Atom Optics

We propose a review of recent developments on entanglement and non-classical effects in collective two-atom systems and present a uniform physical picture of the many predicted phenomena. The collective effects have brought into sharp focus some of the most basic features of quantum theory, such as nonclassical states of light and entangled states of multiatom systems. The entangled states are linear superpositions of the internal states of the system which cannot be separated into product states of the individual atoms. This property is recognized as entirely quantum-mechanical effect and have played a crucial role in many discussions of the nature of quantum measurements and, in particular, in the developments of quantum communications. Much of the fundamental interest in entangled states is connected with its practical application ranging from quantum computation, information processing, cryptography, and interferometry to atomic spectroscopy.

We discuss the problem of creation of a steady-state entanglement in a system of two two-level atoms which are separated by an arbitrary distance r 12 and interact with each other via the dipole-dipole interaction and both are driven by a laser field. Two measures of entanglement, concurrence and negativity, are used to quantify the amount of entanglement in the system. They are compared with the populations of the maximally entangled collective states of the two-atom system. It is shown that considerable amount of entanglement can be created in case of non-identical atoms driven by a strong laser field

In the transmitted beam of a sodium cell with a single feedback mirror highly modulated patterns appear. The patterns possess the dihedral symmetries D6, D2, and D3. More complex patterns consisting of more than one elementary cell show a local hexagonal arrangement. The topological characteristics are very similar to the one of boundary affected patterns predicted in a thin Kerr slice. The instability is due to the competition of diffraction, diffusion, and optical pumping which is influenced by a weak magnetic field. For higher cell-to- mirror distances the observation of an additional length scale indicates a competition between the feedback and a further instability mechanism, probably the counterpropagating beam instability.

We present theoretical and experimental studies of the dynamics of Bose-Einstein condensates in a onedimensional optical lattice and a three-dimensional harmonic trap. For low atom densities and inertial forces, the condensate performs regular Bloch oscillations, and its center-of-mass motion closely follows semiclassical single-particle trajectories, shaped by the lowest-energy band. But in other regimes, the center-of-mass motion disrupts the internal structure of the condensate by generating solitons and vortex rings, which can trigger explosive expansion of the atom cloud. We use images of the atom cloud to provide experimental evidence for this internal disruption, and find that the process occurs most readily in high-density condensates undergoing slow Bloch oscillations.

This talk will describe the principle of cold atom interferometers and review some recent results in the field of precision inertial measurements. It will present different applications in basic science and related to industrial developments.

This thesis presents single photon generation and spectroscopy using quantum dots (q-dots) on optical nanofibers. Optical nanofibers are essentially vacuum-clad silica fibers with sub-wavelength diameter, which can support only the propagation of the fundamental mode through the guided mode. Optical nanofibers are realized using adiabatically tapered single mode optical fibers. Experiments were performed by depositing colloidal core-shell type CdSeTe (ZnS) q-dots on the optical nanofiber surface. A method is developed to deposit single q-dots systematically and reproducibly along the optical nanofiber. In the view point of investigation of fluorescence photon emission characteristics for single q-dots on optical nanofibers, the absolute fluorescence photon-count rates channeled into the nanofiber guided modes and the normalized photon correlations at various excitation laser intensities are measured. The results are able to obtain the product between the fluorescence photon channeli...

In 1999 the DOE Basic Energy Sciences Advisory Committee defined an innovative scientific direction for the new millennium. In the report the panel recognized the scientific opportunity posed by accelerator-based and tabletop sources of short wavelength radiation. The report emphasized that revolutionary science would be enabled by source parameters that include "high degree of coherence, pulse brevity and high pulsed energy" while pushing the frontiers towards the hard x-ray regime. The panel recommended strategic investment in a new light source, which marked the genesis of the world's first x-ray free-electron laser project. This chapter reports on some of the initial atomic physics experiments conducted at the Linac Coherent Light Source (LCLS) at SLAC and addresses the question as to limits of validity of perturbation theory in describing an intense x-ray pulse interacting with matter.

