Photoproduction of ETA mesons from hydrogen at photon energies between 0.8 and 1.45 GeV

We measured the differential cross section of the process γp → pƞ at the 1.5 GeV Caltech electron synchrotron, at photon energies from 0.8 to 1.45 GeV, at various angles between 45° and 100° in the center of mass. A counter-spark chamber array was used to determine the kinematics of all particles in the final state of the partial mode γp → pƞ (ƞ → 2γ). Analysis of 40,000 pictures yielded 6,000 events above a background which varied with energy from 5% to 30% of foreground. The cross section shows an energy dependence confirming earlier results up to 1000 MeV, but with improved statistics; it then remains roughly constant (at 50° C.M.), to 1.45 GeV. The data show a small angular variation, within the limited range covered, at energies between 1000 and 1100 MeV.

Part 1: Longitudinal static and dynamic effects in semiconductor lasers. Part II: Spectral characteristics of passively mode-locked quantum well lasers

In the first part of this thesis a study of the effect of the longitudinal distribution of optical intensity and electron density on the static and dynamic behavior of semiconductor lasers is performed. A static model for above threshold operation of a single mode laser, consisting of multiple active and passive sections, is developed by calculating the longitudinal optical intensity distribution and electron density distribution in a self-consistent manner. Feedback from an index and gain Bragg grating is included, as well as feedback from discrete reflections at interfaces and facets. Longitudinal spatial holeburning is analyzed by including the dependence of the gain and the refractive index on the electron density. The mechanisms of spatial holeburning in quarter wave shifted DFB lasers are analyzed. A new laser structure with a uniform optical intensity distribution is introduced and an implementation is simulated, resulting in a large reduction of the longitudinal spatial holeburning effect.

A dynamic small-signal model is then developed by including the optical intensity and electron density distribution, as well as the dependence of the grating coupling coefficients on the electron density. Expressions are derived for the intensity and frequency noise spectrum, the spontaneous emission rate into the lasing mode, the linewidth enhancement factor, and the AM and FM modulation response. Different chirp components are identified in the FM response, and a new adiabatic chirp component is discovered. This new adiabatic chirp component is caused by the nonuniform longitudinal distributions, and is found to dominate at low frequencies. Distributed feedback lasers with partial gain coupling are analyzed, and it is shown how the dependence of the grating coupling coefficients on the electron density can result in an enhancement of the differential gain with an associated enhancement in modulation bandwidth and a reduction in chirp.

In the second part, spectral characteristics of passively mode-locked two-section multiple quantum well laser coupled to an external cavity are studied. Broad-band wavelength tuning using an external grating is demonstrated for the first time in passively mode-locked semiconductor lasers. A record tuning range of 26 nm is measured, with pulse widths of typically a few picosecond and time-bandwidth products of more than 10 times the transform limit. It is then demonstrated that these large time-bandwidth products are due to a strong linear upchirp, by performing pulse compression by a factor of 15 to a record pulse widths as low 320 fs.

A model for pulse propagation through a saturable medium with self-phase-modulation, due to the a-parameter, is developed for quantum well material, including the frequency dependence of the gain medium. This model is used to simulate two-section devices coupled to an external cavity. When no self-phase-modulation is present, it is found that the pulses are asymmetric with a sharper rising edge, that the pulse tails have an exponential behavior, and that the transform limit is 0.3. Inclusion of self-phase-modulation results in a linear upchirp imprinted on the pulse after each round-trip. This linear upchirp is due to a combination of self-phase-modulation in a gain section and absorption of the leading edge of the pulse in the saturable absorber.

Physical investigations of small particles : (I) aerosol particle charging and flux enhancement and (II) whispering gallery mode sensing

Part I

Particles are a key feature of planetary atmospheres. On Earth they represent the greatest source of uncertainty in the global energy budget. This uncertainty can be addressed by making more measurement, by improving the theoretical analysis of measurements, and by better modeling basic particle nucleation and initial particle growth within an atmosphere. This work will focus on the latter two methods of improvement.

Uncertainty in measurements is largely due to particle charging. Accurate descriptions of particle charging are challenging because one deals with particles in a gas as opposed to a vacuum, so different length scales come into play. Previous studies have considered the effects of transition between the continuum and kinetic regime and the effects of two and three body interactions within the kinetic regime. These studies, however, use questionable assumptions about the charging process which resulted in skewed observations, and bias in the proposed dynamics of aerosol particles. These assumptions affect both the ions and particles in the system. Ions are assumed to be point monopoles that have a single characteristic speed rather than follow a distribution. Particles are assumed to be perfect conductors that have up to five elementary charges on them. The effects of three body interaction, ion-molecule-particle, are also overestimated. By revising this theory so that the basic physical attributes of both ions and particles and their interactions are better represented, we are able to make more accurate predictions of particle charging in both the kinetic and continuum regimes.

