Fabrication

The photonic devices studied in this work were fabricated (see also Methods) on a 200-mm SOI wafer with a 226-nm-thick silicon device slab on top of a 2-m-thick buried oxide (BOX) layer that prevents the optical mode from leaking to the substrate. Photonic wire waveguides^{17, 18, 23, 31, 32, 33, 34, 35, 36} were formed by etching two parallel trenches in the silicon slab down to the BOX layer, as shown in Fig. 1a. The cross-section of such a waveguide was designed to measure 510226 nm, which provides single-mode propagation at telecommunications wavelengths with minimum propagation loss, and simultaneously minimizes the group-velocity dispersion³⁴. In such a high-index-contrast photonic wire, the transverse-electric (TE) optical mode (the electric field in the slab plane) is strongly confined within a cross section of only 0.1 m². This strong confinement results in very small losses in sharp 90° bends with radii of just a few micrometres³², thus opening up the possibility for densely integrated silicon photonic circuits with millimetre-scale footprints.

Figure 1: Scanning electron micrographs of resonantly enhanced optical delay lines based on photonic-wire waveguides.

a, Detailed view of a cleaved coupling section of a bent waveguide bus and a resonator. The photonic-wire waveguide is created by etching two parallel trenches in a Si slab down to the SiO₂ box layer. The waveguide is curved with a bend radius R of 6.5 m. b, Delay line consisting of several ring resonators in an APF configuration in a cascade. Each ring is side-coupled to a common waveguide bus. The gap between the ring resonator and the bus is about 200 nm in the coupling region. c, Delay line composed of several resonators cascaded in a CROW configuration. Each ring is side-coupled to its neighbours with a gap distance of about 200 nm.

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High-index-contrast silicon waveguide ring resonators having extremely small footprints and a high intrinsic quality factor Q have already been demonstrated^{17, 18, 23, 24, 25, 29, 31, 33, 35}. However, as in any resonant system, the enhancement of group delay in a high-Q ring resonator is always associated with a narrowed spectral bandwidth, thus limiting the maximum bit rate of optical signals that can be delayed without distortion. Cascading several ring resonators with relatively low coupling-dominated Q (intrinsic Q should still be high to avoid unwanted losses) is therefore viewed as a winning design strategy for achieving a balance between the footprint, delay and spectral bandwidth. Two complementary designs were chosen for experimental testing, as shown in Fig. 1b and c. The first design is based on a cascade of several identical ring resonators in an APF configuration^{9, 19, 23}, each being side-coupled to a common waveguide bus (Fig. 1b). Although the spectral bandwidth of a cascade is defined by the quality factor of an individual resonator, the total group delay results from a summation of the delays of all individual resonators, because there is no interaction between them. The second design is based on ring resonators side-coupled to each other^{20, 21, 22, 26, 29, 37}, as shown in Fig. 1c. One of the main advantages of such coupled resonator optical waveguides (CROW) (refs.  11 and 38) is a significantly increased spectral bandwidth, because it is defined mainly by the coupling strength between resonators²⁸ (given intrinsic resonator Q and coupling strength identical to the APF design). (See Supplementary Information, section I, for detailed design rules that aim at balancing the footprint, group delay and spectral bandwidth for these two complementary delay lines.) Optical delay lines containing 1, 16, 28, 42, 56 and 100 resonators, in both APF and CROW configurations, were fabricated.

