Fiber Bragg Gratings in the Ultrashort Pulse Regime
Lawrence R. Chen, Seldon D. Benjamin, and Peter W.E. Smith, Dept. of Electrical and Computer Engineering, and John E. Sipe, Dept. of Physics, Univ. of Toronto and the Ontario Laser and Lightwave Research Center, Toronto, Ontario, Canada.
Fiber gratings have numerous applications for optical communications and sensing. They are typically used with incoherent broadband sources or continuous-wave (cw) and quasi-cw (pulsed) sources, whose spectral bandwidth is narrower than... more>>
A New Type of Lens with Binary Subwavelength Structures
Martin Schmitz and Olof Bryngdahl, Univ. of Essen, Essen, Germany.
Cylindrical microlenses are frequently applied in optical technology, for example, collimating light emitted by laser diodes and coupling light in integrated optics. These applications require diffraction-limited microlenses with high numerical apertures (NA).
Microlenses can be refractive or diffractive. Diffractive microlenses offer greater flexibility in their design. With an increase of the NA, the lateral extension of the structure details of diffractive microlenses decreases and it is necessary to use rigorous electromagnetic diffraction theory for their design with high NAs. We have used the volume integral method for this purpose. more>>
Optical Coherence Tomography for the Analysis of Three-dimensional Flow Fields
Michael Böhmer, Heiko Hinrichs, Klaus D. Hinsch, Jan Kick stein, René Netter, Christof Surmann, Dept. of Physics, Oldenburg Univ., Oldenburg, Germany.
Much information about the spatial and temporal structure of fluid flows is gained by optical investigation of the distribution or motion of foreign matter introduced into the flow. Flow visualization, for example, relies on the propagation of smoke clouds or dye tracks. And, in flow velocimetry, the velocity is derived from the motion of tracer particles. Thin-sheet illumination, as in particle image velocimetry (PIV), provides planewise data, unaffected by the numerous particles in other regions of the flow that remain in the dark. Recent interest concerns 3-D and non-stationary flows where a field of considerable spatial depth must be registered instantaneously. Pulsed holography has been introduced to record the deep field of small scattering particles. The velocity vectors are obtained from a detailed evaluation of the positions of reconstructed particle images. Under these conditions, however, the advantage of a dark region in front or behind the area of interest is sacrificed and optical noise deteriorates the evaluation. more>>
Lossless Projection of Light
J. Glückstad and L. Lading, Optics and Fluid Dynamics Dept., Riso National Laboratory, Roskilde, Denmark, and H. Toyoda and T. Hara, Hamamatsu Photonics K.K. Central Research Laboratory, Hamakita City, Japan.
Imaging of phase objects (i.e., visualizing and projecting the information imprinted by a non-absorbing object into the phase of a transmitted light beam) has always been a subject of considerable interest in optics. From a theoretical point of view, it is a fundamental challenge to devise new phase-only imaging methods that provide the most efficient, simple, and robust use of available photons radiated from a given light source. From an application point of view, a phase-only imaging technique is attractive for at least two reasons. First, the majority of the emitted photons will not be dissipated, preventing heat generation and the resulting damaging effects in the optical hardware. Second, photons that are not absorbed by the optics can be efficiently used and transferred to a desired target projection. Consequently, one can use a weak light source to generate a desired light projection, with strength comparable to that generated by a much stronger light source combined with conventional amplitude modulating optics. On the other hand, one can apply a strong light source in a phase-only modulating system without having to be concerned about deteriorating effects due to absorption. more>>
Various Approaches in Super Resolution
David Mendlovic, Zeev Zalevsky, and Adolf W. Lohmann, Faculty of Engineering, Tel-Aviv Univ., Tel-Aviv, Israel.
The resolution of a system is defined as the finest detail that can pass through the system without being distorted. The motivation of the super resolution field is to handle non-resolved details using a given apriori information about the input signal, (e.g., apriori knowledge on object shape, temporal behavior, wavelength behavior, dimensions, and polarization). The super resolution effect is achieved by exchanging degrees of freedom. For instance, let us assume that the spatial apertures of a system are small and some of the signal's information is lost due to this fact. If it is also apriori known that the signal's information is monochromatic, one may convert part of the spatial information into wavelength information, so that the aperture of the system is synthetically expanded. Based on the distinguishing features between the signal information and system's capabilities, one may adapt the space bandwidth (SW) function of the signal to the SW function of the system using the Wigner chart. more>>
Three-dimensional Fluorescence Microscopy by Optical Scanning Holography
T-C. Poon, Virginia Polytechnic Institute and State Univ., Blacksburg, Va.
