Microresonator-based solitons for massively parallel coherent optical communications.

Solitons are waveforms that preserve their shape while propagating, as a result of a balance of dispersion and nonlinearity. Soliton-based data transmission schemes were investigated in the 1980s and showed promise as a way of overcoming the limitations imposed by dispersion of optical fibres. However, these approaches were later abandoned in favour of wavelength-division multiplexing schemes, which are easier to implement and offer improved scalability to higher data rates. Here we show that solitons could make a comeback in optical communications, not as a competitor but as a key element of massively parallel wavelength-division multiplexing. Instead of encoding data on the soliton pulse train itself, we use continuous-wave tones of the associated frequency comb as carriers for communication. Dissipative Kerr solitons (DKSs) (solitons that rely on a double balance of parametric gain and cavity loss, as well as dispersion and nonlinearity) are generated as continuously circulating pulses in an integrated silicon nitride microresonator via four-photon interactions mediated by the Kerr nonlinearity, leading to low-noise, spectrally smooth, broadband optical frequency combs. We use two interleaved DKS frequency combs to transmit a data stream of more than 50 terabits per second on 179 individual optical carriers that span the entire telecommunication C and L bands (centred around infrared telecommunication wavelengths of 1.55 micrometres). We also demonstrate coherent detection of a wavelength-division multiplexing data stream by using a pair of DKS frequency combs-one as a multi-wavelength light source at the transmitter and the other as the corresponding local oscillator at the receiver. This approach exploits the scalability of microresonator-based DKS frequency comb sources for massively parallel optical communications at both the transmitter and the receiver. Our results demonstrate the potential of these sources to replace the arrays of continuous-wave lasers that are currently used in high-speed communications. In combination with advanced spatial multiplexing schemes and highly integrated silicon photonic circuits, DKS frequency combs could bring chip-scale petabit-per-second transceivers into reach.

Kramers-Kronig detection of four 20 Gbaud 16-QAM channels using Kerr combs for a shared phase estimation.

We experimentally demonstrate Kramers-Kronig detection of four 20 Gbaud 16-quadrature-amplitude-modulated (QAM) channels after 50 km fiber transmission using two soliton Kerr combs as signal sources and local oscillators. The estimated carrier phase at the receiver for each of the channels is relatively similar due to the coherence between the frequency comb lines. The standard deviation of the estimated carrier phase difference of the channels is less than 0.08 rad after 50 km single-mode fiber (SMF) transmission. This enables the carrier phase recovery derived from one channel to be shared among multiple channels. In the back-to-back scenario, the bit error rate (BER) performance for shared carrier phase recovery shows an optical signal-to-noise ratio penalty of ${\sim}{0.5}\;{\rm dB}$∼0.5dB compared to the BER performance for carrier phase recovery when derived for each channel independently. BERs below the forward error correction threshold are achieved after 50 km SMF transmission with both independent and shared carrier phase recovery for four 20-Gbaud 16-QAM signals.

Orthogonally polarized frequency comb generation from a Kerr comb via cross-phase modulation.

We experimentally demonstrate that a single microresonator can emit two orthogonally polarized individually coherent combs: (i) a strong polarized soliton comb and (ii) an orthogonally polarized continuous wave seeded weaker comb, generated from the first one via cross-phase modulation, sharing the repetition rate of the soliton comb. Experimental results show that the power of the transverse electric-polarized seed can be well below the threshold of comb generation (e.g., 0.1 mW). In addition, simulations show that a dark pulse could be generated in the anomalous dispersion regime by a bright soliton when the two orthogonally polarized modes have the same group velocity in the microresonator.

Reconfigurable optical generation of nine Nyquist WDM channels with sinc-shaped temporal pulse trains using a single microresonator-based Kerr frequency comb.

Sinc-shaped temporal pulse trains have a spectrally efficient, rectangular Nyquist spectrum. We demonstrate the simultaneous and reconfigurable optical generation of multiple Nyquist-shaped wavelength-division-multiplexed (WDM) channels having temporal sinc-shaped pulse trains as data carriers. The channels are generated through the insertion of coherent lines using cascaded continuous-wave amplitude modulation around the spectral lines of a microresonator-based Kerr optical frequency comb. For each of nine Kerr frequency comb lines, we insert sub-groups of uniform and coherent lines to generate nine WDM channels. The deviations from ideal Nyquist pulses for the nine channels at repetition rates of 6 and 2 GHz are between 4.2%-6.1% and 2%-4.5%, respectively. Each WDM channel is modulated with on-off keying (OOK) at 6 Gbit/s. In addition, we show the reconfigurability of this method by varying the number of WDM channels, the generated sinc-shaped pulse train repetition rates, the duration, and the number of zero-crossings.

