1. Introduction

The synchronization, buffering and storage of wideband data stream in the optical domain are going to become mandatory tasks in optical networks, in order to remove the bottleneck of electronic processing speed and avoid the cost of electrooptical format conversion. To this aim, optical devices capable of introducing arbitrarily large delays are required1. However, in telecom applications, large delays are of interest only if associated with large bandwidth, low loss and low signal distortion, and if the delay can be tuned finely, continuously and easily with flexible devices. Furthermore, the miniaturization down to chip-scale and the integration with other functionalities undoubtedly represent valuable parameters.

The realization of optical delay lines is intrinsically related to the possibility of dynamically controlling, slowing down and ultimately stopping optical pulse propagation. Handling light speed has always represented a classical topic in optics and many different phenomena exhibiting slow-light are known now. The smallest group velocities ever observed were obtained by exploiting electronic resonances in atomic media^2,3, yet requiring impractical low temperatures and exhibiting too narrow spectral bandwidths for high capacity optical links. Vibrational transitions associated to Stimulated Brillouin Scattering (SBS) in glass fibres⁴ have been recently demonstrated to originate slow-light over tens of GHz bandwidth, but with fractional delay below 0.3 bit⁵ and with the need for several km of optical fiber. More recently, tunable delays of several tens of pulses in the GHz range were demonstrated by using double absorption resonance in hot cesium vapor⁶. Even though this result represents the state-of-the-art performance with respect to the bandwidth-delay products, the size of the vapor cell (tens of cm long) and the slow-light mechanism itself are still far from enabling the integration with other optical functions on a common technological platform.

If integration, design flexibility and footprint size have to be taken into account, the exploitation of artificial resonances of optical resonators is expected to outperform slow-light media⁷. The idea underlying coupled resonator Slow-Wave Structures (SWSs)⁸ is forcing lightwave to retrace its path, so that it can be trapped inside optical resonators for as much time as the quality factor (or the finesse) of the resonators is high. From a theoretical point of view, different typologies of resonators can be equivalently used as building blocks for SWSs such as Fabry-Perot cavities^9,10, coupled-ring resonators^11,12 or coupled defect modes in photonic crystals¹³, the main differences only arising from technological issues. State-of-the art devices have been demonstrated by cascading more than ten ring resonators structured as Coupled Resonator Optical Waveguides (CROW) and made of glass¹⁴ and polymer waveguides¹⁵. Optical delay lines including up to 100 microring resonators cascaded in either coupled-resonator or all-pass filter (APF) configurations were recently realized also in silicon-on-insulator (SOI) photonic wire waveguides¹⁶, showing a fractional group delay exceeding 10 bits at 20 Gb/s rate in a device with a footprint below 0.09 mm².

In this contribution, we propose a novel coupled resonator architecture for the realization of tunable Slow-Wave Delay Lines (SWDLs). The structure includes a ring resonator SWS, operating in reflective configuration, which is used to introduce a discrete (digital) delay, the time step being provided by the double-transit across the elementary ring of the structure. The SWS is followed by a ring-resonator phase-shifter that adds a fine continuous (analog), contribution to the overall delay. The spectral and time domain characterization of preliminary devices, fabricated in silicon oxynitride (SiON) technology, is reported, demonstrating a continuously tunable delay from zero to 800 ps on a 2.5 Gbit/s NRZ signal, corresponding to a fractional delay of 2 bits. Before the concluding section, an accurate comparison between the presented results and the state-of-the-art integrated devices is presented.

2 Coupled resonator slow-wave delay lines

The architecture of the proposed reconfigurable SWDL is shown in Fig. 1. It comprises two cascaded all-pass structures, namely S ₁ and S ₂, coupled with the same bus waveguide. The structure S ₁ is a SWS made of N directly coupled ring-resonators, while the structure S ₂ simply consists of a single ring-resonator phase-shifter. All the rings of the two structures are assumed with the same geometrical length L_r. As explained in the following, the SWDL can be used to introduce a continuously tunable and frequency dependent time delay by controlling the individual resonances of the ring resonators.