In optical sectioning microscopy (OSM), 3-D information is collected by recording a series of 2-D images at various focal planes throughout the 3-D specimen.1 However, during the recording of 2-D images, it is critical that exact longitudinal spacing between adjacent 2-D images and the precise registration of these image slides are accurately controlled. Scanning confocal microscopy (SCM) is a radically new microscope design. more>>
Quantum Cascade Distributed Feedback Laser
Claire Gmachl, Jérôme Faist, Federico Capasso, Deborah L. Sivco, James N. Baillargeon, and Alfred Y. Cho, Bell Laboratories, Lucent Technologies, Murray Hill, N.J.
The characteristic absorption lines of most target gases and pollutants in atmospheric sensing applications lie between 3-13 μm wavelengths. Quantum cascade (QC) lasers, are based on an intersubband transition within the conduction band of a cascaded InGaAs/InAlAs multiple quantum-well structure and grown by molecular beam epitaxy (MBE). They are the only available semiconductor laser sources operating in that wavelength range at room temperature (RT), with peak output power up to several 100 mW. These lasers are driven in pulsed mode and their spectrum is inherently multiple-mode. more>>
Non-Markovian Memory Effects in GaN Semiconductor Optical Amplifiers
S. Hughes, Dept. of Physics, Washington State Univ., Pullman, Wash.
The physics of group III nitrides, like A1N and GaN, is currently coming out of its infancy and has been receiving a great deal of attention lately, primarily because of the use in short-wavelength laser diodes. Subsequently, and as a consequence of the growth technology of GaN and related devices, high-efficiency light-emitting diodes have been developed. Moreover, emission wavelengths between 390-430 nm have been observed at room temperature—the lowest ever demonstrated by a semiconductor laser. more>>
Build-up of the Spatial Coherence in a Discharge Pumped Table-top Soft X-ray Laser
M.C. Marconi, J.L.A. Chilla, C.H. Moreno, B.R. Benware, and J.J. Rocca, Dept. of Electrical Engineering, Colorado State Univ., Fort Collins, Colo.
The rapid development of soft X-ray lasers opens the possibility for the widespread use of very intense table-top sources of soft X-ray coherent radiation. Good spatial coherence will be essential in realizing the full potential of these new lasers in nonlinear optics, holography, and interferometry. We have observed, for the first time, a monotonic improvement of the spatial coherence with amplifier length in a soft X-ray laser. more>>
High Power Mid-IR Interband Cascade Lasers
R.Q. Yang, C-H. Lin, B.H. Yang, D. Zhang, S.J. Murry, and S.S. Pei, Space Vacuum Epitaxy Center, Univ. of Houston, Tex.; C.L. Felix, W.W. Bewley, I. Vurgaftman, and J.R. Meyer, Naval Research Laboratory, Washington, D.C.; and A.A. Allerman and S.R. Kurtz, Sandia National Laboratories, Albuquerque,NM
Mid-IR lasers are in demand for a number of commercial, space, and military applications. These include trace gas detection, IR counter measures, IR light detection and ranging (LIDAR) systems, laser surgery, and medical diagnosis. We have recently demonstrated a new type of mid-IR quantum cascade (QC) laser based on interband transitions in type-II quantum wells. This interband cascade (IC) laser takes advantage of the broken-gap band alignment in the InAs/Ga(In)Sb heterostructure to recycle electrons from the valence band back to the conduction band (see Fig. 1), thus enabling sequential photon emissions from active regions stacked in series. However, by sticking to the interband transitions, it circumvented the fast phonon scattering, which limits the performance of devices based on intersubband transitions such as the QC lasers. more>>
Tunable Mid-infrared Sources by Difference Frequency Generation in GaAs Waveguides
A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, Laboratoire Central de Recherches, Thomson CSF, Domaine de Corbeville, France. (A. Fiore is presently at the Dept. of Electrical and Computer Engineering, Univ. of Calif. at Santa Barbara.)