A 87 Rb Bose-Einstein condensate (BEC) is produced in a portable atom-chip system less than 30ϫ 30 ϫ 15 cm, where the ultrahigh vacuum is maintained by a small, 8 L / s, ion pump and nonevaporable getter. An aluminum nitride chip with lithographically patterned copper is used to seal the vacuum system, provide the electrical feedthroughs, and create the magnetic trap potentials. All cooling and trapping processes occur 0.6-2.5 mm from ambient laboratory air. A condensate of about 2000 87 Rb atoms in F =2,m F = 2 is achieved after 4.21 s of rf forced evaporation. A magneto-optical trap lifetime of 30 s indicates the vacuum near the chip surface is about 10 -10 torr. This work suggests that a chip-based BEC-compatible vacuum system can occupy a volume of less than 0.5 L.

We describe recent work at NIST to develop compact, sensitive atomic magnetometers using a combination of precision optical spectroscopy, atomic physics and techniques of microelectro-mechanical systems (MEMS). These instruments have sensor head volumes in the range of a few cubic millimeters but are capable of sensing magnetic fields of a few picotesla per roothertz in the earth's field and as weak as 70 femtotesla per roothertz in a shielded, low-field environment. We discuss the design, fabrication and testing of several of these devices and propose several applications for which such instruments might be of use. I.

We describe recent work at NIST to develop compact, sensitive atomic magnetometers using a combination of precision optical spectroscopy, atomic physics and techniques of microelectro-mechanical systems (MEMS). These instruments have sensor head volumes in the range of a few cubic millimeters but are capable of sensing magnetic fields of a few picotesla per roothertz in the earth's field and as weak as 70 femtotesla per roothertz in a shielded, low-field environment. We discuss the design, fabrication and testing of several of these devices and propose several applications for which such instruments might be of use. I.

We report on the development of a microfabricated atomic magnetic gradiometer based on optical spectroscopy of alkali atoms in the vapor phase. The gradiometer, which operates in the spin-exchange relaxation free regime, has a length of 60 mm and cross sectional diameter of 12 mm, and consists of two chip-scale atomic magnetometers which are interrogated by a common laser light. The sensor can measure differences in magnetic fields, over a 20 mm baseline, of 10 fT/Hz 1/2 at frequencies above 20 Hz. The maximum rejection of magnetic field noise is 1000 at 10 Hz. By use of a set of compensation coils wrapped around the sensor, we also measure the sensor sensitivity at several external bias field strengths up to 150 mG. This device is useful for applications that require both sensitive gradient field information and high common-mode noise cancellation.

We report on the development of a microfabricated atomic magnetic gradiometer based on optical spectroscopy of alkali atoms in the vapor phase. The gradiometer, which operates in the spin-exchange relaxation free regime, has a length of 60 mm and cross sectional diameter of 12 mm, and consists of two chip-scale atomic magnetometers which are interrogated by a common laser light. The sensor can measure differences in magnetic fields, over a 20 mm baseline, of 10 fT/Hz 1/2 at frequencies above 20 Hz. The maximum rejection of magnetic field noise is 1000 at 10 Hz. By use of a set of compensation coils wrapped around the sensor, we also measure the sensor sensitivity at several external bias field strengths up to 150 mG. This device is useful for applications that require both sensitive gradient field information and high common-mode noise cancellation.

Using the techniques of microelectromechanical systems, we have constructed a small low-power magnetic sensor based on alkali atoms. We use a coherent population trapping resonance to probe the interaction of the atoms' magnetic moment with a magnetic field, and we detect changes in the magnetic flux density with a sensitivity of 50 pT Hz -1/2 at 10 Hz. The magnetic sensor has a size of 12 mm 3 and dissipates 195 mW of power. Further improvements in size, power dissipation, and magnetic field sensitivity are immediately foreseeable, and such a device could provide a hand-held battery-operated magnetometer with an atom shot-noise limited sensitivity of 0.05 pT Hz -1/2 .

