Lowest-loss Mode Research Articles

Predictions of resonant mode characteristics for terahertz quantum cascade lasers with distributed feedback utilizing machine learning.

Terahertz quantum cascade lasers (THz QCLs) are the most powerful solid-state THz sources so far and THz QCLs with various distributed feedback (DFB) gratings have demonstrated single-mode emission, collimated beam, frequency tunability and high output power. Resonant mode characteristics of THz QCLs with DFB, including frequency, loss and electric-field distributions, are important for waveguide analysis, fabrication and indication of THz QCLs' radiative performance. Typically, predictions of these characteristics rely on numerical simulations. However, traditional numerical simulations demand a large amount of running time and computing resources, and have to deal with the trade-off between accuracy and efficiency. In this work, machine learning models are designed to predict resonant mode characteristics of THz QCLs with first-order, second-order, third-order DFB and antenna-feedback waveguides according to the four input structural parameters, i.e. grating period, total length of waveguide, duty cycle of grating and length of highly-doped contact layer. The machine learning models are composed of a multi-layer perceptron for predictions of frequency and loss, and an up-sampling convolutional neural network for predictions of electric-field distribution of the lowest-loss mode, respectively. A detailed study on more than 1000 samples shows high accuracy and efficiency of the proposed models, with Pearson correlation coefficients over 0.99 for predictions of lasing frequency and loss, median peak signal-to-noise ratios over 33.74dB for predictions of electric-field distribution, and the required time of prediction is within several seconds. Moreover, the designed models are widely applicable to various DFB structures for THz QCLs. Resonators with graded photonic heterostructures and novel phase-locked arrays are accurately predicted as examples.

Low loss and high performance interconnection between standard single-mode fiber and antiresonant hollow-core fiber

We demonstrate halving the record-low loss of interconnection between a nested antiresonant nodeless type hollow-core fiber (NANF) and standard single-mode fiber (SMF). The achieved interconnection loss of 0.15 dB is only 0.07 dB above the theoretically-expected minimum loss. We also optimized the interconnection in terms of unwanted cross-coupling into the higher-order modes of the NANF. We achieved cross-coupling as low as −35 dB into the LP_{11} mode (the lowest-loss higher-order mode and thus the most important to eliminate). With the help of simulations, we show that the measured LP_{11} mode coupling is most likely limited by the slightly imperfect symmetry of the manufactured NANF. The coupling cross-talk into the highly-lossy LP_{02} mode (>2000 dB/km in our fiber) was measured to be below −22 dB. Furthermore, we show experimentally that the anti-reflective coating applied to the interconnect interface reduces the insertion loss by 0.15 dB while simultaneously reducing the back-reflection below −40 dB over a 60 nm bandwidth. Finally, we also demonstrated an alternative mode-field adapter to adapt the mode-field size between SMF and NANF, based on thermally-expanded core fibers. This approach enabled us to achieve an interconnection loss of 0.21 dB and cross-coupling of −35 dB into the LP_{11} mode.

Superradiance from lattice-confined atoms inside hollow core fibre

Unravelling superradiance, also known as superfluorescence, relies on an ensemble of phase-matched dipole oscillators and the suppression of inhomogeneous broadening. Here we report a superradiance platform that combines an optical lattice free from the ac Stark shift and a hollow-core photonic crystal fibre, enabling an extended atom-light interaction over 2 mm free from the Doppler effect. This system allows control of the atom spatial distribution and spectral homogeneity whilst efficiently coupling the radiation field to an optical fibre. The experimentally-observed and theoretically-corroborated temporal, spectral and spatial dynamic behaviours of the superradiance, e.g., superradiance ringing and density-dependent frequency shift, demonstrate a unique interplay between the trapped atoms and the fibre-guided field with multiple transverse modes. Our theory indicates that the resulting temporal evolution of the guided light shows a minimal beam radius of 3.1 µm which is three times smaller than that of the lowest-loss fibre mode.