Starting from the structure S ₁, an optical signal, incoming from the In port, can propagate along the chain of resonators only if its spectrum is entirely contained within the passing band B=2FSRsin^-1(t₁)/π of the structure⁸, FSR being the rings’ Free Spectral Range and t₁ the field coupling coefficient between two adjacent resonators. If the signal spectrum lies outside B, the signal is directly transferred to the output port without entering S₁ and without any significant delay. When inside the SWS, pulse propagation is slowed down by the factor⁸ $S=\cos (k{L}_r⁄2)⁄\sqrt{t_1^2-{\sin }^2(k{L}_r⁄2)}$, k being the propagation constant in the ring’s waveguide. With the aim to explain the working principle of the structure, let us assume that the first M rings have been set to the same resonant frequency f₀ (M=4 in Fig. 1). The optical signal can propagate along the ring chain only up to the M-th ring, because all the M+n-th (n≥1) offresonance rings act as mirrors. Once arrived at the M-th ring, the signal is reflected backward to the input/output bus waveguide. The delay experienced by the signal is roughly T_d=2M/πB, where T_r=2/πB is the group delay given by the double transit through every elementary resonator of the folded structure. The number of rings resonating at f ₀, and hence the overall delay, can be arbitrarily selected by controlling the round-trip phase-shift of the rings of S₁. Depending on the waveguide technology, this can be conveniently obtained by a thermo-optic, electro-optic or even all-optic control. By selecting M, a discrete, or digital, tunable delay between zero and T_d,max=NT_r=2 N/πB and with a minimum time-step equal to T_r can be achieved. Note that the folded layout enables an easy and complete reconfiguration of the S₁ structure as well as the reduction of the overall dimensions by a factor 2. A remarkable advantage of the proposed structure is that, whatever the desired delay is, the optical signal always propagates at the centre of the SWS bandwidth, where the effects of either dispersion^8,17 or disorder¹⁸ have been demonstrated to be minimum.

 

Fig. 1. Scheme of a continuously tunable SWDL, the coupled resonator SWS S₁ providing a ‘digital’ tunable delay and the all-pass ring S₂ giving an additional ‘analog’ tunable delay.

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The phase-shifter S₂ is cascaded to the coupled resonator SWS S₁ in order to add a continuously variable analog delay. The S₂ delay is selected by simply detuning its resonant frequency with respect to the signal carrier frequency. In this way, it is possible to make the optical signal experience any delay between T_2,max=(1+r₂)/(1-r₂)/FSR at the resonance and T_2,min=(1-r₂)/(1+r₂)/FSR at the anti-resonance frequency, where r₂ is the through port field coupling coefficient of the ring S₂. Straightforwardly, the condition to guarantee a continuously variable delay by the combination of the two cascaded structures S₁ an S₂ is T_2,max-T_2,min>T_r.

3. Experimental results

The reconfigurable SWDL of Fig. 1 was fabricated in integrated optical technology by using high index contrast silicon oxynitride (SiON) waveguides¹⁹. The cross sectional SEM picture of the optical channel waveguide is shown in Fig. 2(a). The waveguide has a square cross section with 2.2 µm×2.2 µm PECVD SiON core with refractive index n _SION=1.513, deposited on a thermal silicon dioxide substrate (n _Si02=1.4456) and covered by BPSG glass (n _BPSG=1.45) as upper-cladding material. By means of cut back measurements, propagation losses of α=0.35 dB/cm at 1550nm were measured for the SWDL waveguide. Lower losses, down to 0.15 dB/cm, have been recently reached on subsequent fabrications by reducing sidewall roughness and improving the thermal annealing process. Fiber to waveguide coupling losses of 0.2 dB per facet can be achieved by using small core fiber with 3.6 µm mode field diameter. The 4.4% index contrast guarantees a minimum bending radius of 500 µm with negligible radiation losses, enabling the realization of ring resonators with a FSR of 100 GHz. Note that, from the point of view of the SWDL performance, the FSR limitation only concerns the minimum achievable device footprint and does not affect neither the group delay per ring T_r (only depending on the SWS bandwidth) nor the insertion loss per ring, of about 2cα/πBn_g, with n_g the waveguide group effective index.