Using the techniques of microelectromechanical systems, we have constructed a small low-power magnetic sensor based on alkali atoms. We use a coherent population trapping resonance to probe the interaction of the atoms' magnetic moment with a magnetic field, and we detect changes in the magnetic flux density with a sensitivity of 50 pT Hz -1/2 at 10 Hz. The magnetic sensor has a size of 12 mm 3 and dissipates 195 mW of power. Further improvements in size, power dissipation, and magnetic field sensitivity are immediately foreseeable, and such a device could provide a hand-held battery-operated magnetometer with an atom shot-noise limited sensitivity of 0.05 pT Hz -1/2 .

We demonstrate a simple technique to significantly improve the long-term frequency stability in atomic clocks based on coherent population trapping (CPT). In this technique, a servo is used to control the local oscillator power level in such a way that the optical spectrum generates no net light shift. This ensures that the clock frequency is always given by the atomic resonance frequency that is not perturbed by the incident light fields.

We demonstrate a simple technique to significantly improve the long-term frequency stability in atomic clocks based on coherent population trapping (CPT). In this technique, a servo is used to control the local oscillator power level in such a way that the optical spectrum generates no net light shift. This ensures that the clock frequency is always given by the atomic resonance frequency that is not perturbed by the incident light fields.

A. Clairon, photograph and biography not available at the time of publication. C. Salomon, photograph and biography not available at the time of publication. N. Dimarcq, photograph and biography not available at the time of publication. P. Petit, photograph and biography not available at the time of publication.

Laser beams with embedded vortices, Bessel or Laguerre-Gaussian modes, provide a unique opportunity for creating elements for atom optics, entangling photons and, potentially, mediating novel quantum interconnects between photons and matter. High-order Bessel modes, for example, contain intensity voids and propagate nearly diffraction-free for tens of meters. These vortices can be exploited to produce dark channels oriented longitudinally (hollow beams)

We demonstrate the critical subsystems of a compact atomic clock based on a microfabricated physics package. The clock components have a total volume below 10 cm 3 , a fractional frequency instability of 6 × 10 -10 /τ 1/2 , and consume 200 mW of power. The physics package is easily adapted to function as a magnetometer with sensitivity below 50 pT Hz -1/2 at 10 Hz.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

The paper summarizes the relative advantages and disadvantages of coherent population trapping (CPT) or intensity optical pumping (IOP) for the implementation of a passive atomic frequency standard using the isotope 87 Rb. This paper outlines the basic principles common to both CPT and IOP when using laser optical pumping, and makes explicit their similarities and their differences. This paper describes experimental results obtained in the same cell on the characteristics of the CPT and IOP 87 Rb-hyperfine-resonance line. The measurements showed that the signal contrast is larger in CPT than in IOP for the same resulting line width; the light shift is smaller in CPT than in IOP, and is easier to control; in principle, a passive frequency standard based on CPT has a smaller size than that based on IOP, due to the absence of a microwave cavity. Conclusions on overall expectations for the future of such frequency standards are drawn.

All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

Theoretical study and computer simulation results for stochastic dynamics of two atoms trapped in an optical dipole trap under action of a probe resonant radiation are presented. The radiation force correlations resulting from our model lead, in addition to cold collisions, to a tendency for atoms escape in pairs from the trap.

Using the techniques of microelectromechanical systems, we have constructed a small low-power magnetic sensor based on alkali atoms. We use a coherent population trapping resonance to probe the interaction of the atoms' magnetic moment with a magnetic field, and we detect changes in the magnetic flux density with a sensitivity of 50 pT Hz -1/2 at 10 Hz. The magnetic sensor has a size of 12 mm 3 and dissipates 195 mW of power. Further improvements in size, power dissipation, and magnetic field sensitivity are immediately foreseeable, and such a device could provide a hand-held battery-operated magnetometer with an atom shot-noise limited sensitivity of 0.05 pT Hz -1/2 .

