Routes to spatiotemporal chaos in Kerr optical frequency combs

Scalable parallel ultrafast optical random bit generation based on a single chaotic microcomb

Random bit generators are critical for information security, cryptography, stochastic modeling, and simulations. Speed and scalability are key challenges faced by current physical random bit generation. Herein, we propose a massively parallel scheme for ultrafast random bit generation towards rates of order 100 terabit per second based on a single micro-ring resonator. A modulation-instability-driven chaotic comb in a micro-ring resonator enables the simultaneous generation of hundreds of independent and unbiased random bit streams. A proof-of-concept experiment demonstrates that using our method, random bit streams beyond 2 terabit per second can be successfully generated with only 7 comb lines. This bit rate can be easily enhanced by further increasing the number of comb lines used. Our approach provides a chip-scale solution to random bit generation for secure communication and high-performance computation, and offers superhigh speed and large scalability.

Synchronization of two chaotic microresonator frequency combs

We explore the synchronization of chaotic microresonator frequency combs, emphasizing the modulation instability state, which is known for its inherent chaotic behaviors. Our study confirms that the synchronization of two such combs is feasible by injecting the output from the lead microresonator into the next microresonator's input. We also identify the optimal parameters for this synchronization. Remarkably, even partial injection from the leader is sufficient for synchronization, paving the way for versatile future system configurations. Such systems could simultaneously utilize distinct spectral components for synchronization and transmission. This work advances our understanding of chaotic microresonator combs, showing them to be pivotal elements in next-generation optical communication systems.

Multimode resonance transition to collapsed snaking in normal dispersive Kerr cavities: bright versus dark solitons

We study the dynamics of Kerr cavity solitons in the normal dispersion regime in the presence of an intracavity phase modulation. The associated parabolic potential introduces multimode resonances, which promote the formation of high-order bright solitons. By gradually reducing the potential strength, bright solitons undergo a transition into dark solitons. We describe this process as a shift from a multimode resonance to a collapsed snaking bifurcation structure. This work offers a comprehensive overview of cavity dynamics and may provide a potential pathway to access multi-stable states by effectively varying the phase modulation.

Infinite ergodicity that preserves the Lebesgue measure

In this study, we prove that a countably infinite number of one-parameterized one-dimensional dynamical systems preserve the Lebesgue measure and are ergodic for the measure. The systems we consider connect the parameter region in which dynamical systems are exact and the one in which almost all orbits diverge to infinity and correspond to the critical points of the parameter in which weak chaos tends to occur (the Lyapunov exponent converging to zero). These results are a generalization of the work by Adler and Weiss. Using numerical simulation, we show that the distributions of the normalized Lyapunov exponent for these systems obey the Mittag-Leffler distribution of order 1/2.

Drifting cavity solitons and dissipative rogue waves induced by time-delayed feedback in Kerr optical frequency comb and in all fiber cavities

Time-delayed feedback plays an important role in the dynamics of spatially extended systems. In this contribution, we consider the generic Lugiato-Lefever model with delay feedback that describes Kerr optical frequency comb in all fiber cavities. We show that the delay feedback strongly impacts the spatiotemporal dynamical behavior resulting from modulational instability by (i) reducing the threshold associated with modulational instability and by (ii) decreasing the critical frequency at the onset of this instability. We show that for moderate input intensities it is possible to generate drifting cavity solitons with an asymmetric radiation emitted from the soliton tails. Finally, we characterize the formation of rogue waves induced by the delay feedback.

Investigation of the local dispersion change in anomalous dispersion microcavity and quantitative analysis of the phase-matching in Kerr comb generation

We numerically simulate Kerr comb generation in an anomalous dispersion microcavity by modal expansion method and demonstrate that the initiation of comb generation is affected by the change of local dispersion possibly caused by avoided mode crossings. We also quantitatively analyze the instantaneous phase matching of different modes and reveal the characteristics of energy distribution in different modes in the dynamics of comb generation. We demonstrate that the local dispersion change can control the Kerr comb to transform between Type I and Type II combs. We also find that local dispersion is closely related to the stability of the power of Kerr comb lines, something that can change the dynamical state of the system near the Hamiltonian-Hopf bifurcation under an anomalous dispersion regime from a quasi-periodic oscillation state to a periodic state (Turing patterns).