 

Fig. 2. Photograph of (a) the SiON waveguide cross section and (b) the first rings of a SWDL realized with directly coupled ring resonators. The diameter of the rings is approximately 1.24 mm, corresponding to FSR=50 GHz.

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Fig. 3. (solid line) experimental and (dashed line) simulated (a) spectral intensity and (b) group delay characteristic of a SWDL with M=2 (blue), 3 (black) and 4 (red) tuned rings. The group delay, normalized to 2.5 Gbit/s NRZ pulse width (400 ps), is referred to as fractional delay.

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Figure 2(b) is a photograph of the initial section of the SiON SWDL. The input waveguide is on the top left and the output port on the bottom right of the photograph. All the rings have the same nominal resonance. The different shape of the first rings is a consequence of the apodization of the coupling coefficients of the directional couplers, which is required to achieve the impedance matching condition between the SWS and the bus waveguide. By this strategy, a flat intensity spectral response as well as a ripple free group delay characteristic can be obtained²⁰. Chromium resistors, acting as thermo-heaters, were deposited on the top of the waveguides to finely control the resonance of every ring by thermo-optic effect. Every resistor is 2 mm long, 9 µm wide, 200 nm thick, giving a measured resistance of about 600 Ω (+/- 10 Ω). The gold electric pads are clearly visible in the middle of the rings. The delay line can be reconfigured simply by changing the voltage applied to the heaters at the typical velocity of thermo-controllers, that has been demonstrated to be well below 1 ms²¹.

Figure 3 discloses in solid lines both the measured spectral intensity (a) and the group delay (b) of the SWDL of Fig. 2(b), for an increasing number of tuned resonators (M=2, 3, 4). With reference to Fig. 1, these measurements give the transmission from the In to the Out port, when only the S₁ section is concerned. The delay line has a useful bandwidth larger than 2.5 GHz over a FSR=50 GHz, corresponding to a finesse 16 and a slowing ratio S=10. The SWDL spectral response of Fig. 3(a) is normalized to the insertion loss of the 2-cm-long bus waveguide, amounting to about 1.2 dB, where 0.25 dB/facet is the contribution of the fiber-to-waveguide coupling loss and 0.7 dB is the bus propagation loss. The transmission spectra of a lossless SWDL would be unitary at any wavelength and for any number of resonators. Under the effect of losses, dips in the spectrum of Fig. 3(a) appear. The insertion loss increases with the number M of tuned resonators, that is with the increasing effective length, or delay, of the SWDL. Higher attenuation is observed at the band-edges, where the group delay of coupled-resonator structures exhibits sharp peaks, which are as much pronounced as the number of resonator increases²². A good agreement between experimental data and the simulations of the nominal structure (dashed lines) was found. The agreement gets worse in the neighbourhood of the band edges, where the delay peaks are expected to be very sensitive to any inaccuracies or disorder, like tolerances on rings coupling coefficients and frequency detuning¹⁸.

The group delay of Fig. 3(b) is normalized to the 400 ps temporal width of a NRZ 2.5 Gbit/s pulse. The reference zero-delay is attributed to the minimum delay of the SWDL, achieved when all the resonators are tuned off-resonance. When four resonators are tuned at the carrier frequency f0 of the input signal (red line in Fig. 3), the folded SWS induces a delay equal to 2 bit lengths (T_d=800 ps), corresponding to an effective geometrical length of about 15.6 cm., with an insertion loss lower than 8 dB. From the measured insertion loss, a ring round-trip loss of 0.2 dB/turn was inferred, where 0.15 dB/turn is the waveguide propagation loss contribution and 0.05 dB is due to excess loss of directional couplers and radiation loss in the ring’s bend. By increasing the number M of tuned rings, both the delay and the insertion loss increase but the intensity spectral shape remains roughly the same obtained with four rings.

