Higher-order Transverse Modes Research Articles

Exploring the effect of transverse patterns on the temporal characteristics in self-mode-locked Nd: YVO[formula omitted] lasers

We investigate the influence of transverse mode distribution on the self-mode-locked (SML) states by employing off-axis pumping in an Nd:YVO4 laser with a linear concave-plano cavity. The higher-order transverse modes in the cavity are excited by adjusting the off-axis pumping displacement, and the dependence of the time characteristics of the SML laser on the transverse modes is analyzed. When the laser cavity length is 50 mm, and the off-axis displacement is adjusted offsets in the radial x and y directions to be (0,0) μ m, (45,58) μ m, and (80,0) μ m, the laser is operated in the longitudinal SML state with a repetition rate of 2.72 GHz, the amplitude modulation mode-locked pulse with a modulation frequency of 0.68 GHz and a repetition rate of 2.72 GHz, and the total-self-mode-locked with a repetition rate of 0.68 GHz, respectively. The corresponding transverse mode patterns are TEM00, TEM00+TEM01+TEM10 superposition, and TEM00+TEM10+TEM20 superposition. Finally, numerical simulations reconstruct the experimental mode-locked pulse and the corresponding transverse mode patterns based on the theory of coherent superposition of laser modes.

Minimizing the influence of higher-order transverse modes on the precision of cavity ring-down measurements

In cavity ring-down (CRD) measurements, the excitation of higher-order transverse modes and their random occurrence together with the fundamental mode inside the ring-down cavity (RDC) inevitably induce measurement errors of the decay time constant, which lead to a reduction in the measurement precision of the CRD instrument. To analyze and minimize the influence of higher-order transverse mode excitations on the CRD measurement precision, in this paper we report on the experimental observations of the impact of mode matching lens, aperture inside the cavity and trigger threshold on the excitation probability of fundamental and higher-order transverse mode excitations. The theoretical analysis and experimental results showed that when the optical misalignment is negligibly small, the occurrence probability of higher-order transverse mode excitations can be effectively suppressed by using a single lens between the laser and RDC to match preferably the fundamental model of the laser beam into the RDC, or inserting an aperture of an appropriate diameter inside the RDC, or using a high trigger threshold to record only CRD events with high amplitudes, or the combination of these approaches. For example, when the mode-matching lens is located at the optimal experimental position, and combined with the 2.2 mm diameter aperture, a 100% suppression of the excitation of high-order transverse modes can be achieved. Our results demonstrated that these methods effectively eliminated the decay time constant determination errors caused by the higher-order transverse mode excitations and therefore improved the precision of CRD experiments for high reflectance measurements. In practice the combination of mode-matching and appropriate trigger threshold setting is preferable for highly precise and yet fast CRD measurements.

Spatial rogue waves in the actively Q-switched Nd:YAG laser under low Kerr nonlinearity.

We report the generation of spatial rogue waves in an actively Q-switched Nd:YAG laser. We observed that spatial rogue waves can emerge when the laser operates in a low-power regime below the self-focusing limit, while the lasing takes place at a large number of high-order transverse modes. These results suggest that the main mechanism leading to rogue waves generation is the modal overlap while large Kerr nonlinearity in the cavity is not a necessary factor in the process of spatial rogue waves formation. We have also investigated the spatio-temporal and coherence properties of the observed rogue waves.

Phase-locked terahertz quantum cascade laser array integrated with a Talbot cavity.

Increasing the power of a quantum cascade laser by widening laser ridges will lead to the degradation of the beam quality because of the operation of high-order transverse modes. We report on a phase-locked array scheme of terahertz quantum cascade laser (THz QCL) utilizing Talbot effect. By adjusting the absorbing boundary width of each ridge in the array, stable operation of the fundamental supermode is realized. A five-element array shows 4 times power amplification than that of a single ridge device. Due to the large power amplification efficiency, stable mode selection, and simple fabricating process, the phase-locked array scheme is very promising to further improve the performance of THz QCL.