Nonlinear frequency conversion provides coherent sources in frequency regions where lasers are difficult to obtain. GaAs and AlGaAs have very high second order susceptibilities [χ(2)(GaAs) = 240 pm/V in the near-infrared] and are widely transparent in the infrared. These facts, together with the possibility of integration with sources, make these materials attractive for nonlinear frequency converters. Frequency conversion in GaAs-based waveguides may lead to widely tunable infrared sources by difference frequency generation (DFG), frequency converters around 1.55 μm, and all-optical processing at 1.55 μm. For the nonlinear conversion process to be efficient, the phase velocities of the interacting waves must be matched. In most nonlinear materials, this is achieved by using the natural birefringence of the crystal: Different waves travel with different polarizations, and the effect of dispersion is compensated by the birefringence. However, GaAs and AlGaAs are isotropic materials, so birefringence phase-matching cannot be used. An artificial, "form" birefringence can be induced by stacking layers with different refractive indices. In this case, the two polarizations, parallel and normal to the layers, experience different interface boundary conditions, so their effective phase velocities are different. To maximize the birefringence, a multilayer with high index contrast is required. We have recently demonstrated, that huge form birefringence and phase-matching can be achieved in multilayer GaAs/(Al oxide) waveguides, obtained by selective lateral oxidation of GaAs/AlAs heterostructures. more>>
Self-Focusing, Switching, and Spatial Solitons in Quasi-Phase-Matched Quadratic Media
Yuri S. Kivshar and Ole Bang, Optical Sciences Centre, Australian National Univ., Canberra, Australia, and Carl Balslev Clausen, Technical Univ. of Denmark, Lyngby, Denmark.
Recently, the study of effects produced by the parametric wave mixing in quadratic nonlinear optical materials has attracted growing attention because of exciting prospects for all-optical switching devices. Many of the theoretically predicted effects, such as large nonlinear phase-shifts and spatial two-component soli-tons (fundamental and second harmonic, mutually trapped), have already been observed experimentally, e.g., in a KTP bulk crystal and LiNbO3 slab waveguides. However, for the quadratic nonlinearity to be effective, the wavevector mismatch between the fundamental and second harmonic must be small. So far the efficiency has been quite low, mainly due to restrictions imposed by the use of birefringent phase-matching techniques, and consequently, the required input power has been high. more>>
Optics of Polymer Dispersed Liquid Crystals
L. Vicari, Istituto Nazionale per la Fisica della Materia, Univ. di Napoli "Federico II" Dip. Scienze Fisiche, Facoltà d'Ingegneria, Napoli, Italy.
Polymer dispersed liquid crystals (PDLC) are liquid crystal microdroplets dispersed in a polymeric binder. Optoelectronic films that switch from an opalescent to transparent state are commonly realized by them. Appropriate choices of materials and manufacturing procedures ensure that the liquid crystals in the film are in a nematic phase at room temperature and the molecules assume a bipolar orientation inside each droplet. Molecules are roughly parallel to a direction that is assumed as the droplet director. Droplets appear as optically uniaxial spheres, randomly oriented. Due to the refractive index mismatch with the surrounding medium, the droplets produce a strong light scattering when their size is close to the wavelength of visible light. more>>
Electromagnetically Induced Transparency in Solids
Yang Zhao, Dept. of Electrical and Computer Engineering, Wayne State Univ., Detroit, Mich., and Philip Hemmer, Rome Laboratory, Hanscom AFB, Mass.
Field-induced quantum interference can lead to lasing without inversion (LWI) and electromagnetically induced transparency (EIT) for the resonant enhancement of nonlinear effects with reduced absorption. Until recently, experimental studies of quantum interference have mainly focused on atomic gas media. Now EIT is reported in ruby and Pr+ doped YSO, using three-level systems wherein two of the levels are coupled by a strong electromagnetic field. These results significantly advance the understanding of quantum coherence and interference in solids, and serve as a valuable intermediate step in the development of inversion-less solid-state lasers and low power optical switches. more>>
Optical Doppler Tomography
Zhongping Chen, Thomas E. Milner, Shyam Srinivas, and J. Stuart Nelson, Beckman Laser Institute and Medical Clinic, Univ. of California at Irvine.