Thermal measurements showed that, to shift the rings resonances, the power required by every thermo-heater is about 12 mW/GHz, corresponding to 1.45 °C/GHz for a 2-mm long heater. Despite of the presence of a Peltier thermo-cooler placed below the chip, a small thermal crosstalk was observed during the reconfiguration of the structure. However, thanks to the quite high finesse of the resonators, a small temperature variation (<4 °C to induce a frequency shift of 2.5 GHz) is sufficient to drive resonators outside the SWS passing band, thus limiting the effects of the thermal cross-talk.

Time domain measurements were carried out to evaluate the time delay and the envelope distortion given by the SWDL. To this aim, a SWS with bandwidth B=6.25 GHz (FSR=50 GHz) was used to entirely accommodate the spectrum of a 2.5 Gbit/s NRZ data stream. The structure has finesse F=8 and provides a slowing ratio S=6. Figure 4 shows in the right column the measured eye diagrams at the output of the SWDL for the case M=0 (a), M=1 (b), M=2 (c) and M=3 (d). In the left column, the results of numerical simulations are reported, where the input signal (blue line) is described by a supergaussian envelope of order 5. The simulated output pulses (red line) of Fig. 4(a)–4(d) are in very nice agreement with the experimental data with respect to both the delay and the distortion experienced by the pulse. As predicted by the theory, each additional resonator provides a delay T_r=2/πB≈100 ps. Despite of the distortion of the leading and trailing pulse edges, which increases with the length M of the SWDL, the measured eye remains well open, with a small intersymbol interference and only slightly attenuated (less than 3 dB for 300 ps delay). These distortions are mainly due to the peaks of group delay and attenuation at the band edges of the SWDL and are expected to disappear if a smoother input pulse is used, for instance by filtering the electric signal sent to the electro-optical modulator. The best way to finely tune the various rings to the correct position is in the time domain by maximizing the eye opening rather than impose a flat intensity spectral response. In this way also the group delay characteristic is optimized and the pulse shape preserved.

As discussed in Sec. 2, the continuous delay is achieved with the addition of a single resonator phase shifter, named S₂ in Fig. 1, cascaded to the coupled resonator SWS S₁. As shown in Fig. 5(a), a resonator with FSR=50 GHz and field coupling coefficient r₂=0.65 can introduce a delay comprised between T_2,max=94 ps at resonance (no frequency detuning) and T_2,min=4 ps at anti-resonance frequencies (FSR/2 frequency detuning). The 90 ps range of tunability almost covers the 100 ps time step of the digital SWDL described in Fig. 4. Figure 5(b) shows the eye pattern of a 2.5 Gbit/s NRZ signal propagating through the resonator whose spectral group delay is reported in Fig. 5(a). Three frequency detunings of the ring’s resonant frequency with respect to the signal carrier are reported, 3.5 GHz (b₁), 2 GHz (b₂) and 0 (b₃), introducing 50 ps, 69 ps and 90 ps delay, respectively. For more than 4 GHz frequency detuning, the pulse experiences less than 50 ps delay with no envelope distortion, because of the smoothness of the ring’s frequency response far from resonance. In the linear part of the group delay characteristic, the slope of the delay versus frequency is around 10 ps/GHz. Therefore, in order to achieve 1 ps resolution in the delay tunability, the resonator temperature must be controlled with an accuracy of ΔT _1ps=n_gΔf/K_Thf≈0.1 °C, where n_g=1.534 and K_th=1.04e-5 are the measured SiON waveguide effective group index and thermooptic coefficient, respectively. Note that this temperature accuracy is typically guaranteed by the state-of-the-art thermo-heaters, thus enabling both the stability and the fine adjustment of the delay. As shown by Fig. 5(b₃), the envelope distortion is maximum at the resonance, where a small oscillation in the leading edge of the pulse and a sharp overshoot in the trailing edge appear. These effects are the consequence of the third order dispersion, which is the dominant dispersion contribution at ring’s resonance. Nonetheless, the eye diagram aperture remains practically unaffected. Figures 5(b₁) and 5(b₂) show also that the second order dispersion, arising where the group delay slope versus frequency is different from zero, carries negligible pulse envelope distortion.

