Room-temperature quantum optomechanics using an ultralow noise cavity.

At room temperature, mechanical motion driven by the quantum backaction of light has been observed only in pioneering experiments in which an optical restoring force controls the oscillator stiffness1,2. For solid-state mechanical resonators in which oscillations are controlled by the material rigidity, the observation of these effects has been hindered by low mechanical quality factors, optical cavity frequency fluctuations3, thermal intermodulation noise4,5 and photothermal instabilities. Here we overcome these challenges with a phononic-engineered membrane-in-the-middle system. By using phononic-crystal-patterned cavity mirrors, we reduce the cavity frequency noise by more than 700-fold. In this ultralow noise cavity, we insert a membrane resonator with high thermal conductance and a quality factor (Q) of 180 million, engineered using recently developed soft-clamping techniques6,7. These advances enable the operation of the system within a factor of 2.5 of the Heisenberg limit for displacement sensing8, leading to the squeezing of the probe laser by 1.09(1) dB below the vacuum fluctuations. Moreover, the long thermal decoherence time of the membrane oscillator (30 vibrational periods) enables us to prepare conditional displaced thermal states of motion with an occupation of 0.97(2) phonons using a multimode Kalman filter. Our work extends the quantum control of solid-state macroscopic oscillators to room temperature.

Lithium tantalate photonic integrated circuits for volume manufacturing.

Electro-optical photonic integrated circuits (PICs) based on lithium niobate (LiNbO3) have demonstrated the vast capabilities of materials with a high Pockels coefficient1,2. They enable linear and high-speed modulators operating at complementary metal-oxide-semiconductor voltage levels3 to be used in applications including data-centre communications4, high-performance computing and photonic accelerators for AI5. However, industrial use of this technology is hindered by the high cost per wafer and the limited wafer size. The high cost results from the lack of existing high-volume applications in other domains of the sort that accelerated the adoption of silicon-on-insulator (SOI) photonics, which was driven by vast investment in microelectronics. Here we report low-loss PICs made of lithium tantalate (LiTaO3), a material that has already been adopted commercially for 5G radiofrequency filters6 and therefore enables scalable manufacturing at low cost, and it has equal, and in some cases superior, properties to LiNbO3. We show that LiTaO3 can be etched to create low-loss (5.6 dB m-1) PICs using a deep ultraviolet (DUV) stepper-based manufacturing process7. We demonstrate a LiTaO3 Mach-Zehnder modulator (MZM) with a half-wave voltage-length product of 1.9 V cm and an electro-optic bandwidth of up to 40 GHz. In comparison with LiNbO3, LiTaO3 exhibits a much lower birefringence, enabling high-density circuits and broadband operation over all telecommunication bands. Moreover, the platform supports the generation of soliton microcombs. Our work paves the way for the scalable manufacture of low-cost and large-volume next-generation electro-optical PICs.

Ultrafast tunable lasers using lithium niobate integrated photonics.

Early works1 and recent advances in thin-film lithium niobate (LiNbO3) on insulator have enabled low-loss photonic integrated circuits2,3, modulators with improved half-wave voltage4,5, electro-optic frequency combs6 and on-chip electro-optic devices, with applications ranging from microwave photonics to microwave-to-optical quantum interfaces7. Although recent advances have demonstrated tunable integrated lasers based on LiNbO3 (refs. 8,9), the full potential of this platform to demonstrate frequency-agile, narrow-linewidth integrated lasers has not been achieved. Here we report such a laser with a fast tuning rate based on a hybrid silicon nitride (Si3N4)-LiNbO3 photonic platform and demonstrate its use for coherent laser ranging. Our platform is based on heterogeneous integration of ultralow-loss Si3N4 photonic integrated circuits with thin-film LiNbO3 through direct bonding at the wafer level, in contrast to previously demonstrated chiplet-level integration10, featuring low propagation loss of 8.5 decibels per metre, enabling narrow-linewidth lasing (intrinsic linewidth of 3 kilohertz) by self-injection locking to a laser diode. The hybrid mode of the resonator allows electro-optic laser frequency tuning at a speed of 12 × 1015 hertz per second with high linearity and low hysteresis while retaining the narrow linewidth. Using a hybrid integrated laser, we perform a proof-of-concept coherent optical ranging (FMCW LiDAR) experiment. Endowing Si3N4 photonic integrated circuits with LiNbO3 creates a platform that combines the individual advantages of thin-film LiNbO3 with those of Si3N4, which show precise lithographic control, mature manufacturing and ultralow loss11,12.