The same revised theory that was used above to model ion charging can also be applied to the flux of neutral vapor phase molecules to a particle or initial cluster. Using these results we can model the vapor flux to a neutral or charged particle due to diffusion and electromagnetic interactions. In many classical theories currently applied to these models, the finite size of the molecule and the electromagnetic interaction between the molecule and particle, especially for the neutral particle case, are completely ignored, or, as is often the case for a permanent dipole vapor species, strongly underestimated. Comparing our model to these classical models we determine an “enhancement factor” to characterize how important the addition of these physical parameters and processes is to the understanding of particle nucleation and growth.

Part II

Whispering gallery mode (WGM) optical biosensors are capable of extraordinarily sensitive specific and non-specific detection of species suspended in a gas or fluid. Recent experimental results suggest that these devices may attain single-molecule sensitivity to protein solutions in the form of stepwise shifts in their resonance wavelength, \lambda_{R}, but present sensor models predict much smaller steps than were reported. This study examines the physical interaction between a WGM sensor and a molecule adsorbed to its surface, exploring assumptions made in previous efforts to model WGM sensor behavior, and describing computational schemes that model the experiments for which single protein sensitivity was reported. The resulting model is used to simulate sensor performance, within constraints imposed by the limited material property data. On this basis, we conclude that nonlinear optical effects would be needed to attain the reported sensitivity, and that, in the experiments for which extreme sensitivity was reported, a bound protein experiences optical energy fluxes too high for such effects to be ignored.

Nonlinear optics and wavelength translation via cavity-optomechanics

The field of cavity-optomechanics explores the interaction of light with sound in an ever increasing array of devices. This interaction allows the mechanical system to be both sensed and controlled by the optical system, opening up a wide variety of experiments including the cooling of the mechanical resonator to its quantum mechanical ground state and the squeezing of the optical field upon interaction with the mechanical resonator, to name two.

In this work we explore two very different systems with different types of optomechanical coupling. The first system consists of two microdisk optical resonators stacked on top of each other and separated by a very small slot. The interaction of the disks causes their optical resonance frequencies to be extremely sensitive to the gap between the disks. By careful control of the gap between the disks, the optomechanical coupling can be made to be quadratic to first order which is uncommon in optomechanical systems. With this quadratic coupling the light field is now sensitive to the energy of the mechanical resonator and can directly control the potential energy trapping the mechanical motion. This ability to directly control the spring constant without modifying the energy of the mechanical system, unlike in linear optomechanical coupling, is explored.

Next, the bulk of this thesis deals with a high mechanical frequency optomechanical crystal which is used to coherently convert photons between different frequencies. This is accomplished via the engineered linear optomechanical coupling in these devices. Both classical and quantum systems utilize the interaction of light and matter across a wide range of energies. These systems are often not naturally compatible with one another and require a means of converting photons of dissimilar wavelengths to combine and exploit their different strengths. Here we theoretically propose and experimentally demonstrate coherent wavelength conversion of optical photons using photon-phonon translation in a cavity-optomechanical system. For an engineered silicon optomechanical crystal nanocavity supporting a 4 GHz localized phonon mode, optical signals in a 1.5 MHz bandwidth are coherently converted over a 11.2 THz frequency span between one cavity mode at wavelength 1460 nm and a second cavity mode at 1545 nm with a 93% internal (2% external) peak efficiency. The thermal and quantum limiting noise involved in the conversion process is also analyzed and, in terms of an equivalent photon number signal level, are found to correspond to an internal noise level of only 6 and 4 times 10x^-3 quanta, respectively.

We begin by developing the requisite theoretical background to describe the system. A significant amount of time is then spent describing the fabrication of these silicon nanobeams, with an emphasis on understanding the specifics and motivation. The experimental demonstration of wavelength conversion is then described and analyzed. It is determined that the method of getting photons into the cavity and collected from the cavity is a fundamental limiting factor in the overall efficiency. Finally, a new coupling scheme is designed, fabricated, and tested that provides a means of coupling greater than 90% of photons into and out of the cavity, addressing one of the largest obstacles with the initial wavelength conversion experiment.