Edge-wave method for calculating the output mode of strip unstable resonators.

We develop an edge-wave method for calculating the output mode of a positive branch off-axis unstable resonator. According to the iterative property of the edge-wave function, the transmission line of the apertures is adopted to solve the Fox-Li iteration for calculating the lowest loss mode on the output plane. Furthermore, the so-called mask effect is eliminated by revising the edge-wave function derived from the last order aperture, so that the modified formula can be utilized to calculate the output mode directly. The method can be employed in most cases, with an exception at the mode crossing point.

CW laser light condensation

We present a first experimental demonstration of classical CW laser light condensation (LC) in the frequency (mode) domain that verifies its prediction (Fischer and Weill, Opt. Express20, 26704 (2012)). LC is based on weighting the modes in a noisy environment in a loss-gain measure compared to an energy (frequency) scale in Bose-Einstein condensation (BEC). It is characterized by a sharp transition from multi- to single-mode oscillation, occurring when the spectral-filtering (loss-trap) has near the lowest-loss mode ("ground-state") a power-law dependence with an exponent smaller than 1. An important meaning of the many-mode LC system stems from its relation to lasing and photon-BEC.

Double antiresonant hollow core fiber--guidance in the deep ultraviolet by modified tunneling leaky modes.

Guiding light inside the hollow cores of microstructured optical fibers is a major research field within fiber optics. However, most of current fibers reveal limited spectral operation ranges between the mid-visible and the infrared and rely on complicated microstructures. Here we report on a new type of hollow-core fiber, showing for the first time distinct transmission windows between the deep ultraviolet and the near infrared. The fiber, guiding in a single mode, operates by the central core mode being anti-resonant to adjacent modes, leading to a novel modified tunneling leaky mode. The fiber design is straightforward to implement and reveals beneficial features such as preselecting the lowest loss mode (Gaussian-like or donut-shaped mode). Fibers with such a unique combination of attributes allow accessing the extremely important deep-UV range with Gaussian-like mode quality and may pave the way for new discoveries in biophotonics, multispectral spectroscopy, photo-initiated chemistry or ultrashort pulse delivery.

The approximate analytic solution for the mode of strip negative branch unstable resonators

In this paper, the formula of the edge wave (EW) which is applicable for strip negative branch unstable resonators is derived. It is shown that the lowest-loss mode can be represented as the superposition of these EWs in an explicit form, the validity is verified by numerical comparison with the classic power method.

Analysis of resonator modes in two-dimensional laser cavities containing a left-handed material

Resonator modes in two-dimensional laser cavities with curved end mirrors filled with a left-handed material were investigated numerically using the extended Fox-Li mode calculation method. The results reveal that the phase profile on the curved end mirrors of a left-handed cavity is inverted relative to that of a cavity filled with a right-handed material. Furthermore, we show that the phase on the end mirrors takes discrete values of zero and ±π under stable resonator conditions, while it varies continuously under unstable resonator conditions. The differences between stable and unstable resonators significantly alter the far-field patterns of the lowest-loss modes.

When does single-mode lasing become a condensation phenomenon?

We present a generic route to classical light condensation (LC) in linear photonic mode systems, such as cw lasers, with different grounds from regular Bose-Einstein condensation (BEC). LC is based on weighting the modes in a noisy environment (spontaneous emission, etc.) in a loss-gain scale, rather than in photon energy. It is characterized by a sharp transition from a multi- to single-mode oscillation. The study uses a linear multivariate Langevin formulation which gives a mode occupation hierarchy that functions like Bose-Einstein statistics. Condensation occurs when the spectral filtering has near the lowest-loss mode a power law dependence with exponent smaller than 1. We then discuss how condensation can occur in photon systems, its relation to lasing and the difficulties to observe regular photon-BEC in laser cavities. We raise the possibility that experiments on photon condensation in optical cavities fall in a classical LC or lasing category rather than being a thermal-quantum BEC phenomenon.