A photonic integrated continuous-travelling-wave parametric amplifier.

The ability to amplify optical signals is of pivotal importance across science and technology typically using rare-earth-doped fibres or gain media based on III-V semiconductors. A different physical process to amplify optical signals is to use the Kerr nonlinearity of optical fibres through parametric interactions1,2. Pioneering work demonstrated continuous-wave net-gain travelling-wave parametric amplification in fibres3, enabling, for example, phase-sensitive (that is, noiseless) amplification4, link span increase5, signal regeneration and nonlinear phase noise mitigation6. Despite great progress7-15, all photonic integrated circuit-based demonstrations of net parametric gain have necessitated pulsed lasers, limiting their practical use. Until now, only bulk micromachined periodically poled lithium niobate (PPLN) waveguide chips have achieved continuous-wave gain16,17, yet their integration with silicon-wafer-based photonic circuits has not been shown. Here we demonstrate a photonic-integrated-circuit-based travelling-wave optical parametric amplifier with net signal gain in the continuous-wave regime. Using ultralow-loss, dispersion-engineered, metre-long, Si3N4 photonic integrated circuits18 on a silicon chip of dimensions 5 × 5 mm2, we achieve a continuous parametric gain of 12 dB that exceeds both the on-chip optical propagation loss and fibre-chip-fibre coupling losses in the telecommunication C band. Our work demonstrates the potential of photonic-integrated-circuit-based parametric amplifiers that have lithographically controlled gain spectrum, compact footprint, resilience to optical feedback and quantum-limited performance, and can operate in the wavelength ranges from visible to mid-infrared and outside conventional rare-earth amplification bands.

Topological lattices realized in superconducting circuit optomechanics.

Cavity optomechanics enables the control of mechanical motion through the radiation-pressure interaction1, and has contributed to the quantum control of engineered mechanical systems ranging from kilogramme-scale Laser Interferometer Gravitational-wave Observatory (LIGO) mirrors to nanomechanical systems, enabling ground-state preparation2,3, entanglement4,5, squeezing of mechanical objects6, position measurements at the standard quantum limit7 and quantum transduction8. Yet nearly all previous schemes have used single- or few-mode optomechanical systems. By contrast, new dynamics and applications are expected when using optomechanical lattices9, which enable the synthesis of non-trivial band structures, and these lattices have been actively studied in the field of circuit quantum electrodynamics10. Superconducting microwave optomechanical circuits2 are a promising platform to implement such lattices, but have been compounded by strict scaling limitations. Here we overcome this challenge and demonstrate topological microwave modes in one-dimensional circuit optomechanical chains realizing the Su-Schrieffer-Heeger model11,12. Furthermore, we realize the strained graphene model13,14 in a two-dimensional optomechanical honeycomb lattice. Exploiting the embedded optomechanical interaction, we show that it is possible to directly measure the mode functions of the hybridized modes without using any local probe15,16. This enables us to reconstruct the full underlying lattice Hamiltonian and directly measure the existing residual disorder. Such optomechanical lattices, accompanied by the measurement techniques introduced, offer an avenue to explore collective17,18, quantum many-body19 and quench20 dynamics, topological properties9,21 and, more broadly, emergent nonlinear dynamics in complex optomechanical systems with a large number of degrees of freedom22-24.

Integrated photonics enables continuous-beam electron phase modulation.

Integrated photonics facilitates extensive control over fundamental light-matter interactions in manifold quantum systems including atoms1, trapped ions2,3, quantum dots4 and defect centres5. Ultrafast electron microscopy has recently made free-electron beams the subject of laser-based quantum manipulation and characterization6-11, enabling the observation of free-electron quantum walks12-14, attosecond electron pulses10,15-17 and holographic electromagnetic imaging18. Chip-based photonics19,20 promises unique applications in nanoscale quantum control and sensing but remains to be realized in electron microscopy. Here we merge integrated photonics with electron microscopy, demonstrating coherent phase modulation of a continuous electron beam using a silicon nitride microresonator. The high-finesse (Q0 ≈ 106) cavity enhancement and a waveguide designed for phase matching lead to efficient electron-light scattering at extremely low, continuous-wave optical powers. Specifically, we fully deplete the initial electron state at a cavity-coupled power of only 5.35 microwatts and generate >500 electron energy sidebands for several milliwatts. Moreover, we probe unidirectional intracavity fields with microelectronvolt resolution in electron-energy-gain spectroscopy21. The fibre-coupled photonic structures feature single-optical-mode electron-light interaction with full control over the input and output light. This approach establishes a versatile and highly efficient framework for enhanced electron beam control in the context of laser phase plates22, beam modulators and continuous-wave attosecond pulse trains23, resonantly enhanced spectroscopy24-26 and dielectric laser acceleration19,20,27. Our work introduces a universal platform for exploring free-electron quantum optics28-31, with potential future developments in strong coupling, local quantum probing and electron-photon entanglement.

