C. Martijn de Sterke’s research while affiliated with The University of Sydney and other places

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Publications (463)


Observation of fractional evolution in nonlinear optics
  • Preprint
  • File available

October 2024

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20 Reads

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Justin Widjaja

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Y. Long Qiang

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C. Martijn de Sterke

The idea of fractional derivatives has a long history that dates back centuries. Apart from their intriguing mathematical properties, fractional derivatives have been studied widely in physics, for example in quantum mechanics and generally in systems with nonlocal temporal or spatial interactions. However, systematic experiments have been rare due to challenges associated with the physical implementation. Here we report the observation and full characterization of a family of temporal optical solitons that are governed by a nonlinear wave equation with a fractional Laplacian. This equation has solutions with unique properties such as non-exponential tails and a very small time-bandwidth product.

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All-optical damping forces enhanced by metasurfaces for stable relativistic lightsail propulsion

August 2024

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5 Reads

Lightsails are a promising spacecraft concept that can reach relativistic speeds via propulsion by laser light, allowing travel to nearby stars within a human lifetime. The success of a lightsail mission requires that any motion in the plane transverse to the propagation direction is bounded and damped for the entire acceleration phase. Here, we demonstrate that a previously unappreciated relativistic force, which generalizes the Poynting-Robertson effect, can passively damp this transverse motion. We show that this purely optical effect can be enhanced by two orders of magnitude compared to plane mirror sails by judicious design of the scattering response. We thus demonstrate that exploiting relativistic effects may be a practical means to control the motion of lightsails.


(a) Schematic illustration of the laser cavity. LD, laser diode; WDM, wavelength division multiplexer; Iso, isolator; PC, polarization controller; FP, fiber polarizer; SPS, spectral pulse shaper; OC, output coupler. (b) Measured output spectrum. Inset shows the applied net-cavity dispersion, following Eq. (1). (c) Simulated output spectrum. Inset shows the corresponding temporal intensity (solid blue). The dashed line indicates the common envelope.
Temporal evolution of the simulated output pulse over $50$ 50 consecutive roundtrips when the laser operates in the (a) phase-locked and (c) phase-unlocked regimes. Temporal intensity profile after $25$ 25 (solid blue) and $55$ 55 (red dashed) roundtrips for the (b) phase-locked and (d) phase-unlocked regimes. The black dashed line indicates the hyperbolic secant envelope.
(a) Simulated and (b) measured averaged output spectra of the phase-locked (blue) and phase-unlocked (red dashed) operating regimes. The green area indicates the bandwidth over which the energy is calculated. Energies of $100$ 100 consecutive roundtrips for the phase-locked (blue dots) and phase-unlocked (red diamonds) regime, extracted from (c) numerical simulations and (d) experimental measurements. The solid red curve corresponds to a cosine fit with a period of $11.8$ 11.8 and $14.5$ 14.5 roundtrips, for the simulations and experiments, respectively.
RF spectra of the output pulse train centered around the first two harmonics, when the laser operates in the (a) phase-locked and (b) phase-unlocked regimes. Inset: zoom around the first cavity harmonic.
Phase-locked and phase-unlocked multicolor solitons in a fiber laser

July 2024

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75 Reads

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1 Citation

Multicolor solitons are nonlinear pulses composed of two or more solitons centered at different frequencies, propagating with the same group velocity. In the time domain, multicolor solitons consist of an envelope multiplying a more rapidly varying fringe pattern that results from the interference of these frequency components. Here, we report the observation in a fiber laser of a novel, to the best of our knowledge, type of dynamics in which different frequency components still have the same group velocity but have different propagation constants. This causes the relative phases between the constituent spectral components to change upon propagation, corresponding to the fringes moving under the envelope. This leads to small periodic energy variations that we directly measure. Our experimental results are in good agreement with realistic numerical simulations based on an iterative cavity map.


