Phase-locked, pre-amplified optical injection locking at low input powers.

Optical injection locking generally occurs when light from a master laser is unidirectionally injected into a slave laser, such that the injected light overcomes spontaneous emission inside the cavity, and forces the slave laser to behave as a frequency copy of the master. Here, we study the limits of stability for optically pre-amplified optical injection locking in the case of large added noise on the input field and in the presence of a phase locked loop which minimizes the frequency offset between master and slave lasers. We present a set of modified rate equations which we use to describe the physics of the system near the limit of stable injection locking, and report on phase slips which occur due to injected noise momentarily destabilizing the system. We then provide experimental evidence to support the behavior seen in simulation, and are able to successfully recover a CW wave at -80 dBm black box input power (-70 dBm for phase slip free operation), providing 20 dBm of output power from the injection locked slave laser.

Low-noise phase-sensitive optical parametric amplifier with lossless local pump generation using a digital dither optical phase-locked loop.

The low noise figure of phase-sensitive amplifiers (PSAs) is attractive for optically pre-amplified measurement and communication systems. However, a major practical implementation difficulty pertains to the requirement of phase-locked signal, idler, and pump waves. Previously, injection locking to a co-propagating weak pump pilot or tapping portions of the received signal (lossy) for carrier re-generation have been used. Here we present a novel, lossless approach without any pump pilot, that generates a phase-locked receiver-local pump within the PSA using a digital dither-based optical phase-locked loop. We experimentally demonstrate a 2 dB noise figure with a low 0.3 dB penalty due to imperfect locking. By comparing the phase-locking performance in a PSA to that in a 50/50-coupler, we discuss and predict potential performance improvements connected to loop delay and laser phase characteristics.

Thermorefractive noise reduction of photonic molecule frequency combs using an all-optical servo loop.

Phase and frequency noise originating from thermal fluctuations is commonly a limiting factor in integrated photonic cavities. To reduce this noise, one may drive a secondary "servo/cooling" laser into the blue side of a cavity resonance. Temperature fluctuations which shift the resonance will then change the amount of servo/cooling laser power absorbed by the device as the laser moves relatively out of or into the resonance, and thereby effectively compensate for the fluctuation. In this paper, we use a low noise laser to demonstrate this principle for the first time in a frequency comb generated from a normal dispersion photonic molecule micro-resonator. Significantly, this configuration can be used with the servo/cooling laser power above the usual nonlinearity threshold since resonances with normal dispersion are available. We report a 50 % reduction in frequency noise of the comb lines in the frequency range of 10 kHz to 1 MHz and investigate the effect of the secondary servo/cooling noise on the comb.

Widely tunable narrow linewidth laser source based on photonic molecule microcombs and optical injection locking.

We demonstrate a method to generate a widely and arbitrarily tunable laser source with very narrow linewidth. By seeding a coupled-cavity microcomb with a highly coherent single-frequency laser and using injection locking of a Fabry-Perot laser to select a single output comb tone, a high power, high side mode suppression ratio output wave is obtained. The system is demonstrated across 1530 -1585 nm with a linewidth below 8 kHz, having 5 dBm output power and sidemode suppression of at least 60 dB. Prospects of extending the performance are also discussed.

Coherent combining of low-power optical signals based on optically amplified error feedback.

In free-space optical communication links, the combining of optical signals from multiple apertures is a well-known method to collect more power for improved sensitivity or mitigation of atmospheric disturbances. However, for analog optical combining no detailed analysis has been made in cases when the optical signal power is very low (<-60 dBm) as would be the case in very long-haul free-space links. We present a theoretical and experimental study of analog coherent combining of noise-limited signals from multiple independent apertures by applying low frequency optical phase dithering to actively compensate the relative phases. It is experimentally demonstrated that a 97% combining efficiency of four 10 GBaud QPSK signals is possible with a signal power per aperture exceeding -80 dBm, in fair agreement with theory. We also discuss the scaling aspects to many apertures.

Phase-sensitively amplified wavelength-division multiplexed optical transmission systems.

The throughput and reach in fiber-optic communication links are limited by in-line optical amplifier noise and the Kerr nonlinearity in the optical transmission fiber. Phase-sensitive amplifiers (PSAs) are capable of amplifying signals without adding excess noise and mitigating the impairments caused by the Kerr nonlinearity. However, the effectiveness of Kerr nonlinearity mitigation depends on the dispersion pre-compensation in each span. This paper investigates dense wavelength-division multiplexed PSA-amplified links using joint processing with a less complex digital domain Volterra nonlinear equalizer at the receiver. Both numerically and with experiments, it is shown that this significantly reduces the impact of the dispersion pre-compensation in each span. Also, with simulations, a substantial improvement in transmission reach is demonstrated for PSA links.