High-coherence hybrid Si/III-V semiconductor lasers

The relentlessly increasing demand for network bandwidth, driven primarily by Internet-based services such as mobile computing, cloud storage and video-on-demand, calls for more efficient utilization of the available communication spectrum, as that afforded by the resurging DSP-powered coherent optical communications. Encoding information in the phase of the optical carrier, using multilevel phase modulationformats, and employing coherent detection at the receiver allows for enhanced spectral efficiency and thus enables increased network capacity. The distributed feedback semiconductor laser (DFB) has served as the near exclusive light source powering the fiber optic, long-haul network for over 30 years. The transition to coherent communication systems is pushing the DFB laser to the limits of its abilities. This is due to its limited temporal coherence that directly translates into the number of different phases that can be imparted to a single optical pulse and thus to the data capacity. Temporal coherence, most commonly quantified in the spectral linewidth Δν, is limited by phase noise, result of quantum-mandated spontaneous emission of photons due to random recombination of carriers in the active region of the laser.

In this work we develop a generically new type of semiconductor laser with the requisite coherence properties. We demonstrate electrically driven lasers characterized by a quantum noise-limited spectral linewidth as low as 18 kHz. This narrow linewidth is result of a fundamentally new laser design philosophy that separates the functions of photon generation and storage and is enabled by a hybrid Si/III-V integration platform. Photons generated in the active region of the III-V material are readily stored away in the low loss Si that hosts the bulk of the laser field, thereby enabling high-Q photon storage. The storage of a large number of coherent quanta acts as an optical flywheel, which by its inertia reduces the effect of the spontaneous emission-mandated phase perturbations on the laser field, while the enhanced photon lifetime effectively reduces the emission rate of incoherent quanta into the lasing mode. Narrow linewidths are obtained over a wavelength bandwidth spanning the entire optical communication C-band (1530-1575nm) at only a fraction of the input power required by conventional DFB lasers. The results presented in this thesis hold great promise for the large scale integration of lithographically tuned, high-coherence laser arrays for use in coherent communications, that will enable Tb/s-scale data capacities.

Tools for the study of dynamical spacetimes

This thesis covers a range of topics in numerical and analytical relativity, centered around introducing tools and methodologies for the study of dynamical spacetimes. The scope of the studies is limited to classical (as opposed to quantum) vacuum spacetimes described by Einstein's general theory of relativity. The numerical works presented here are carried out within the Spectral Einstein Code (SpEC) infrastructure, while analytical calculations extensively utilize Wolfram's Mathematica program.

We begin by examining highly dynamical spacetimes such as binary black hole mergers, which can be investigated using numerical simulations. However, there are difficulties in interpreting the output of such simulations. One difficulty stems from the lack of a canonical coordinate system (henceforth referred to as gauge freedom) and tetrad, against which quantities such as Newman-Penrose Psi_4 (usually interpreted as the gravitational wave part of curvature) should be measured. We tackle this problem in Chapter 2 by introducing a set of geometrically motivated coordinates that are independent of the simulation gauge choice, as well as a quasi-Kinnersley tetrad, also invariant under gauge changes in addition to being optimally suited to the task of gravitational wave extraction.

Another difficulty arises from the need to condense the overwhelming amount of data generated by the numerical simulations. In order to extract physical information in a succinct and transparent manner, one may define a version of gravitational field lines and field strength using spatial projections of the Weyl curvature tensor. Introduction, investigation and utilization of these quantities will constitute the main content in Chapters 3 through 6.

For the last two chapters, we turn to the analytical study of a simpler dynamical spacetime, namely a perturbed Kerr black hole. We will introduce in Chapter 7 a new analytical approximation to the quasi-normal mode (QNM) frequencies, and relate various properties of these modes to wave packets traveling on unstable photon orbits around the black hole. In Chapter 8, we study a bifurcation in the QNM spectrum as the spin of the black hole a approaches extremality.

Resonance cones and mode conversion in a warm magnetized bounded plasma

The warm plasma resonance cone structure of the quasistatic field produced by a gap source in a bounded magnetized slab plasma is determined theoretically. This is initially determined for a homogeneous or mildly inhomogeneous plasma with source frequency lying between the lower hybrid frequency and the plasma frequency. It is then extended to the complicated case of an inhomogeneous plasma with two internal lower hybrid layers present, which is of interest to radio frequency heating of plasmas.