Excess noise in strip off-axis confocal unstable resonators

The lowest-loss mode and higher-order modes in strip off-axis confocal unstable resonators are calculated by the eigenvector method. The moduli of all pairs of the adjacent order eigenvalues exhibit crossing behavior. For the lowest- and next-lowest-loss modes, crossings occur when the equivalent Fresnel number N eq is close to s + 0.08 (s positive integer), and the lowest-loss mode profile calculated by the Fox–Li iteration is no longer self-reproducing, but the superposition of both eigenmodes with unfixed complex weights varies as the number of iterations. Numerical calculations of excess noise factors K in strip off-axis confocal unstable resonators are described in detail. The value of K shows an irregular resonance switching against N eq. The hybrid model presented by van Eijkelenborg et al. is modified in this paper, and shows a good quantitative agreement with nonorthogonality theory.

Mode calculations in asymmetrically aberrated laser resonators using the Huygens–Fresnel kernel formulation

A theoretical framework is presented for calculating three-dimensional resonator modes of both stable and unstable laser resonators. The resonant modes of an optical resonator are computed using a kernel formulation of the resonator round-trip Huygens-Fresnel diffraction integral. To substantiate the validity of this method, both stable and unstable resonator mode results are presented. The predicted lowest loss and higher order modes of a semi-confocal stable resonator are in agreement with the analytic formulation. Higher order modes are determined for an asymmetrically aberrated confocal unstable resonator, whose lowest loss unaberrated mode is consistent with published results. The three-dimensional kernel method provides a means to evaluate multi-mode configurations with two-dimensional aberrations that cannot be decomposed into one-dimensional representations.

High-quality lowest-loss-mode lasing in GaAs quasi-stadium laser diodes having unstable resonators

We obtained high-quality lowest-loss-mode lasing in quasi-stadium laser diodes having unstable resonators that consisted of two curved end mirrors and two straight sidewall mirrors. The laser diodes were fabricated by applying a reactive ion etching technique to a metal-organic chemical-vapor deposition-grown graded-index separate-confinement heterostructure single-quantum-well GaAs/AlGaAs structure. The electrode contact area of the laser diodes was formed along unstable periodic orbits, along which the optical beams are localized. Highly directional fan-out beams corresponding to the numerically obtained lowest loss mode were emitted from the end mirrors under CW operation at room temperature.

Birefringence-induced bifocusing for selection of radially or azimuthally polarized laser modes

We develop a round-trip matrix diagonalization method for quantitative description of selection of radially or azimuthally polarized beams by birefringence-induced bifocusing in a simple laser resonator. We employ different focusing between radially and tangentially polarized light in thermally stressed laser rods to obtain low-loss stable oscillation in a radially polarized Laguerre-Gaussian, LG(0,1)*, mode. We derive a free-space propagator for the radially and azimuthally polarized LG(0,1)* modes and explain basic principles of mode selection by use of a round-trip matrix diagonalization method. Within this method we calculate round-trip diffraction losses and intensity distributions for the lowest-loss transverse modes. We show that, for the considered laser configuration, the round-trip loss obtained for the radially polarized LG(0,1)* mode is significantly smaller than that of the azimuthally polarized mode. Our experimental results, obtained with a diode side-pumped Nd:YAG rod in a flat-convex resonator, confirm the theoretical predictions. We achieved a pure radially polarized LG(0,1)* beam with M(2)=2.5 and tens of watts of output power.

Resonant directional coupling of hollow Bragg fibers.

Coupling between the lowest-loss TE01 modes of two touching hollow-core Bragg fibers is considered with a view to designing a directional coupler. We have found that for fibers with core radii larger than 10 microm one can identify broad frequency ranges in which intermodal coupling strength exceeds supermode radiation losses by an order of magnitude, thus opening the possibility of building a directional coupler. We attribute such unusually strong intermode coupling both to the resonant effects in the intermirror cavity and a proximity interaction between the leaky modes localized in the mirror.