In addition to the group delay, spectral bandwidth and footprint, another metric of utmost importance in a delay line is signal attenuation, or the total insertion loss. There are two major loss mechanisms in bent photonic wires and hence ring resonators: the propagation loss caused by light scattering at rough sidewalls of the waveguide, and bending loss caused by the leakage of the optical mode at the bend. Figure 2a represents the loss spectra of the propagation (black curve, left vertical axis) and bending (red curve, right vertical axis) losses measured separately in photonic wire waveguides with multiple bends of 6.5 m radius (see also Methods). At a wavelength around 1,550 nm, the propagation loss is measured to be as small as 1.7  0.1 dB cm^-1, which compares favourably with the best results published to date^{31, 32, 33, 35}. This is a direct result of significantly reduced sidewall surface roughness due to an optimized fabrication process (see Methods). As measured using top-down atomic force microscopy (AFM), confirmed with sidewall AFM and line-edge roughness analysis of scanning electron microscopy (SEM) images (see Methods), the sidewall surface roughness is found to be as small as  = 1.1 nm, corresponding to just a few monolayers of silicon, and the correlation length is about 60 nm. The bending loss around 1,550 nm is measured to be as small as 0.005  0.0005 dB per 90° bend. Measured propagation and bending losses allow the estimation of a roundtrip loss of 0.03 dB for a single-ring resonator with a bending radius of 6.5 m and total perimeter of 55 m. As the transverse-magnetic (TM) mode suffers from much larger bending and propagation loss close to the cutoff and is stripped off after propagation through just a few bends, the effects of polarization conversion on spectral response in the bends and rings^{36, 39, 40} can be neglected.

Figure 2: Optical characterization of losses in waveguides, bends and cascaded ring resonators in an APF configuration.

a, Propagation loss (black curve, left vertical axis) and bending loss (red curve, right vertical axis) measured in photonic wire waveguides. Spectra are measured with 60-pm resolution as described in the Methods section. b, Experimental transmission spectra of a single ring resonator (black curve) and of 56 cascaded ring resonators (red curve) in an APF configuration. The horizontal axis corresponds to wavelength detuning with respect to a central wavelength around 1,550 nm. Spectra are measured using a tunable laser with 20-pm resolution, as described in the Methods section. Owing to the spread of the resonant wavelengths of individual resonators in a cascade, the resonance of a 56-ring APF delay line appears to be much wider than that of a single resonator. The black arrows depict the 3-dB spectral bandwidth (BW) of the APF delay line. The magenta curve shows the calculated transmission spectrum of an APF delay line consisting of a single resonator, using the resonator parameters as measured in the Supplementary Information (section II). The blue curve is the result of a convolution of a single resonator spectrum with a gaussian distribution of resonant wavelengths with a standard deviation  = 0.4 nm, according to equation (1).

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Delay line based on APF configuration

The black curve in Fig. 2b represents an experimental transmission spectrum of a single-ring resonator in an APF configuration. The on-resonance insertion loss is only about 2.3 dB, thus preventing the accurate extraction of the major optical parameters of a resonator: roundtrip attenuation factor (a), and self-coupling (r) and cross-coupling (t) coefficients²⁵. Instead, additional measurements of transmission spectra were performed on a structure with an identical ring resonator side-coupled to two waveguide buses (see Supplementary Information, section II, for details), permitting accurate extraction of a = 0.996, r = 0.965 and t = 0.269. These parameters completely describe the response of a resonator with a quality factor Q of 14,000 and group delay of 45 ps on resonance. With a free spectral range of about 11 nm, such a quality factor implies a resonator finesse of 100 (ref. 41), which corresponds approximately to 55 roundtrips^{12, 41} that light travels at resonance (light build-up factor¹²). The intrinsic quality factor Q can be estimated from the measured loaded Q and the attenuation factor as 70,000, which is close to the 80,000 estimated from propagation and bending losses.

The red curve in Fig. 2b represents the transmission spectrum of 56 APF resonators. The transmission resonance appears to be much wider than that of a single resonator, with the maximum attenuation reaching 22 dB around zero detuning. This broadening is a result of a spread of individual resonances and, in principle, can be caused by deviation of the coupling⁴², the width of the waveguides²², and the resonators' perimeters. Our estimations have shown that, for our design, a change of gap distance by as much as 5 nm would result in, at most, a 3–5% change in the quality factor and less than 0.03 nm resonance shift, which is less than the bandwidth of an individual resonator (0.11 nm). The broadening is explained therefore by a small variation of the waveguide widths and/or perimeters of the rings.

Assuming that resonance wavelengths of individual resonators are distributed randomly (no interaction between resonators), the spectrum in Fig. 2b can be viewed as just a probability distribution. Then the response of 56 resonators can be simulated by convoluting the transmission spectrum of an individual resonator, T₀() (magenta curve in Fig. 2b), and a gaussian distribution of the resonant wavelengths according to

Fitting of the experimental spectrum (red curve) with equation (1) (blue curve) gives a standard deviation of 0.4 nm. This is a remarkable result, because it corresponds to a standard deviation of the resonant wavelengths of only 0.025% of the central wavelength. This, in turn, corresponds to the same variation of the optical roundtrip path lengths. Correspondingly, either the perimeters of the rings or the widths of the photonic wire waveguides are varied with standard deviations of 12 nm or 0.5 nm (just one monolayer), respectively.