Scalable and reconfigurable optical tapped-delay-line for multichannel equalization and correlation using nonlinear wave mixing and a Kerr frequency comb.

We experimentally demonstrate a scalable and reconfigurable optical tapped-delay-line (TDL) for multichannel equalization and correlation of 20-Gbaud quadrature-phase-shift-keyed (QPSK) signals using nonlinear wave mixing and a microresonator Kerr frequency comb. The optical TDL mainly consists of two stages: one being a multicasting of the original signals in a periodically poled lithium niobate (PPLN) waveguide with Kerr comb lines functioning as mutually coherent pumps, while the other is a coherent multiplexing of the delayed and weighted signal replicas in a second PPLN. A two- or three-tap optical TDL is demonstrated to simultaneously equalize a distorted QPSK data signal, reducing the error vector magnitude (EVM) from 22.5% to either 19.9% or 18.2%, and search two- or three-symbol patterns on another QPSK signal.

Effects of erbium-doped fiber amplifier induced pump noise on soliton Kerr frequency combs for 64-quadrature amplitude modulation transmission.

We experimentally investigate the effects of erbium-doped fiber amplifier induced pump noise on soliton Kerr frequency combs for 64-quadrature amplitude modulation (QAM) transmission. We find that the optical carrier-to-noise ratios (OCNRs) of the comb lines across the C-band almost linearly depend on the pump OCNR and are similar for a constant input pump power and noise. For a specific three-soliton state, despite higher comb line power, there is no noticeable OCNR improvement compared to the single-soliton comb. When the ASE noise on the pump is varied by 10 dB in the stable single-soliton state, the comb linewidths remain relatively unchanged and similar to the pump linewidth. Furthermore, four lines of the single-soliton Kerr comb produced by a pump light at an OCNR larger than 52 dB are used as coherent light sources to transmit 20-Gbaud 64-QAM signals over a 25-km fiber with bit error rate below the forward-error correction threshold.

Pump-linewidth-tolerant wavelength multicasting using soliton Kerr frequency combs.

We experimentally demonstrate pump-linewidth-tolerant wavelength multicasting using microresonator-based soliton Kerr frequency combs. When Kerr comb lines serve as coherent pumps in a periodically poled lithium niobate waveguide, the linewidth of the multicast signal almost remains that of the original signal at different linewidths of Kerr combs, ranging from 100 kHz to 1 MHz. However, in conventional multicasting where free-running (FR) pumps are used, the linewidth of the converted signal significantly increases. Furthermore, the error vector magnitude (EVM) performance demonstrates eight-fold error-free multicasting of 10 Gbaud 16-quadrature amplitude modulation signals, even when the linewidths of the Kerr combs are as broad as 1 MHz (no Kalman filtering algorithm in the receiver). In contrast, the EVM performance of the signal copy is degraded with an FR laser as a dummy pump.

Dependence of a microresonator Kerr frequency comb on the pump linewidth.

We experimentally investigate the dependence of Kerr comb generation, comb linewidth, and coherent system performance on the pump linewidth in a microresonator. We find that the generation of the primary comb can have a larger tolerance to the pump linewidth compared with that of the low-phase-noise comb. In addition, the linewidths of the generated combs are almost linearly dependent on the pump linewidth in the primary and low-phase-noise states. Furthermore, the optical signal-to-noise ratio penalty between the pump and generated Kerr combs in a coherent communication system is less than 0.2 dB in both the primary and low-phase-noise states, showing that Kerr frequency combs in these two states can have similar coherent system performance to the pump.

Tunable insertion of multiple lines into a Kerr frequency comb using electro-optical modulators.

We experimentally insert a flexible number of electro-optical (EO) comb lines into a Kerr frequency comb via EO modulation and demonstrate the use of combined Kerr and EO combs as light sources in coherent communications. The number of EO lines inserted into the Kerr comb can be varied by changing the modulation frequency. Additionally, the inserted EO comb is found to have similar coherence to that of the Kerr comb, as indicated by their linewidths. The high coherence of both the Kerr and EO combs has further been demonstrated in a communication experiment in which the comb lines are encoded with 10 Gbaud quadrature phase-shift-keyed signals. The increased number of comb lines after EO modulation indicates the possibility of obtaining more data channels in optical communications.

Dual-pump generation of high-coherence primary Kerr combs with multiple sub-lines.

We experimentally generate high-coherence primary Kerr combs with multiple sub-lines by using dual pumps and demonstrate the application of a primary comb state in multichannel communications. We find that more than 10 primary comb lines can be generated within the spectrum of modulation instability gain in our microring resonator. The generation is also verified by numerical simulations and the measured linewidth confirms the high coherence of the generated primary comb lines. We also demonstrate the high-coherence characteristics in a coherent communication experiment, in which each comb line is encoded with 20 Gbaud quadrature phase-shift-keyed signals.