Overcoming the quantum limit of optical amplification in monolithic waveguides.

Optical amplifiers are essential in numerous photonic applications. Parametric amplifiers, relying on a nonlinear material to create amplification, are uniquely promising as they can amplify without generating excess noise. Here, we demonstrate amplification based on the third-order nonlinearity in a single chip while, in addition, reporting a noise figure significantly below the conventional quantum limit when operated in phase-sensitive mode. Our results show the potential of nanophotonics for realizing continuous-wave parametric amplification that can enable applications in optical communications, signal processing, and quantum optics across a wide range of frequencies.

Modulation format dependence on transmission reach in phase-sensitively amplified fiber links.

We quantify the maximum transmission reach for phase-insensitive amplifier (PIA) and phase-sensitive amplifier (PSA) links with different modulation formats and show that the maximum transmission reach increase (MTRI) when using PSAs compared to PIAs is enhanced for higher-order modulation formats. The higher-order modulation formats are more susceptible to smaller phase rotations from nonlinearities, and PSAs are efficient in mitigating these smaller phase distortions. Numerical simulations were performed for single- and multi-span PIA and PSA links with single and multiple wavelength channels. We obtain a significant enhancement in the MTRI with PSAs compared to PIAs when using higher-order modulation formats for both the single- and multi-channel systems in single- and multi-span links. We verify the enhancement with a single-span, single-channel system experiment. We also demonstrate, for the first time, a 64-QAM modulation format fiber transmission in phase-sensitively amplified link, with a 13.3-dB maximum allowable span loss increase compared to a phase-insensitively amplified link.

One photon-per-bit receiver using near-noiseless phase-sensitive amplification.

Space communication for deep-space missions, inter-satellite data transfer and Earth monitoring requires high-speed data connectivity. The reach is fundamentally dictated by the available transmission power, the aperture size, and the receiver sensitivity. A transition from radio-frequency links to optical links is now seriously being considered, as this greatly reduces the channel loss caused by diffraction. A widely studied approach uses power-efficient formats along with nanowire-based photon-counting receivers cooled to a few Kelvins operating at speeds below 1 Gb/s. However, to achieve the multi-Gb/s data rates that will be required in the future, systems relying on pre-amplified receivers together with advanced signal generation and processing techniques from fibre communications are also considered. The sensitivity of such systems is largely determined by the noise figure (NF) of the pre-amplifier, which is theoretically 3 dB for almost all amplifiers. Phase-sensitive optical amplifiers (PSAs) with their uniquely low NF of 0 dB promise to provide the best possible sensitivity for Gb/s-rate long-haul free-space links. Here, we demonstrate a novel approach using a PSA-based receiver in a free-space transmission experiment with an unprecedented bit-error-free, black-box sensitivity of 1 photon-per-information-bit (PPB) at an information rate of 10.5 Gb/s. The system adopts a simple modulation format (quadrature-phase-shift keying, QPSK), standard digital signal processing for signal recovery and forward-error correction and is straightforwardly scalable to higher data rates.

Waveguide tapering for improved parametric amplification in integrated nonlinear Si3N4 waveguides.

In this paper, we propose and numerically investigate waveguide tapering to improve optical parametric amplification in integrated nonlinear Si3N4 circuits. The phase matching condition of parametric amplification changes along the length of uniform Si3N4 waveguides, due to the non-negligible propagation loss, potentially causing peak-gain wavelength shifts of more than 20 nm. By tapering the waveguide width along propagation, we can achieve a 2.5 dB higher maximum parametric gain thanks to the improved phase matching, which can also broaden the amplification bandwidth. Therefore, the length of an optimally tapered Si3N4 waveguide can be 23% shorter than a uniform one in the case of a 3.0 dB/m propagation loss and a single continuous-wavelength pump. Quasi-continuous tapers are efficient to approximate continuous ones and might simplify the fabrication of long tapered nonlinear Si3N4 waveguides, which are promising for optical signal processing and optical communications.

Enhanced analog-optical link performance with noiseless phase-sensitive fiber optical parametric amplifiers.