Delay line based on CROW configuration

The red, blue and black curves in Fig. 3a–d represent transmission spectra of three delay lines composed of 28, 42 and 100 cascaded ring resonators in a CROW configuration. In the spectrum of a 28-ring CROW (red line), the transmission intensity varies in the passband within 2–5 dB, forming a nearly periodic sequence of ripples (Fig. 3a). Such Fabry–Perot-type ripples (also shown in the blown-up portion of the spectrum in Fig. 3b) arise owing to the finite-size effect⁴³. The period between the ripples (about 0.08 nm as seen in Fig. 3b) corresponds to a phase shift of 2. Correspondingly, when plotting positions of the maxima and minima of these ripples against their number, the phase shift across the passband (or dispersion diagram) can be restored as shown by the red circles in Fig. 3e. Because the standard deviation of individual resonances,  = 0.4 nm, is significantly less than the total 2-nm bandwidth of the passband, coherent propagation is preserved, as seen from the continuity of a relative phase across the passband. However, frequency mismatch between the resonators results in modulation of the ripple amplitude, which is reminiscent of a Vernier effect⁴⁴. With an increase in the number of rings in the CROW, the ripple modulation becomes larger, sometimes reaching 10–20 dB in the spectrum of the 100-ring CROW (black curve in Fig. 3a). In some locations, in particular close to the passband edges, it exceeds 25–30 dB, indicating light localization in a series of rings. However, ripples can still be seen in 42- and even in 100-ring CROWs, as shown in Fig. 3c and d, with significantly decreased periods of about 0.05 nm and 0.03 nm, that allow extraction of the dispersion diagrams as shown in Fig. 3e (blue and black circles). Dispersion appears to be fairly flat across the whole passband, suggesting a large operational bandwidth of the delay line.

Figure 3: Optical characterization of losses and phase in cascaded ring resonators in a CROW configuration.

a, Transmission spectra of 28 (red curve) and 100 (black curve) cascaded ring resonators in a CROW configuration. Spectra are measured with 2-pm resolution as described in the Methods section. Dotted rectangles in the red and black curves represent parts of the spectra that are blown-up in b and d, respectively. b–d, Blown-up portions of spectra of 28-, 42- and 100-ring CROWs taken close to zero detuning wavelength. The spectra represent periodic ripples, with periodicity of 0.08 nm, 0.05 nm and 0.03 nm, respectively. The scale bars in b–d are as given in c. e, Dispersion diagrams of CROWs with 28 (red circles), 42 (blue circles) and 100 (black circles) cascaded rings extracted from transmission spectra. Relative phase (vertical axis) is measured by counting the maxima and minima of periodic ripples in transmission spectra starting from the shortest wavelength edge of corresponding passbands. The 28- and 42-ring CROWs are composed of rings having 6.5-m radii, gap distances of 200 nm and coupling lengths of 7 m (design identical to the APF configuration). The design of the 100-ring CROW is modified as described in the Supplementary Information (section I), with ring radii of 9 m and coupling distance 8 m. These modifications result in a passband bandwidth almost the same as for the 28- and 42-ring CROWs.

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Pulse Propagation

The red and black curves in Fig. 4a show the time-domain measurements of a 1-Gbps pseudo-random bit stream (PRBS) of optical pulses in a non-return-to-zero (NRZ) format, transmitted through a delay line with 56 cascaded APF rings. When the laser is tuned to a wavelength far from resonance, the light travels along the waveguide bus with negligible interaction with the rings, and the transmitted-pulse waveform (black curve) is therefore mainly delayed by the waveguide bus. The waveform of pulses transmitted on-resonance (red curve) is faithfully reproduced as expected, because the spectral bandwidth of the delay line is much larger than is required to accommodate a 1-Gbps signal. Hence, the time difference between the arrivals of the sharp fronts can be ascribed to the group delay, which exceeds 510  10 ps for pulses tuned on-resonance (red curve). Similar measurements were performed on a complementary delay line composed of 100 cascaded ring resonators in a CROW configuration. The group delay measured near the centre of the transmission band (blue curve in Fig. 4a) is 220 ps, about half the delay of the APF line, as expected (see Supplementary Information, section I). Figure 4a also shows analogous measurements performed on a reference photonic-wire waveguide (green curve) with multiple bends to reduce its footprint. The total length is chosen to be 4 cm, to produce almost the same group delay as in the APF line.

