The realization of an integrated delay line using tapered Bragg gratings in a drop-filter configuration is presented. The device is fabricated on silicon-on-insulator (SOI) rib waveguides using a Deep-UV 248 nm lithography. The continuous delay tunability is achieved using the thermo-optical effect, showing experimentally that a tuning range of 450 ps can be obtained with a tuning coefficient of −51 ps/°C. Furthermore the system performance is considered, showing that an operation at a bit rate of 25 Gbit/s can be achieved, and could be extended to 80 Gbit/s with the addition of a proper dispersion compensation.
©2012 Optical Society of America
Optical delay lines constitute an important component for several applications in optical signal processing. In the field of optical communications they are required for bit synchronization for multiplexing and interleaving , equalization and dispersion compensation  and data buffering in optical switches . Other possible applications concern the optical beam forming in phased-array antennas  or optical coherence tomography . In all cases a continuous tunability is required, together with a wide bandwidth and a large tunability range. Furthermore an amplitude and phase preservation of the signal is highly desirable to avoid distortion.
Different approaches for the implementation of optical tunable delay lines were proposed, mostly based on fiber Bragg gratings [6,7]. However the realization of integrated devices on silicon is an important step for the realization of more complex integrated systems for fast optical signal processing. Integrated delay lines have been realized making use of all-pass filters (APF)  or coupled resonator optical waveguides (CROW) [9,10], both based on ring resonators. Slow light effects in photonic crystal waveguides were used as well for the aim [10–12]. Delays larger than 100 ps could be achieved, however with relatively high losses and limited bandwidth, limiting the potential application field. Recently integrated delay lines based on Bragg gratings on rib waveguides have been proposed , with combination of a p-i-n junction to perform the tuning via free-carrier plasma effect. This solution would provide a high tuning range with much lower losses, however not yet experimentally proved.
In this paper we demonstrate the realization of optical delay lines based on tapered Bragg gratings in a drop filter configuration, which allows in-line operation without the necessity of an external circulator to out-couple the delayed signal. The tuning is obtained exploiting the thermo-optical effect in silicon.
In a chirped Bragg grating different wavelengths are reflected at different positions along the grating length, with a consequent delay difference between them. The wavelength reflected at the end of the grating will exhibit a delay difference of Δτ = 2nLg/c with respect to the wavelength reflected at the beginning of the grating, where Lg is the overall grating length, n the waveguides effective index and c the speed of light in vacuum.
Considering the wavelength of the input signal fixed and within the reflection bandwidth of the grating, the added delay is then τ = 2nz1/c, where z1 is the position where the reflection takes place. If the grating is properly uniformly perturbated in a way to slightly shift the reflection bandwidth, the unchanged wavelength of the input signal will be reflected at a different position z2, corresponding to a different added delay. With the perturbation a delay difference of Δτ = 2n(z1 – z2)/c is achieved.
It was shown that the thermo-optical effect produces a shift of 80 pm/°C of the reflection bandwidth of a Bragg grating [14,15]. Our idea is therefore to heat the Bragg grating uniformly and hence vary the position where the signal is reflected within the grating and consequently the added delay.
To implement the chirp in silicon rib waveguides a waveguide tapering was proposed [16,17], linearly varying the rib width along the grating (see Fig. 1(a) ). A linear variation of the effective index and hence of the reflected wavelength is produced. This solution is more robust than varying the grating period [15,17]. To out-couple the reflected signal without an optical circulator, whose integration is not trivial, we inserted the tapered grating in the drop-filter structure described in  (see Fig. 2(b) ). It allows to separate the delayed signal and forward it to a separate output waveguide. Furthermore the use of two grating pairs G1 and G2 permits to double the achievable delay.
3. Fabrication and characterization
The proposed device was manufactured using a double lithographic process based on Deep-UV 248 nm lithography, a planar technology which proved to be able to reliably pattern stitching-free gratings with a length of several millimeters and very high performances . First the gratings were realized with a double patterning lithography on the plain substrate, subsequently the rib waveguides were added with a second lithographic step. Waveguides were fabricated using a SOI substrate with a silicon guiding layer thickness of 1.4 µm on a 1 µm thick buried oxide. They were designed with a rib width of 1.5 µm and a rib height of 0.5 µm to assure single mode operation and linear loss around 0.2 dB/cm. All the gratings exhibit a period of 224 nm and an etching depth of 50 nm. A taper of Δw = 150 nm over a grating length of 1 cm was chosen to implement the chirp. The high overlay precision of the DUV exposure and the full control over the etching depth allow to precisely determine insertion loss, bandwidth and grating strength .