Direct visualization of physiological processes provides important information to the clinician for the diagnosis and treatment of disease. High spatial resolution noninvasive techniques for imaging in vivo blood flow dynamics and tissue structure are currently not available as a diagnostic tool in clinical medicine. Such techniques could have a significant impact for biomedical research and clinical diagnostics. Techniques such as Doppler ultrasound and laser Doppler flowmetry (LDF) are currently used in medical diagnostics for blood flow velocity determination. Doppler ultrasound uses the principle that the frequency of ultrasonic waves backscattered by moving particles are Doppler shifted. However, the relatively long acoustic wavelengths required for deep tissue penetration limits the spatial resolution to approximately 200 μm. Although LDF has been used to measure mean blood perfusion in the peripheral microcirculation, strong optical scattering in biological tissue limits spatially resolved flow measurements by LDF. more>>
Laser-induced Crystallization of Supersaturated Urea Solutions
Bruce A. Garetz, Janice E. Aber, Noel L. Goddard, Rod G. Young, and Allan S. Myerson, Polytechnic Univ., Brooklyn, N.Y.
Supersaturated solutions and vapors contain an excess of dissolved or evaporated substances, and therefore are not thermodynamically stable. A slight perturbation, such as a knock or a dust particle, can cause such a solution to crystallize or vapor to condense. The study of the light-induced condensation of supersaturated vapors dates back to the work of Tyndall in the 1860s. More recent interest has involved laser-induced chemical vapor deposition and the precipitation of laser-induced "snow." In all these cases, the absorption of visible or ultraviolet light caused a photochemical reaction forming some new substance that acted as the nucleus for the growth of the condensed phase more>>
Miniature Hologram on Optical Waveguide
Ming Li, National Research Council Canada, Institute for Microstructural Science, Ottawa, Canada, and Anders Larsson, Chalmers Univ. of Technology, Dept. of Optoelectronics, Gothenburg, Sweden.
A novel scheme to build a miniature, synthetic (or 'computer-generated') hologram on the surface of an optical waveguide has been proposed and experimentally demonstrated. Such a hologram is not much larger than the tip of a human hair. This new type of computer-generated hologram is capable of coupling light out of an optical waveguide, thereby leading to its name, off-plane computer-generated waveguide hologram (OP-CGWH), and simultaneously forming a predefined image at a certain distance above the waveguide surface. more>>
Second Harmonic Generation in a Photonic Crystal
Jordi Martorell, R. Vilaseca, and J. Trull, Universitat Politecnica de Catalunya, Terrassa, Barcelona, Spain, and R. Corbalán, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain
Photonic crystals emerged at the end of the last decade as a new frame to control the interaction between radiation and matter. more>>
Progress in Three-dimensional Photonic Bandgap Structures at Visible Wavelengths
S.G. Romanov, N.P Johnson, and R.M. De La Rue, Optoelectronics Research Group, Dept. of Electronics and Electrical Engineering, Univ. of Glasgow, Glasgow, Scotland, U.K.
So far, only 3-D photonic structures demonstrating an incomplete bandgap have been reported for wavelengths shorter than 1 μm. We have used a template method to approach a complete 3-D photonic bandgap (PBG) structure in the visible range. more>>
Two-dimensional Photonic Crystals for the Visible Spectrum
A. Rosenberg, R.J. Tonucci, H.B. Lin, and A.J. Campillo, Naval Research Lab., Optical Sciences Division, Washington, D.C.
Electronic band structure is a familiar concept in solid-state physics. It arises from the interaction of electrons with the crystal's periodic potential, which varies on a length scale comparable to the electronic de Broglie wavelength. The electronic band structure is largely responsible for many of the crystal's physical properties. Ten years ago, the analogous concept of photonic band structure was used to explain the optical properties of an engineered material whose refractive index varies with a periodicity comparable to the wavelength of a photon. more>>
Asymmetric Resonant Optical Cavities
A. Douglas Stone, Applied Physics, Yale Univ., New Haven, Conn, and Jens U. Nöckel, Max-Planck-Institut f. Physik kom-plexer Systeme, Dresden, Germany.