In the first case, the potential is obtained as a sum of multiply reflected warm plasma resonance cones, each of which has a similar structure, but a different size, amplitude, and position. An important interference between nearby multiply-reflected resonance cones is found. The cones are seen to spread out as they move away from the source, so that this interference increases and the individual resonance cones become obscured far away from the source.

In the second case, the potential is found to be expressible as a sum of multiply-reflected, multiply-tunnelled, and mode converted resonance cones, each of which has a unique but similar structure. The effects of both collisional and collisionless damping are included and their effects on the decay of the cone structure studied. Various properties of the cones such as how they move into and out of the hybrid layers, through the evanescent region, and transform at the hybrid layers are determined. It is found that cones can tunnel through the evanescent layer if the layer is thin, and the effect of the thin evanescent layer is to subdue the secondary maxima of cone relative to the main peak, while slightly broadening the main peak and shifting it closer to the cold plasma cone line.

Energy theorems for quasistatic fields are developed and applied to determine the power flow and absorption along the individual cones. This reveals the points of concentration of the flow and the various absorption mechanisms.

Nanofabrication for On-Chip Optical Levitation, Atom-Trapping, and Superconducting Quantum Circuits

Researchers have spent decades refining and improving their methods for fabricating smaller, finer-tuned, higher-quality nanoscale optical elements with the goal of making more sensitive and accurate measurements of the world around them using optics. Quantum optics has been a well-established tool of choice in making these increasingly sensitive measurements which have repeatedly pushed the limits on the accuracy of measurement set forth by quantum mechanics. A recent development in quantum optics has been a creative integration of robust, high-quality, and well-established macroscopic experimental systems with highly-engineerable on-chip nanoscale oscillators fabricated in cleanrooms. However, merging large systems with nanoscale oscillators often require them to have extremely high aspect-ratios, which make them extremely delicate and difficult to fabricate with an "experimentally reasonable" repeatability, yield and high quality. In this work we give an overview of our research, which focused on microscopic oscillators which are coupled with macroscopic optical cavities towards the goal of cooling them to their motional ground state in room temperature environments. The quality factor of a mechanical resonator is an important figure of merit for various sensing applications and observing quantum behavior. We demonstrated a technique for pushing the quality factor of a micromechanical resonator beyond conventional material and fabrication limits by using an optical field to stiffen and trap a particular motional mode of a nanoscale oscillator. Optical forces increase the oscillation frequency by storing most of the mechanical energy in a nearly loss-less optical potential, thereby strongly diluting the effects of material dissipation. By placing a 130 nm thick SiO₂ pendulum in an optical standing wave, we achieve an increase in the pendulum center-of-mass frequency from 6.2 to 145 kHz. The corresponding quality factor increases 50-fold from its intrinsic value to a final value of Q_m = 5.8(1.1) x 10⁵, representing more than an order of magnitude improvement over the conventional limits of SiO₂ for a pendulum geometry. Our technique may enable new opportunities for mechanical sensing and facilitate observations of quantum behavior in this class of mechanical systems. We then give a detailed overview of the techniques used to produce high-aspect-ratio nanostructures with applications in a wide range of quantum optics experiments. The ability to fabricate such nanodevices with high precision opens the door to a vast array of experiments which integrate macroscopic optical setups with lithographically engineered nanodevices. Coupled with atom-trapping experiments in the Kimble Lab, we use these techniques to realize a new waveguide chip designed to address ultra-cold atoms along lithographically patterned nanobeams which have large atom-photon coupling and near 4π Steradian optical access for cooling and trapping atoms. We describe a fully integrated and scalable design where cold atoms are spatially overlapped with the nanostring cavities in order to observe a resonant optical depth of d₀ ≈ 0.15. The nanodevice illuminates new possibilities for integrating atoms into photonic circuits and engineering quantum states of atoms and light on a microscopic scale. We then describe our work with superconducting microwave resonators coupled to a phononic cavity towards the goal of building an integrated device for quantum-limited microwave-to-optical wavelength conversion. We give an overview of our characterizations of several types of substrates for fabricating a low-loss high-frequency electromechanical system. We describe our electromechanical system fabricated on a Si₃N₄ membrane which consists of a 12 GHz superconducting LC resonator coupled capacitively to the high frequency localized modes of a phononic nanobeam. Using our suspended membrane geometry we isolate our system from substrates with significant loss tangents, drastically reducing the parasitic capacitance of our superconducting circuit to ≈ 2.5$ fF. This opens up a number of possibilities in making a new class of low-loss high-frequency electromechanics with relatively large electromechanical coupling. We present our substrate studies, fabrication methods, and device characterization.

