1. Introduction

The field of ultrafast optics has revolutionized modern science and technology including ultrafast spectroscopy, optical frequency metrology, high-speed optical and electrical testing, ultrahigh-speed optical communications and many forms of biomedical imaging [1]. Today’s ubiquitous source of ultrafast pulses, the titanium:sapphire (Ti:sapph) laser, provides high quality, wavelength-tunable (100’s of nm) optical pulse trains; however, these expensive, power-hungry, table-top systems are limited to primarily the more demanding scientific explorations rather than many potential commercial applications. Rack-mountable fiber lasers and, more recently, chip-scale ultrafast optical sources represent a reduction in size, weight, power and cost (SWaP-C) over their Ti:sapph counterparts, however are limited by an optical gain window of tens of nm’s as dictated by the typical ion dopant electronic transitions or III-V semiconductor transitions. In contrast, for optical parametric oscillators (OPO), the gain profile is dictated by the phase matching bandwidth, which can be controlled through engineering the nonlinear device geometry. Therefore OPOs can greatly extend the limited gain bandwidth of fiber lasers. Parametric oscillators using the χ⁽³⁾ nonlinearity, which provide oscillating signals that can be close in frequency to the pump, can be readily realized in optical waveguide geometries allowing for robust alignment, compact size, and greatly enhanced nonlinearity. Such parametric oscillators have been demonstrated in various nonlinear mediums such as highly nonlinear optical fiber and chalcogenide and crystalline silicon (c-Si) on-chip waveguides [2–6]. Among these platforms, using silicon and its mature CMOS fabrication technology to realize such an OPO can greatly increase the practicality of wavelength tunable ultrafast sources by enabling robust and resource-efficient sources and further supporting the move towards low SWaP-C systems. However, c-Si-based OPOs have been limited to the mid-IR range [6, 7] due to deleterious nonlinear loss mechanisms of two-photon absorption (TPA) and TPA-induced free-carrier absorption (FCA) present in c-Si at telecommunications wavelengths.

Hydrogenated amorphous silicon (a-Si:H) recently emerged as an exceptional material for CMOS-compatible nonlinear optics due to its ultrahigh nonlinearity [8, 9] and reduced impact of TPA as compared to c-Si [10]. For example, we have demonstrated a-Si:H waveguides with effective nonlinearities as large as 3000 W⁻¹m⁻¹, representing a value of effective nonlinearity that is 5 orders of magnitude larger than highly nonlinear fiber and an order of magnitude larger than high-nonlinearity c-Si waveguides [8]. Furthermore, a high nonlinear figure of merit (FOM) of > 5 (ten times larger than c-Si) was measured in several studies [11, 12], showing a-Si:H’s potential for efficient nonlinear interactions with large nonlinear phase shifts. Using a highly nonlinear a-Si:H waveguide, we previously demonstrated continuous-wave (CW) frequency conversion [8] and temporal demultiplexing [13] with ultra-low pump powers. Additionally, when operating at lower repetition rates to mitigate free carrier loss, parametric amplification as high as 26.5 dB was achieved at telecommunications wavelengths over a ~11.6-THz bandwidth by Kuyken et al [14]. This large parametric amplification is made possible by the large nonlinear FOM of a-Si:H.

Here, we investigate the extremely high nonlinearity and negligible TPA of a-Si:H waveguides for ultrabroad-bandwidth parametric amplification and oscillation. We observe parametric amplification spanning 500 nm (60 THz) representing the largest on-chip parametric gain bandwidth demonstrated to date in any integrated material system, and additionally we realize the first silicon OPO operating in the near-IR. We demonstrate simple wavelength tuning of this source through the time-dispersion-tuned technique over the majority of the waveguide’s dispersion-engineered gain bandwidth from 1370 nm to 1810 nm, while maintaining an extremely low SWaP-C device. Finally, through dispersion engineering of the OPO cavity we are able to generate pulses as short as 300 fs from this source.