A new and useful type of optical resonator has been proposed based on the principles of chaos theory. The asymmetric resonant cavity (ARC) is an extension of the concept of spherical or cylindrical dielectric resonators that have high-Q "whispering gallery" (WG) modes trapped by total internal reflection. In the ARC, such a cylinder or sphere is deformed substantially, but in a smooth and convex manner, leading to an oval cross-section (see Fig. la, page 38). more>>
Plug and Play Quantum Cryptography
B. Huttner, A. Muller, G. Ribordy, W. Tittel, H. Zbinden, and N. Gisin, Group of Applied Physics, Univ. of Geneva, Geneva, Switzerland.
Quantum cryptography relies on the interplay between classical cryptography and quantum mechanics to ensure the confidentiality of information carried by unprotected channels. It could well become the first practical application of quantum mechanics at the single quantum level. more>>
Optical Nonlinearities of Quantum-Confined Excitons in Semiconductor Microcavities
F. Jahnke, M. Kira, and S.W. Koch, Dept. of Physics and Material Sciences Center, Philipps-Univ. Marburg, Marburg, Germany, and G. Khitrova and H.M. Gibbs, Optical Sciences Center, Univ. of Arizona, Tucson, Ariz.
Radiatively coupled excitons in quantum wells and microcavities show many properties similar to atoms in the micromaser. For example, excitonic normal-mode coupling resembles vacuum-field Rabi oscillations and effects of radiative coupling between excitons in multiple quantum wells are similar to superradiance of atoms. However, the physical nature of the effects is different. For effects involving few atoms, the quantum properties of the light are important. Reflection, transmission, and absorption experiments in semiconductor microcavities can be described within a semi-classical theory. Also, measurements of the number of photons necessary to see nonlinear effects indicate that current semiconductor experiments are far from the quantum statistical limit, so that interpretations based on quantum ladders, as in Reference 3, are not appropriate. The saturation mechanisms in atoms (e.g., power broadening or local field effects) are completely different from those in semiconductors (phase space filling and Coulomb interaction between carriers). more>>
Self-aligned Dual-Beam Optical Laser Trap Using Photorefractive Phase Conjugation
W. Wang, A.E. Chiou, G.J. Sonek, and M.W. Berns
In 1969, Ashkin demonstrated that two counter-propagating focused laser beams form a stable 3-D trap for small dielectric spheres (see Fig. 1a). In 1985, a stable single-beam gradient optical trap (see Fig. 1b) was successfully demonstrated. Since then, optical laser traps in both dual- and single-beam geometries have been developed and used extensively for sample micromanipulation and force transduction. more>>
Nanoquakes at Work: A Quantum Conveyor Belt for Photons
Achim Wixforth, Sektion Physik, Geschw. Scholl Platz, München, Germany.
The combination of surface acoustic waves (SAWs) and the superior optical properties of band gap engineered semiconductor layer systems yields a completely new and promising approach toward another generation of optoelectronic devices. more>>
Novel Methods for Diagnosing Mixing and Laser-Fusion Target Performance Using X-ray Spectroscopy of an Embedded Titanium Layer
Barukh Yaakobi, Frederic J. Marshall, David K. Bradley, Jacques A. Delettrez, Robert S. Craxton, and Reuben Epstein, Laboratory for Laser Energetics, Univ. of Rochester, Rochester, N.Y.
In current direct-drive laser fusion experiments, shell
targets containing thermonuclear fuel (D-T) are uniformly
irradiated by a powerful multi-beam laser, leading to compression and heating. Imperfect irradiation uniformity results in hydrodynamically unstable implosions, which lead to mixing of target layers and reduction in heating and compression. Recent experiments
on the 60-beam OMEGA laser system at the Laboratory for Laser Energetics show that the inclusion of a thin titanium layer within the shell yields novel and significant diagnostic signatures of target behavior. more>>
Do Interacting Spatial Solitons Conserve Angular Momentum?
Ming-Feng Shih, Mordechai Segev, Princeton Univ., Princeton, N.J.; Greg Salamo, Univ. of Arkansas, Fayetteville, Ark.; and Yuri Kivshar, Australian National Univ., Canberra, Australia
Optical spatial solitons have attracted substantial research interest since the 1960s, in part because they hold a promise of controlling light by light. Among all soliton studies, collisions between solitons is one of the most fascinating features, since, in many aspects, solitons interact like particles, maintaining their identities and conserving energy and linear momenta.1 Before 1990, all soliton interaction studies were limited to collisions in a single plane since practically all of the observed stable solitons before that time were 1-D. more>>
Allan W. Snyder, Institute of Advanced Studies, Australian National Univ., Canberra, Australia.