We review recent work at NIST to develop highly miniaturized instruments based on spectroscopy of room-temperature alkali atoms confined in a microfabricated vapor cell. These instruments combine moderate performance, especially over long time periods, with small size, low power dissipation and potentially low cost. Atomic clocks with a fractional frequency stability below 10 −11 over time periods from a few seconds to a few hours have been demonstrated in the laboratory [1] and are now nearing commercial reality [2]. These "chip-scale" atomic clocks operate using under 100 mW of electrical power and are contained in a volume of about 10 cm 3. Processes used in this early clock technology were adapted to make compact atomic magnetometers, with similar size and power requirements [3]. These magnetometers have a sensitivity of about 1pT / √ Hz in earth's field and have been demonstrated to be as low as 10 f T / √ Hz in a low-field environment. We discuss in particular two recent developments in chip-scale atomic magnetometry, both utilizing methods to enhance the instrument sensitivity by suppressing spin-exchange collisions between alkali atoms [4]. The first is an instrument in which the sensor head is interrogated using light fields transmitted through optical fibers, and is therefore completely free from metallic elements. The absence of metal near the sensor head leads to reduced magnetic noise originating from thermal currents and a simple sensor head design. A sensitivity of 130 f T / √ Hz is obtained for signals at a frequency of 100 Hz. The second development is the use of flux concentrators to enhance the sensitivity of a magnetometer based on a micromachined alkali vapor cell. We observe enhancement of the sensitivity by a factor of approximately ten to a sensitivity of 10 f T / √ Hz. Further improvements in sensitivity appear possible through the use of more sophisticated pumping and probing schemes. We conclude with an evaluation of the prospects for the use of microfabricated atomic magnetometers in biomagnetic imaging and nuclear magnetic resonance.

A magneto-optical trap of neutral atoms is essentially a dissipative quantum system. The fast thermal atoms continuously dissipate their energy to the environment via spontaneous emissions during the cooling. The atoms are, therefore, strongly coupled with the vacuum reservoir and the laser field. The vacuum fluctuations as well as the field fluctuations are imparted to the atoms as random photon recoils. Consequently, the external and internal dynamics of atoms becomes stochastic. In this paper, we have investigated the stochastic dynamics of the atoms in a magneto-optical trap during the loading process. The time series analysis of the fluorescence signal shows that the dynamics of the atoms evolves, like all dissipative systems, from deterministic to the chaotic regime. The subsequent disappearance and revival of chaos was attributed to chaos synchronization between spatially different atoms in the magneto-optical trap.