In this paper, we investigate the enhancement of analog optical link performance with noiseless phase-sensitive fiber optical parametric amplifiers. The influence of different noise sources in the link impacts the quality of analog optical signals, especially with low optical signal power, which has not been investigated before. Theoretically, the increase in signal-to-noise ratio and spurious-free dynamic range can be up to ∼6 dB and ∼4 dB, respectively, if the noise figure of optical pre-amplifier drops 3 dB when the received optical power is less than -65 dBm. In addition, experiments based on a 1.3 dB-noise-figure phase-sensitive fiber optical parametric amplifier and conventional optical pre-amplifiers are implemented, and the measured results agree with the theoretical expectations. This illustrates that noiseless phase-sensitive optical amplification may pave the way to long-haul distribution of analog optical signals and find applications in microwave-photonic systems.

Phase-coherent lightwave communications with frequency combs.

Fiber-optical networks are a crucial telecommunication infrastructure in society. Wavelength division multiplexing allows for transmitting parallel data streams over the fiber bandwidth, and coherent detection enables the use of sophisticated modulation formats and electronic compensation of signal impairments. Optical frequency combs can replace the multiple lasers used for the different wavelength channels. Beyond multiplexing, it has been suggested that the broadband phase coherence of frequency combs could simplify the receiver scheme by performing joint reception and processing of several wavelength channels, but an experimental validation in a fiber transmission experiment remains elusive. Here we demonstrate and quantify joint reception and processing of several wavelength channels in a full transmission system. We demonstrate two joint processing schemes; one that reduces the phase-tracking complexity and one that increases the transmission performance.

High-Q Si3N4 microresonators based on a subtractive processing for Kerr nonlinear optics.

Microresonator frequency combs (microcombs) are enabling new applications in frequency synthesis and metrology - from high-speed laser ranging to coherent optical communications. One critical parameter that dictates the performance of the microcomb is the optical quality factor (Q) of the microresonator. Microresonators fabricated in planar structures such as silicon nitride (Si3N4) allow for dispersion engineering and the possibility to monolithically integrate the microcomb with other photonic devices. However, the relatively large refractive index contrast and the tight optical confinement required for dispersion engineering make it challenging to attain Si3N4 microresonators with Qs > 107 using standard subtractive processing methods - i.e. photonic devices are patterned directly on the as-deposited Si3N4 film. In this work, we achieve ultra-smooth Si3N4 microresonators featuring mean intrinsic Qs around 11 million. The cross-section geometry can be precisely engineered in the telecommunications band to achieve either normal or anomalous dispersion, and we demonstrate the generation of mode-locked dark-pulse Kerr combs as well as soliton microcombs. Such high-Qs allow us to generate 100 GHz soliton microcombs, demonstrated here for the first time in Si3N4 microresonators fabricated using a subtractive processing method. These results enhance the possibilities for co-integration of microcombs with high-performance photonic devices, such as narrow-linewidth external-cavity diode lasers, ultra-narrow filters and demultiplexers.

Analysis of nonlinearity mitigation using phase-sensitive optical parametric amplifiers.

Phase-sensitive optical parametric amplifiers (PSAs) can provide low-noise optical amplification while simultaneously mitigating nonlinear distortions caused by the Kerr effect. However, nonlinearity mitigation using PSAs is affected by link parameters, and imperfect link design results in residual nonlinear distortions. In this paper, we use first-order perturbation theory to describe these residual nonlinear distortions, and develop a way to mitigate them using a modified third-order Volterra nonlinear equalizer (VNLE) in the receiver. Using numerical simulations, we show that our proposed VNLE reduces the residual nonlinear distortions in links using in-line PSAs for several combinations of symbol rates and modulation formats, and can increase the maximum transmission distance by up to 80%. We also perform a proof-of-concept experiment and confirm that our modified VNLE can mitigate the residual nonlinear distortions on a 10-Gbaud 16QAM signal after transmission through a 10×80-km link with in-line PSAs.

Overhead-optimization of pilot-based digital signal processing for flexible high spectral efficiency transmission.

We present a low-complexity fully pilot-based digital signal processing (DSP) chain designed for high spectral efficiency optical transmission systems. We study the performance of the individual pilot algorithms in simulations before demonstrating transmission of a 51×24 Gbaud PM-64QAM superchannel over distances reaching 1000 km. We present an overhead optimization technique using the system achievable information rate to find the optimal balance between increased performance and throughput reduction from adding additional DSP pilots. Using the optimal overhead of 2.4%, we report 9.3 (8.3) bits/s/Hz spectral efficiency, or equivalently 11.9 (10.6) Tb/s superchannel throughput, after 480 (960) km of transmission over 80 km spans with EDFA-only amplification. Moreover, we show that the optimum overhead depends only weakly on transmission distance, concluding that back-to-back optimization is sufficient for all studied distances. Our results show that pilot-based DSP combined with overhead optimization can increase the robustness and performance of systems using advanced modulation formats while still maintaining state-of-the-art spectral efficiency and multi-Tb/s throughput.