The polarization of the recoil proton in ETA photoproduction

We measured the recoil proton polarization in the process γp → pη at the 1.5 GeV Caltech electron synchrotron, at photon energies from 0.8 to 1.1 GeV, and at center-of-mass production angles around 90°. A counter-spark chamber array was used to determine the kinematics of all particles in the final state of the partial mode γp → pη (η → 2γ). The protons' polarization was determined by measuring an asymmetry in scattering off carbon. Analysis of 280,000 pictures yielded 2400 useful scatters with a background which was 30% of the foreground. The polarization results show a sizeable opposite parity interference at 830 MeV, 950 MeV, and 1100 MeV.

Reggeization of some unequal mass processes involving higher spins : the reactions pion-nucleon going to (V,Nucleon), pion-nucleon going to (V,delta-hyperon), and photon-proton going to (positive pion,neutron)

Recent theoretical developments in the reggeization of inelastic processes involving particles with high spin are incorporated into a model of vector meson production. A number of features of experimental differential cross sections and density matrices are interpreted in terms of this model.

The method chosen for reggeization of helicity amplitudes first separates kinematic zeros and singularities from the parity-conserving amplitudes and then applies results of Freedman and Wang on daughter trajectories to the remaining factors. Kinematic constraints on helicity amplitudes at t = 0 and t = (M – M_Δ)² are also considered.

It is found that data for reactions of types πN→VN and πN→VΔ are consistent with a model of this type in which all kinematic constraints at t = 0 are satisfied by evasion (vanishing of residue functions). As a quantitative test of the parametrization, experimental differential cross sections of vector meson production reactions dominated by pion trajectory exchange are compared with the theory. It is found that reduced residue functions are approximately constant, once the kinematic behavior near t = (M – M_Δ)² has been removed.

The alternative possibility of conspiracy between amplitudes is also discussed; and it is shown that unless conspiracy is present, some amplitudes allowed by angular momentum conservation will not contribute with full strength in the forward direction. An example, γp→π⁺n in which the data for dσ/dt indicate conspiracy, is studied in detail.

Spontaneous and stimulated light emission due to radiative recombination in forward biased lead telluride P-N junctions

Since the discovery in 1962 of laser action in semiconductor diodes made from GaAs, the study of spontaneous and stimulated light emission from semiconductors has become an exciting new field of semiconductor physics and quantum electronics combined. Included in the limited number of direct-gap semiconductor materials suitable for laser action are the members of the lead salt family, i.e . PbS, PbSe and PbTe. The material used for the experiments described herein is PbTe . The semiconductor PbTe is a narrow band- gap material (E_g = 0.19 electron volt at a temperature of 4.2°K). Therefore, the radiative recombination of electron-hole pairs between the conduction and valence bands produces photons whose wavelength is in the infrared (λ ≈ 6.5 microns in air).

The p-n junction diode is a convenient device in which the spontaneous and stimulated emission of light can be achieved via current flow in the forward-bias direction. Consequently, the experimental devices consist of a group of PbTe p-n junction diodes made from p –type single crystal bulk material. The p - n junctions were formed by an n-type vapor- phase diffusion perpendicular to the (100) plane, with a junction depth of approximately 75 microns. Opposite ends of the diode structure were cleaved to give parallel reflectors, thereby forming the Fabry-Perot cavity needed for a laser oscillator. Since the emission of light originates from the recombination of injected current carriers, the nature of the radiation depends on the injection mechanism.

The total intensity of the light emitted from the PbTe diodes was observed over a current range of three to four orders of magnitude. At the low current levels, the light intensity data were correlated with data obtained on the electrical characteristics of the diodes. In the low current region (region A), the light intensity, current-voltage and capacitance-voltage data are consistent with the model for photon-assisted tunneling. As the current is increased, the light intensity data indicate the occurrence of a change in the current injection mechanism from photon-assisted tunneling (region A) to thermionic emission (region B). With the further increase of the injection level, the photon-field due to light emission in the diode builds up to the point where stimulated emission (oscillation) occurs. The threshold current at which oscillation begins marks the beginning of a region (region C) where the total light intensity increases very rapidly with the increase in current. This rapid increase in intensity is accompanied by an increase in the number of narrow-band oscillating modes. As the photon density in the cavity continues to increase with the injection level, the intensity gradually enters a region of linear dependence on current (region D), i.e. a region of constant (differential) quantum efficiency.

