Comb Modes Research Articles

Purely dipolar versus dipolar-exchange modes in cylindrical nanorods

Properties of purely dipolar and dipolar-exchange modes in finite circular rods are investigated numerically, with the sample static magnetization assumed to be uniform and parallel to the rod axis; we study magnetic excitations propagating along this direction. In particular, we demonstrate size-exchange effects induced by modifying the rod aspect ratio (the diameter to length ratio) and the strength of the exchange coupling. Untypical groups of purely dipolar modes are shown to occur in smooth rods: bulk-dead modes, characterized by a dead-amplitude region inside the rod, and comb modes, in which a nearly “dead” region is found at the sample borders, while numerous (“comb-like”) oscillations take place in the bulk. These two mode groups fade to disappear when the sample geometry evolves toward the thin-film one, or when the exchange becomes dominant. The existence of these untypical modes is related to local demagnetizing field profile nonhomogeneity, particularly to two edge wells found in the field profile. The bulk-dead modes are low-frequency modes confined to the well regions only (and therefore double-degenerated), while modes with higher frequency values (subjected to an interference within the barrier) become fast-oscillating comb modes. When the contribution of the exchange grows to prevail, the “dipolar” nonhomogeneity becomes negligible with respect to the total (exchange and dipolar) energy, and only the typically exchange-related bulk and surface modes are found to subsist.

Determination of absolute mode number using two mode-locked laser combs in optical frequency metrology

The mode number of the comb line involved in the optical frequency measurement was determined using two mode-locked, erbium-doped fiber laser combs operated at different repetition rates independently of the frequency fluctuation of the laser under measurement (LUM). A simple measurement process is presented to determine the difference in mode number between the two laser combs and the comb mode number, yielding the absolute frequency of the LUM.

Widely tunable single-mode quantum cascade lasers with two monolithically coupled Fabry-Pérot cavities

The authors report on tunable, miniaturized, two-segment coupled cavity quantum cascade lasers fabricated in a process with a single dry etch step. They observed controllable vernier-effect-based mode switching, induced by the spectral shift of the short cavity’s Fabry-Pérot mode comb due to Joule heating. With the help of this discontinuous tuning mechanism, single-mode operation with routinely ∼20dB side mode suppression ratio was achieved over a broad spectral range. The authors measured a quasicontinuous tuning range of 12cm−1 (138nm) and an entire single-mode tuning range of 16.5cm−1 (190nm), centered around 933cm−1 (10.7μm).

Experimental characterization of an Yb3+-doped fiber ring laser with frequency-shifted feedback

We present experimental characteristics of an Yb3+-doped fiber ring laser operating with frequency-shifted feedback (FSF) through an acousto-optic modulator (AOM) and seeded by both a stationary continuous-wave (CW) laser and spontaneous emission. We show the spectrum and output characteristics for operations with several effective gain bandwidths, as established by Fabry–Perot etalons inside the cavity. Observation using a high finesse Fabry–Perot interferometer shows that, as expected from earlier work, although the spectrum of the FSF laser without seeding is continuous, when seeded by a CW-laser the spectrum consists of a comb of discrete modes, each offset from the seed by an integer number of AOM frequency shifts. The experimental results are in excellent quantitative agreement with the theory developed earlier [L. Yatsenko, B.W. Shore, K. Bergmann, Opt. Commun. 236 (2004) 183].

New magnetostatic modes in small nonellipsoidal magnetic particles

AbstractMagnetostatic normal modes are investigated here in elongated rods. The dipolar field resulting from the dipole–dipole interactions is calculated numerically in points of the axis connecting opposite rod face centers (central axis ) by collecting individual contributions to this field coming from each of the atomic planes perpendicular to the central axis. The applied magnetic field is assumed to be oriented along the central axis, and the magnetization to be uniform throughout the sample. The frequency spectrum of magnetostatic waves propagating in the direction of the applied field is found numerically by solving the Landau–Lifshitz equation of motion with the spatially nonhomogeneous dipolar field taken into account; the mode amplitude profiles are depicted as well. While energetically highest modes have bulk‐extended character, the modes forming the lower part of the spectrum are localized in the subsurface region (bulk‐dead modes ). Between these two mode types, magnetostatic modes of a new type (comb modes ) are found to occur, characterized by two clearly discernible regions: a zone of fast amplitude oscillations inside the rod, and narrow slow‐oscillation regions at the borders. Absorbing virtually no energy from an applied alternating field, comb modes will have no significant contribution to the magnetic noise. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Influence of ridge geometry on lateral mode stability of (In/Al)GaN laser diodes