Resonant Coupling of Hermite-Gaussian Transverse Modes in the Triangular Cavity of a Cavity Ring-down Spectroscope

During resonance in resonant cavities, such as those used in laser or cavity ring-down spectroscopes (CRDS), resonant coupling between higher-order transverse modes and fundamental modes can seriously affect the quality of the beam and introduce measurement errors. Several coupling models, such as thermal deformation coupling and scattering coupling, have been established according to existing coupling theory and specific application scenarios; however, these coupling models have not been attributed to a unified theory. In this paper, we reveal that the same resonant coupling excitation factors exist under different types of environmental perturbation. The conditions and range of resonant coupling in a CRDS ring-down cavity are systematically analyzed, and a preferential coupling model of the middle-order modes is proposed. The time-domain characteristics of the CRDS are used in experiments to analyze the resonant coupling between the modes in a weak energy system. The order and coupling range of the middle-order modes involved in resonant coupling are verified using the modal filtering characteristics of the triangular cavity; this paper presents a unified explanation for various types of resonant coupling and also provides a new approach to resonant coupling experiments performed in high-finesse resonant cavities.

Coherent control of transverse modes in semiconductor laser frequency combs via radio-frequency injection

Increasing the output power of semiconductor laser frequency combs, while maintaining a single-lobe far-field characteristic is of great interest for mid-infrared sensing applications. Broadening of the ridge waveguide represents the most common approach for power scaling, however, the excitement of higher-order transverse modes often limits general applicability. Here, we demonstrate that the coherent control of the longitudinal laser modes enables control over the transverse modes of a quantum cascade laser. Modulating the laser in a frequency range 60 ± 3 MHz above the free-running laser beatnote and applying modulation powers above 25 dBm provides reliable fundamental transverse mode operation, observable as single-lobe, Gaussian-like characteristic in the recorded far-field. Furthermore, coherent comb operation for both fundamental and higher-order transverse mode states is demonstrated.

Clarification for the fields of different radially polarized Laguerre-Gaussian light beams.

Radially polarized light beams have found many applications in particle manipulation, laser processing, and microscopy. Just as with linear polarization, radially polarized light beams can have higher-order transverse modes that involve Laguerre polynomials. Fields of a radially polarized Laguerre-Gaussian light beam have been calculated before, even beyond the paraxial approximation. However, there are in fact multiple solutions to the paraxial wave equation that involve Laguerre polynomials with different properties and propagation characteristics. We therefore clarify the discrepancies among three valid radially polarized solutions to the paraxial wave equation that involve Laguerre polynomials.

Electro-optically tunable single-frequency lasing from neodymium-doped lithium niobate microresonators.

Tunable light sources are a key enabling technology for many applications such as ranging, spectroscopy, optical coherence tomography, digital imaging and interferometry. For miniaturized laser devices, whispering gallery resonator lasers are a well-suited platform, offering low thresholds and small linewidths, however, many realizations suffer from the lack of reliable tuning. Rare-earth ion-doped lithium niobate offers a way to solve this issue. Here we present a single-frequency laser based on a neodymium-doped lithium niobate whispering gallery mode resonator that is tuned via the linear electro-optic effect. Using a special geometry, we suppress higher-order transverse modes and hence ensure single-mode operation. With an applied voltage of just 68 V, we achieve a tuning range of 3.5 GHz. The lasing frequency can also be modulated with a triangular control signal. The freely running system provides a frequency and power stability of better than Δ ν=20MHz and 6 %, respectively, for a 30-minute period. This concept is suitable for full integration with existing photonic platforms based on lithium niobate.

Scalable single-mode surface-emitting laser via open-Dirac singularities.

