### Simulton Formation in Nonlinear Resonators

Formation and propagation of solitary pulses in nonlinear resonators, for instance in mode-locked lasers and micro-resonators have attracted increasing research interest because they play an important role in realization of femtosecond frequency comb sources. In our recent theoretical and experimental studies, we have discovered a new regime of optical parametric oscillator operation where formation of simultons, i.e. simultaneous dark/bright solitons, is the main pulse shaping mechanism. This new regime of light-matter interaction in nonlinear resonators can lead to significant pulse shortening through half-harmonic generation that can enable on-chip generation of extremely short-pulse frequency combs in the mid-IR. Since such a nonlinear process happens in a regime where most of the conventional assumptions of nonlinear optics are not valid, we developed the theory to understand and design devices based on it, and we have demonstrated the experimental proof-of-concept [1]. Simulton-based resonators can enable enormous opportunities for realization of scalable solutions for molecular spectroscopic applications.

[1] M. Jankowski et al., “Temporal Simultons in Optical Parametric Oscillators.”** *** Physical Review Letters* 120 (2018), 053904.

### Optical Ising Machines

Finding the ground states of the Ising Hamiltonian maps to various combinatorial optimization problems in biology, medicine, wireless communications, artificial intelligence and social network. So far, no efficient classical and quantum algorithm is known for these problems and intensive research is focused on creating physical systems—Ising machines—capable of finding the absolute or approximate ground states of the Ising Hamiltonian. In parallel to the fast- growing exploratory efforts on quantum computing, we proposed and demonstrated that Ising machines can be implemented using a network of optical parametric oscillators, where the collective quantum-noise driven phase bifurcation in the network can be a computational resource for tackling these hard problems. We showed some numerical analysis of the idea [1], demonstrated the first proof-of-concept of an optical Ising machine [2], and developed a large-scale OPO-based Ising machine [3] that can be programmed arbitrary Ising problems; we demonstrated its promising computational performance on thousands of problems. We have also numerically showed possibility of quantum entanglement in these optical networks and their potential in implementation of other quantum systems and architectures [4].

[1] Z. Wang et al., “Coherent Ising machine based on degenerate optical parametric oscillators.” ** Physical Review A** 88.6 (2013): 063853.

[2] A. Marandi et al., “Network of time-multiplexed optical parametric oscillators as a coherent Ising machine.” ** Nature Photonics** 8.12 (2014): 937-942.

[3] P. McMahon* and A. Marandi* et al., “A fully programmable 100-spin coherent Ising machine with all-to-all connections.” ** Science** 354.6312 (2016): 614-617.

[4] K. Takata et al., “Quantum correlation in degenerate optical parametric oscillators with mutual injections.” ** Physical Review A** 92.4 (2015): 043821.

### Half-harmonic generation of few-cycle mid-IR frequency combs

Half-harmonic generation is a nonlinear optical process that is the inverse of second harmonic generation, in which photons are split into pairs of identical photons. This process can occur in optical parametric oscillators at degeneracy, and we have demonstrated how such process can be utilized to generate optical frequency combs in the mid-IR using the well-developed near-IR frequency combs [1, 2]. These coherent broadband sources cover the molecular fingerprint region of the optical spectrum, enabling direct sensing of several molecular species simultaneously; a capability that has potential applications in areas such as non-invasive medical breath analysis and environmental analysis of greenhouse gases. We have demonstrated some of the most efficient sources of mid-IR frequency combs with the shortest pulses and broadest bandwidths using half-harmonic generation, and a two-octave phase-locked down-conversion of frequency combs by cascading them [3, 4, 5] .

[1] N. C. Leindecker et al., “Broadband degenerate OPO for mid-infrared frequency comb generation.” ** Optics Express** 19.7 (2011): 6296-6302.

[2] A. Marandi et al., “Coherence properties of a broadband femtosecond mid-IR optical parametric oscillator operating at degeneracy.” ** Optics Express **20.7 (2012): 7255-7262.

[3] A. Marandi et al., “Cascaded half-harmonic generation of femtosecond frequency combs in the mid-infrared.” ** Optica** 3.3 (2016): 324-327.

[4] E. Sorokin et al., “Efficient half-harmonic generation of three-optical-cycle mid-IR frequency comb around 4 µm using OP-GaP.” * Optics Express *26.8 (2018): 9963-9971.

[5] N. Leindecker et al., “Octave-spanning ultrafast OPO with 2.6-6.1 µm instantaneous bandwidth pumped by femtosecond Tm-fiber laser.” ** Optics Express** 20.7 (2012): 7046-7053.