Photonic integrated circuits (PICs) capable of ultra-fast, signal processing are recognized as being fundamental for future applications involving ultra-short optical pulse propagation, including the ability to meet the exponentially growing global fiber-optic telecommunications bandwidth demand. Integrated all-optical signal processors would carry substantial benefits in terms of performance, cost, footprint, and energy efficiency. Here, we demonstrate an optical pulse compressor based on an integrated nonlinear chirper, capable of operating on a sub-picosecond (> 1Tb/s) time scale. It is CMOS compatible and based on a 45cm long, high index doped silica glass waveguide we achieve pulse compression at relatively low input peak powers, due to the high nonlinearity and low linear and nonlinear losses of the device. The flexibility of this platform in terms of nonlinearity and dispersion allows the implementation of several compression schemes.
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Temporally compressing optical pulses is fundamental to many applications ranging from telecom networks [1,2] to optical metrology and imaging, where the wide bandwidth of sub-picosecond optical pulses is particularly suited to optical coherence tomography techniques . For telecommunications applications, the sub-picosecond optical pulses that are required for future terabit, time domain multiplexed (TDM) systems, are currently difficult to obtain directly from commercially available high repetition rate laser sources. In order to circumvent this issue, a number of different pulse compression schemes exploiting ultrafast nonlinearities have been demonstrated. For example, nonlinear pulse compression can be realized by spectrally broadening transform limited optical pulses via nonlinear propagation in a normally dispersive optical fiber followed by a re-phasing via linear anomalous dispersion . In the so called “adiabatic soliton compression scheme” , an input pulse matching a soliton solution is compressed by exploiting a fiber having a slowly varying group velocity dispersion (GVD). Pulse compression can also be realized via nonlinear frequency conversion [6–8] or by using higher-order soliton excitations  far above the fundamental soliton energy, where the soliton is compressed by self-phase modulation in an anomalously dispersive medium.
Fundamental to many of these approaches is the generation of a significant nonlinear chirp, which requires a strong third order-nonlinearity. For these reasons, highly nonlinear materials such as chalcogenide glasses (ChG) [10,11] and semiconductors (silicon and AlGaAs [12–15]) have attracted significant attention. Their high refractive indices also allow for the fabrication of waveguides with tightly confined modes, i.e. modes with small effective area Aeff, thus enhancing the effective nonlinear parameter (k0, n2 are the vacuum wave number and the Kerr nonlinear coefficient, respectively) as well as enabling tight bends with negligible loss . However, in spite of these advantages, significant challenges still need to be addressed. Silicon exhibits inherent nonlinear losses due to two-photon absorption (TPA) and the associated free carriers , while chalcogenide glasses suffer from an immature fabrication technology. In addition the compensation of the high material GVD and the desired single-mode operation requires tightly confined waveguides that can result in significant scattering losses [14,18]. Not surprisingly, a practical photonic integrated circuit capable of generating the required nonlinear chirp for optical pulse compression has not been demonstrated, in spite of its importance.
Recently , we reported CW nonlinear optics in a high-index, doped silica glass integrated platform, achieving low power frequency conversion via four wave mixing, and subsequently  demonstrated a low power, multi-wavelength integrated hyper-parametric oscillator. In this paper, we use this platform to demonstrate the first integrated optical pulse compressor capable of operation on sub-picosecond pulses. We achieve optical pulse compression of over 50%, down to pulse widths of under 400fs, at peak pulse powers well below 100W. This glass system has an optical refractive index that can be varied (according to the fabrication process) from 1.45 to 1.8 at 1550nm – a similar range to that of silicon nitride [21–23] – with a low absolute GVD (lower than 20ps2/km) at telecom wavelengths, together with negligible nonlinear losses. Further, this platform is CMOS compatible, with the ability to produce low loss waveguides (in this case, 0.06dB/cm) in the 1550nm wavelength range without the need for high temperature annealing. The comparatively high index contrast allows very tight modal field confinement (1.5x1.5 μm2 and below) and low bend radii (30 μm) with GVD magnitude and sign easily adjustable by tailoring the waveguide width .