Master-slave carrier recovery for M-QAM multicore fiber transmission.

Master-slave carrier recovery is a digital signal processing technique that uses correlated phase noise in multi-channel receivers to eliminate redundant carrier recovery blocks. In this paper we experimentally investigate the performance of master-slave carrier recovery for multicore fiber transmission in the presence of inter-channel nonlinear interference. Using a triple parallel loop setup we jointly receive three spatial channels in a 7-core fiber for transmission distances of up to 1600 km. We find that an increased launch power causes a moderate penalty on the slave channels. Furthermore, we study the penalty from a non-zero inter-core skew.

Low-loss high-Q silicon-rich silicon nitride microresonators for Kerr nonlinear optics.

Silicon nitride is a dielectric material widely used for applications in linear and nonlinear optics. It has an ultra-broad transparency window, low intrinsic loss, and a refractive index that allows for moderate optical field confinement in waveguides. The chemical composition of this material can be precisely set during the fabrication process, leading to an extra degree of freedom for tailoring the optical and mechanical properties of photonic chips. Silicon-rich silicon nitride waveguides are appealing for nonlinear optics, because they have a higher nonlinear Kerr coefficient and refractive index than what is possible with stoichiometric silicon nitride. This is a direct consequence of the increased silicon content. However, silicon-rich silicon nitride waveguides typically display higher absorption losses. In this Letter, we report low-loss (∼0.4 dB/cm) silicon-rich silicon nitride waveguides. The structures feature high optical confinement and can be engineered with low anomalous dispersion. We find an optimum silicon composition that, through an annealing process, overcomes optical losses associated to N-H bonds in the telecom band. Based on this technology, we successfully fabricate microresonators with mean quality factors (Q) ∼0.8×106 in the C and L bands. Broadband coherent microresonator frequency combs are generated in this platform, indicating its potential for efficient Kerr nonlinear optics.

Improved mitigation of self-phase modulation induced impairments in 28 GBaud phase-sensitive amplified links.

The improved mitigation of self-phase modulation (SPM) induced nonlinear impairments by the use of a multi-span dispersion map optimization in 28 GBaud phase-sensitive amplifier (PSA) links is numerically investigated. We show that a four-span dispersion map optimized PSA link provides 2.1 times reach improvement over a single-span optimized PSA link with a total nonlinear phase shift tolerance increase from 2.1 radians to 8.8 radians. Furthermore, the optimized PSA link increases the maximum transmission reach by 6.9 times compared to a single-span optimized in-line dispersion managed phase-insensitive amplifier (PIA) link and 4.3 times reach extension is achieved compared to a dispersion unmanaged PIA link.

Optical injection locking at sub nano-watt powers.

We demonstrate optical injection locking (OIL) at record low injection power of -65 dBm using EDFA-based pre-amplification and an electrical phase locked loop (PLL). Investigating the phase noise characteristics of OIL, we find that at low injection powers the slave laser linewidth and injection ratio strongly influence the phase noise of the locked slave output. By introducing an EDFA pre-amplifier, the minimum locking power for OIL is reduced. Moreover, using this pre-amplifier we find that there exists an optimum injection power into the slave where the output phase noise is minimized and is below the phase noise without EDFA. We evaluate an OIL-based pump recovery in a phase sensitive amplifier (PSA) receiver system aimed at free-space communications.

Publisher Correction: Long-haul optical transmission link using low-noise phase-sensitive amplifiers.

The original version of this Article incorrectly listed an affiliation of Samuel L.I. Olsson as 'Thomas Johann Seebeck Department of Electronics, Tallinn University of Technology, Tallinn 19086, Estonia', instead of the correct 'Present address: Nokia Bell Labs, 791 Holmdel Road, Holmdel, NJ 07733, USA'. Similarly, Egon Astra had an incorrect affiliation of 'Present address: Nokia Bell Labs, 791 Holmdel Road, Holmdel, NJ 07733, USA', instead of the correct 'Thomas Johann Seebeck Department of Electronics, Tallinn University of Technology, Tallinn 19086, Estonia'. This has been corrected in both the PDF and HTML versions of the Article.