Massively parallel coherent laser ranging using a soliton microcomb.

Coherent ranging, also known as frequency-modulated continuous-wave (FMCW) laser-based light detection and ranging (lidar)1 is used for long-range three-dimensional distance and velocimetry in autonomous driving2,3. FMCW lidar maps distance to frequency4,5 using frequency-chirped waveforms and simultaneously measures the Doppler shift of the reflected laser light, similar to sonar or radar6,7 and coherent detection prevents interference from sunlight and other lidar systems. However, coherent ranging has a lower acquisition speed and requires precisely chirped8 and highly coherent5 laser sources, hindering widespread use of the lidar system and impeding parallelization, compared to modern time-of-flight ranging systems that use arrays of individual lasers. Here we demonstrate a massively parallel coherent lidar scheme using an ultra-low-loss photonic chip-based soliton microcomb9. By fast chirping of the pump laser in the soliton existence range10 of a microcomb with amplitudes of up to several gigahertz and a sweep rate of up to ten megahertz, a rapid frequency change occurs in the underlying carrier waveform of the soliton pulse stream, but the pulse-to-pulse repetition rate of the soliton pulse stream is retained. As a result, the chirp from a single narrow-linewidth pump laser is transferred to all spectral comb teeth of the soliton at once, thus enabling parallelism in the FMCW lidar. Using this approach we generate 30 distinct channels, demonstrating both parallel distance and velocity measurements at an equivalent rate of three megapixels per second, with the potential to improve sampling rates beyond 150 megapixels per second and to increase the image refresh rate of the FMCW lidar by up to two orders of magnitude without deterioration of eye safety. This approach, when combined with photonic phase arrays11 based on nanophotonic gratings12, provides a technological basis for compact, massively parallel and ultrahigh-frame-rate coherent lidar systems.

Controlling free electrons with optical whispering-gallery modes.

Free-electron beams are versatile probes of microscopic structure and composition1,2, and have revolutionized atomic-scale imaging in several fields, from solid-state physics to structural biology3. Over the past decade, the manipulation and interaction of electrons with optical fields have enabled considerable progress in imaging methods4, near-field electron acceleration5,6, and four-dimensional microscopy techniques with high temporal and spatial resolution7. However, electron beams typically couple only weakly to optical excitations, and emerging applications in electron control and sensing8-11 require large enhancements using tailored fields and interactions. Here we couple a free-electron beam to a travelling-wave resonant cavity mode. The enhanced interaction with the optical whispering-gallery modes of dielectric microresonators induces a strong phase modulation on co-propagating electrons, which leads to a spectral broadening of 700 electronvolts, corresponding to the absorption and emission of hundreds of photons. By mapping the near-field interaction with ultrashort electron pulses in space and time, we trace the lifetime of the the microresonator following a femtosecond excitation and observe the spectral response of the cavity. The natural matching of free electrons to these quintessential optical modes could enable the application of integrated photonics technology in electron microscopy, with broad implications for attosecond structuring, probing quantum emitters and possible electron-light entanglement.

Monolithic piezoelectric control of soliton microcombs.