Single-aperture cavities are a key component of lasers that are instrumental for the amplification and emission of a single light mode. However, the appearance of high-order transverse modes as the size of the cavities increases has frustrated efforts to scale-up cavities while preserving single-mode operation since the invention of the laser six decades ago1-8. A suitable physical mechanism that allows single-mode lasing irrespective of the cavity size-a 'scale invariant' cavity or laser-has not been identified yet. Here we propose and demonstrate experimentally that open-Dirac electromagnetic cavities with linear dispersion-which in our devices are realized by a truncated photonic crystal arranged in a hexagonal pattern-exhibit unconventional scaling of losses in reciprocal space, leading to single-mode lasing that is maintained as the cavity is scaled up in size. The physical origin of this phenomenon lies in the convergence of the complex part of the free spectral range in open-Dirac cavities towards a constant governed by the loss rates of distinct Bloch bands, whereas for common cavities it converges to zero as the size grows, leading to inevitable multimode emission. An unconventional flat-envelope fundamental mode locks all unit cells in the cavity in phase, leading to single-mode lasing. We name such sources Berkeley surface-emitting lasers (BerkSELs) and demonstrate that their far-field corresponds to a topological singularity of charge two, in agreement with our theory. Open-Dirac cavities unlock avenues for light-matter interaction and cavity quantum electrodynamics.

Acoustic Vibration Modes of Gold–Silver Core–Shell Nanoparticles

Bimetallic Au/Ag core–shell cuboid nanoparticles (NPs) exhibit a complex plasmonic response dominated by a dipolar longitudinal mode and higher-order transverse modes in the near-UV, which may be exploited for a range of applications. In this paper, we take advantage of the strong signature of these modes in the NP ultrafast transient optical response, measured by pump-probe transient absorption (TA) spectroscopy, to explore the NP vibrational landscape. The fast Fourier transform analysis of the TA dynamics reveals specific vibration modes in the frequency range 15–150 GHz, further studied by numerical simulations based on the finite element method. While bare Au nanorods exhibit extensional and breathing modes, the bimetallic NPs undergo more complex motions, involving the displacement of facets, edges and corners. The amplitude and frequency of these modes are shown to depend on the Ag shell thickness, as the silver load modifies the NP aspect ratio and mass. Moreover, the contributions of the vibrational modes to the experimental TA spectra are shown to vary with the probe laser wavelength at which the signal is monitored. Using the combined simulations of the NP elastic and optical properties, we elucidate this influence by analyzing the effect of the mechanisms involved in the acousto-plasmonic coupling.

Self-consistent transverse modes in a geometric-phase-plate-assisted optical resonator

We propose a geometric phase plate (GPP) assisted optical resonator to tailor and discriminate intracavity transverse modes. Theoretical analysis demonstrates that the resonator has well-defined self-consistent resonator modes when the GPP is placed at the self-imaging position of the resonator mirror. By engineering phases carried by the GPP, we show configuration functions including breaking the symmetry of transverse-mode structures in forward and backward propagations, generating purely high-order transverse modes, and discriminating degenerate Laguerre-Gaussian modes. Furthermore, we conduct numerical simulation based on the iterative Fox-Li method. Our design provides a tool for efficiently shaping laser modes at a source, which has potential application in such technologies as optical imaging, optical tweezers, optical communication, and quantum information processing.

Monolithic elliptical dome Fabry–Perot microcavities exhibiting large birefringence

We report on the experimental and theoretical characterization of elliptically shaped Fabry–Perot microcavities fabricated through a controlled thin-film buckling process. Due to the highly astigmatic nature of the buckled mirrors, the cavity modes are well described as elliptical Hermite–Gaussian beams. In addition to lifting the typical degeneracy of higher-order transverse spatial modes, the cavities exhibit large polarization-mode splitting greater than 25 GHz in the 1550 nm wavelength range. This large, controllable, and highly predictable birefringence makes these cavities of interest for emerging applications in cavity quantum optics that rely on non-degenerate polarization modes.