2. The device
Our device consists of a 45cm long spiral waveguide integrated on a silicon wafer together with a reference waveguide of 1mm length (See Fig. 1 ). The films were deposited by using chemical vapor deposition and patterned with high resolution optical lithography followed by reactive ion etching. The entire chip is only ~6.5 mm x 6.5 mm in size and it is pigtailed to single mode fibers (pigtail losses of 3dB), whereas the 45cm long spiral waveguide is contained within a square area as small as 2.5mm x 2.5mm. The waveguide core (see the SEM picture in Fig. 1a) consists of n = 1.7 (at 1550nm) doped silica glass with a rectangular cross section of 1.45 μm x 1.50 μm, surrounded by silica glass. At λ = 1550nm, the (experimentally measured) group velocity dispersion is anomalous and as small as  for the TE polarized light, with a zero dispersion crossing near 1600nm, and a nonlinear coefficient of γ = 220 W−1km−1, 200 times higher than the value reported in standard single mode fibers (SMF) [5,25].
Figure 2 shows the experimental setup used to demonstrate pulse compression. We used a standard fiber laser (Pritel FFL, see Fig. 2) generating a train of Gaussian pulses with a field temporal beam waist t0 = 0.94ps (FWHM = 1.10ps), a pulse chirp (in terms of total dispersion) Dp = 0.17ps/nm, at a repetition rate of 16.9MHz, and a central wavelength of λ = 1550nm.
A polarization controller and an attenuator enabled the control of both the input polarization and power, the latter being measured by using a power meter coupled to a 1%-99% fiber splitter. The pulse autocorrelation and spectrum were collected using a standard intensity autocorrelation and an optical spectrum analyzer (OSA). The total length of the SMF used was 8m: 7.33m from the laser to the chip input, and an additional 0.66m at the chip output. Most of the source initial chirp from the laser was compensated in propagating the 7.33m to the chip, and the final input pulse residual chirp was estimated to be equivalent to propagating approximately 2m in a SMF.
In Fig. 3 , we show the optical pulse autocorrelation and spectrum obtained at the output of the chip, after passing through the 0.66m long output SMF. These graphs indicate that the pulse is clearly compressed as its energy (or input peak power) increases. We obtained an experimental value of the pulse width compression by fitting the intensity autocorrelation to a Gaussian field, i.e. (see Eq. (1) and related definitions below), which results in a waist T0 (power FWHM = 1.1774* T0) spanning from 0.65ps to 0.40ps for pulse energies (peak power) varying from 15pJ (19W) to 71.2pJ (98W). At 71.2pJ the pulse width at the input section is estimated to be around 0.6ps. We estimated the temporal focusing power of the waveguide by fitting the parabolic term Γ of the total nonlinear phase shift obtaining a maximum nonlinear phase shift of φ0 = 2.2rad and a curvature Γ = 0.046ps2/rad.
The pulse spectrum (Fig. 3b) clearly shows the double peak signature of an ongoing self-phase modulation (SPM) arising at high powers [5,25].We also performed the experiments using a reference 1mm long waveguide, in order to verify that the compression was due to the nonlinear chirp acquired by the 45cm waveguide and did not take place in the input or output fiber pigtails. Figure 4 clearly shows that for this experiment there is only a very weak pulse compression (0.65ps to 0.58ps), with a similarly weak SPM spectral signature at very high excitation energies, confirming that the compression seen in Fig. 3 is due almost solely to the nonlinear on-chip chirp.
In order to model the observed phenomena, we followed a standard  approach for optical waveguides based on a (1 + 1) nonlinear Schrödinger equation for dissipative-dispersive systems. In particular, we define z and t as the propagation and the temporal coordinate respectively, while the propagation of the optical pulse is represented by the envelope, through the equation:Equation (1) was integrated via a finite difference approach using the measured source output pulse chirp. Our simulations take into account the insertion losses of the all optical components in the setup, the optical nonlinearity, and the dispersion for both the SMF (, , ) and the waveguide (, ). We also included the experimentally measured coupling losses from the fiber pigtails to the chip, inferring an additional loss of 1-1.5dB due to the input polarization mode mismatch.
