Nonlinear optical response of heme solutions.

Heme is the prosthetic group for cytochrome that exists in nearly all living organisms and serves as a vital component of human red blood cells (RBCs). Tunable optical nonlinearity in suspensions of RBCs has been demonstrated previously, however, the nonlinear optical response of a pure heme (without membrane structure) solution has not been studied to our knowledge. In this work, we show optical nonlinearity in two common kinds of heme (i.e., hemin and hematin) solutions by a series of experiments and numerical simulations. We find that the mechanism of nonlinearity in heme solutions is distinct from that observed in the RBC suspensions where the nonlinearity can be easily tuned through optical power, concentration, and the solution properties. In particular, we observe an unusual phenomenon wherein the heme solution exhibits negative optical nonlinearity and render self-collimation of a focused beam at specific optical powers, enabling shape-preserving propagation of light to long distances. Our results may have potential applications in optical imaging and medical diagnosis through blood.

Efficient direct mapping of the nonlinear optical response via modulated Airy beams.

We report a scheme to achieve efficient direct mapping of the nonlinear optical response into a spatial beam profile. Compared with previous methods where a standard two-dimensional Airy beam was used as a probe, a modulated beam configuration allows for an improved mapping efficiency, stemming from the induced nonlinearity caused by the applied modulation. We find that the mapping efficiency along different orientations is highly related to the beam patterns and the type of nonlinearity. The improvement of the mapping quality and new, to the best of our knowledge, features found in simulations are further verified in experiments by testing a photorefractive nonlinearity. Our results represent a further step towards an effective tool for the direct measurement of the nonlinear optical response with low power consumption.

Unveiling the Link between Airy-like Self-Acceleration and Diametric Drive Acceleration.

We theoretically reveal the link between two types of self-acceleration mechanisms widely emerging in wave dynamics and experimentally demonstrate such a connection via pulse interactions in nonlinear optical fibers. We find that, in order to realize a pulse pair subjected to a diametric drive acceleration, one of the two components can be directly obtained from a self-accelerating Airy-like pulse under appropriate conditions. Such a form of synchronized acceleration cannot be achieved by approaches previously used to generate diametric drive acceleration. Our results generalize the fundamental concept of diametric drive acceleration and may bring about unconventional approaches to control self-accelerating waves.

Dynamically Emerging Topological Phase Transitions in Nonlinear Interacting Soliton Lattices.

We demonstrate dynamical topological phase transitions in evolving Su-Schrieffer-Heeger lattices made of interacting soliton arrays, which are entirely driven by nonlinearity and thereby exemplify an emergent nonlinear topological phenomenon. The phase transitions occur from the topologically trivial-to-nontrivial phase in periodic succession with crossovers from the topologically nontrivial-to-trivial regime. The signature of phase transition is the gap-closing and reopening point, where two extended states are pulled from the bands into the gap to become localized topological edge states. Crossovers occur via decoupling of the edge states from the bulk of the lattice.

Third-order Riemann pulses in optical fibers.

We introduce the concept of third-order Riemann pulses in nonlinear optical fibers. These pulses are generated when properly tailored input pulses propagate through optical fibers in the presence of higher-order dispersion and Kerr nonlinearity. The local propagation speed of these optical wave packets is governed by their local amplitude, according to a rule that remains unchanged during propagation. Analytical and numerical results exhibit a good agreement, showing controllable pulse steepening and subsequent shock wave formation. Specifically, we found that the pulse steepening dynamic is predominantly determined by the action of higher-order dispersion, while the contribution of group velocity dispersion is merely associated with a shift of the shock formation time relative to the comoving frame of the pulse evolution. Unlike standard Riemann waves, which exclusively exist within the strong self-defocusing regime of the nonlinear Schrödinger equation, such third-order Riemann pulses can be generated under both anomalous and normal dispersion conditions. In addition, we show that the third-order Riemann pulse dynamics can be judiciously controlled by a phase chirping parameter directly included in the initial chirp profile of the pulse.

Tunable self-similar Bessel-like beams of arbitrary order.

We predict that Bessel-like beams of arbitrary integer order can exhibit a tunable self-similar behavior (that take an invariant form under suitable stretching transformations). Specifically, by engineering the amplitude and the phase on the input plane in real space, we show that it is possible to generate higher-order vortex Bessel-like beams with fully controllable radius of the hollow core and maximum intensity during propagation. In addition, using a similar approach, we show that it is also possible to generate zeroth-order Bessel-like beams with controllable beam width and maximum intensity. Our numerical results are in excellent agreement with our theoretical predictions.

Optical generation and control of spatial Riemann waves.

We extend the concept of Riemann waves (RWs) to the spatial domain and demonstrate for the first time, to the best of our knowledge, Riemann beams with a propagation scenario allowing controllable shock formation in a nonlinear optical system. Similar to their standard counterparts, "shifted" RWs are characterized by a local propagation speed proportional to their local amplitude. Their steepening dynamics can be judiciously controlled by means of an additional phase term. In particular, RWs are generated by properly tailoring the initial phase of an optical beam propagating through a thermal solution of an m-cresol/nylon mixture that exhibits a giant self-defocusing nonlinearity. The experimental results show a controllable steepening and shock wave behavior, in good agreement with the prediction from the simple inviscid Burgers equation.

Optimal compression and energy confinement of optical Airy bullets.