High-speed actuation of laser frequency1 is critical in applications using lasers and frequency combs2,3, and is a prerequisite for phase locking, frequency stabilization and stability transfer among optical carriers. For example, high-bandwidth feedback control of frequency combs is used in optical-frequency synthesis4, frequency division5 and optical clocks6. Soliton microcombs7,8 have emerged as chip-scale frequency comb sources, and have been used in system-level demonstrations9,10. Yet integrated microcombs using thermal heaters have limited actuation bandwidths11,12 of up to 10 kilohertz. Consequently, megahertz-bandwidth actuation and locking of microcombs have only been achieved with off-chip bulk component modulators. Here we demonstrate high-speed soliton microcomb actuation using integrated piezoelectric components13. By monolithically integrating AlN actuators14 on ultralow-loss Si3N4 photonic circuits15, we demonstrate voltage-controlled soliton initiation, tuning and stabilization with megahertz bandwidth. The AlN actuators use 300 nanowatts of power and feature bidirectional tuning, high linearity and low hysteresis. They exhibit a flat actuation response up to 1 megahertz-substantially exceeding bulk piezo tuning bandwidth-that is extendable to higher frequencies by overcoming coupling to acoustic contour modes of the chip. Via synchronous tuning of the laser and the microresonator, we exploit this ability to frequency-shift the optical comb spectrum (that is, to change the comb's carrier-envelope offset frequency) and make excursions beyond the soliton existence range. This enables a massively parallel frequency-modulated engine16,17 for lidar (light detection and ranging), with increased frequency excursion, lower power and elimination of channel distortions resulting from the soliton Raman self-frequency shift. Moreover, by modulating at a rate matching the frequency of high-overtone bulk acoustic resonances18, resonant build-up of bulk acoustic energy allows a 14-fold reduction of the required driving voltage, making it compatible with CMOS (complementary metal-oxide-semiconductor) electronics. Our approach endows soliton microcombs with integrated, ultralow-power and fast actuation, expanding the repertoire of technological applications of microcombs.

Integrated turnkey soliton microcombs.

Optical frequency combs have a wide range of applications in science and technology1. An important development for miniature and integrated comb systems is the formation of dissipative Kerr solitons in coherently pumped high-quality-factor optical microresonators2-9. Such soliton microcombs10 have been applied to spectroscopy11-13, the search for exoplanets14,15, optical frequency synthesis16, time keeping17 and other areas10. In addition, the recent integration of microresonators with lasers has revealed the viability of fully chip-based soliton microcombs18,19. However, the operation of microcombs requires complex startup and feedback protocols that necessitate difficult-to-integrate optical and electrical components, and microcombs operating at rates that are compatible with electronic circuits-as is required in nearly all comb systems-have not yet been integrated with pump lasers because of their high power requirements. Here we experimentally demonstrate and theoretically describe a turnkey operation regime for soliton microcombs co-integrated with a pump laser. We show the appearance of an operating point at which solitons are immediately generated by turning the pump laser on, thereby eliminating the need for photonic and electronic control circuitry. These features are combined with high-quality-factor Si3N4 resonators to provide microcombs with repetition frequencies as low as 15 gigahertz that are fully integrated into an industry standard (butterfly) package, thereby offering compelling advantages for high-volume production.

An optical-frequency synthesizer using integrated photonics.

Optical-frequency synthesizers, which generate frequency-stable light from a single microwave-frequency reference, are revolutionizing ultrafast science and metrology, but their size, power requirement and cost need to be reduced if they are to be more widely used. Integrated-photonics microchips can be used in high-coherence applications, such as data transmission 1 , highly optimized physical sensors 2 and harnessing quantum states 3 , to lower cost and increase efficiency and portability. Here we describe a method for synthesizing the absolute frequency of a lightwave signal, using integrated photonics to create a phase-coherent microwave-to-optical link. We use a heterogeneously integrated III-V/silicon tunable laser, which is guided by nonlinear frequency combs fabricated on separate silicon chips and pumped by off-chip lasers. The laser frequency output of our optical-frequency synthesizer can be programmed by a microwave clock across 4 terahertz near 1,550 nanometres (the telecommunications C-band) with 1 hertz resolution. Our measurements verify that the output of the synthesizer is exceptionally stable across this region (synthesis error of 7.7 × 10-15 or below). Any application of an optical-frequency source could benefit from the high-precision optical synthesis presented here. Leveraging high-volume semiconductor processing built around advanced materials could allow such low-cost, low-power and compact integrated-photonics devices to be widely used.

Towards efficient broadband parametric conversion in ultra-long Si3N4 waveguides.

Broadband continuous-wave parametric gain and efficient wavelength conversion is an important functionality to bring on-chip. Recently, meter-long silicon nitride waveguides have been utilized to obtain continuous-traveling-wave parametric gain, establishing the great potential of photonic-integrated-circuit-based parametric amplifiers. However, the effect of spiral structure on the performance and achievable bandwidth of such devices have not yet been studied. In this work, we investigate the efficiency-bandwidth performance in up to 2 meter-long waveguides engineered for broadband operation. Moreover, we analyze the conversion efficiency fluctuations that have been observed in meter-long Si3N4 waveguides and study the use of temperature control to limit the fluctuations.