Dipole–dipole energy transfer in free space. (a) Calculated free space mutual impedance Z21parl02\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left| {{\text{Z}}_{{21_{{{\text{parl}}}} }}^{0} } \right|^{2}$$\end{document} normalized by its maximum for two parallel antennas with finite lengths L. The black dotted curve corresponds to the energy transfer between ideal point dipoles from Green’s function theory, which serves as a reference. Blue markers are experimental data recorded for L = λ/30. The shaded area indicates the region considered in (c) to compute the exponent n. (b) Relative error (log10 scale) of the normalized mutual impedance compared to point dipoles as a function of the dipole length and mutual separation. (c) Distance dependence 1/Rⁿ of the energy transfer averaged over the region 0.12 < kR < 0.57 (shaded area in (a)) as a function of the dipole length. (d) Bicolor map showing the {antenna length − antenna separation} regions where the exponent n of the energy transfer distance dependence 1/Rⁿ deviates by more or less than 5% with respect to the 1/R⁶ dependence predicted by Green’s function theory.
Influence of the antenna length on the energy transfer enhancement near a PEC mirror. (a) Setup and notations for parallel dipoles. (b) Energy transfer enhancement (with respect to free space) as a function of the distance to the PEC mirror for ideal point dipoles (black dotted line, Green’s function theory) and dipoles of finite lengths L (color lines, our analytical model). The separation between antennas is kR = 1 (R = 10 mm, 5 GHz frequency). (c) Relative error in the energy transfer enhancement of finite antennas compared to point dipoles. The right axis indicates the real part of the antenna input impedance. (d)–(f) are similar as (a)–(c), but for perpendicular dipoles. The grey area in (f) corresponds to the region of parameters which is physically impossible due to finite dipole lengths.
Experimental validation of the antenna length influence on the energy transfer enhancement near a PEC mirror. (a)–(c) are for parallel dipoles and (d)–(f) for perpendicular dipoles, as pictured in the top schematics. Blue triangles are experimental results, orange curves are the result of our analytical model and the dotted black curves are predictions from Green’s function theory. The antenna length normalized by the wavelength L/λ varies for each line, as indicated on the graph, and the separation is kept constant to the antenna length R = L. The root mean square errors σ between the experimental results and the Green’s theory predictions are shown in each graph.
Microwave analogy of Förster resonance energy transfer and effect of finite antenna length

May 2024

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37 Reads

The near-field interaction between quantum emitters, governed by Förster resonance energy transfer (FRET), plays a pivotal role in nanoscale energy transfer mechanisms. However, FRET measurements in the optical regime are challenging as they require nanoscale control of the position and orientation of the emitters. To overcome these challenges, microwave measurements were proposed for enhanced spatial resolution and precise orientation control. However, unlike in optical systems for which the dipole can be taken to be infinitesimal in size, the finite size of microwave antennas can affect energy transfer measurements, especially at short distances. This highlights the necessity to consider the finite antenna length to obtain accurate results. In this study, we advance the understanding of dipole–dipole energy transfer in the microwave regime by developing an analytical model that explicitly considers finite antennas. Unlike previous works, our model calculates the mutual impedance of finite-length thin-wire dipole antennas without assuming a uniform current distribution. We validate our analytical model through experiments investigating energy transfer between antennas placed adjacent to a perfect electric conductor mirror. This allows us to provide clear guidelines for designing microwave experiments, distinguishing conditions where finite-size effects can be neglected and where they must be taken into account. Our study not only contributes to the fundamental physics of energy transfer but also opens avenues for microwave antenna impedance-based measurements to complement optical FRET experiments and quantitatively explore dipole–dipole energy transfer in a wider range of conditions.


Optics and Photonics in Sydney: introduction to the focus issue

May 2024

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19 Reads

This focus issue provides an overview of current applied optics research activities in the Sydney region in Australia, illustrating the breadth and depth of the research carried out in the region. Below we first give an overview of some of the history of optics research in Sydney and then brief descriptions of the 10 papers in the issue.