We report on an approach to generate non-diffractive and non-dispersive Airy3 bullets with enhanced spatio-temporal energy confinement. By appropriately reshaping the initial spectral components in the Fourier domain, the resulting optical bullets show a significant enhancement of their central lobe intensity while exhibiting a reduced spatio-temporal outspread of the surrounding sub-lobes - typical of Airy3 bullets. Numerically, we demonstrate that when propagating in dispersive media within a linear regime, such optimized Airy3 bullets maintain the peculiar properties of their "standard" counterparts, including curved trajectories, non-spreading features and self-healing. We foresee direct applications in novel and non-disruptive optical techniques for imaging, tomography and spatio-temporally resolved spectroscopy.

Experimental Generation of Riemann Waves in Optics: A Route to Shock Wave Control.

We report the first observation of Riemann (simple) waves, which play a crucial role for understanding the dynamics of any shock-bearing system. This was achieved by properly tailoring the phase of an ultrashort light pulse injected into a highly nonlinear fiber. Optical Riemann waves are found to evolve in excellent quantitative agreement with the remarkably simple inviscid Burgers equation, whose applicability in physical systems is often challenged by viscous or dissipative effects. Our method allows us to further demonstrate a viable novel route to efficiently control the shock formation by the proper shaping of a laser pulse phase. Our results pave the way towards the experimental study, in a convenient benchtop setup, of complex physical phenomena otherwise difficult to access.

Engineering topological interface states in metal-wire waveguides for broadband terahertz signal processing.

Innovative terahertz waveguides are in high demand to serve as a versatile platform for transporting and manipulating terahertz signals for the full deployment of future six-generation (6G) communication systems. Metal-wire waveguides have emerged as promising candidates, offering the crucial advantage of sustaining low-loss and low-dispersion propagation of broadband terahertz pulses. Recent advances have opened up new avenues for implementing signal-processing functionalities within metal-wire waveguides by directly engraving grooves along the wire surfaces. However, the challenge remains to design novel groove structures to unlock unprecedented signal-processing functionalities. In this study, we report a plasmonic signal processor by engineering topological interface states within a terahertz two-wire waveguide. We construct the interface by connecting two multiscale groove structures with distinct topological invariants, i.e., featuring a π-shift difference in the Zak phases. The existence of this topological interface within the waveguide is experimentally validated by investigating the transmission spectrum, revealing a prominent transmission peak in the center of the topological bandgap. Remarkably, we show that this resonance is highly robust against structural disorders, and its quality factor can be flexibly controlled. This unique feature not only facilitates essential functions such as band filtering and isolating but also promises to serve as a linear differential equation solver. Our approach paves the way for the development of new-generation all-optical analog signal processors tailored for future terahertz networks, featuring remarkable structural simplicity, ultrafast processing speeds, as well as highly reliable performance.

Periodic self-accelerating beams by combined phase and amplitude modulation in the Fourier space.

We propose and demonstrate the generation of periodic self-accelerating beams through both phase and amplitude modulation in the Fourier space. For small amplitude variations, an accelerating beam still follows a smooth convex trajectory, which can be traced by acting on the spectral phase only. However, large modulations such as those generated from the Heaviside function with a zero amplitude distribution partially modify the convex trajectory due to the appearance of straight-line paths. Furthermore, periodic self-accelerating beams along convex trajectories are realized by employing an array of "spectral wells" in both the paraxial and nonparaxial regimes.

Spectrum to distance mapping via nonlinear Airy pulses.

We theoretically and experimentally study the phenomena related to self-phase modulation of Airy pulses in fibers. During nonlinear evolution, most spectral components of the Airy pulses concentrate into one or two peaks for normal and anomalous dispersion, respectively. The resulting peaks self-shift along the propagation, effectively mapping the longitudinal coordinate into the frequency domain. The frequency shift can be precisely controlled by simply acting on the spectral cubic phase structure without the need to alter the fiber length.

Reshaping the trajectory and spectrum of nonlinear Airy beams.

We demonstrate theoretically and experimentally that a finite Airy beam changes its trajectory while maintaining its acceleration in nonlinear photorefractive media. During this process, the spatial spectrum reshapes dramatically, leading to negative (or positive) spectral defects on the initial spectral distribution under a self-focusing (or defocusing) nonlinearity.

Nonlinear control of photonic higher-order topological bound states in the continuum.

Higher-order topological insulators (HOTIs) are recently discovered topological phases, possessing symmetry-protected corner states with fractional charges. An unexpected connection between these states and the seemingly unrelated phenomenon of bound states in the continuum (BICs) was recently unveiled. When nonlinearity is added to the HOTI system, a number of fundamentally important questions arise. For example, how does nonlinearity couple higher-order topological BICs with the rest of the system, including continuum states? In fact, thus far BICs in nonlinear HOTIs have remained unexplored. Here we unveil the interplay of nonlinearity, higher-order topology, and BICs in a photonic platform. We observe topological corner states that are also BICs in a laser-written second-order topological lattice and further demonstrate their nonlinear coupling with edge (but not bulk) modes under the proper action of both self-focusing and defocusing nonlinearities. Theoretically, we calculate the eigenvalue spectrum and analog of the Zak phase in the nonlinear regime, illustrating that a topological BIC can be actively tuned by nonlinearity in such a photonic HOTI. Our studies are applicable to other nonlinear HOTI systems, with promising applications in emerging topology-driven devices.

Efficient Optical Energy Harvesting in Self-Accelerating Beams.

We report the experimental observation of energetically confined self-accelerating optical beams propagating along various convex trajectories. We show that, under an appropriate transverse compression of their spatial spectra, these self-accelerating beams can exhibit a dramatic enhancement of their peak intensity and a significant decrease of their transverse expansion, yet retaining both the expected acceleration profile and the intrinsic self-healing properties. We found our experimental results to be in excellent agreement with the numerical simulations. We expect further applications in such contexts where power budget and optimal spatial confinement can be important limiting factors.