Transverse Cavity Modes Research Articles

Diffraction loss analysis of a plane-parallel optical cavity with a phase step and a slit aperture

A model for calculating the round trip diffraction loss in a plane-mirror cavity with an intracavity phase step and an infinite slit aperture is developed. The round trip remaining intensity fraction for the low order transverse cavity modes can be calculated for any given location of the slit aperture and the phase step along the cavity and for any given phase delay on the phase step. The diffraction loss on the slit aperture is found to be a periodic function of the phase delay on the phase step. Transformation of the lasing spectrum emitted from a broadband pulsed dye laser on moving the phase step along the oscillator cavity is reproduced theoretically. The lasing spectrum affected by the phase step is interpreted as the wavelength dependence of the remaining intensity fraction for the principal transverse mode.

Optical characterization and selective addressing of the resonant modes of a micropillar cavity with a white light beam

We have performed white-light reflectivity measurements on GaAs/AlAs micropillar cavities with diameters ranging from 1 {\mu}m up to 20 {\mu}m. We are able to resolve the spatial field distribution of each cavity mode in real space by scanning a small-sized beam across the top facet of each micropillar. We spectrally resolve distinct transverse optical cavity modes in reflectivity. Using this procedure we can selectively address a single mode in the multimode micropillar cavity. Calculations for the coupling efficiency of a small-diameter beam to each mode are in very good agreement with our reflectivity measurements.

Three-Mode Optoacoustic Parametric Amplifier: A Tool for Macroscopic Quantum Experiments

We introduce the three-mode optoacoustic parametric amplifier (OAPA), a close analog of the optical parametric amplifier, for macroscopic quantum mechanics experiments. The radiation pressure reaction of light on the reflective surface of an acoustic resonator provides a nonlinearity similar to the Kerr effect in the optical parametric amplifier. The OAPA can be tuned to operate in a positive gain regime where acoustic signals are amplified or in a negative gain regime where acoustic modes are cooled. Compared with conventional optoacoustic devices, (i) the OAPA incorporates two transverse cavity modes such that the carrier and sideband fields simultaneously resonate, and (ii) it is less susceptible to the laser phase and amplitude noise. These two features significantly ease the experimental requirements for cooling of acoustic modes to their quantum-ground state and creating entangled pairs of phonons and photons.

Evolution from modal to spatially incoherent emission of a broad-area VCSEL

Broad-area vertical-cavity surface-emitting lasers (BA-VCSELs) can exhibit a state of spatially incoherent emission, as we recently reported in [M. Peeters et al., Opt. Express, 13, 9337 (2005)]. Here, we experimentally study the evolution of a BA-VCSEL under pulsed operation from well-defined modal emission with a multitude of transverse cavity modes to such spatially incoherent emission. The transition is studied using a high-speed intensified CCD camera and differential image analysis with which single-shot measurements of the imaged nearfield, farfield, spatial coherence, and spectral emission properties are acquired. This combination of experimental characterization tools allows for a detailed description of the BA-VCSEL's emission behavior, which is necessary for an in-depth understanding of the processes involved. We find the interplay between the thermal chirp and the build-up of a spatially distributed thermal lens to be decisive for the break-up of the global cavity modes.

Dynamic all-optical tuning of transverse resonant cavity modes in photonic bandgap fibers

Photonic bandgap fibers for transverse illumination containing half-wavelength microcavities have recently been designed and fabricated. We report on the fabrication and characterization of an all-optical tunable microcavity fiber. The fiber is made by incorporating a photorefractive material inside a Fabry-Perot cavity structure with a quality factor Q >200 operating at 1.5 microm. Under short-wavelength transverse external illumination, a 2 nm reversible shift of the cavity resonant mode is achieved. Dynamic all-optical tuning is reported at frequencies up to 400 Hz. Experimental results are compared with simulations based on the amplitude and kinetics of the transient photodarkening effect measured in situ in thin films.

Optical Cavity Effects in ZnO Nanowire Lasers and Waveguides

Wide band gap semiconductor nanostructures with near-cylindrical geometry and large dielectric constants exhibit two-dimensional ultraviolet and visible photonic confinement (i.e., waveguiding). Combined with optical gain and suitable resonant feedback, the waveguiding behavior facilitates highly directional lasing at room temperature in controlled-growth nanowires. We have characterized the nanowire emission in detail with high-resolution optical microscopy. The waveguiding behavior of individual zinc oxide (ZnO) nanowires depends on the wavelength of the emitted light and the directional coupling of the photoluminescence (PL) to the emission dipoles of the nanowire. Polarization studies reveal two distinct regimes of PL characterized by coupling to either guided (bound) or radiation modes of the waveguide, the extent of which depends on wire dimensions. Pumping with high pulse energy engenders the transition from spontaneous to stimulated emission, and analysis of the polarization, line width, and line spacing of the laser radiation facilitates identification of the transverse and longitudinal cavity modes and their gain properties. Interpretation of the lasing spectra as a function of pump fluence, with consideration of ZnO material properties and ultrafast excitation dynamics, demonstrates a transition from exciton (fluence 1 IJ/cm 2 ) and gain saturation behavior (fluence > 3 IJ/cm 2 ) modified by the constraints of the nanoscale cylindrical cavity.