Architecture for integrated RF photonic downconversion of electronic signals.

Electronic analog to digital converters (ADCs) are running up against the well-known bit depth versus bandwidth trade off. Towards this end, radio frequency (RF) photonic-enhanced ADCs have been the subject of interest for some time. Optical frequency comb technology has been used as a workhorse underlying many of these architectures. Unfortunately, such designs must generally grapple with size, weight, and power (SWaP) concerns, as well as frequency ambiguity issues which threaten to obscure critical spectral information of detected RF signals. In this work, we address these concerns via an RF photonic downconverter with potential for easy integration and field deployment by leveraging a novel, to the best of our knowledge, hybrid microcomb/electro-optic comb design.

Single-frequency violet and blue laser emission from AlGaInN photonic integrated circuit chips.

Chip-based, single-frequency and low phase-noise integrated photonic laser diodes emitting in the violet (412 nm) and blue (461 nm) regime are demonstrated. The GaN-based edge-emitting laser diodes were coupled to high-quality on-chip micro-resonators for optical feedback and mode selection resulting in laser self-injection locking with narrow emission linewidth. Multiple group III-nitride (III-N) based photonic integrated circuit chips with different waveguide designs including single-crystalline AlN, AlGaN, and GaN were developed and characterized. Single-frequency laser operation was demonstrated for all studied waveguide core materials. The best side-mode suppression ratio was determined to be ∼36 dB at 412 nm with a single-frequency laser emission linewidth of only 3.8 MHz at 461 nm. The performance metrics of this novel, to the best of our knowledge, type of laser suggest potential implementation in next-generation, portable quantum systems.

Space-time wave packets with reduced divergence and tunable group velocity generated in free space after multi-mode fiber propagation.

Previously, space-time wave packets (STWPs) have been generated in free space with reduced diffraction and a tunable group velocity by combining multiple frequency comb lines each carrying a single Bessel mode with a unique wave number. It might be potentially desirable to propagate the STWP through fiber for reconfigurable positioning. However, fiber mode coupling might degrade the output STWP and distort its propagation characteristics. In this Letter, we experimentally demonstrate STWP generation and propagation over 1-m graded-index multi-mode fiber. Fiber mode coupling is mitigated by pre-distortion according to the inverse matrix of the fiber mode coupling matrix. Measurement of the STWP at the fiber output shows that its group velocity can vary from 1.0042c to 0.9967c by tuning the wave number of the Bessel mode on each frequency. The measured time-averaged intensity profiles show that the beam radius remains similar after 150-mm free-space propagation after exiting the fiber.

Microresonator-based solitons for massively parallel coherent optical communications.

Solitons are waveforms that preserve their shape while propagating, as a result of a balance of dispersion and nonlinearity. Soliton-based data transmission schemes were investigated in the 1980s and showed promise as a way of overcoming the limitations imposed by dispersion of optical fibres. However, these approaches were later abandoned in favour of wavelength-division multiplexing schemes, which are easier to implement and offer improved scalability to higher data rates. Here we show that solitons could make a comeback in optical communications, not as a competitor but as a key element of massively parallel wavelength-division multiplexing. Instead of encoding data on the soliton pulse train itself, we use continuous-wave tones of the associated frequency comb as carriers for communication. Dissipative Kerr solitons (DKSs) (solitons that rely on a double balance of parametric gain and cavity loss, as well as dispersion and nonlinearity) are generated as continuously circulating pulses in an integrated silicon nitride microresonator via four-photon interactions mediated by the Kerr nonlinearity, leading to low-noise, spectrally smooth, broadband optical frequency combs. We use two interleaved DKS frequency combs to transmit a data stream of more than 50 terabits per second on 179 individual optical carriers that span the entire telecommunication C and L bands (centred around infrared telecommunication wavelengths of 1.55 micrometres). We also demonstrate coherent detection of a wavelength-division multiplexing data stream by using a pair of DKS frequency combs-one as a multi-wavelength light source at the transmitter and the other as the corresponding local oscillator at the receiver. This approach exploits the scalability of microresonator-based DKS frequency comb sources for massively parallel optical communications at both the transmitter and the receiver. Our results demonstrate the potential of these sources to replace the arrays of continuous-wave lasers that are currently used in high-speed communications. In combination with advanced spatial multiplexing schemes and highly integrated silicon photonic circuits, DKS frequency combs could bring chip-scale petabit-per-second transceivers into reach.

Polarization selective ultra-broadband wavelength conversion in silicon nitride waveguides.

