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NASA NTRS1984

Rotationally-induced Birkeland current systems

Rotational effects which are negligible in earth's magnetosphere become dominant in the magnetospheres of the outer planets where they give rise to Birkeland current circuits coupling the ionospheric and magnetospheric motions. The centrifugal force of corotation produces an azimuthal ring current in the magnetosphere while the Coriolis force produces a current parallel to the plasma flow. The acceleration current also becomes significant when deviations from strict corotation are appreciable. In general, none of these currents are divergence-free, and closure is provided by ionospheric conduction currents via connecting Birkeland currents. Thus the ionospheric conductivity regulates magnetospheric motions much as it does in the terrestrial case. The effects of such currents have been clearly observed in the magnetospheres of Jupiter and Saturn. Birkeland current circuits also transmit planetary angular momentum to external sinks such as conducting satellites (e.g., Io), plasma production sites (e.g., the Io torus), and/or the surrounding solar wind (as proposed for Uranus).

Hill, T. W.↗

NASA NTRS1983

Ion trajectories in a space-charge wave on a relativistic electron beam

The motion of an ion in a space-charge wave on a strongly magnetized electron beam is investigated. The motions of the ion perpendicular and parallel to the beam direction are coupled by a nonlinear term in the ion Hamiltonian that is proportional to the wave amplitude, and this coupling causes the motion of the ion to deviate significantly from that of a linear harmonic oscillator in certain resonant regions of phase space. A sequence of canonical transformations is employed to investigate the motion of the ion in these regions. It is determined that wave amplitudes that are too small to trap beam electrons are too small to cause these resonances to overlap. When this overlap does not occur, the motion is found not to be discernibly ergodic in any three-dimensional subspace of the energy hypersurface because there exists a third constant of the motion in addition to the total energy and angular momentum. The numerically integrated ion trajectories are studied using surface-of-section techniques in order to verify these findings. It is found that the third constant of the motion constrains an ion initially trapped in a potential well of the wave to remain trapped in this well. It is concluded that ergodic behavior poses no threat at attempts at collective ion acceleration in space-charge waves on an electron beam.

Russell, D. A.↗

NASA NTRS1988

GOES dynamic propagation of attitude

The spacecraft in the next series of Geostationary Operational Environmental Satellites (GOES-Next) are Earth pointing and have 5-year mission lifetimes. Because gyros can be depended on only for a few years of continuous use, they will be turned off during routine operations. This means attitude must, at times, be determined without benefit of gyros and, often, using only Earth sensor data. To minimize the interruption caused by dumping angular momentum, these spacecraft have been designed to reduce the environmental torque acting on them and incorporate an adjustable solar trim tab for fine adjustment. A new support requirement for GOES-Next is that of setting the solar trim tab. Optimizing its setting requires an estimate of the unbalanced torque on the spacecraft. These two requirements, determining attitude without gyros and estimating the external torque, are addressed by replacing or supplementing the gyro propagation with a dynamic one, that is, one that integrates the rigid body equations of motion. By processing quarter-orbit or longer batches, this approach takes advantage of roll-yaw coupling to observe attitude completely without Sun sensor data. Telemetered momentum wheel speeds are used as observations of the unbalanced external torques. GOES-Next provides a unique opportunity to study dynamic attitude propagation. The geosynchronous altitude and adjustable trim tab minimize the external torque and its uncertainty, making long-term dynamic propagation feasible. This paper presents the equations for dynamic propagation, an analysis of the environmental torques, and an estimate of the accuracies obtainable with the proposed method.

Markley, F. Landis↗

DOE OSTI2025

Photoredox Catalysis with Spin Magnetic Field Effects: A Scheme for Chiral Resolution