Cold atoms in a high-Qring cavity

We report the confinement of large clouds of ultracold ${}^{85}\mathrm{Rb}$ atoms in a standing-wave dipole trap formed by the two counterpropagating modes of a high-$Q$ ring cavity. Studying the properties of this trap, we demonstrate loading of higher-order transverse cavity modes and excite recoil-induced resonances.

Cavity-enhanced optical bottle beam as a mechanical amplifier

We analyze the resonant cavity enhancement of a hollow ``optical bottle beam'' for the dipole-force trapping of dark-field-seeking species. We first improve upon the basic bottle beam by adding further Laguerre-Gaussian components to deepen the confining potential. Each of these components itself corresponds to a superposition of transverse cavity modes, which are then enhanced simultaneously in a confocal cavity to produce a deep optical trap needing only a modest incident power. The response of the trapping field to displacement of the cavity mirrors offers an unusual form of mechanical amplifier in which the Gouy phase shift produces an optical Vernier scale between the Laguerre-Gaussian beam components.

Optimization of the mode matching in pulsed cavity ringdown spectroscopy by monitoring non-degenerate transverse mode beating

A simple and reliable method is presented for optimizing the mode matching of a laser beam to the high-finesse cavity used in pulsed cavity ringdown spectroscopy (CRDS). The method is based on minimizing the excitation of higher-order transverse cavity modes through monitoring the non-degenerate transverse mode beating which becomes visible with induced cavity asymmetry caused by slight misalignment. No additional instrument is required other than a pinhole aperture, thus this method can be applied for CRDS experiments in the whole wavelength range. Measurements of the CRDS absorption spectrum of acetylene (C2H2) near 571 nm demonstrate that the mode-matching optimization improves the sensitivity of pulsed CRDS.

Effect of magnetopause leakage on the lifetime of magnetospheric cavity modes

Magnetospheric cavity modes can decay through various loss processes. Energy leakage across the magnetopause is one such process that is commonly neglected. Here we consider what the actual effect of the neglected magnetopause leakage might be on cavity mode lifetime and hence on coupled transverse mode wave growth. First, we review the linear theory of fast mode wave reflection at a tangential discontinuity to show that magnetopause leakage is significant. For realistic subsolar magnetopause conditions we estimate that 20–60% of magnetospheric fast mode wave Poynting flux incident on the magnetopause is transmitted through the magnetopause and out of the magnetospheric cavity. Second, we demonstrate the effect of magnetopause leakage on magnetospheric cavity modes using an MHD simulation. The simulation is of a box‐like cavity with a dipolar variation of the magnetospheric magnetic field and realistic conditions at the subsolar magnetopause, based upon in situ spacecraft observations. The simulation results show that a purely fast mode cavity oscillation decays due to leakage of fast mode wave energy across the magnetopause. The decay rate that arises from magnetopause leakage is comparable to that found in previous simulations from coupling of fast mode energy into transverse mode field line resonances. Thus we conclude that magnetopause leakage is likely to enhance the decay rate of fast and transverse cavity mode oscillations and should be taken into account in field line resonance theory and especially its application to observations.

Determination and optimization of mode matching into optical cavities by heterodyne detection

We report on a novel high-sensitivity method to characterize and improve mode matching into optical cavities. This method is based on heterodyne detection of cylindrical transverse cavity modes. A specially designed annular-segmented photodiode is used to measure the amplitude of nonresonant modes reflected by the cavity. Our measurements allow us to optimize cavity mode matching to nearly 99.98% and will play an important diagnostic role in gravitational-wave detectors.

Spontaneous rotation of laser patterns

Through a study of the spontaneous rotation of laser patterns, a phenomenon that appears in class-A lasers with a cylindrically symmetric configuration and a homogeneous active medium, we found that class-A lasers support the spontaneous creation of three types of rotational patterns. We derived analytically a general cooperative relation to describe the spontaneous rotation of these patterns. This relation contains three characteristic frequencies: the central carrier frequency, the rotational frequency of the pattern, and the frequency spacing between the transverse cavity modes.

Thermal lens determination of end-pumped solid-state lasers using primary degeneration modes

A simple method using the singularities of an optical resonator to determine the thermal lens of end-pumped laser crystals is reported in this letter. At certain resonator parameters the transverse structures of the laser beam become a superposition of many transverse cavity modes of equal resonance frequencies. Because the resonator parameters depend on the thermally induced lens in the active medium, the strength of the lens can be determined by means of measuring the shift of the degeneration resonator length depending on the pumping power. The method is applied to an end-pumped Nd:YAG laser.