2. The a-Si:H waveguide design and fabrication

The geometry of the a-Si:H waveguide used in this investigation is engineered to have anomalous group velocity dispersion (GVD) for broad-bandwidth phase-matching of the parametric amplification process. The cross-section of the designed waveguide is 205 nm by 500 nm with a waveguide length of 8 mm. The a-Si:H waveguide is fabricated using standard CMOS-compatible techniques at the Center for Nanoscale Science and Technology’s NanoFab at the National Institute of Standards and Technology. After a standard cleaning, the a-Si:H film is deposited by plasma-enhanced chemical vapor deposition (PECVD) on a silicon wafer with 3 µm thermal oxide. The a-Si:H film deposition chamber parameters are: a gas flow of 1200 sccm made up of helium with 5% silane is kept at a pressure of 900 mT with 50 W RF power. The substrate is maintained at 300°C during the deposition. A thin layer of silicon dioxide (~150 nm) is deposited as a hard mask to reduce deleterious effects from direct etching with resists. Electron-beam lithography followed by chlorine-based inductively coupled plasma (ICP) etching is used for waveguide patterning. A thick silicon dioxide layer (~1 µm) is deposited via PECVD over the waveguide to serve as an optical cladding. Inverse adiabatic tapers on both ends of the waveguide are made for optical coupling [15]. The scanning electron microscope (SEM) image of the fabricated waveguide is shown in Fig. 1(a) (before cladding), depicting a smooth and near-vertical sidewall of the waveguide. The calculated quasi-TE-mode electric field profile of the waveguide is shown in Fig. 1(b). The material optical properties of the deposited a-Si:H film (shown in Fig. 1 (c)) are characterized by an ellipsometer and then imported to finite difference method simulation software to calculate the effective index and dispersion of the waveguide. The calculated GVD as a function of wavelength as calculated by a finite-difference mode solver is plotted in Fig. 1(d) with a value of ~200 ps/(nm∙km) near a wavelength of 1550 nm. The effective area as function of the wavelength of the waveguide is plotted in Fig. 1(e). The propagation loss of the waveguide is characterized to be −3.2 dB/cm for the quasi-TE-mode at wavelength of 1550 nm. Additionally, we measure the propagation loss of the waveguide to be −4 dB/cm at 1450 nm and −4 dB/cm at 1700 nm. Thus we observe little wavelength dependence of the loss over the wavelength range we can measure.

 

Fig. 1 (a) Scanning electron micrograph of an a-Si:H waveguide before the silicon dioxide cladding. A 150-nm silicon dioxide hard mask is on top of the waveguide. (b) Modeled electric field profile of the waveguide in the quasi-TE mode. (c) Complex refractive index of bulk a-Si:H material as measured by an ellipsometer. (d) Material group-velocity dispersion (GVD) of the a-Si:H material as calculated from the measured ellipsometry data (blue) and calculated total GVD for the designed a-Si:H waveguide (205 nm × 500 nm × 8 mm), showing anomalous GVD over telecommunication wavelengths (red). (e) Calculated effective area of the fundamental TE mode as a function of wavelength.

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We find that the samples degrade over time (~months) if continually exposed to visible light. It is likely that this degradation is due to a process that is well-known in the solar cell community as the Staebler–Wronski effect and can be readily avoided by isolating the sample from visible light by adding an opaque cover for packaging. For example, we store our samples in opaque packaging when not in use and have observed no degradation after greater than three years of use. Critically, we do not observe waveguide damage by the telecommunication wavelength light used in the experiments. We find no correlation between degradation and exposure to high average power infrared light in the waveguide.