 

Fig. 4. Simulated pulse propagation (left column) and experimental eye pattern (right column) of a 2.5 Gbit/s NRZ optical signal delayed by a SWDL for an increasing number of rings tuned to resonance: M=0 (a), M=1 (b), M=2 (c) and M=3 (d). A total delay of 300 ps is induced without significant pulse distortion.

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Fig. 5. (a) Theoretical group delay of a ring resonator phase-shifter with FSR=50 GHz and r₂=0.65; (b) Experimental eye pattern of a 2.5 Gbit/s NRZ optical signal delayed by the resonator shown in (a) for three different detuning of the ring’s resonant frequency with respect to the signal carrier: 3.5 GHz (b₁), 2 GHz (b₂) and 0 (b₃).

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4. Discussion

It is interesting to compare the performance of the proposed reconfigurable SWDL with the state-of-the-art architectures based on integrated ring-resonators and employed as optical buffers or delay lines. The main properties of the devices under investigation are summarized in Tab. 1. In Ref. [15], a CROW with 12 coupled ring resonators realized in polymethyl methacrylate (PMMA) was presented, showing a maximum delay of 110 ps over a bandwidth of 17 GHz. In Ref. [16] optical delay lines based on silicon wire waveguides in either CROW or APF configurations were reported. The figures of merit reported here refer to the APF configuration only, enabling more than 500 ps delay with 56 resonators and significantly outperforming the SOI CROW architecture.

Three figures of merit can be defined to compare the proposed structures:

- the ratio T_d/IL [ns/dB] between the delay and the insertion loss;

- the ratio T_d/A [ns/mm²] between the delay and the device footprint;

- the ratio T_d/T_b N between the delay and the bit time duration, normalized to the number N of resonators (normalized fractional delay).

As shown in Tab. 1, SOI APFs largely show the best footprint parameter (5.6 ns/mm², more than 30 times higher than the SiON SWDL one), thanks to the ultra tight waveguide bending enabled by silicon photonic wires. Note that the footprint parameter scales up with the waveguide index contrast (around 140 % in SOI waveguides, 11 % in PMMA waveguides and 4.4% SiON waveguides); therefore, it is mainly dependent on the employed technology rather than on the circuit design.

If losses are concerned, the best result is achieved by SiON SWDL, where T_d/IL=0.1 ns/dB, more than 4 times higher than the SOI APS one. The poor value of the PMMA CROW (<0.003 ns/dB) is due to the extremely high loss of the waveguide (>17 dB/cm) mainly arising from sidewall roughness. It is worthwhile to point out here that, for any structure (not necessarily involving slow light), the theoretical upper limit for the delay to insertion loss ratio is fixed by (T_d/IL)_max=ng/cα. Therefore, it only depends on the ratio between the waveguide group index and the waveguide propagation loss. For the SiON waveguide discussed in this work, this condition gives 0.146 ns/dB, very close to measured value 0.1 ns/dB. As mentioned in Sec. 3, the discrepancy is probably due to the additional loss carried by ring-to-ring couplers and waveguide bending. In recent fabrications, propagation losses have been reduced down to 0.15 dB/cm, so that a delay-loss ratio higher than 0.2 ns/dB (reported in brackets in Tab. 1) is expected to be reached in future SWDLs. From the point of view of pulse attenuation, it corresponds to an attenuation per bit delay equal to 2 dB/bit in a 2.5 Gbit/s system, or even better 0.5 dB/bit in a 10 Gbit/s system. It is easy to verify that SOI structures can reach the same performance only if losses are reduced below 0.6 dB/cm, three times less than the state-of-the art value of 1.7 dB/cm [16].