Quantities that break both mirror symmetry and time-reversal symmetry, such as the orbital angular momentum, are known to connect molecular chirality with an applied magnetic field. This concept has led to observations such as magneto-chiral dichroism and chirality-induced spin selectivity (CISS). However, being small, these effects often require additional amplification procedures such as flow chemistry to achieve bulk enantioseparation. In this work, we demonstrate how the magnetic field effect on photogenerated radical pairs, which also breaks time-reversal symmetry, can be harnessed for enantiopurification. Fundamental to this process is the collective decay of the singlet and triplet radical-pair states made possible by an applied magnetic field. Because opposite enantiomers exhibit spin-orbit coupling matrix elements of opposite signs, the singlet and triplet decay channels interfere constructively in one enantiomer. Meanwhile, molecules of the other enantiomer are funnelled into the first enantiomer through excited-state chirality inversion, achieving (dynamic kinetic) chiral resolution. Using an axially chiral binaphthyl derivative and a borane photosensitizer as prototype, we predict an appreciable enantiomeric excess (e.e.) of 90% to be possible at steady state, attained within hundreds of milliseconds when irradiated by a laser. Importantly, our analytical results showcase regimes of perfect enantioselectivity (100% e.e.), accessible by further chemical optimization of the photosensitizer for which general strategies are discussed. Altogether, this work illustrates a so-far untapped but powerful control knob for photoredox catalysis based on spin chemistry principles.

Magnetic properties↗

NASA NTRS2018

Polarization-Controlled Directional Multiphoton Photoemission from Hot Spots on Single Au Nanoshells

Directional photoemission from single Au nanoshells is demonstrated in the low-intensity, multiphoton regime. Thisdirectionality is shown to be due to the plasmonic excitation of highly photoemissive, nanometer scale surface regions, which are characterized by correlated momentum mapping, scanning electron microscopy (SEM), and laser polarization-dependence studies. Furthermore, the photoelectron flux from a single nanoshell can be systematically rotated by over 90Â° in momentum space simply by polarization-controlled coupling to different hot spots. Photoelectrondistributions are directly characterized in momentum space via velocity map imaging (VMI) of the two-dimensional transverse (px, py) momentum components for single nanoshells. For the majority of nanoshells studied, the photoemission is directionally orthogonal to the laser polarization, which implicates nanoscale crevice-shaped "hotspots" clearly observed in the correlated SEM/VMI studies, with the near-field plasmonic nature of these crevices clarified further via finite-element simulations. These results rationalize the large photoemission enhancements observed in previous Au nanoshell studies, but more importantly provide a novel experimental access to directionally tunable electron emission from nanoscale sources. The ability to control photoemission/photocurrent angular distributions at the nanoscale with only modest optical fields indicates a new parameter for optimizing nanoplasmonic system performance and suggests new plasmonic applications such as ultrafast, polarization-controlled photoelectric/photovoltaic switches.

Pettine, Jacob↗

DOE OSTI2025

Dynamical control in a prethermalized molecular ultracold plasma: Local dissipation drives global relaxation

Prethermalization occurs as an important phase in the dynamics of isolated many-body systems when coupled degrees of freedom relax in a subspace separated from a state of complete thermodynamic equilibrium by a gap in energy or other conserved quantity. Slow equilibration from a prethermal phase can localize the dynamics of natural and model systems despite high dimensionality and limited disorder. Here, we report the signature of an enduring prethermal regime of arrested relaxation in the molecular ultracold plasma that forms following the avalanche of a state-selected Rydberg gas of nitric oxide. For a wide range of initial conditions, this system enters a critical phase in which a density of NO + and electrons balances a population of Rydberg molecules. Electron collisions mix orbital angular momentum, scattering Rydberg electrons to states of very high ℓ . The rapid predissociation of molecules in states of low- ℓ purifies this high- ℓ ensemble. The angular momentum barrier that separates NO + ions and electrons creates an extraordinary gap between the plasma states of n ≈ ℓ , with measured n > 200 and penetrating states of ℓ = 0 , 1 , and 2. Evolution to a statistically equilibrated state of N and O atoms cannot occur without Rydberg electron penetration, and this gap blocks relaxation for a millisecond or more. A weak radiofrequency (RF) field drives ℓ -mixing electron collisions that erase this gap, causing wholesale dissipation. Remarkably, a local quantum-state transition promoting an exceedingly small fraction of the molecules in the prethermalized ensemble to a predissociative state also acts with a global effect, driving the entire system to a dissipative equilibrium. Using the Lindblad master equation, we illustrate qualitatively similar dynamics for a toy model of an open quantum system that consists of a localized set of spins on which dissipation acts at a single site as a gateway to equilibrium. Published by the American Physical Society 2025