3. Optical parametric amplification

Single pass amplification of our waveguide is measured using a degenerate pump-probe four-wave mixing (FWM) experiment. A 90-MHz mode-locked fiber laser centered at 1558 nm is split with a 90/10 coupler. The pump pulse is generated by sending 90% of the laser into a ~200-GHz optical filter followed by an EDFA. The pump average power is ~0.34 mW (2.5 W peak power) and the pulse width is measured by an autocorrelator to be 1.5 ps. The signal is generated by sending 10% of the mode-locked fiber laser into an EDFA and subsequently 5 meters of highly nonlinear fiber to generate broad-bandwidth continuum. A free-space tunable filter (~200-GHz bandwidth) is used to isolate the signal wavelength. A wavelength division multiplexer (WDM) combines the signal and pump arms for input into the chip. Fiber-to-chip coupling is achieved by a lensed fiber (input) and lens collimator (output) assembly. The amplification as a function of wavelength is measured by tuning the signal wavelength and recording the respective on/off optical gain spectrum and is plotted in Fig. 2 (c), red points. With a pump wavelength of 1558 nm, a peak on/off gain value of ~17 dB is obtained for a signal at 1480 nm and the on/off gain bandwidth extends over more than 220 nm. Due to the experimental setup whereby the 90-MHz laser provides both pump and signal, the spectral power is split between the two inputs. Therefore, an external EDFA is required to boost the peak pump power. However, due to undesired SPM inside the EDFA, the maximum peak pump power is limited for a given pulse width. Use of a longer pump pulse (6.1 ps) partially alleviates this effect and the input pump peak power can be increased to 3.6 W. The on/off gain is again measured for the longer pulse width (blue points, Fig. 2 (c)). Despite the higher peak power, the peak gain is observed to be similar to the 2.5-W, 1.5-ps-long pulse likely due to the larger carrier-induced loss produced by longer pulses. However, the resulting gain bandwidth is wider because the phase matching occurs at farther wavelength detuning due to the increased self- and cross-phase modulation. The calculated phase mismatch and gain spectrum are plotted in Fig. 2 (a) including the effects of the full device dispersion and (b) including the effects of the full device dispersion and two-photon absorption, however carrier effects are neglected in both cases. We observe that the secondary peaks that appear with the 6.1-ps-pulse pump originate from additional phase-matched wavelengths from the impact of fourth-order dispersion (β₄) [16]. The combination of phase matching bands of β₂ and β₄ and nonlinear phase shift results in broad bandwidth amplification of 500 nm, corresponding to 60 THz in total bandwidth.

 

Fig. 2 (a) The calculated linear phase mismatch as function of signal wavelength. The blue and red dash lines represent the nonlinear phase (2γP) at peak pump powers of 3.6 W and 2.5 W, respectively. The 4 phase matching (PM) points in the case of the 3.6 W pump power are shown by arrows. (b) Simulated parametric gain spectrum for peak pump powers of 3.6 W and 2.5 W. The carrier-related nonlinear loss is neglected in the simulation. (c) Measured single pass on/off gain of the a-Si:H waveguide using a 1.5-ps pump with peak power of 2.5 W and 6.1-ps pump with peak power of 3.6 W. Amplification is achieved from 1326 nm - 1523 nm and 1577 nm - 1885 nm.

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Finally, we note that the experimental gain spectrum exhibits significant asymmetry versus wavelength with less gain on the long wavelength side of the pump. From our simulations, we find that this asymmetry is not explained by dispersion, wavelength dependent linear propagation loss, or wavelength dependent effective nonlinearity. The origin of this asymmetry is likely wavelength dependent loss from photo-generated carriers [17] and also explains the larger observed asymmetry for the longer pump pulses, which should produce more carriers. However, we note that the nature of photogenerated carriers in a-Si:H and their impacts on nonlinear optical interactions are still not well understood with several experimental observations that contradict well understood free-carrier effects in crystalline silicon nonlinear devices [18]. Thus we reserve more extensive simulations of the parametric gain process including carrier effects in these devices for future work pending more thorough characterization of the impact of carriers.