It should be noted that, although the finesse of the resonators used in the APF structure [16] (F=100) is much higher than those of the SiON SWDL (F=16), the effective slowing ratio S is almost the same. The reason is that, in the APF case, the overall transmission resonance is much wider than that of the single resonator, this broadening resulting from a spread of individual resonances caused by imperfections in the width of the waveguides and the resonators’ lengths. The high slowing factor of the PMMA CROW demonstrates that, even in the absence of an active control of the waveguide refractive index, the rings resonances are very close to their nominal value.

Furthermore, SiON SWDLs show also a much higher normalized fractional delay T_d/T_bN with respect to SOI APFs, this figure of merit giving the amount of delay carried by every resonator of the structure. In the case of the PMMA CROW this parameter is not available, since time domain measurements were not reported. The better result of the SiON SWDL is strictly related to the double transit inside the structure, whose reflective configuration doubles the contribution of every rings to the overall delay.

The reflective architecture enables also an easy and complete reconfiguration of the proposed SWDL. From this point of view, it is worthwhile to stress that full reconfiguration and continuously variable delays have not been demonstrated so far in neither APF nor CROW, both operating in transmission configuration.

Table 1. Figure of merits of state-of -the art slow-wave delay lines

View Table

A final consideration concerns the maximum length of the proposed SWDLs. As well known, apart from propagation loss, the maximum achievable delay T _d,max, setting also the maximum number of storable pulses (i.e. bits) D_max, is limited by the SWDL chromatic dispersion¹⁷. For a pulse with bandwidth B_p propagating at resonance, no more than N=6.7(B/B_p)³ resonators can be cascaded to avoid unacceptable distortions²². Since the number of cavities covered by a gaussian pulse is approximately N_1b=π(B/B_p), the maximum number of storable bits in the SWDL is D_max=2.1(B/B_s)². Note that 1/N_1b, representing the storage efficiency of the SWDL, is directly related to the normalized fractional delay T_d/T_b N and increases when the bandwidth of the structure approaches the pulse bandwidth. For the folded structure of Fig. 4, where B=6.25 GHz, up to 13 bits with B _p=2.5 GHz could be accommodated in 52 resonators, corresponding to an overall delay of more than 5 ns. While loss limitations mainly depend on the waveguide characteristics (α and n_g), dispersion limitations mainly depend on the circuit properties and can be reduced by dispersion compensating architectures²³.

5. Conclusion

In conclusion, a simple and flexible scheme for the realization of fully tunable integrated optical delay lines based on slow-wave propagation has been proposed. Experimental results, in both the spectral and time domain, have been presented, demonstrating the feasibility of the structure in 4.4% index contrast SiON technology. A continuously variable delay from almost zero to 800 ps over a bandwidth of more than 2.5 GHz was achieved, corresponding to a fractional delay of 2 bits in a 2.5Gbit/s data stream. Both loss and bandwidth performance is expected to be improved in next fabrications, down to 0.5 dB per bit delay and up to 10Gbit/s modulation speed. A comparative analysis with the state-of-the-art devices shows that, to date, the proposed SiON SWDL shows the best figures of merit. This result derives from both the simpler and mature technological process, providing very low waveguide attenuation, and from the original reflective architecture, enabling an easy and complete tuneability. Clearly, the SiON technology can not compete with the ultra high confinement achievable by using SOI waveguides. However, as far as the required integration scale does not force the use of semiconductor platforms, a medium index contrast glass platform, such as SiON, could represent the best trade-off between compactness and optical performance.