Periodic arrays of magnetic microtraps patterned on a magnetic film provide a potential complementary tool to conventional optical lattices. Such magnetic lattices allow a high degree of design flexibility, low technical noise and state-selective trapping of atoms. This thesis reports the trapping of ultracold 87 Rb atoms in 0.7 µm-period triangular and square magnetic lattices integrated on an atom chip as a step towards using magnetic lattices as a platform for simulating condensed matter and quantum many-body phenomena in nontrivial lattice geometries. The new generation sub-micron period magnetic lattices are produced by patterning a Co/Pd multi-atomic layer magnetic film deposited on a silicon substrate using electron-beam lithography and reactive ion-etching. The magnetic microstructures include 0.7 µm-period 2D square and triangular lattices and 1D 0.7 µm-period and 5 µm-period lattices. The four magnetic microstructures are mounted on an atom chip containing two Z-shaped and two U-shaped current-carrying wires fabricated by chemical etching on a direct bonded copper (DBC) board. The current-carrying wires are required for initial preparation of the ultracold 87 Rb atoms, allowing the creation of a Bose-Einstein condensate in a Z-wire trap and loading into the magnetic lattice. The magnetic lattice potential is produced by applying a bias magnetic field to the magnetic lattice structures which in the case of the 0.7 µm-period lattice produce extremely tight magnetic microtraps with trap frequencies up to about 800 kHz and trap bottoms at estimated distances down to about 90 nm from the chip surface. The atom-surface interaction is studied by measuring the atom loss when atoms in the Z-wire magnetic trap are brought to various distances very close to the chip surface. The interaction of the atoms with the magnetic trapping potential is investigated by launching the Z-wire trap cloud vertically towards the magnetic lattice structures under different bias magnetic fields. The key results presented in this thesis are the successful loading of ultracold atoms into the 0.7 µm-period 2D triangular and square magnetic lattices. The mea-This thesis could not have been completed without constant help and support from my colleagues, friends and family members and now, with a grateful heart, I would like to express my appreciation to all of them. First and foremost, my sincerest gratitude is to my supervisor Emeritus Professor Peter Hannaford who has provided valuable guidance and encouragement, as well as constant motivations to me throughout my research. I will always remember his helping hand from my very first steps in the PhD program to the final writing of this thesis. I feel truly lucky to have the opportunity to do my PhD studies under his supervision. Next, I wish to say thank you to my co-supervisor Professor Russell McLean and Professor Andrei Sidorov for all of their involvements in my research. Without their precious discussions, suggestions and contributions, I doubt I could have gone this far. I would also like to express my thanks to Prof. Saulius Juodkazis, Armandas Balcytis and Pierrette Michaux from the Centre for Micro-Photonics at Swinburne for their contributions to the fabrication of the magnetic lattice atom chip; to Prof. Shannon Whitlock at the University of Strasbourg for his fruitful suggestions and contributions to the project; to Prof. Manfred Albrecht at the Universität Augsburg, Germany for supplying the state-of-art Co/Pd multi-atomic layer film; and to Dr. James Wang for his support and guidance during the characterization of the patterned Co/Pd films. I appreciated the help of Dr. Ivan Herrara, one of the best former postdoc fellows in our group. From the time I was very new to the lab, I have benefited so much from the experience and knowledge that Ivan has kindly passed on to me to improve the quality of my research. Besides, it would be a huge remiss without mentioning Yibo Wang, the former PhD student in our group, who has been a great colleague, as well as a close friend since I first came to the lab. I would like to thank Professor Lap Van Dao, Dr Khuong Dinh and former PhD vi students Prince Surendran, Alessandro Brolis and Smitha Jose for sharing their insightful view and critical comments on the experiments. Also, I would like to thank other people in the Centre, especially Research Support Coordinator Tatiana Tchernova for assistance with all administrative work. Last but not least, I wish to send my sincere appreciation to my family for all their love and support. Their encouragement, advice and guidance has been invaluably precious from the very early stage of my studies. vii viii Declaration The work presented in this thesis entitled "Trapping Ultracold Atoms in Submicron Period Magnetic Lattices" has been carried out in the Centre for Quantum and Optical Science (CQOS) at Swinburne University of Technology in Melbourne, Australia between October 2014 and May 2018. The thesis contains no material that has been accepted for the award of any other degree or diploma. To the best of my knowledge, the thesis contains no material previously published or written by another author, except where due reference is made in the text of the thesis.

Microgravity eases several constraints limiting experiments with ultracold and condensed atoms on ground. It enables extended times of flight without suspension and eliminates the gravitational sag for trapped atoms. These advantages motivated numerous initiatives to adapt and operate experimental setups on microgravity platforms. We describe the design of the payload, motivations for design choices, and capabilities of the Bose-Einstein Condensate and Cold Atom Laboratory (BECCAL), a NASA-DLR collaboration. BECCAL builds on the heritage of previous devices operated in microgravity, features rubidium and potassium, multiple options for magnetic and optical trapping, different methods for coherent manipulation, and will offer new perspectives for experiments on quantum optics, atom optics, and atom interferometry in the unique microgravity environment on board the International Space Station.

database and to 1.47 for the characters database. However, it must be noted that in our case only two parameters are used to characterise each BP. Some examples of retrieval results are shown in Figs. 2-4. It can be appreciated that recognition is successful even when additional BPs appear, like in the square and elliptic shapes. (CICYT), under Project No. TlC098-0562. We would also like to thank F.S. Chang and S.Y. Chen, from Yuan-Ze University (Republic of China), for their help and for providing the databases used in this work.

In this paper, the problem of identifying variations in the nature of atomic clock noise is addressed. Two methods are proposed. One method is based on a generalized likelihood ratio test (GLRT), and the other is based on the dynamic Allan variance (DAVAR), which is a representation of the instantaneous clock stability that is able to point out possible nonstationary behaviors. Both methods efficiently track variations in the experimental clock data and, thus, appear as suitable tools for the detection of atomic clock anomalies.