Analysis of mode structure in hollow dielectric waveguide fibers.

In this paper, we analyze the electromagnetic mode structure of an OmniGuide fiber-a hollow dielectric waveguide in which light is confined by a large index-contrast omnidirectional dielectric mirror. In particular, we find that the modes in an OmniGuide fiber are similar to those in a hollow metallic waveguide in their symmetries, cutoff frequencies, and dispersion relations. We show that the differences can be predicted by a model based on a single parameter-the phase shift upon reflection from the dielectric mirror. The analogy to the metal waveguide extends to the transmission properties, resulting in the identification of the TE01 mode as the lowest-loss mode of the OmniGuide fiber.

Quasi-stadium laser diodes with an unstable resonator condition.

We have observed lasing in a complicated eigenmode of a quasi-stadium laser diode with an unstable resonator consisting of two curved end mirrors obeying an unstable resonator condition and two straight sidewall mirrors. The laser was fabricated by application of a reactive-ion-etching technique to a molecular beam epitaxy-grown graded-index separate-confinement heterostructure single-quantum-well GaAs/AlGaAs structure. The far-field pattern shows that the lasing mode corresponds to the complicated lowest-loss mode obtained numerically by an extended Fox-Li method.

Hexagonal dielectric resonators and microcrystal lasers

We study long-lived resonances (lowest-loss modes) in hexagonally shaped dielectric resonators in order to gain insight into the physics of a class of microcrystal lasers. Numerical results on resonance positions and lifetimes, near-field intensity patterns, far-field emission patterns, and effects of rounding of corners are presented. Most features are explained by a semiclassical approximation based on pseudointegrable ray dynamics and boundary waves. The semiclassical model is also relevant for other microlasers of polygonal geometry.

Direct generation of Bessel beams.

Two implementations are identified to create a Bessel beam directly, i.e. without the spatial filtering of an initially Gaussian beam. The first implementation is based on a resonator configuration whose lowest-loss transverse mode is a Bessel beam. Numerical simulation to corroborate the geometrical optical arguments is presented. The second implementation is based on the theorem that the angular-plane wave spectrum of a Bessel beam is composed of a cone of wave vectors. This cone is also generated through a phase-matching condition in a four-wave mixing process. This leads to the conclusion that anti-Stokes radiation generated in a nonlinear material will leave the substrate under the form of a Bessel beam.

Fractal modes of unstable lasers with polygonal and circular mirrors

The lowest-loss modes of unstable lasers are fractals, emerging asymptotically in the limit of high Fresnel number. The fractality depends on the shape of the feedback mirror. An explicit asymptotic theory can be constructed for the lowest-loss mode, in terms of a superposition of successively magnified edge waves. For polygonal mirrors, the superposition is anisotropic, and gives rise to a mode | u( x, y)| whose graph is a surface with fractal dimension 3, consistent with previous analysis for strip (one-dimensional) mirrors. For circular mirrors, the lowest-loss mode is dominated by focusing of edge waves at the centre of the mirror; the resulting superposition of circular waves gives rise to a mode |u( r )| whose graph is a curve with fractal dimension 3/2.

Theory of unstable laser modes: edge waves and fractality

For large Fresnel numbers N, unstable laser modes are highly irregular and resemble fractals. To explore this, we derive an explicit formula for the lowest-loss mode of a one-dimensional laser (i.e. where the cavity is two dimensional) in terms of edge-diffracted waves, and demonstrate its accuracy for large N. Between the size a of the mirror (outer scale), and the inner scale a/ N, there is no distinguished scale, and the graph of mode intensity has a fractal dimension close to 2. Near the inner scale, the scaling is scale dependent, and the crossover is described by an explicit formula for a `local fractal dimension' D( K), describing the mode on scales near Δx= a/(2 πNK). As K increases through the inner scale K=1, D( K) decreases from 2 when K≪1 to 1 when K≫1 (reflecting the smoothness of the mode on fine scales).