Figure 4: Measured time delay of different types of delay lines at varying bit rates.

a, Group delay measurements using 1-Gbps NRZ optical pulses in different delay lines. The reference trace (black curve) is measured on an APF delay line consisting of 56 cascaded ring resonators with the laser wavelength tuned by 2 nm out of resonance. Off-resonance delay introduced by ring resonators is negligible and is defined mainly by transmission through a 0.45-cm bus waveguide. The red curve shows a time trace measured for the same APF delay line with 56 ring resonators when the laser wavelength is tuned exactly at resonance. An on-resonance group delay of 510  10 ps is observed. The blue curve shows the optical pulse transmitted through a delay line containing 100 resonators in a CROW configuration when the laser wavelength is tuned to the centre of the CROW passband. A group delay of 220  10 ps is measured. The green curve depicts the optical pulse delayed by 500 ps in a delay line based on a bent photonic-wire waveguide with total length 4 cm. The measurements shown in b–d are all performed on an APF delay line composed of 56 resonators in cascade. b, The black curve shows the 3 Gbps NRZ optical bit stream when the laser wavelength is detuned from the resonance by 2 nm. On-resonance (red curve), the bits are delayed with a fractional delay of 1.7 bits with negligible signal distortion. c, Off-resonance (black curve) and on-resonance (red curve) NRZ optical bit stream at 12 Gbps. A fractional delay of 6 bits is measured with noticeable signal distortions. d, Off-resonance (black curve) and on-resonance (red curve) NRZ optical bit stream at 20 Gbps. A fractional delay of 10 bits is measured with significant signal distortions.

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The 510-ps group delay measured in the APF delay line not only significantly exceeds previously demonstrated resonantly enhanced on-chip delays using optical resonators^{9, 27}, but, most importantly, this delay is achieved within a much smaller footprint of only 0.09 mm². The spread of the resonance wavelengths results in a much broader bandwidth of the delay line. To explore the operation of the delay line at higher bit rates, a set of measurements was performed as shown in Fig. 4b–d. At a bit rate of 3 Gbps (Fig. 4b) no significant distortion of the delayed pulses is observed. The buffering capacity of the delay line, expressed as the number of bits contained within the line, exceeds 1.7 bit slots. The buffering capacity expands to 6 bits with an increase of the bit rate to 12 Gbps (see Fig. 4c), although some distortion of the delayed pulses becomes noticeable. The signals further deteriorate at 20 Gbps, as seen in Fig. 4d; however, a delay of 10 individual bits can still be clearly distinguished, implying that the information is transmitted at the group velocity if the bandwidth of the resonant medium permits. This is in contrast with previous demonstrations of slow light delays in resonant atomic media, where the very narrow resonance does not allow effective transmission of information contained in the sharp fronts forming individual bits⁴⁵.

Bit error rate measurements

Various approaches have been proposed to estimate the maximum operational bit rate for a delay line (see also Supplementary Information, section I, refs. 6–8, 46, 47), which gives rise to some uncertainty in comparing performance. In our APF delay line, the 3-dB spectral bandwidth suggests a maximum allowable bit rate of 27 Gbps, which is larger than observed. Because the input optical power was kept low enough (less than -4 dBm) to avoid significant nonlinear effects (such as two-photon absorption and self-phase modulation⁴⁸, as well as four-wave mixing⁴⁹, Raman amplification⁵⁰ and so on), a plausible explanation for the data degradation at high bit rates observed in Fig. 4 is the effect of large group delay dispersion (GDD). The maximum group delay ripple within 0.1 nm around zero detuning was measured to be about 65 ps, which gives a GDD of roughly 650 ps nm^-1, resulting in another estimate⁴⁶ of the highest bit rate of 15 Gbps.