As a contribution to the current intense research efforts on wide band-gap semiconductor devices which are directed towards the development of commercial blue laser diodes, in this issue's Editor's Choice the optimization of the waveguide structure, to achieve stable laser mode operation, is investigated. The cover picture shows the near-field intensity distribution of the fundamental and first order lateral modes of a blue (Al,In)GaN laser diode together with the double longitudinal mode comb associated with these modes. The first author, Ulrich T. Schwarz, works on optical spectroscopy, characterization, and simulation of blue laser diodes and LEDs. Apart from semiconductor optoelectronics, the focus of his scientific interest is on modern optics, covering propagation invariant Bessel beams, Ince-Gaussian beams and optical vortices.

Influence of ridge geometry on lateral mode stability of (Al,In)GaN laser diodes

AbstractHeight and width of the ridge forming the laser diode waveguide determine threshold current density and lateral mode stability. We measure the optical near‐field of the laser mode and simulate the two–dimensional mode distribution including waveguide losses and optical gain. The simulations show that weak guiding and not current spreading is the major cause for increased threshold current densities in weakly guided laser diodes. The near‐field measurements show fundamental and higher order modes for nominally identical ridge laser diodes. We demonstrate that asymmetric losses in the waveguide bias the lateral mode competition towards higher order modes for an intermediate range of index guiding. This asymmetric damping is specific for (Al,In)GaN laser diodes due to absorption introduced in the p‐waveguide by magnesium doping. This competition of lateral modes can also be seen spectrally as two longitudinal mode combs of different optical gain. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Cavity-enhanced absorption spectroscopy with a mode-locked diode-pumped vertical external-cavity surface-emitting laser

We present a first demonstration of `mode-locked' cavity-enhanced absorption spectroscopy (ML-CEAS) using a mode-locked diode-pumped, vertical external-cavity, surface-emitting semiconductor laser (DP-VECSEL). This laser, operating around 1.04 μm, was modeloked using a semiconductor saturable absorber mirror (SESAM) and provided an emission spectrum possessing a regular comb of modes with a broad and smooth envelope. Matching this comb with the comb of resonances of a high finesse cavity allowed efficient transmission of the laser spectrum by the cavity. Thanks to the enhancement of absorption by the cavity, on this transmitted spectrum we could observe weak absorption lines by a gas placed inside the cavity.

A bulk microfabricated multi-axis capacitive cellular force sensor using transverse comb drives

This paper presents design, fabrication and calibration results for a novel 2-DOF capacitive force sensor capable of resolving forces up to 490 µN with a resolution of 0.01 µN in x, and up to 900 µN with a resolution of 0.24 µN in y. A simple fabrication process using deep reactive ion etching (DRIE) on silicon-on-insulator (SOI) wafers forms the 3D high aspect ratio structure. A transverse mode comb drive movement is used to greatly improve device sensitivity. Among other advantages of the developed process is a dice-free release of wafer structures, allowing fragile structures to be individually packaged. Notching or footing effects and bowing effects are well-known problems in DRIE on SOI wafers. Techniques to overcome notching and bowing effects using a PlasmaTherm SLR-770 etcher are presented that do not require hardware modifications. The application of the force sensor is for providing real-time force feedback during individual cell manipulation tasks.

Optical frequency standards and measurements

We describe the performance characteristics and frequency measurements of two high-accuracy high-stability laser-cooled atomic frequency standards. One is a 657-nm (456-THz) reference using magneto-optically trapped Ca atoms, and the other is a 282-nm (1064-THz) reference based on a single Hg/sup +/ ion confined in an RF-Paul trap. A femtosecond mode-locked laser combined with a nonlinear microstructure fiber produces a broad and stable comb of optical modes that is used to measure the frequencies of the reference lasers locked to the atomic standards. The measurement system is referenced to the primary frequency standard NIST F-1, a Cs atomic fountain clock. Both optical standards demonstrate exceptional short-term instability (/spl ap/5/spl times/10/sup -15/ at 1 s), as well as excellent reproducibility over time. In light of our expectations for the future of optical frequency standards, we consider the present performance of the femtosecond optical frequency comb, along with its limitations and future requirements.