Wang, Ruoxi↗

NASA NTRS1977

The magnetic attitude control of the Atmosphere Explorer-E spacecraft

The Atmosphere Explorer-E spacecraft was launched in November 1975, as the last of the Atmosphere Explorer series. It is a dual spin satellite and has on-board magnetic coils to maintain the spin axis of the spacecraft within 2 degrees of orbit normal. There is a constraint on the total angular momentum to keep it at a constant level, at around 1200 in-lb-sec +/-10 percent. On the previous AE satellites, the attitude and momentum were controlled separately, with dipoles mounted parallel to the spin axis for pure attitude control, and with coils in the spin plane to desaturate the momentum wheel. Due to the near-equatorial orbit of the AE-E spacecraft, spin axis coils would be inefficient, because the dipoles would have been closely aligned with the geomagnetic field vector. For this reason it was decided to control both attitude and momentum magnitude with dipoles in the spin plane. However, for spin plane coils the attitude and momentum control are strongly coupled, which required a special control theory to be worked out.

Grell, M. G.↗

DOE OSTI2020

The effect of non-linear mutual friction on pulsar glitch sizes and rise times

ABSTRACT Observations of pulsar glitches have the potential to provide constraints on the dynamics of the high density interior of neutron stars. However, to do so, realistic glitch models must be constructed and compared to the data. We take a step towards this goal by testing non-linear models for the mutual friction force, which is responsible for the exchange of angular momentum between the neutron superfluid and the observable normal component in a glitch. In particular, we consider a non-linear dependence of the drag force on the relative velocity between superfluid vortices and the normal component, in which the contributions of both kelvin and phonon excitations are included. This non-linear model produces qualitatively new features, and is able to reproduce the observed bimodal distribution of glitch sizes in the pulsar population. The model also suggests that the differences in size distributions in individual pulsars may be due to the glitches being triggered in regions with different pinning strengths, as stronger pinning leads to higher vortex velocities and a qualitatively different mutual friction coupling with respect to the weak pinning case. Glitches in pulsars that appear to glitch quasi-periodically with similar sizes may thus be due to the same mechanisms as smaller events in pulsars that have no preferred glitch size, but simply originate in stronger pinning regions, possibly in the core of the star.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Theoretical methods to design and test quantum simulators for the compact Abelian Higgs model

The lattice compact Abelian Higgs model is a nonperturbative regularized formulation of low-energy scalar quantum electrodynamics. In 1+1 dimensions, this model can be quantum simulated using a ladder-shaped optical lattice with Rydberg-dressed atoms. In this setup, one spatial dimension is used to carry the angular momentum of the quantum rotors. One can use truncations corresponding to spin-2 and spin-1 to build local Hilbert spaces associated with the links of the lattice. We argue that ladder-shaped configurable arrays of Rydberg atoms can be used for the same purpose. We make concrete proposals involving two and three Rydberg atoms to build one local spin-1 space (a qutrit). We show that the building blocks of the Hamiltonian calculations are models with one and two spins. We compare target and simulators using perturbative and numerical methods. The two-atom setup provides an easily controllable simulator of the one-spin model while the three-atom setup involves solving nonlinear equations. We discuss approximate methods to couple two spin-1 spaces. The article provides analytical and numerical tools necessary to design and build the proposed simulators with current technology.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Distinguishing resonance symmetries with energy-resolved photoion angular distributions from ion-pair formation in O 2 following two-photon absorption of a 9.3 eV femtosecond pulse

We present a combined experimental and theoretical study on the photodissociation dynamics of ion-pair formation in O 2 following resonant two-photon absorption of a 9.3 eV femtosecond pulse, where the resulting O + ions are detected using 3-D momentum imaging. Ion-pair formation states of $^3\Sigma^-_g$ and $^3\Pi_g$ symmetry are accessed through predissociation of optically dark continuum Rydberg states converging to the B $^2\Sigma^-_g$ ionic state, which are resonantly populated via a mixture of both parallel-parallel and parallel-perpendicular two-photon transitions. This mixture is evident in the angular distribution of the dissociation relative to the light polarization, and varies with the kinetic energy release (KER) of the fragmenting ion-pair. The KER-dependent photoion angular distribution reveals the underlying two-photon absorption dynamics involved in the ion-pair production mechanism and indicates the existence of two nearly degenerate continuum resonances possessing different symmetries, which can both decay by coupling to ion-pair states of the same total symmetry through internal conversion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Measuring autoionization decay lifetimes of optically forbidden inner valence excited states in neon atoms with attosecond noncollinear four-wave-mixing spectroscopy