The predicted pulse compression is immediately evident in Fig. 5 where the theoretical pulse duration (expressed in terms of a Gaussian-fit waist) as a function of the input pulse energy is traced for the experiments conducted by using the spiral waveguide (red plots), and also for those that use only the 1mm reference waveguide (black plot). In the same figure the dots represent a Gaussian fit to the experimental data. The compression obtained is largely due to the nonlinear chirp acquired inside the spiral waveguide and not from the input or output SMF. The slight decrease in pulse width as a function of the input pulse energy in the reference plot (Fig. 5) is due to a small nonlinear chirp acquired in the input fiber. Figure 6 shows the pulse width as a function of the propagation distance for a pulse energy of 15.0 pJ (a) and 71.2 pJ (b). In this plot the 7.33m input fiber is followed by the 0.45m waveguide and then by the 0.66m output fiber pigtail. We observe that after the chip, the pulse width decreases dramatically for high energies along the short output fiber due to its anomalous dispersion.
We stress that the role played by the output fiber is simply to compensate the nonlinear chirp induced by the integrated device. Although in this work this is not performed on-chip, the total required dispersion is quite low, at around Dout = 10fs/nm. This level of dispersion can be easily achieved on-chip by many means, such as engineering the waveguide parameters, for example.
It is well known  that the post-compensation of nonlinear dispersion is not suitable for high compression ratios as it induces both the formation of a pedestal in the temporal field profile and a pulse breaking at high intensities. However, we would like to stress that generally the small total dispersion required at the output (in the presented case around 1.1 x 10−2 ps/nm) could have been compensated on-chip by a suitable design, e.g. by using dispersion engineered waveguides or through the well known approach of all-pass filters . These approaches allow for the implementation of the adiabatic soliton compression scheme, enabling high compression ratios according to which a dispersion “tapering”, along the waveguide length, essentially “squeezes” (adiabatically) the soliton width by adjusting the dispersion/nonlinearity tradeoff along the fiber length. Performing this in an integrated device would offer much greater flexibility in designing and fabricating linearly tapered waveguide segments to achieve the desired geometry and performances.
Our platform easily allows for GVDs spanning in the range β2≈ ± 70ps2/km by simply engineering the waveguide width and height (See Fig. 7 ). Figure 8 shows an example of the predicted pedestal-free compression (which exceeds 200%) by varying linearly the waveguide width from W = 1.75μm to W = 1.40μm, for a fixed height H = 1.7μm. The graph is obtained by launching a fundamental soliton pulse at the waveguide input assuming. Equation (1) was used to model the propagation, assuming linear losses of 0.06 dB/cm and accounting for the dependence of β2 and γ on the waveguide width. As the compression ratio and the maximum width of the input pulse are limited by propagation, the very low losses of these waveguides enable the use of much longer waveguide lengths: for example, adiabatic compression ratios exceeding 4x of sub-ps pulses can be achieved for waveguide lengths of 1.5m. We stress that although we neglect the effects of waveguide bending in the estimation of the GVD, the high index contrast in this platform (>0.25) allows for very tight bend radii (<100µm), with negligible impact on the GVD arising from waveguide geometry.
Finally, while this work focuses on a proof of concept using low repetition rate pulses, the principle of operation of this device is unaffected by the pulse repetition rate. Whereas the low-duty-cycle output makes it more suitable for non-telecom applications such as optical coherence tomography, the technique of compressing pulses in lower repetition rate data streams and then time multiplexing them up to extremely high bit rates is well know . Hence, the fact that we demonstrate operation of our device with pulsewidths commensurate with a full on-off keyed (return-to-zero) data stream at >1Tb/s implies that the application of this device to high bit rate data signals of ~1Tb/s should be straightforward.
In conclusion, we have demonstrated a sub-picosecond temporal optical pulse compressor. It is based on a waveguide pulse chirper in a CMOS compatible high index doped silica glass platform. This device combines a high nonlinearity with extremely low linear and nonlinear losses, and paves the way for fully integrated, cost effective, optical pulse compressors and regenerators operating at terabit/s bit rates and beyond, as well as for many other applications such as metrology and optical coherence tomography.
This work was supported by the Australian Research Council (ARC) Centres of Excellence program, Le Fonds Québécois de la Recherche sur la Nature et les Technologies (FQRNT), the Natural Sciences and Engineering Research Council of Canada (NSERC), NSERC Strategic Projects, and the INRS. M. Peccianti and L. Razzari acknowledge a Marie Curie Outgoing International Fellowship (contracts PIOF-GA-2008-221262 and 040514, respectively).
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