Optical solitons have potential importance for long distance telecommunications (temporal solitons), as well as for all optical devices (spatial solitons) where light itself guides, steers, or manipulates light in bulk material without any intervening fabricated structures. more>>
Lluis Torner and Maria C. Santos, Laboratory of Photonics, Univ. Politècnica de Catalunya, Barcelona, Spain, and Dumitru Mihalache, Dumitru Mazilu, and Lucian C. Crasovan, Dept. of Theoretical Physics, Institute of Atomic Physics, Bucharest, Romania
By and large, optical "walking solitons" are localized, trapped short pulses or focused beams propagating in a nonlinear medium that, for whatever reason, may slow down or accelerate relative to the temporal or spatial group velocity of the frame of reference from where they are launched. They therefore "walk" off the corresponding temporal or spatial slot. Walking solitons might have all the possible shapes of known solitary waves—bright, dark, grey, or exotic—and propagate in any nonlinear material that allows the formation of solitary waves. However, their nature, properties, and overall relevance depend critically on the optical setting where they form, and on the mechanism that makes them walk. more>>
A Compact All-Solid-State Sub-5-fsec Laser
Andrius Baltuŝka, Maxim S. Pshenichnikov, Róbert Szipöcs, and Douwe A. Wiersma
Recent developments in solid-state lasers, chirp-mirror technology, and methods of pulse characterization made it possible to design an all-solid-state laser that delivers sub-5-fsec pulses at a 1-MHz repetition rate. more>>
Spatiotemporal Shaping of Terahertz Pulses
Jake Bromage, Stojan Radic, G.P. Agrawal, and Carlos R. Stroud, Jr.
It has been demonstrated in a number of laboratories over the past several years that when a GaAs crystal is subject to a dc voltage bias and simultaneously illuminated by a fsec laser pulse whose photon energy exceeds the crystal's bandgap, a small antenna is formed that radiates a THz pulse. The pulse typically contains only a fraction of a cycle to a few cycles of oscillation. These pulses have found a variety of uses in ultrafast spectroscopy of atoms, molecules, and solids, far-infrared time-domain spectroscopy, study and control of Rydberg atoms, T-ray imaging of optically opaque materials, and impulse ranging studies. more>>
Infrared Streak Camera
L.D. Noordam and M. Drabbels, FOM Institute for Atomic and Molecular Physics, Amsterdam, The Netherlands.
Streak cameras are being used in many fields of science because of their excellent time resolution and high sensitivity. The spectral range at which conventional streak camera systems operate is limited by the spectral response of their particular photocathode. For most photocathode materials, sensitivity is limited to wavelengths shorter than 1.5 μm. Beyond this, the quantum efficiency of the photocathode becomes negligible. Therefore, the temporal profile of mid- and far-infrared light pulses, e.g., from IR laser systems, cannot be measured directly using a conventional streak camera. more>>
Ultrashort Pulse Autocorrelator
Jinendra K. Ranka and Alexander L. Gaeta, School of Applied and Engineering Physics, Cornell Univ., and Andrius Baltuŝka-Maxim S. Pshenichnikov, and Douwe A. Wiersma, Ultrafast Laser and Spectroscopy Laboratory, Univ. of Groningen, Groningen, The Netherlands.
The standard technique for characterizing an optical pulse in the range of a few picoseconds to sub-10-fsec in duration is to measure its intensity autocorrelation. The measurement of such an autocorrelation requires a material whose nonlinear optical response scales uniformly with the square of the incident pulse intensity over a bandwidth greater than that of the pulse. The most common approach is to detect the amount of second-harmonic light generated by a χ(2) crystal in a Michelson-type autocorrelator as one arm is scanned. more>>
20 Femtosecond Visible Pulses Go Tunable by Noncollinear Parametric Amplification
T. Wilhelm and E. Riedle, Institut fur Medizinische Optik, Ludwig-Maximilians-Universität München, München, Germany.
The past few years have revolutionized ultrafast spectroscopy and femtosecond technology. Based on the modelocked Ti:sapphire laser and on amplifiers using the same active material, extremely powerful and stable systems are now available with pulse lengths below 10 fsec. more>>