We experimentally demonstrate broadband degenerate continuous-wave four-wave mixing in long silicon nitride (Si3N4) waveguides for operation both in the telecommunication L-band and the thulium band near 2 µm by leveraging polarization dependence of the waveguide dispersion. Broadband conversion is typically demonstrated in short milimeter long waveguides as the bandwidth is linked to the interaction length. This makes it challenging to simultaneously push bandwidth and efficiency, imposing stringent constraints on dispersion engineering. In this work, we show conversion bandwidths larger than 150 nm in the L-band when pumping in the transverse magnetic (TM) mode and larger than 120 nm at 2 µm when using transverse electric excitation, despite the use of 0.5 m long waveguides. In addition, we also show how extreme polarization selectivity can be leveraged in a single waveguide to enable switchable distant phase-matching based on higher-order dispersion. Relying on this approach, we demonstrate the selective conversion of light from the telecom band to the O-band for TM polarization or to the mid-infrared light up to 2.5 µm in TE. Our experiments are in excellent agreement with simulations, showing the high potential of the platform for broadband and distant conversion beyond the telecom band.

Generation of OAM-carrying space-time wave packets with time-dependent beam radii using a coherent combination of multiple LG modes on multiple frequencies.

Space-time (ST) wave packets, in which spatial and temporal characteristics are coupled, have gained attention due to their unique propagation characteristics, such as propagation invariance and tunable group velocity in addition to their potential ability to carry orbital angular momentum (OAM). Through experiment and simulation, we explore the generation of OAM-carrying ST wave packets, with the unique property of a time-dependent beam radius at various ranges of propagation distances. To achieve this, we synthesize multiple frequency comb lines, each assigned to a coherent combination of multiple Laguerre-Gaussian (LGℓ,p) modes with the same azimuthal index but different radial indices. The time-dependent interference among the spatial modes at the different frequencies leads to the generation of the desired OAM-carrying ST wave packet with dynamically varying radii. The simulation results indicate that the dynamic range of beam radius oscillations increases with the number of modes and frequency lines. The simulated ST wave packet for OAM of orders +1 or +3 has an OAM purity of >95%. In addition, we experimentally generate and measure the OAM-carrying ST wave packets with time-dependent beam radii. In the experiment, several lines of a Kerr frequency comb are spatially modulated with the superposition of multiple LG modes and combined to generate such an ST wave packet. In the experiment, ST wave packets for OAM of orders +1 or +3 have an OAM purity of >64%. In simulation and experiment, OAM purity decreases and beam radius becomes larger over the propagation.

Synthesis of near-diffraction-free orbital-angular-momentum space-time wave packets having a controllable group velocity using a frequency comb.

Novel forms of light beams carrying orbital angular momentum (OAM) have recently gained interest, especially due to some of their intriguing propagation features. Here, we experimentally demonstrate the generation of near-diffraction-free two-dimensional (2D) space-time (ST) OAM wave packets (ℓ = +1, +2, or +3) with variable group velocities in free space by coherently combining multiple frequency comb lines, each carrying a unique Bessel mode. Introducing a controllable specific correlation between temporal frequencies and spatial frequencies of these Bessel modes, we experimentally generate and detect near-diffraction-free OAM wave packets with high mode purities (>86%). Moreover, the group velocity can be controlled from 0.9933c to 1.0069c (c is the speed of light in vacuum). These ST OAM wave packets might find applications in imaging, nonlinear optics, and optical communications. In addition, our approach might also provide some insights for generating other interesting ST beams.

Tunability of space-time wave packet carrying tunable and dynamically changing OAM value.

Space-time (ST) wave packets have gained much interest due to their dynamic optical properties. Such wave packets can be generated by synthesizing frequency comb lines, each having multiple complex-weighted spatial modes, to carry dynamically changing orbital angular momentum (OAM) values. Here, we investigate the tunability of such ST wave packets by varying the number of frequency comb lines and the combinations of spatial modes on each frequency. We experimentally generate and measure the wave packets with tunable OAM values from +1 to +6 or from +1 to +4 during a ∼5.2-ps period. We also investigate, in simulation, the temporal pulse width of the ST wave packet and the nonlinear variation of the OAM values. The simulation results show that: (i) a pulse width can be narrower for the ST wave packet carrying dynamically changing OAM values using more frequency lines; and (ii) the nonlinearly varying OAM value can result in different frequency chirps along the azimuthal direction at different time instants.