4. Optical parametric oscillation

To harness the broad-bandwidth parametric gain achieved in the a-Si:H waveguide, the device is placed in a resonant-cavity to observe optical parametric oscillation. The experimental setup for oscillation is depicted in Fig. 3(a). A 90-MHz mode-locked fiber laser pump wave is centered at 1558 nm with a pulse width measured by auto-correlation to be 1.5 ps. In the OPO configuration, the laser output is used exclusively as the pump, and the peak pump power can be increased using the mode-locked laser’s built-in amplifier without the external EDFA used in the single-pass setup. Fiber-to-chip coupling is achieved by a lensed fiber (input coupling loss −8.5 dB) and lens-collimator assembly (output coupling loss −3.5 dB). The asymmetry in coupling loss is due to the two different methods used: a lensed fiber for the input and free-space lenses for the output. We use a lensed fiber on the input for simplicity, however the use of free-space optics affords greater flexibility for mode-matching and thus lower coupling loss. If lower round-trip loss was desired in a fully fiber-coupled system then greater optimization of the fiber mode-size can be employed. A half-wave plate and polarization beam splitter are used to control the output coupling ratio of the fiber cavity. The length of the cavity (created mostly from SMF-28) is chosen to match the repetition rate of the pump (~2.3 m), and a polarization controller and free-space tunable delay are included in the cavity. The feedback light is combined with the pump using a broad WDM (1554-1563 nm). Due to the breadth of the WDM the pump pulse temporal width is unaffected. We calculate the total round trip cavity loss to be −16.5 dB, which is dominated by the fiber-to-fiber loss (−14.6 dB) from coupling into and out of the photonic chip. Once the single pass gain exceeds the round-trip loss, the cavity achieves oscillation, and a sample oscillation trace is shown in Fig. 3(b) where the peak pump power in the waveguide is 2.5 W. To demonstrate thresholding of the oscillation with our device, the output of the oscillating mode (1470 nm in this case) as a function of input pump energy is plotted in Fig. 3(c), revealing an oscillation threshold of 1.53 pJ with slope efficiency of ~4.4%. The inset shows the evolution of the spectrum as the coupled pump energy increases. The pulse width of the oscillation output is measured through cross-correlation with a 1.5 ps reference pulse. The cross-correlation trace is shown in Fig. 3(d). The de-convolved pulse width of the oscillating mode is measured to be ~1.1 ps.

 

Fig. 3 Demonstration of the a-Si:H optical parametric oscillator. (a) Experimental setup for the optical parametric oscillator (OPO). (PC: polarization controller. WDM: wavelength division multiplexer. OSA: optical spectrum analyzer. PBS: polarization beam splitter. λ/2: half-wave plate. Red line: single mode fiber) (b) Optical spectrum of the OPO when oscillation wavelength is at 1460 nm. (c) Output energy of the OPO (at 1470 nm) as a function of coupled pump energy. The oscillation threshold is 1.53 pJ with a slope efficiency of ~4.4%. Inset: output spectrum as function of coupled pump energy. (d) Cross-correlation trace between oscillation (1476 nm) and a strong 1.5 ps pump. The de-convolved pulse width for the oscillation output is 1.1ps.

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As the majority of the cavity is built from single-mode fiber (SMF-28), the cavity exhibits net anomalous group-velocity dispersion and tuning of the oscillating wavelength through the time-dispersion-tuning technique is simply achieved through changing the physical length of the OPO cavity [2–5]. The total dispersion of the cavity is 0.042 ps/nm at 1550 nm and the inclusion of the tunable free-space delay in the OPO cavity allows for such wavelength tuning of the oscillating wave while the pump at the wavelength of 1558 nm remains fixed. The optical spectrum of the oscillating mode is recorded for different cavity lengths and Fig. 4 shows the overlaid spectra from this measurement. We are able to tune the fundamental oscillating mode continuously from 1370 nm to 1515 nm, and 1600 nm to 1810 nm (with the gap in the tuning range corresponding to the pump’s fixed location), corresponding to an overall wavelength tuning range of 42 THz (355 nm). For large wavelength detuning, a higher pump peak power (~4.8 W) is used to extend the gain bandwidth to achieve oscillation.

 

Fig. 4 Overlaid tuning spectra of the oscillation mode of the OPO at short wavelength side (1370 nm ~1515 nm), and long wavelength side (1600 nm ~1810 nm) for a 1558-nm pump laser.