Frequency-comb-assisted broadband precision spectroscopy with cascaded diode lasers.

Frequency-comb-assisted diode laser spectroscopy, employing both the accuracy of an optical frequency comb and the broad wavelength tuning range of a tunable diode laser, has been widely used in many applications. In this Letter, we present a novel method using cascaded frequency agile diode lasers, which allows us to extend the measurement bandwidth to 37.4 THz (1355-1630 nm) at megahertz resolution with scanning speeds above 1 THz/s. It is demonstrated as a useful tool to characterize a broadband spectrum for molecular spectroscopy, and in particular it enables us to characterize the dispersion of integrated microresonators up to the 4th-order.

Demonstration of optical multicasting using Kerr frequency comb lines.

We experimentally demonstrate optical multicasting using Kerr frequency combs generated from a Si3N4 microresonator. We obtain Kerr combs in two states with different noise properties by varying the pump wavelength in the resonator and investigate the effect of Kerr combs on multicasting. Seven-fold multicasting of 20 Gbaud quadrature phase-shift-keyed signals and four-fold multicasting of 16-quadrature amplitude modulation signals have been achieved when low-phase-noise combs are input into a periodically poled lithium niobate waveguide. In addition, we find that the wavelength conversion efficiency in the PPLN waveguide for chaotic combs with high noise is similar to that for low-noise combs, while the signal quality of the multicast copy is significantly degraded.

Raman Self-Frequency Shift of Dissipative Kerr Solitons in an Optical Microresonator.

The formation of temporal dissipative Kerr solitons in microresonators driven by a continuous-wave laser enables the generation of coherent, broadband, and spectrally smooth optical frequency combs as well as femtosecond pulse sources with compact form factors. Here we report the observation of a Raman-induced soliton self-frequency shift for a microresonator dissipative Kerr soliton also referred to as the frequency-locked Raman soliton. In amorphous silicon nitride microresonator-based single soliton states the Raman effect manifests itself by a spectrum that is sech^{2} in shape and whose center is spectrally redshifted from the continuous wave pump laser. The shift is theoretically described by the first-order shock term of the material's Raman response, and we infer a Raman shock time of ∼20 fs for amorphous silicon nitride. Moreover, we observe that the Raman-induced frequency shift can lead to a cancellation or overcompensation of the soliton recoil caused by the formation of a coherent dispersive wave. The observations are in agreement with numerical simulations based on the Lugiato-Lefever equation with a Raman shock term. Our results contribute to the understanding of Kerr frequency combs in the soliton regime, enable one to substantially improve the accuracy of modeling, and are relevant to the understanding of the fundamental timing jitter of microresonator solitons.

Practical continuous-variable quantum key distribution with composable security.

A quantum key distribution (QKD) system must fulfill the requirement of universal composability to ensure that any cryptographic application (using the QKD system) is also secure. Furthermore, the theoretical proof responsible for security analysis and key generation should cater to the number N of the distributed quantum states being finite in practice. Continuous-variable (CV) QKD based on coherent states, despite being a suitable candidate for integration in the telecom infrastructure, has so far been unable to demonstrate composability as existing proofs require a rather large N for successful key generation. Here we report a Gaussian-modulated coherent state CVQKD system that is able to overcome these challenges and can generate composable keys secure against collective attacks with N ≈ 2 × 108 coherent states. With this advance, possible due to improvements to the security proof and a fast, yet low-noise and highly stable system operation, CVQKD implementations take a significant step towards their discrete-variable counterparts in practicality, performance, and security.

Homodyne-based quantum random number generator at 2.9 Gbps secure against quantum side-information.

Quantum random number generators promise perfectly unpredictable random numbers. A popular approach to quantum random number generation is homodyne measurements of the vacuum state, the ground state of the electro-magnetic field. Here we experimentally implement such a quantum random number generator, and derive a security proof that considers quantum side-information instead of classical side-information only. Based on the assumptions of Gaussianity and stationarity of noise processes, our security analysis furthermore includes correlations between consecutive measurement outcomes due to finite detection bandwidth, as well as analog-to-digital converter imperfections. We characterize our experimental realization by bounding measured parameters of the stochastic model determining the min-entropy of the system's measurement outcomes, and we demonstrate a real-time generation rate of 2.9 Gbit/s. Our generator follows a trusted, device-dependent, approach. By treating side-information quantum mechanically an important restriction on adversaries is removed, which usually was reserved to semi-device-independent and device-independent schemes.