Phase coherent vacuum-ultraviolet to radio frequency comparison with a mode-locked laser

We demonstrate a versatile new technique that provides a phase coherent link between optical frequencies and the radio frequency domain. The regularly spaced comb of modes of a mode-locked femtosecond laser is used as a precise ruler to measure a large frequency gap between two different multiples (harmonics or subharmonics) of a laser frequency. In this way, we have determined a new value of the hydrogen 1S-2S two-photon resonance, f(1S-2S) = 2 466 061 413 187.29(37) kHz, representing now the most accurate measurement of an optical frequency.

Optical frequency measurement across a 104-THz gap with a femtosecond laser frequency comb

The frequency-domain mode comb of a Ti:sapphire femtosecond laser centered at 350 THz is broadened to 150 THz (full width at -30 dBc) by self-phase modulation in a single-mode optical fiber. By phase locking continuous-wave lasers to elements of the comb near 1064 and 778 nm, we measure the 104-THz frequency gap between these two lasers with a relative uncertainty of 2.7 x 10(-11) in 1 s.

Surface-emitting lasers coupled to external cavities with a phase plate: dependence on the orientation of the plate axes

We study a vertical-cavity surface-emitting laser with external feedback through a quarter-wavelength plate. We show that the effect of a rotation of the quarter-wavelength plate is to shift one comb of modes with respect to the other one. The dependence of the frequency on the rotation angle is calculated and shown to be in good agreement with experimental results.

Frequency stabilization and control of a mode-locked dye laser

The mode comb of a synchronously pumped mode-locked dye laser is stabilized in frequency by locking one of its modes to a transmission maximum of a reference Fabry–Perot interferometer. The frequency error signal, obtained by a conventional modulation–demodulation technique, is fed back to permanently readjust the cavity length of the laser via an integrating servo amplifier and a piezo-positioned end mirror. Insertion of an appropriate loop filter prevents loop oscillations on the dominant mechanical resonance of the transducer–mirror combination. A special ramp automatic reset function is introduced to avoid saturation of the servo amplifier. To verify the improvement in laser stability the emission spectrum was scanned with a high-resolution optical spectrum analyzer. A laser linewidth of 3 MHz has been achieved. Extended linear sweeps of the stabilized mode comb for spectroscopic measurements were realized by simultaneously tuning the reference cavity and tilting the intracavity etalon.

Design of a phase-locked multimode SAW oscillator

A 60-100 MHz multimode SAW (surface acoustic wave) oscillator with comb spacing Deltaf=10 MHz used a low-loss SPUDT (single-phase unidirectional transducer) comb filter in conjunction with two varactor-based control elements and two feedback loops, for mode selection and stability enhancement over long dwell times. The end aim is to reduce close-in phase noise over that of the unlocked oscillator, corresponding to improved intermediate-term time-domain stability. Frequency deviation was less than 20 Hz over two hours in each of the five comb modes.

Sampling effect of distributed reflector arrays within a single-phase unidirectional SAW transducer

A noteworthy feature of the group-type single-phase unidirectional transducer is that it can permit wideband low-loss surface-acoustic-wave (SAW) comb filter operation. This is shown to be due to the sampling imposed by the distributed reflector gratings. The capability is illustrated theoretically and experimentally for a 65-MHz comb filter on 128 degrees Y-X lithium niobate, with 5 comb modes of 585-kHz bandwidth each, together with 2.6-dB minimum insertion loss and overall 50% fractional bandwidth.

Inter-intramode correlation spectroscopy: A new experimental technique to study mode interaction in semiconductor lasers

A new experimental method to study modal interaction in semiconductor lasers is presented. The inter-intramode correlation spectroscopy investigates correlations between intensity and phase fluctuations having their origin in different longitudinal modes. First results for GaAs/(GaAl)As multimode lasers reveal correlated frequency fluctuations of the total longitudinal mode comb. Refractive index fluctuations and intermode coupling are discussed as the origin for these intramodal fluctuations.