CONTROL OVER HIGHER-ORDER TRANSVERSE MODES IN A WAVEGUIDE-BASED QUASI-OPTICAL RESONATOR

Subject and Purpose. The problems under consideration concern selection and focusing of higher-order modes in a waveguide-based dielectric laser. The purpose is to clarify the physics underlying the behavior of, and permitting control over, continuous terahertz-frequency laser beams of various spatial polarizations. Methods and Methodology. The mode parameters of the waveguide-based laser resonator involving an inhomogeneous phase-stepped mirror were calculated in a matrix technique. To analyze the propagation and focusing of the laser beams that can be excited in a variety of diffraction zones by the wave modes of a waveguide-based quasi-optical resonator, a vectorial Rayleigh–Sommerfeld theory was used. The pertinent experimental studies were performed with the use of known measurement methods suitable for the terahertz frequency range. Results. A method for selecting the higher-order EH12q-mode of a terahertz-range laser resonator has been suggested, substantiated theoretically and approbated in experiment. It envisages placing an additional element to perform control over the system’s modal structure, namely a (2.3…2.8) λ-wide groove on the surface of one of the resonator mirrors. This measure can significantly increase losses for all undesirable modes. At the same time, the losses for the higher EH12q-mode remain practically unchanged, which creates conditions for its predominant excitation. Theoretical and experimental studies of moderate and ‘sharp’ focusing in free space of higher-order modes with different spatial polarizations of a dielectric waveguide-based resonator have been carried out. Conclusion. As has been shown, the proposed phase-stepped mirror with a groove can effectively select the higher-order transverse modes that may be required. The linearly polarized EH12q-mode has maximum field intensity in the focal region of the lens employed. For azimuthally polarized TE02q- and TE03q-modes the central lobes, noticeably shifted from the focus of the lens, have a field maximum. An increase in the axial intensity is observed upon ‘sharp’ focusing in the field distribution of the radially polarized TM02q- and TM03q-modes. In this case their central lobes, like those of the higher TE0nq-modes, are noticeably shifted from the lens focus.

High-Power InGaN Laser Array With Advanced Lateral-Corrugated Waveguides

Both high-beam-quality and high-power operation of InGaN laser array are realized by lateral-corrugated waveguides (LCWG) with reduced higher-order transverse modes. In our proposed structure, the number of higher-order modes supported by the waveguide and scattered by the LCWG is smaller than that of a conventional LCWG, which suppresses the deterioration of quantum efficiency. This contributes to high-power operation for laser processing, since the maximum output power of an array is sensitive to the efficiency. Even at 55 W from a single InGaN array chip, averaged lateral beam-quality factor of 4.9 is successfully obtained for individual emissions in the array.

Characteristics of multi-mode lasing in cesium lead bromide perovskite microwires with an isosceles right triangle cross-section.

The CsPbBr3 microwires with unique isosceles right triangle cross-sections are commonly observed via chemical vapor deposition method. In this work, we study the correlations between measured multi-mode lasing behaviors and the simulation of the mode patterns inside the triangular-rod microcavity. We confirm that lasing action with higher-order transverse modes can well sustain, even when these modes experience large optical loss due to the isosceles triangle cross-section. By comparing the experimental and simulation results, the higher-order transverse modes tend to show up prior to the fundamental transverse modes for wider microwires. We attribute this behavior to the nonuniform field distribution caused by the high absorption efficiency of CsPbBr3. We also elaborate on the difficulties to sustain the whispering gallery mode in the CsPbBr3 triangular-rod microcavity, which implies that the lateral dimension and geometry of the cavity should be considered carefully for the future design of low threshold wire-based laser devices.

Fully differential higher order transverse mode piezoelectric membrane resonators for enhanced liquid-phase quality factors

This paper investigates the characteristics of higher-order transverse mode fully clamped membrane resonators that are piezoelectrically transduced as a class of resonators that completely seal the domain above the resonator from the domain below. Such isolation between the top and bottom of a resonator is preferable when encasing the device in a microfluidic cell for liquid-phase sensing measurements, a setup that can be beneficial for sensing applications. Most fully clamped membrane resonators are hampered by low liquid-phase quality factor (Q) and large motional resistance (R m). This paper describes the design of higher-order transverse (2, 2) mode square membrane and (2, 0) mode circular membrane resonators, and the effect of device scaling on liquid-phase Q and R m. We show a best-case liquid-phase R m of 54 kΩ and Q of 270 among the various membrane sizes tested. This level of liquid-phase Q is higher than some contour mode resonators. Compared to other fully clamped membrane resonators in the literature, the results here represent a significant improvement in both R m and Q, highlighting the potential of these membrane resonators for liquid-phase mass sensing applications.