For practical applications, however, the quality of the buffered information has to be quantified by the bit error rate (BER). The BER of the delayed 20-Gbps data stream can be estimated directly from the pulse traces in Fig. 4d. The signal Q-parameter (ref. 47) is estimated to be 2.2, which corresponds approximately to a BER of 10^-2, implying one error per 100 received bits, or 90% chance of error-free buffering of all 10 bits in the APF delay line. More accurate measurements of the BER (described in detail in the Methods) of the APF delay line at 510-ps group delay are shown in Fig. 5a (blue dots). The BER degrades to 10^-4 at 10 Gbps, but improves significantly at lower bit rates with an almost 'open eye' diagram at 8 Gbps (panel c). The rigorous definition of the maximum operational bit rate is then based on a requirement of the maximum allowable BER for a given application. Selecting a BER threshold of 10^-9 (as is typical for telecommunications applications), the APF delay line presented here operates error-free up to 5 Gbps.

Figure 5: BER and eye diagram measurements.

a, Bit error rate measured for different delay lines (see Methods) while the optical power at the receiver is maintained at -7 dBm. Red and blue dots correspond to BER measurements performed for a CROW delay line with 100 cascaded ring resonators and an APF delay line with 56 cascaded rings, respectively, when the laser wavelength is tuned to maximum group delay. The magenta dots show the BER measured for a 4-cm bent photonic-wire waveguide delay line. b–d, 8-Gbps NRZ eye diagrams measured for 2³¹-1 PRBS (see Methods) when the laser wavelength is tuned to maximum group delays: Eye diagram for the 100-resonator CROW configuration at 220-ps delay (b); eye diagram for the 56-resonator APF configuration at 510-ps delay (c); eye diagram for the 4-cm bent photonic wire waveguide at 500-ps delay (d). Scale bars for b–d are as shown in d.

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According to the same criterion, the maximum bit rate for error-free operation of the CROW delay line composed of 100 resonators (red dots in Fig. 5a) is measured as 4 Gbps. The BER degrades much faster than that of the APF with the eye diagram almost closed at 8 Gbps (panel b). Such fast BER degradation results from both GDD-induced phase distortions and amplitude distortions. Indeed, a GDD as large as 10,000 ps nm^-1 is expected from the fast periodic group delay ripples^{28, 29, 43} that accompany amplitude ripples in the transmission spectrum with a period of only 0.03 nm (see Supplementary Information, section I). Large modulation of the transmission spectrum in Fig. 3a induced by the Vernier effect also adds significantly to the BER degradation owing to amplitude distortion of the data stream. If, in principle, the group delay ripples can be minimized by apodization of cross-coupling coefficients for just a few of the first rings in CROW (refs. 21, 37 and 43), more precise control of individual resonators is needed to achieve better alignment of resonances and to avoid the Vernier effect.

Fabrication of photonic delay lines based on photonic wires

All the photonic devices mentioned in this work were fabricated on 10   cm p-type SOI 200-mm wafers from SOITEC with 2-m BOX layer and a thin silicon layer of thickness d = 226 nm on a standard CMOS fabrication line, as described elsewhere¹⁰. Compared to previous demonstrations³², double thermal oxidation steps were used to reduce the sidewall roughness of the photonic-wire waveguides. First, about 10 nm of silicon was dry-oxidized to produce approximately 20 nm of thermal oxide on the photonic wire sidewalls. This was followed by removal of sidewall oxide using a short buffered oxide etch. The wafer was then cleaned and another 10 nm of silicon was oxidized. The oxide formed in the second oxidation step was kept permanently.

Measurements of waveguide sidewall roughness

The surface roughness on the sidewall of the photonic-wire waveguide was characterized using three different methods that gave complementary information. The first and most reliable method is conventional top-down AFM. In this case, the wafer was cleaved along the waveguide longitudinal direction and turned by 90° along the longitudinal axis so that the sidewall of the waveguide was on the horizontal plane. The sidewall surface roughness was measured on several areas of approximately 200 nm  200 nm. Standard deviation as small as  = 1.1 nm and a correlation length of about 60 nm were measured. However, the accuracy of the correlation length measurements was limited by the relatively small scanning area.