Schematic of the picobalance and Gaussian beam. a) The picobalance comprises a photothermal excitation laser beam (405 nm laser drawn in blue), which is used to excite the cantilever. The position of each laser can be adjusted independently in three orthogonal directions using piezo‐based positioners. The picobalance is mounted on and compatible with an inverted optical microscope. b) Detail from a) showing the cantilever and the Gaussian beams reaching the cantilever. The cantilever can be in either air or in water. The microscope objective is underneath the cantilever. c) Gaussian beam propagating downward in the z‐direction. The main Gaussian beam parameters are indicated with their actual values for the photothermal beam. The beam waist w0 =  3.65 µm, where the beam radius is smallest. The Rayleigh range z0 =  103 µm corresponds to the propagation distance where the cross section of the beam is twice that at the beam waist. The confocal parameter is twice the Rayleigh range.
Photothermal efficiency as a function of the relative longitudinal position of the cantilever. a) Amplitude and phase response of a cantilever versus frequency for two different cantilever positions. The blue lines correspond to resonance curves (amplitude and phase) of the cantilever when the cantilever is located at the beam waist according to the optical microscope. The red lines show equivalent information as the blue lines but for the optimal position along the propagation axis of the photothermal beam. The measurements are performed in water with a R500 TL cantilever. b) Cantilever amplitude at resonance for different relative longitudinal cantilever positions for different optical powers of the photothermal beam. The origin of the axis is chosen to be at the position of maximum (optimal) photothermal efficiency, which is indicated by the dashed line (shaded in blue). The other dashed line (shaded in orange) indicates the longitudinal position at which the cantilever is at the apparent beam waist. The measurements are performed in water with a R500 TL cantilever. c) The images show, top: optical image of a cantilever and photothermal beam at the optimal position, bottom: optical image of the cantilever at the apparent beam waist. d) Results for similar measurements as in (b), but for different cantilever types in both air and water environments. The enhancement factors of the resonance amplitude at the optimal longitudinal position compared to that at the apparent beam waist are shown. All results were conducted for at least two independent cantilever probes and measurements for each probe were repeated at least twice. For each laser position five consecutive resonance curves were acquired.
Identifying the true position of the photothermal beam waist. a) Schematic setup for measuring the residual optical power of the photothermal excitation beam beneath the cantilever in which the longitudinal position of the photothermal laser with respect to the cantilever is changed. To avoid interference, the infrared laser is switched off during these measurements. It is switched back on immediately afterward to read out the cantilever oscillation amplitude. b) Top views schematic of the photothermal beam spot size at the cantilever for two different relative longitudinal cantilever positions. c) Cantilever (R500 TL) resonant oscillation amplitude and residual optical laser power versus longitudinal position measured using the setup in (a). The apparent beam waist position is marked with a dashed line shaded orange and the real beam waist position is shown with a dash line shaded in blue. d) Schematic of the photothermal Gaussian beam profile with the Gaussian focal shift, Rayleigh range, confocal range, and beam waist indicated.
Beams of different wavelengths generated by a laser diode. a) Schematic of two superimposed beams of different wavelengths generated by a laser diode. The principal beam comprises the intended 405 nm light, yet the diode also generates light above 450 nm (spurious beam). The location of the beam waists of the principal and spurious beams differs by 2450 µm in our setup. b) Power spectra in the range 350–850 nm of the 405 nm laser diode use in the experiments without the 450 nm longpass (LP) filter (blue curve) and with the 450 nm LP filter (red curve). All measurements are normalized with respect to the peak laser power measured without LP filter.
The detailed parameters of the cantilevers used in the experiment, including manufacturer, model, morphology, nominal dimensions, types of materials and coating layers. The oscillation information was obtained from the experiment.
Optimization and Artifacts of Photothermal Excitation of Microresonators

April 2024

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50 Reads

The excitation of microresonators using focused intensity modulated light, known as photothermal excitation, is gaining significant attention due to its capacity to accurately excite microresonators without distortions, even in liquid environments, which is driving key advancements in atomic force microscopy and related technologies. Despite progress in the development of coatings, the conversion of light into mechanical movement remains largely inefficient, limiting resonator movements to tens of nanometers even when milliwatts of optical power are used. Moreover, how photothermal efficiency depends on the relative position of a microresonator along the propagation axis of the photothermal beam remains poorly studied, hampering the understanding of the conversion of light into mechanical motion. Here, photothermal measurements are performed in air and water using cantilever microresonators and a custom‐built picobalance, to determine how photothermal efficiency changes along the propagation beam axis. It is identified that far out‐of‐band laser emission can lead to visual misidentification of the beam waist, resulting in a drop of photothermal efficiency of up to one order of magnitude. The measurements also unveil that the beam waist is not always the position of highest photothermal efficiency, and can reduce the efficiency up to 20% for silicon cantilevers with trapezoidal cross section.