High-power single-mode triple-ridge waveguide semiconductor laser based on supersymmetry

To achieve a high-power single-transverse mode laser, we here propose a supersymmetry-based triple-ridge waveguide semiconductor laser structure, which is composed of an electrically pumped main broad-ridge waveguide located in the middle and a pair of lossy auxiliary partner waveguides. The auxiliary partner waveguides are designed to provide dissipative modes that can phase match and couple with the higher-order modes in the main waveguide. By appropriately manipulating the gain–loss discrimination of the modes in the laser cavity, one can effectively suppress all the undesired higher-order transverse modes while keeping the fundamental one almost unaffected, thereby ensuring stable single-mode operation with a larger emitting aperture and accordingly a higher output power than a conventional single-transverse-mode ridge waveguide diode laser.

Experimental demonstration of spatial rogue waves in the passively Q-switched Nd:YAG laser

The generation of spatial rogue waves, or "hot spots," is demonstrated experimentally in the passively Q-switched Nd:YAG laser system operating in a low-power regime well below the self-focusing limit. Here, we report the dependence of rogue wave statistics on the number of transverse modes that interact in the laser cavity. Our observations show that spatial rogue waves are most likely to occur when the laser exhibits complex output beam configurations that are formed by a large number of interacting high-order transverse modes. These results confirm the hypothesis that one of the main factors affecting the emergence of spatial rogue waves in solid-state lasers is the number of laser transverse modes.

Parametric sideband generation in CMOS-compatible oscillators from visible to telecom wavelengths

We present an approach for generating widely separated first sidebands based solely on the four-wave-mixing process in optical parametric oscillators built on complementary metal–oxide–semiconductor-compatible photonic chips. Using higher-order transverse modes to perform dispersion engineering, we obtain zero-group-velocity dispersion near 796 nm. By pumping the chip in the normal dispersion region, at 795.6 nm, we generate a signal field in the visible band (at 546.2 nm) and the corresponding idler field in the telecom band (at 1465.3 nm), corresponding to a frequency span of approximately 346 THz. We show that the spectral position of signal and idler can be tailored by exploiting a delicate balance between second- and fourth-order dispersion terms. Furthermore, we explicitly demonstrate a change in the parametric oscillation dynamics when moving the pump field from the anomalous to normal dispersion, where the chip ceases producing multiple sidebands adjacent to the pump field and generates widely separated single sidebands. This provides a chip-scale platform for generating single-sideband fields separated by more than one octave, covering the visible and telecom spectral regions.

Multiple stopbands and wavefield asymmetry of surface water waves in non-Bragg structures

In this paper, we use laboratory wave tank experiments to study the effect of asymmetry and defects on the bandgaps of surface water waves and use the finite element numerical method to validate our results. We demonstrate here that breaking the mirror symmetry around the midplane of a periodic structure introduces multiple bandgaps in the spectrum caused by the involvement of high-order transverse modes. The results show that the presence of a defect in the structure leads to the formation of a strong defect mode in the Bragg gap, which is localized around the defect element and a weak mode in the induced non-Bragg gap. The results show that the bandgap excited by symmetry breaking is much narrower due to the weak mode coupling. In addition, at the non-Bragg resonance frequency in the defect state, the transverse water surface wavefield distribution around the defect is asymmetric about the midplane of the channel. The multiple transmission modes in the spectrum of the structure can be applied in the design of Bragg reflection-based wave attenuation structures that can help protect shorelines and coastal infrastructure. The asymmetry of the surface wavefield in the non-Bragg gap can be applied in the development of energy harvesting technologies. Due to the generality of wave phenomena in periodic structures, the findings of this research provide a basis for more research in physical acoustics and optics and may lead to the development of cutting-edge appliances, such as bandpass filters.