Data obtained from measurements of the stimulated-mode light-intensity profile and the far-field diffraction pattern (both in the direction perpendicular to the junction-plane) indicate that the active region of high gain (i.e. the region where a population inversion exists) extends to approximately a diffusion length on both sides of the junction. The data also indicate that the confinement of the oscillating modes within the diode cavity is due to a variation in the real part of the dielectric constant, caused by the gain in the medium. A value of τ ≈ 10^-9 second for the minority- carrier recombination lifetime (at a diode temperature of 20.4°K) is obtained from the above measurements. This value for τ is consistent with other data obtained independently for PbTe crystals.

Data on the threshold current for stimulated emission (for a diode temperature of 20. 4°K) as a function of the reciprocal cavity length were obtained. These data yield a value of J’_th = (400 ± 80) amp/cm² for the threshold current in the limit of an infinitely long diode-cavity. A value of α = (30 ± 15) cm^-1 is obtained for the total (bulk) cavity loss constant, in general agreement with independent measurements of free- carrier absorption in PbTe. In addition, the data provide a value of n_s ≈ 10% for the internal spontaneous quantum efficiency. The above value for n_s yields values of t_b ≈ τ ≈ 10^-9 second and t_s ≈ 10^-8 second for the nonradiative and the spontaneous (radiative) lifetimes, respectively.

The external quantum efficiency (n_d) for stimulated emission from diode J-2 (at 20.4° K) was calculated by using the total light intensity vs. diode current data, plus accepted values for the material parameters of the mercury- doped germanium detector used for the measurements. The resulting value is n_d ≈ 10%-20% for emission from both ends of the cavity. The corresponding radiative power output (at λ = 6.5 micron) is 120-240 milliwatts for a diode current of 6 amps.

Photoproduction of charged pion pairs from hydrogen at photon energies between 800 and 1500 MeV

The reaction γ + p p + π⁺ + π^- has been studied for photon energies between 800 and 1500 MeV and for dipion masses between 510 and 900 MeV. The bremsstrahlung beam from the Caltech synchrotron was passed through a liquid hydrogen target and spark chambers were used to detect the three final particles. In addition, the proton energy was determined by a range measurement. Approximately 40,000 photographs were taken, yielding 3018 acceptable events. The results were fit to an incoherent combination of the N*(1238) resonance, the p^o (750) resonance, and three-body phase space, with various models being tried for p^o production. The total cross section for p^o production is consistent with previous experiments. However, the angular dependence of the cross section is slightly more peaked in the forward direction, and the ratio of p^o production to phase space production is larger than previously observed.

However, since this experiment was only sensitive to the production angles cos θ cm ≥ .75, statistical fluctuations and/or an anisotropic distribution of background production have a severe influence on the p^o to background ratio. Of the p^o models tested, the results prefer p^o production by the one pion exchange mechanism with a very steep form factor dependence. The values of the mass and width of the p^o found here are consistent with previous experiments.

I. Baryon-antibaryon phase transition at high temperature. II. Inclusive virtual photon-hadron reactions in the parton model

Part I

Present experimental data on nucleon-antinucleon scattering allow a study of the possibility of a phase transition in a nucleon-antinucleon gas at high temperature. Estimates can be made of the general behavior of the elastic phase shifts without resorting to theoretical derivation. A phase transition which separates nucleons from antinucleons is found at about 280 MeV in the approximation of the second virial coefficient to the free energy of the gas.

Part II

The parton model is used to derive scaling laws for the hadrons observed in deep inelastic electron-nucleon scattering which lie in the fragmentation region of the virtual photon. Scaling relations are obtained in the Bjorken and Regge regions. It is proposed that the distribution functions become independent of both q² and ν where the Bjorken and Regge regions overlap. The quark density functions are discussed in the limit x→1 for the nucleon octet and the pseudoscalar mesons. Under certain plausible assumptions it is found that only one or two quarks of the six types of quarks and antiquarks have an appreciable density function in the limit x→1. This has implications for the quark fragmentation functions near the large momentum boundary of their fragmentation region. These results are used to propose a method of measuring the proton and neutron quark density functions for all x by making measurements on inclusively produced hadrons in electroproduction only. Implications are also discussed for the hadrons produced in electron-positron annihilation.