Coupled mode theory for plasmonic couplers

April 2024

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96 Reads

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2 Citations

Photonic integrated circuits play an increasingly important role in several emerging technologies. Their functionality arises from a combination of integrated components, e.g., couplers, splitters, polarization rotators, and wavelength selective filters. Efficient and accurate simulation of these components is crucial for circuit design and optimization. In dielectric systems, design procedures typically rely on coupled-mode theory (CMT) methods, which then guide subsequent refined full-wave calculations. Miniaturization to deep sub-wavelength scales requires the inclusion of lossy plasmonic (metal) components, making optimization more complicated by the interplay between coupling and absorption. Even though CMT is well developed, there is no consensus as to how to rigorously and quantitatively implement it for lossy systems. Here we present an intuitive coupled-mode theory framework for quantitative analysis of dielectric–plasmonic directional and adiabatic couplers, whose large-scale implementation in 3D is prohibitively slow with full-wave methods. This framework relies on adapting existing coupled mode theory approaches by including loss as a perturbation. This approach will be useful in designing dielectric–plasmonic circuits, providing a first reference point for anyone using techniques such as inverse design and deep learning optimization methods.



Rational design of an integrated directional coupler for wideband operation

February 2024

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34 Reads

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1 Citation

We consider a design procedure for directional couplers for which the coupling length is approximately wavelength-independent over a wide bandwidth. We show analytically that two coupled planar waveguides exhibit a maximum in the coupling strength, which ensures both wideband transmission and minimal device footprint. This acts as a starting point for mapping out the relevant part of phase space. This analysis is then generalized to the fully three-dimensional geometry of rib waveguides using an effective medium approximation. This forms an excellent starting point for fully numerical calculations and leads to designs with unprecedented bandwidths and compactness.


Modulation instability with high-order dispersion: fundamental limitations of pattern formation

February 2024

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77 Reads

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2 Citations

We theoretically and numerically investigate modulation instability in the presence of even, high-order dispersion, focusing on general trends rather than on specific results for a particular dispersion order. We show that high-order dispersion leads to increasingly poor phase matching between the three central waves (i.e. the pump and the ±1 sidebands) and the higher sideband orders, inhibiting in effect four-wave mixing frequency generation. For sufficiently large dispersion orders, the problem in effect can reduce to a three-wave system. Our predictions are in excellent agreement with numerical simulations and show that high-order dispersion imposes a fundamental limit on modulation instability dynamics.


Citations (53)


... Specifically, for β 3 = 0, generalized dispersion Kerr solitons (GDKSs) where identified, and a closed-form solution of their meta-envelope (ME) was obtained in the long-pulse limit [18]. Such objects have been observed in mode-locked laser cavities [19,[36][37][38], and extensions to multiple domains of anomalous dispersion have been addressed [27,39]. In the long-pulse limit, a simplified model based on two incoherently coupled nonlinear Schrödinger equations (NSEs) applies, admitting two-frequency soliton pairs (TFSPs) as solutions [28]. ...

Reference:

Optical Solitary Wavelets
Phase-locked and phase-unlocked multicolor solitons in a fiber laser

... The most direct approach is arguably end-fire coupling from the gap waveguide edge 35 -however, in the present configuration the huge mismatch between the guided mode and a diffraction limited free space beam leads to low coupling efficiencies. Another approach adapted at near-infrared frequencies, which is also suited for photonic integration, is directional-or adiabatic-coupling, 36 whose underlying formalism relies on matching the propagation constants of two adjacent modes, 37 and is agnostic to the physical dimensions of the waveguides. Most recently for example, a millimeter-wave mode converter was shown to efficiently transfer signals from a silicon waveguide to an antenna of ∼ 10 µm lateral dimensions placed directly on top. ...