Longitudinal–transverse mode interplay and conical emission in microchip lasers

Field confinement in a microchip laser with transversely varying gain and plane–plane cavity mirrors is theoretically discussed with a semiclassical treatment. We show that the common notion of a transverse cavity mode becomes closely linked to that of a longitudinal cavity mode owing to the key role that detuning of the longitudinal cavity frequency from the atomic resonance plays in the formation of the transverse field profile. In particular, we show that as the pump size decreases the laser emission is pulled toward the atomic resonance frequency on the negative detuning side. Strong mode pulling is interpreted as being due to the index-antiguiding effect induced by the pump and manifests itself as a ring pattern in the far-field spatial intensity.

Spatiotemporal pattern formation and chaos in passive optical systems

The interaction and competition of transverse cavity modes in passive optical systems can lead to the formation of spatial field structures whose symmetry differs from that of the empty cavity, while the time behaviour can become irregular. After having introduced dynamical equations in which the spatial dependence of the electric field is described by frequency-degenerate Gauss-Laguerre (GL) modes, the stationary solutions corresponding to a single or many modes are calculated and their stability is discussed. A scan of the parameter space allows for the identification of several interesting dynamical regimes. An extensive study of the chaotic states is performed in order to understand the relation between GL mode excitation and the relevant active degrees of freedom. Based on this analysis, the conditions for the onset of spatiotemporal chaos, for its characterisation and experimental observation are finally discussed.

Transverse pattern variations in a laser with a parabolic excitation profile

Transverse intensity profiles from a model for a laser with a parabolic transverse excitation profile are shown to change from symmetric to asymmetric patterns, with bistability between some patterns, as the frequency spacing between the transverse cavity modes is decreased. The parabolic excitation profile suppresses some of the nonlinear coupling of the transverse modes that predominates when the excitation profile is uniform. Nonetheless there are substantial qualitative similarities between the results for uniform and parabolic excitation, suggesting some generic governing principles for the pattern formation caused by mode competition and mode correlation.

Transverse laser patterns. I. Phase singularity crystals.

We analyze the interaction and the competition of a set of transverse cavity modes, which belong to a frequency-degenerate family. The laser turns out to be able to realize several different stationary spatial patterns, which differ in the transverse configuration of the intensity or of the field and are met by varying the values of the control parameters. A striking feature that emerges in almost all steady-state patterns is the presence of dark points, in which both the real and the imaginary part of the electric field vanish and such that, if one covers a closed loop around one of these points, the field phase changes by a multiple of 2\ensuremath{\pi}, which corresponds to the topological charge of the point. We show in detail the analogy of these phase singularities to the vortex structures well known in such fields as, for example, hydrodynamics, superconductivity, and superfluidity. In our case, at steady state, these singularities are arranged in the form of regular crystals, nd the equiphase lines of the field exhibit a notable similarity to the field lines of the electrostatic field generated by a corresponding set of point charges. We analyze in detail the patterns that emerge in the cases 2p+l=2 and 2p+l=3, where p and l are the radial and angular modal indices, respectively, and we compare the results with the experimental observations obtained from a ${\mathrm{Na}}_{2}$ laser. The observed patterns agree in detail with those found by theory; in particular, they exhibit the predicted phase singularities in each pattern. The transitions from one pattern to another, that one observes under variation of the control parameters, basically agree with those predicted by theory.

Instabilities in a bimode CO 2 laser with a saturable absorber

We report on the observation of mode hopping in a bimode CO 2 laser with a saturable absorber. When the control parameters are changed, the output intensity of this laser shows a succession of periodic regimes that may become completely erratic. Each of these regimes may be explained considering the role played alternatively by two unstable fixed points corresponding to the steady state intensity of each mode. In a particular range of the parameter space, a description of multipeaked regimes is given using the Farey arithmetic, and it ressembles that observed in the Belousov-Zhabotinskii reaction. Transverse effects are observed that result from the nonlinear coupling of transverse cavity modes with both the active and passive media.

Stochastic noise in TEM_00 laser beam position

The centroid of a single-transverse-mode laser beam fluctuates in position because of spontaneous emission of the laser medium into higher transverse cavity modes.

Spatial and temporal instabilities in aCO2laser

We show experimentally the appearance of time-dependent and stationary complex spatial structures in a ${\mathrm{CO}}_{2}$ laser. A comparison of the data with a theoretical model supports the notion that the observed phenomena result from the nonlinear interaction of transverse cavity modes with the active medium. The simultaneous appearance of spatial and temporal instabilities hints to the interesting prospect that one may be able to study turbulence in a laser system.