It is well established that a light beam can carry angular momentum and therefore when using optical tweezers it is possible to exert torques to twist or rotate microscopic objects. Both spin and orbital angular momentum can be transferred. This transfer can be achieved using birefringent particles exposed to a Gaussian circularly polarized beam. In this case, a transfer of spin angular momentum will occur. The change in spin, and hence the torque, can be readily measured optically. On the other hand, it is much more challenging to measure orbital angular momentum and torque. Laguerre-Gauss mode decomposition, as used for orbital angular momentum encoding for quantum communication, and rotational frequency shift can be used, and are effective methods in a macro-environment. However, the situation becomes more complicated when a measurement is done on microscale, especially with highly focused laser beams. We review the methods for the measurement of the angular momentum of light in optical tweezers, and the challenges faced when measuring orbital angular momentum. We also demonstrate one possible simple method for a quantitative measurement of the orbital angular momentum in optical tweezers.

We have investigated the influence of frequency chirps of the excitation pulses in a time-domain optical Ramsey-Bordé atom-interferometer used in an optical clock with ultracold calcium atoms. With optical interferometry, we identify a ringing in the excitation pulses to be responsible for the observed frequency shifts. Using these results, the uncertainty of the latest frequency measurement could be reduced to 1.2 10 14 .

An optical wavelength/frequency standard using the intercombination line 3 P 1 0 1 S 0 of calcium at 657 nm as clock transition is described. An ensemble of cold 40 Ca atoms was prepared in a magneto-optical trap utilizing the cooling transition 1 P 1 0 1 S 0 at 423 nm. The reference signal for the frequency stabilization was generated by time separated field excitation of the clock transition. Sub-kHz resolution close to the natural linewidth of the transition was observed. The frequency of the standard Ca determined against the primary cesium (Cs) atomic clock by a phase-coherent chain is Ca = 455 986 240 494:13 kHz with a total relative uncertainty of 2:5 2 10 013 .

Recently, gyroscopes based on ring-shaped condensate interferometers have been proposed [1]. They offer the advantages of long interaction times within confined physical dimensions. Phase errors can arise, however, from the technical difficulty of controlling noise effects such as mechanical vibrations, trap potential fluctuations, and initial condensate motion. To deal with these problems, we propose a gyroscope based on two dual interferometers consisting of condensates moving in a near-circular trajectory through a common harmonic potential. We show that in such a system, many sources of phase noise cancel to high order, with the primary limitation expected to be from residual asymmetry in the trapping potential. We will present theoretical results for noise sensitivity and our experimental progress towards implementing such a system. [1] Burke, J. H. T. and C. A. Sackett, "Scalable Bose-condensate Sagnac interferometer in a linear trap." Phys. Rev. A 80 061603(R) (2009) and references therein.

A magneto-optical trap of neutral atoms is essentially a dissipative quantum system. The fast thermal atoms continuously dissipate their energy to the environment via spontaneous emissions during the cooling. The atoms are, therefore, strongly coupled with the vacuum reservoir and the laser field. The vacuum fluctuations as well as the field fluctuations are imparted to the atoms as random photon recoils. Consequently, the external and internal dynamics of atoms becomes stochastic. In this paper, we have investigated the stochastic dynamics of the atoms in a magneto-optical trap during the loading process. The time series analysis of the fluorescence signal shows that the dynamics of the atoms evolves, like all dissipative systems, from deterministic to the chaotic regime. The subsequent disappearance and revival of chaos was attributed to chaos synchronization between spatially different atoms in the magneto-optical trap.

We study the classical and quantum dynamics of a Fermi accelerator realized by an atom bouncing off a modulated atomic mirror. We find that in a window of the modulation amplitude dynamical localization occurs in both position and momentum. A recent experiment [A. Steane, P. Szriftgiser, P. Desbiolles, and J. Dalibard, Phys. Rev. Lett. 74, 4972 (1995)] shows that this system can be implemented experimentally.

Laser beams with embedded vortices, Bessel or Laguerre-Gaussian modes, provide a unique opportunity for creating elements for atom optics, entangling photons and, potentially, mediating novel quantum interconnects between photons and matter. High-order Bessel modes, for example, contain intensity voids and propagate nearly diffraction-free for tens of meters. These vortices can be exploited to produce dark channels oriented longitudinally (hollow beams)