High resolution top-down SEM images were used to analyse the line-edge roughness (LER) over longer distances and verify the top-down AFM data. Although the limited SEM resolution did not permit accurate measurements of roughness below 5 nm, the correlation length was found to lie within the range 60–100 nm, in agreement with the AFM measurements. Analysis of the SEM images and the LER data also revealed rare occurrence of larger features with maximum profile extension of approximately 15 nm. The spatial distances corresponding to these large features were estimated with a third method capable of scanning the waveguide sidewalls directly to produce three-dimensional topography data (Dimension X3D AFM scanner, Veeco). Although the resolution is lower than that of a top-down AFM, sidewall scans over longer distances confirmed the presence of similar large features spatially separated by distances exceeding 500 nm.

Measurements of transmission spectra and insertion losses

TE-polarized (electric field in the silicon slab plane) transmission spectra of the delay lines were measured using a tunable diode laser (New Focus, Velocity 6328H and 6330), using 2–20 pm resolution, with a wavelength tuning range between 1,519 and 1,631 nm. The polarized light is first coupled to a polarization-maintaining (PM) fibre. Coupling to and from the photonic chip is realized through microlensed and tapered PM fibres aligned with the input–output on-chip inverted taper couplers³² using xyz piezo-translational stages. The coupling loss from a lensed fibre to a silicon photonic-wire waveguide is less than 1 dB (ref. 32). The total fibre-to-fibre loss (or insertion loss) in a reference structure with a 4.5-mm straight silicon photonic-wire waveguide with inverted taper couplers at both ends is below 3 dB. In all the transmission spectra shown in Figs. 2 and  3, transmission is normalized to the insertion loss of a 4.5-mm straight waveguide structure.

The propagation loss of the photonic wires was determined by comparing the transmission spectra of photonic wires of length 1.5 cm and 5.1 cm, folded in a serpentine manner, with identical numbers of 10-m bends. The 90° bending loss of bends with 6.5 m radius was obtained separately by comparing the transmission spectra of two photonic wires with the same total optical length but containing 40 and 280 bends, respectively. For loss measurements, the broadband LED light source Agilent 83437A was used, and transmission spectra were recorded with 60-pm resolution using an Agilent 86140B optical spectrum analyser.

Measurements of time delays

To measure the time delay in the optical delay line, the incoming light signal was provided by a JDSU tunable laser modulator (TLM) with a 3-dB modulation bandwidth of 15 GHz. A pulse pattern generator (Anritsu MP1763C for up to 12 Gbps bit rates and SHF BPG44 for 20 Gbps) was used to provide the modulation signal to the TLM. The output delayed optical signals were first amplified by a JDSU OA400 erbium-doped fibre amplifier (EDFA) with a small signal gain of 27 dB, filtered with a series of tunable optical filters with a 3-dB bandwidth of 1.1 nm and detected by the Agilent Infinium DCA 86100A wide-bandwidth oscilloscope with a 65 GHz optical plug-in. The delay time for a given device were measured by comparing two traces taken with the TLM source wavelength tuned to the resonance and out of resonance.

Measurements of BERs

A 2³¹-1 PRBS was generated by the Anritsu pulse pattern generator MP1763C to modulate the JDSU TLM modulator unit. Instead of detecting the optical signals in the time domain using an Agilent oscilloscope, the delayed, amplified and filtered optical signals were coupled into a 10-Gbps optical receiver with a sensitivity of -15 dBm. The electrical signals generated were detected by an Anritsu bit-error-detector MP1764A.

In general, BER strongly depends on the output optical power. The output optical power of the APF delay line with 56 resonators after light was delayed by 510 ps was -34 dBm, limited by the maximum input power possible before the onset of significant nonlinear effects. To make a fair comparison of BER dependence on a bit rate for various optical delay lines, the delayed optical signal power was always kept at -34 dBm using an optical attenuator in the detection circuit. With the EDFA gain kept constant, the power at the receiver was maintained identical at -7 dBm for all delay lines measured.