Attosecond noncollinear four-wave-mixing spectroscopy with one attosecond extreme ultraviolet (XUV) pulse and two few-cycle near-infrared (NIR) pulses was used to measure the autoionization decay lifetimes of inner valence electronic excitations in neon atoms. After a 43-48-eV XUV photon excites a 2s electron into the 2s2p 6 (np) Rydberg series, broadband NIR pulses couple the 2s2p 6 3p XUV-bright state to neighboring 2s2p 6 3s and 2s2p 6 3d XUV-dark states. Controllable delays of one or both NIR pulses with respect to the attosecond XUV pulse reveal the temporal evolution of either the dark or bright states, respectively. Experimental lifetimes for the 3s, 3p, and 3d states are measured to be 7±2, 48±8, and 427±40 fs, respectively, with 95% confidence. Accompanying calculations with two independent ab initio theoretical methods, newstock and astra, verify the findings. The results support the expected trend that the autoionization lifetime should be longer for states that have a smaller penetration in the radial region of the 2s core hole, which in this case is for the higher angular momentum Rydberg orbitals. In conclusion, the underlying theory thus links the lifetime results to electron correlation and provides an assessment of the direct and exchange terms in the autoionization process.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Quarkonium semiclassical transport in quark-gluon plasma: factorization and quantum correction

We study quarkonium transport in the quark-gluon plasma by using the potential nonrelativistic QCD (pNRQCD) effective field theory and the framework of open quantum systems. We argue that the coupling between quarkonium and the thermal bath is weak using separation of scales, so the initial density matrix of the total system factorizes and the time evolution of the subsystem is Markovian. We derive the semiclassical Boltzmann equation for quarkonium by applying a Wigner transform to the Lindblad equation and carrying out a semiclassical expansion. We resum relevant interactions to all orders in the coupling constant at leading power of the nonrelativistic and multipole expansions. The derivation is valid for both weakly coupled and strongly coupled quark-gluon plasmas. We find reaction rates in the transport equation factorize into a quarkonium dipole transition function and a chromoelectric gluon distribution function. For the differential reaction rate, the definition of the momentum dependent chromoelectric gluon distribution function involves staple-shaped Wilson lines. For the inclusive reaction rate, the Wilson lines collapse into a straight line along the real time axis and the distribution becomes momentum independent. The relation between the two Wilson lines is analogous to the relation between the Wilson lines appearing in the gluon parton distribution function (PDF) and the gluon transverse momentum dependent parton distribution function (TMDPDF). The centrality dependence of the quarkonium nuclear modification factor measured by experiments probes the momentum independent distribution while the transverse momentum dependence and measurements of the azimuthal angular anisotropy may be able to probe the momentum dependent one. We discuss one way to indirectly constrain the quarkonium in-medium real potential by using the factorization formula and lattice calculations. The leading quantum correction to the semiclassical transport equation of quarkonium is also worked out. The study can be easily generalized to quarkonium transport in cold nuclear matter, which is relevant for quarkonium production in eA collisions in the future Electron-Ion Collider.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Controlling $H_{3}^{+}$ Formation From Ethane Using Shaped Ultrafast Laser Pulses