The characterization of the fabricated samples was performed with a modulation phase shift method. A polarization controller allowed setting the polarization of the propagating light, and an efficient in- and out-coupling was achieved using lensed fibers. Facets were covered with an anti-reflection coating to avoid undesired resonances. The device transmissivity was calculated as the ratio between the power transmitted by the drop-filter (port Out3, see Fig. 1(b)), and the one measured from a common waveguide, isolating the grating performance from the waveguide characteristics . Using a Peltier element and a temperature controller, the temperature of the measured sample could be varied with a precision of 0.1°C, allowing to tune the optical delay.
On Fig. 2 the transmission spectra and the respective group delay measured and the output of the drop filter (reflection of the cascaded grating pairs) for different temperatures between 32°C and 41°C are shown. At the starting temperature of 32°C a bandwidth of 1.2 nm centered at λ = 1535.4 nm was measured, with an insertion loss varying from 1.7 dB at the short-wavelength side and 6 dB at the long-wavelength side of the transmission bandwidth, corresponding to a reflection at the end of the grating. Over this bandwidth a linear increase of the group delay of 500 ps was measured, corresponding to 250 ps for each grating pair. A noticeable group delay ripple can be observed and is due to the absence of a grating apodization.
As expected, the increase of the device temperature produces a shift of 80 pm/°C of the Bragg wavelength to larger values, keeping the spectrum shape unchanged. If the wavelength of the input signal is placed in the middle region where the transmission is kept high for all temperatures, the delay applied to it can be tuned. Choosing a wavelength within this range, e.g. λs = 1535.8 nm, the signal delay can be varied between almost 0 and 440 ps (see Fig. 3 ). The tuning is linear within the temperature range between 32°C and 38°C, with a tuning coefficient of −51 ps/°C. For larger temperatures the effect of the group delay ripple predominates producing a sharper decrease of the group delay. Since the grating reflection spectrum is not perfectly flat, the signal experienced different losses at different temperatures, varying between 1.7 and 6 dB.
4. System performances
To evaluate the performance of the measured tunable delay line in real systems, different emulations with the VPItransmissionMaker simulation software were performed using the experimental data previously shown. Two limitations for data stream transmission are intrinsic in the device. First of all, the chirped gratings introduce a chromatic dispersion on the signal of 500 ps/nm. Furthermore, as previously discussed, the larger the tuning rage of the delay, the larger the required temperature variation, with a consequent larger shift of the grating spectrum and a reduction of the usable bandwidth. Both phenomena affect the signal bandwidth and hence the data rate which can be transmitted without errors.
On Fig. 4 the virtual setup used to estimate the system performance of the device is shown. The input signal consists on a QPSK modulated signal with a stream of 1018 random symbols. After propagating along a standard fiber span (80 km @ 17 ps/nm·km), a dispersion compensating fiber and an EDFA, the signal is coupled into the tunable delay line (TDL). To estimate the effect of the dispersion, the delayed signal is then coupled to a fictitious drop filter (CDC), analogous to the one described, but with reversed chirp in order to compensate the added dispersion. This filter is obtained by mirroring and properly shifting the measured spectra achieving a transmission bandwidth centered around λs and a dispersion of −500 ps/nm. The filter is not tuned, in order to add always a fixed extra delay of 270 ps.
Figure 5(a) shows the bit error rate (BER) for different data rates with and without dispersion compensation. In the former case it can be observed that the dispersion added by the tunable delay line strong affects the quality of the signal, leading to a BER larger than 10−3 for data rates beyond 25 Gbit/s. The performance can be strongly improved if the dispersion compensation is included. In this case a safe data transmission until 80 Gbit/s can be achieved.
Finally the transmission of a bit sequence at a data rate of 10 Gbit/s was emulated, to verify the delay tuning. On Fig. 5(b) the output signal for three different tuning temperatures is shown. At 40°C, corresponding to a delay close to zero (see Fig. 3), only the delay of 270 ps added by the dispersion compensator filter can be seen. Decreasing the temperature to 36°C and 32°C the signal is delayed of 197 ps and 417 ps respectively. The dispersion experienced by the signal is not equal at all temperatures, leading to a slight distortion of the signal shape, which anyway does not compromise a good detection.
We presented the realization of integrated delay lines based on tapered Bragg gratings in SOI rib waveguides. The delay can be furthermore continuously tuned varying the operating temperature, exploiting the thermo-optical effect. A comparison of the achieved device performances with the state of the art of integrated delay lines is shown on Table 1 . The device demonstrated in this work exhibits a large tuning range (until 450 ps) comparable to the one achievable with APFs  or in chirped gratings tuned with free-carrier plasma effect , but with a lower insertion loss and the possibility to operate at larger data rates, until 25 Gbit/s. We demonstrated also that the maximum affordable data rate can be increased up to 80 Gbit/s adding an analogous drop-filter with reversed grating taper for the dispersion compensation.
The financial support of the German Research Foundation (DFG) in the frame of the research group FOR653 is gratefully acknowledged.
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