the image plane was used with a ×20 microscope objective lens. The camera used 12-bit analog-to-digital conversion for electronic readout, resulting in quantization levels between 0 and 4,095 arbitrary digital units (ADU). A typical 0.25% noise in the 12-bit ADU scale translates, in the logarithmic scale, to 10 dB noise within the 36 dB full range. A typical infrared camera image of light propagating in a silicon photonic chip, with analog-to-digital converter settings that avoid saturation as well as readout noise at the lower levels, resulted in only 20 dB of usable information. In generating spectroscopic imaging data, the wavelength of the tunable laser was scanned in steps of 0.002 nm and a sequence of infrared camera images (320 × 256 pixels) was acquired at each wavelength. A portion of a representative image is shown in Fig. 4a. Corresponding to the imaged field-of-view, a binaryvalued computational image mask of each racetrack was constructed in Matlab, consisting of a two-dimensional array of either 1 or 0 for each entry, with 1 indicating the presence of a ring at the particular coordinate location. The mask for each ring was multiplied, in turn, with the infrared image acquired at a particular wavelength, and the camera readout values along the racetrack perimeter were averaged, yielding a single number that represented the amplitude of the optical excitation of an individual resonator at that wavelength. This spectrally and spatially resolved measurement is shown in Fig. 3b.
Received 19 September 2013; accepted 17 February 2014; published online 30 March 2014
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Acknowledgements The authors thank J.B. Pendry, D. Wiersma, P. Lodahl, C. Lopez, Y. Vlasov and H. Cao for discussions. This work was supported by the US National Science Foundation (grants ECCS 092539, 1028553, 1153716 and 1201308) and the Center for Integrated Access Networks—a National Science Foundation Engineering Research Center. J.R.O. acknowledges support from the Agency for Science, Technology and Research (A*STAR), Singapore. All statements of fact, opinion or conclusions contained herein are those of the authors and should not be construed as representing the official views or policies of the US Government.
Author contributions S.M. conceived the study, coordinated the project and wrote the manuscript with input from all authors. J.R.O. designed the lithographic layout for the devices, which were fabricated by X.L. and L.G.Q. Measurements were performed by S.M. and J.R.O. All authors reviewed the manuscript.
Additional information Supplementary information is available in the online version of the paper. Reprints and permissions information is available online at www.nature.com/reprints. Correspondence and requests for materials should be addressed to S.M.
Competing financial interests The authors declare no competing financial interests.
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