An adaptive learning algorithm coupled with 3D momentum-based feedback is used to identify intense laser pulse shapes that control $H_{3}^{+}$ formation from ethane. Specifically, we controlled the ratio of D 2 H + to $D_{3}^{+}$ produced from the D 3 C-CH 3 isotopologue of ethane, which selects between trihydrogen cations formed from atoms on one or both sides of ethane. We are able to modify the D 2 H + :$D_{3}^{+}$ ratio by a factor of up to three. In addition, two-dimensional scans of linear chirp and third-order dispersion are conducted for a few fourth-order dispersion values while the D 2 H + and $D_{3}^{+}$ production rates are monitored. The optimized pulse is observed to influence the yield, kinetic energy release, and angular distribution of the D 2 H + ions while the $D_{3}^{+}$ ion dynamics remain relatively stable. We subsequently conducted COLTRIMS experiments on C 2 D 6 to complement the velocity map imaging data obtained during the control experiments and measured the branching ratio of two-body double ionization. Two-body $D_{3}^{+}$ + $C_{2}D_{3}^{+}$ is the dominant final channel containing $D_{3}^{+}$ ions, although the three-body D + $D_{3}^{+}$ + $C_{2}D_{2}^{+}$ final state is also observed.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS1995

Hydrodynamics of coalescing binary neutron stars: Ellipsoidal treatment

We employ an approximate treatment of dissipative hydrodynamics in three dimensions to study the coalescence of binary neutron stars driven by the emission of gravitational waves. The stars are modeled as compressible ellipsoids obeying a polytropic equation of state; all internal fluid velocities are assumed to be linear functions of the coordinates. The hydrodynamics equations then reduce to a set of coupled ordinary differential equations for the evolution of the principal axes of the ellipsoids, the internal velocity parameters, and the binary orbital parameters. Gravitational radiation reaction and viscous dissipation are both incorporated. We set up exact initial binary equilibrium configurations and follow the transition from the quasi-static, secular decay of the orbit at large separation to the rapid dynamical evolution of the configurations just prior to contact. A hydrodynamical instability resulting from tidal interactions significantly accelerates the coalescence at small separation, leading to appreciable radial infall velocity and tidal lag angles near contact. This behavior is reflected in the gravitational waveforms and may be observable by gravitational wave detectors under construction. In cases where the neutron stars have spins which are not aligned with the orbital angular momentum, the spin-induced quadrupole moment can lead to precession of the orbital plane and therefore modulation of the gravitational wave amplitude even at large orbital radius. However, the amplitude of the modulation is small for typical neutron star binaries with spins much smaller than the orbital angular momentum.

Lai, Dong↗

DOE OSTI2021

Correlation between Spin and Orbital Dynamics during Laser-Induced Femtosecond Demagnetization

Spin and orbital angular momenta are two intrinsic properties of an electron and are responsible for the physics of a solid. How the spin and orbital evolve with respect to each other on several hundred femtoseconds is largely unknown, but it is at the center of laser-induced ultrafast demagnetization. In this paper, we introduce a concept of the spin–orbital correlation diagram, where spin angular momentum is plotted against orbital angular momentum, much like the position-velocity phase diagram in classical mechanics. We use four sets of highly accurate time-resolved X-ray magnetic circular dichroism data to construct four correlation diagrams for iron and cobalt. To our surprise, a pattern emerges. The trace on the correlation diagram for iron is an arc, and at the end of demagnetization, it has a pronounced cusp. The correlation diagram for cobalt is different and appears more linear but with kinks. We carry out first-principles calculations with two different methods: time-dependent density functional theory (TDDFT) and time-dependent Liouville density functional theory. These two methods agree that the experimental findings for both Fe and Co are not due to experimental errors. It is the spin–orbit coupling that correlates the spin dynamics to the orbital dynamics. Microscopically, Fe and Co have different orbital occupations, which leads to distinctive correlation diagrams. We believe that this correlation diagram presents a useful tool to better understand spin and orbital dynamics on an ultrafast time scale. A brief discussion on the magnetic anisotropy energy is also provided.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2003

Earth System Dynamics: The Determination and Interpretation of the Global Angular Momentum Budget using the Earth Observing System