Coupled mode theory for plasmonic couplers

... Reducing this dependence reduces the complexity and cost of the circuit of which they are part and makes the couplers more robust against fabrication imperfections. Passarelli et al. [10] describe a systematic procedure combining an approximate analytic method and sophisticated numerical simulations that leads to directional couplers with very wide bandwidths. ...

Rational design of an integrated directional coupler for wideband operation

... As is customary in most optics and photonics meetings, a number of papers report novel nonlinear phenomena and effects. These include nonlinear wave-mixing, supercontinuum generation, FIR/THz generation, and high-order harmonic generation [6][7][8][9][10][11]. Additionally, modulation stability [12], solitons, and soliton interactions are investigated in various nonlinear systems such as silica optical microresonators [13], electrically active multiferroic guiding structures [14], and MXene-based mode-locked fiber lasers [15]. The investigation of optical nonlinearity in heme solutions is also explored, leading to the observation of soliton-like self-collimation of a focused beam under appropriate conditions for long-distance propagation [16]. ...

Modulation instability with high-order dispersion: fundamental limitations of pattern formation

... In many of these applications, high-energy, high-peak-power ultrashort pulses are always attractive [30,31], since they can greatly alleviate the burdens on subsequent pulse amplifiers. Benefiting from the large effective core area and plenty of spatial mode channels of multimode fibers, STML fiber lasers are very promising for high-energy ultrashort pulse generation [32]. ...

The bright prospects of optical solitons after 50 years
  • Citing Article
  • October 2023

Nature Photonics

... Hyperbolic metamaterials [59][60][61][62][63], metasurfaces [64] and epsilon-near-zero elements [65][66][67][68][69][70] can enhance spontaneous emission of quantum emitters and even realize strong coupling between quantum emitters and light field. In particular, the metasurface in the microwave domain [71] and the epsilon-near-zero waveguide [72] can enhance the FRET. However, the enhancement factor of the FRET rate is relatively small, since the electric fields in these architectures can't be concentrated into several hot spots where the quantum emitters locate. ...

Experimental evidence of Förster energy transfer enhancement in the near field through engineered metamaterial surface waves

... Also, photonics-assisted generation of nonlinear frequency-modulated continuous waves designed to decrease the correlation peak-to-sidelobe ratio of broadband radar signals have been demonstrated [9]. In a broader context, optical pulses with general spectral phase profiles attract continuous attention due to its unique linear [10,11] and nonlinear [12] propagation properties, and temporal or spectral pulse engineering can be combined with spatial beam conformation to generate spatio-temporal wavepackets with unconventional behavior under both dispersion and diffraction [13][14][15]. ...

Experimental observation of linear pulses affected by high-order dispersion

... This kind of dispersion has also been shown in dispersion engineered fibers [3] and resonators [4][5][6], as well as with reconfigurable spatial light modulators [7]. PQS have shown to be stable and to have decaying oscillatory tails and, importantly, an advantageous energy width scaling with respect to conventional solitons arising from quadratic dispersion [8][9][10]. Additionally, the existence of multi-pulse solitary waves has been numerically identified in regimes with both quadratic and quartic dispersion [11]. ...

Even-order dispersion solitons: A pedagogical note
  • Citing Article
  • May 2023

Optics Communications

... The microsatellites are to be equipped with a light sail and accelerated using Earth-based laser arrays to 20% of the speed of light [1,2]. Before this project can become a reality, many engineering challenges must be overcome, involving the thermal management of the light sail [3][4][5][6], ensuring its stability in the acceleration process [7][8][9][10], and accounting for different forces acting on the sail [11]. Another critical aspect concerns the materials from which the light sail should be made. ...

Self-Stabilization of Light Sails by Damped Internal Degrees of Freedom
  • Citing Article
  • February 2022

Physical Review Applied

... We note that the use of semi-analytic, approximate methods in the design and analysis of photonic devices is well established (see, e.g., [22][23][24]). Here we apply it to the design of wavelength-independent couplers, for which, to the best of our knowledge, it has not previously been used. ...

Plasmonic Sensors beyond the Phase Matching Condition: A Simplified Approach

Sensors