On the phase noise performance of microwave and millimeter-wave signals generated with versatile Kerr optical frequency combs

We investigate the phase noise performance of micro- and millimeter-wave signals generated using a ultra-high Q whispering gallery mode disk-resonator with Kerr nonlinearity. Our study focuses on the stability of the optical spectra and on the performances of the corresponding microwave and millimeter-wave beat notes in terms of power and phase noise. The blue slope of an optical mode of the resonator, allowing for the generation of optical frequency combs, is accurately explored in order to identify various comb patterns. Each of these patterns is characterized in the optical and radio-frequency domains. Phase noise levels below -100 dBc/Hz at 10 kHz offset have been achieved for beat notes in the radio-frequency spectrum at 12 GHz, 18 GHz, 24 GHz, 30 GHz, and 36 GHz with the same resonator.

Phase-locking transition in Raman combs generated with whispering gallery mode resonators

We investigate the mechanisms leading to phase locking in Raman optical frequency combs generated with ultrahigh Q crystalline whispering gallery mode disk resonators. We show that several regimes can be triggered depending on the pumping conditions, such as single-frequency Raman lasing, multimode operation involving more than one family of cavity eigenmodes, and Kerr-assisted Raman frequency comb generation. The phase locking and coherence of the combs are experimentally monitored through the measurement of beat signal spectra. These phase-locked combs, which feature high coherence and wide spectral spans, are obtained with pump powers in the range of a few tens of mW. In particular, Raman frequency combs with multiple free-spectral range spacings are reported, and the measured beat signal in the microwave domain features a 3 dB linewidth smaller than 50 Hz, thereby indicating phase locking.

Universal nonlinear scattering in ultra-high Q whispering gallery-mode resonators

Universal nonlinear scattering processes such as Brillouin, Raman, and Kerr effects are fundamental light-matter interactions of particular theoretical and experimental importance. They originate from the interaction of a laser field with an optical medium at the lattice, molecular, and electronic scale, respectively. These nonlinear effects are generally observed and analyzed separately, because they do not often occur concomitantly. In this article, we report the simultaneous excitation of these three fundamental interactions in mm-size ultra-high Q whispering gallery mode resonators under continuous wave pumping. Universal nonlinear scattering is demonstrated in barium fluoride and strontium fluoride, separately. We further propose a unified theory based on a spatiotemporal formalism for the understanding of this phenomenology.

Optimally coherent Kerr combs generated with crystalline whispering gallery mode resonators for ultrahigh capacity fiber communications

Optical Kerr frequency combs are known to be effective coherent multiwavelength sources for ultrahigh capacity fiber communications. These combs are the frequency-domain counterparts of a wide variety of spatiotemporal dissipative structures, such as cavity solitons, chaos, or Turing patterns (rolls). In this Letter, we demonstrate that Turing patterns, which correspond to the so-called primary combs in the spectral domain, are optimally coherent in the sense that for the same pump power they provide the most robust carriers for coherent data transmission in fiber communications using advanced modulation formats. Our model is based on a stochastic Lugiato-Lefever equation which accounts for laser pump frequency jitter and amplified spontaneous emission noise induced by the erbium-doped fiber amplifier. Using crystalline whispering-gallery-mode resonators with quality factor Q∼10^{9} for the comb generation, we show that when the noise is accounted for, the coherence of a primary comb is significantly higher than the coherence of their solitonic or chaotic counterparts for the same pump power. In order to confirm this theoretical finding, we perform an optical fiber transmission experiment using advanced modulation formats, and we show that the coherence of the primary comb is high enough to enable data transmission of up to 144  Gbit/s per comb line, the highest value achieved with a Kerr comb so far. This performance evidences that compact crystalline photonic systems have the potential to play a key role in a new generation of coherent fiber communication networks, alongside fully integrated systems.

Extension of spatiotemporal chaos in glow discharge-semiconductor systems

Generation of chaos in response systems is discovered numerically through specially designed unidirectional coupling of two glow discharge-semiconductor systems. By utilizing the auxiliary system approach, [H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, Phys. Rev. E 53, 4528-4535 (1996)] it is verified that the phenomenon is not a chaos synchronization. Simulations demonstrate various aspects of the chaos appearance in both drive and response systems. Chaotic control is through the external circuit equation and governs the electrical potential on the boundary. The expandability of the theory to collectives of glow discharge systems is discussed, and this increases the potential of applications of the results. Moreover, the research completes the previous discussion of the chaos appearance in a glow discharge-semiconductor system [D. D. Šijačić U. Ebert, and I. Rafatov, Phys. Rev. E 70, 056220 (2004).].