The objective of this investigation has been to examine the mass and momentum exchange between the atmosphere, oceans, solid Earth, hydrosphere, and cryosphere. The investigation has focused on changes in the Earth's gravity field, its rotation rate, atmospheric and oceanic circulation, global sea level change, ice sheet change, and global ground water circulation observed by contemporary sensors and models. The primary component of the mass exchange is water. The geodetic observables provided by these satellite sensors are used to study the transport of water mass in the hydrological cycle from one component of the Earth to another, and they are also used to evaluate the accuracy of models. As such, the investigation is concerned with the overall global water cycle. This report provides a description of scientific, educational and programmatic activities conducted during the period July 1, 1999 through June 30,2000. Research has continued into measurements of time-varying gravity and its relationship to Earth rotation. Variability of angular momentum and the related excitation of polar motion and Earth rotation have been examined for the atmosphere and oceans at time-scales of weeks to several years. To assess the performance of hydrologic models, we have compared geodetic signals derived from them with those observed by satellites. One key component is the interannual mass variability of the oceans obtained by direct observations from altimetry after removing steric signals. Further studies have been conducted on the steric model to quantify its accuracy at global and basin-scales. The results suggest a significant loss of water mass from the Oceans to the land on time-scales longer than 1-year. These signals are not reproduced in any of the models, which have poorly determined interannual fresh water fluxes. Output from a coupled atmosphere-ocean model testing long-term climate change hypotheses has been compared to simulated errors from the Gravity Recovery and Climate Experiment (GRACE) mission. Results indicate that GRACE will be able to observe seasonal signals at half-wavelengths ranging from 1000 to 10000 km, and may be able to observe secular trends at half- wavelengths of greater than 2000-3000 km for soil moisture and snow depth if they are as large as some of the climate experiments predict.

Source record↗

DOE OSTI2024

Controlling 4 f antiferromagnetic dynamics via itinerant electronic susceptibility

Optical manipulation of magnetism holds promise for future ultrafast spintronics, especially with lanthanides and their huge, localized 4 f magnetic moments. These moments interact indirectly by spin polarizing the conduction electrons (the Ruderman-Kittel-Kasuya-Yosida exchange interaction), influenced by interatomic orbital overlap, and the conduction electron's susceptibility around the Fermi level. Here, we study this influence in a series of 4 f antiferromagnets, Gd T 2 Si 2 ( T = Co, Rh, Ir), using ultrafast resonant x-ray diffraction. We observe a twofold increase in the ultrafast intersublattice angular momentum transfer rate between the materials, originating from modifications in the conduction electron susceptibility, as confirmed by first-principles calculations. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗

NASA NTRS2008

Compact Dielectric-Rod White-Light Delay Lines

Optical delay lines of a proposed type would be made from rods of such dielectric materials as calcium fluoride, fused silica, or sapphire. These would offer advantages over prior optical delay lines, as summarized below. Optical delay lines are key components of opto-electronic microwave oscillators, narrow-band opto-electronic microwave filters, evanescent-field optical biochemical detectors, and some Fourier-Transform spectrum analyzers. Heretofore, optical delay lines used in such applications have been of two types: resonators and coiled long optical fibers, both of which have disadvantages: Resonators are compact, but excitation must be provided by narrow-band lasers. Wide-band (including noisy) laser light cannot be coupled efficiently to narrow-band resonators. When light is coupled into a narrowband resonator from a source of reasonably high power, a significant amount of optical energy circulates within the resonator, causing nonlinear loss and significant noise. Typically, a coil-type optical delay line is made of fused-silica fiber, which exhibits fundamental loss. To overcome the limit imposed by the optical loss in fused silica, it would be necessary to use fibers having crystalline cores. Although space is saved by winding fibers into coils, fiber-coil delay lines are still inconveniently bulky. The proposed compact dielectric-rod delay lines would exploit the special class of non-diffracting light beams that are denoted Bessel beams because their amplitudes are proportional to Bessel functions of the radii from their central axes. High-order Bessel beams can have large values of angular momentum. They can be generated with the help of whispering-gallery-mode optical resonators, as described, for example, in "Simplified Generation of High-Angular-Momentum Light Beams" (NPO-42965) NASA Tech Briefs, Vol. 31, No. 3 (March 2007), page 8a. In a delay line according to the proposal, the dielectric rod would be dimensioned to function as a multimode waveguide. Suitably chosen high-angular-momentum modes in such a waveguide exhibit low group velocity (hence, long delay) and no resonance. Such a delay line could perform well at any wavelength or range of wavelengths within the transparency wavelength band of the dielectric material, and the maximum possible group delay achievable through suitable design would be limited only by the optical loss in the rod material.

Maleki, Lute↗