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In the aforementioned configuration, the fundamental oscillating mode is limited to a maximum wavelength of 1810 nm; however, through cascaded FWM, light can be generated at wavelengths outside of the parametric gain bandwidth. Figure 5(a) shows an example spectrum of the cascaded FWM process when the pump power is increased. When the oscillating wave ( + 1 mode) interacts with the pump and undergoes FWM, an idler is generated on the opposite side of the pump (−1 mode). These two waves mix with the pump wave to generate light at additional wavelengths ( + 2, −2, −3, −4 modes) through cascaded FWM. By adjusting the delay to increase the separation of the oscillating mode from the pump and further increasing the pump power, Fig. 5(b) shows the cascaded + 2 mode generated at a wavelength of 1900 nm. Currently, our waveguide favors a cascade towards shorter wavelengths as illustrated by Fig. 5(a). This asymmetry potentially results from higher-order dispersion, increased loss at longer wavelengths, or reduced nonlinearity at longer wavelengths due to delocalization of the mode as shown in Fig. 1(e). We anticipate that the efficiency of a cascaded process towards longer wavelengths can be increased in future work through the use of a larger waveguide cross-section, with potential spectroscopic applications in short-wave infrared and mid-infrared biological sensing and environmental monitoring.

 

Fig. 5 Generated output wavelength extension through cascaded FWM. (a) Optical spectrum with increased pump power when + 1 represents the oscillating mode. Cascaded FWM generates idlers at + 2, −1, −2, −3, −4 modes. (b) Oscillating wave ( + 1 mode) near 1700 nm with cascaded FWM ( + 2 mode) for light generation at ~1900 nm.

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As a final demonstration of the utility of this source, we show the potential for ultra-short pulse generation. The OPO cavity is modified to include both SMF-28 (1.6 m) and dispersion compensating fiber (DCF) (70 cm, Corning Vascade S1000 Fiber with D = −38 ps/(nm∙km)) to minimize the net round-trip second-order dispersion. We calculate the total dispersion of this new cavity to be 0.003 ps/nm at 1550 nm. With this new cavity, the oscillation wavelength is tuned to 1467 nm (inset of Fig. 6) to maximize the bandwidth of the oscillating mode, which is extended to > 30 nm. As shown in Fig. 6, we measure the pulse width of this oscillation output through cross-correlation with a 250-fs reference pulse and the de-convolved pulsewidth of the oscillating mode is measured to be ~300 fs. Notably, the pulse width of the OPO pump laser is maintained at 1.5 ps for this demonstration representing the generation of an oscillating pulse that is 5 times shorter than the pump pulse. Furthermore, given the large parametric gain bandwidth of this device we anticipate that oscillating pulses well below 100 fs can be generated with improved cavity dispersion management to correct for higher-orders of dispersion within the cavity.

 

Fig. 6 Cross-correlation trace of the oscillation mode (1467 nm) with a 250-fs reference pulse. The de-convolved pulse width for the oscillation mode is ~300 fs assuming a sech² pulse shape. The side peak in the trace is the cross-correlation of the cascaded FWM idler. Inset: the output spectrum of the reduced net dispersion OPO cavity. The bandwidth of the oscillation mode is greater than 30 nm, allowing ultra-short pulse generation.

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5. Conclusion and outlook

In this paper, we report the first silicon-based optical parametric oscillator centered at telecommunications wavelengths. The broad bandwidth parametric gain enables wavelength tuning over the greater part of the extended telecommunications bands (E, S, C, L, and U) and beyond providing a robust near-infrared ultrafast wavelength-tunable light source that can greatly extend the wavelength agility of ultrafast erbium-doped fiber lasers and semiconductor lasers. Furthermore, the oscillation threshold (1.53 pJ) and the high levels of parallelism made possible through CMOS device fabrication indicates that a vast multitude of synchronized wavelength-agile sources can be created using a single pump laser, an intriguing possibility for scaling many ultrafast technologies. Finally, we have recently observed that parametric amplification can be achieved in these waveguides at repetition rates > 1 GHz [19]. Thus we anticipate that the use of higher repetition rate pump lasers (> 1 GHz) and hybrid integration with an ultralow-loss waveguide material to form a sufficiently low loss cavity (e.g. silicon nitride [20]) will provide a path towards integration of the full OPO cavity on chip.