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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 19:19:46 +0000Spontaneously radiating atom in cavity fields
https://resolver.caltech.edu/CaltechETD:etd-09102002-134828
Authors: Buczek, Carl James
Year: 1965
DOI: 10.7907/CCD3-4P11
Spontaneous emission competes with stimulated emission in many interactions of light with matter. In the usual analyses which describe the interaction of an atom with a coherent optical field, the spontaneous emission characteristics, e.g., probability and spectral distribution, are not determined. The spontaneous emission from an atom which interacts with a coherent light wave is considered. The competition between coherent photons and spontaneous photons is treated in detail for a system consisting of a stationary atom, an open cavity and spatial fields. In the model chosen, a multilevel atom which spontaneously decays by interacting with spatial fields has two nondegenerate states coupled by an interaction with a single mode of the cavity. The Laplace-transformed Schrodinger equation is solved for specified initial conditions of the system. It is found that the interaction with the coherent field modifies the spectral distribution of spontaneous radiation from the atom. For spontaneous transitions involving an atomic state which interacts with the coherent field, the spectral distributions can no longer be described by Lorentzian functions. The new distributions exhibit a broadening and splitting for strong interactions between the atom and the coherent field. It is shown that the qualitative features of these distributions can be predicted from the energy-level diagram of the atom-cavity system. The net probability of the system gaining a coherent or cavity photon is calculated by integrating over the emitted spontaneous frequencies. The equivalence of this approach to the method of computing probabilities by integrating over time is demonstrated by using Parseval's theorem.https://thesis.library.caltech.edu/id/eprint/3421An Analysis of Perturbed Confocal Resonators
https://resolver.caltech.edu/CaltechETD:etd-01132003-084119
Authors: Asmus, John Fredrich
Year: 1965
DOI: 10.7907/74wn-7319
<p>An analytical technique is developed for computing mode functions and associated diffraction losses of perturbed multimode optical resonators. It is based upon a consistent field formulation of resonance in an open two-mirror system.</p>
<p>To illustrate the method the theory of confocal resonators is extended to include configurations differing from the confocal case by small geometrical perturbations. This involves computing and expanding a perturbed Green's function for such near confocal resonators. Diffraction losses for certain statistical and deterministic perturbations are computed and related to disturbances arising from an imperfect figure, polish or alignment of the mirrors.</p>
<p>The design and construction of a stable laser spectrometer consisting of a single mode tuneable gas laser and a swept interferometer are described. Measurements of the diffraction losses of perturbed confocal resonators are found to be in agreement with the above analysis.</p>
https://thesis.library.caltech.edu/id/eprint/147Nonlinear effects in traveling wave laser amplifiers
https://resolver.caltech.edu/CaltechETD:etd-09122002-090900
Authors: Close, Donald Henry
Year: 1965
DOI: 10.7907/Y5FC-GV56
Using semiclassical radiation theory, a formalism similar to that used by Lamb in his "Theory of an Optical Maser" is developed for studying the amplification of vector traveling waves in a laser-type medium. The effect of the medium on the waves is given in terms of space (or time) dependent field amplitudes and phases and a nonlinear index of refraction. With particular emphasis on typical gaseous media, the effects of Doppler broadening are treated in detail for arbitrary ratios of natural to Doppler linewidths. Polarization and propagation vectors in various directions are considered, and the nonlinear effects are found to make an isotropic medium effectively anisotropic.
Lowest order nonlinear effects (due to a polarization cubic in the field amplitudes) are studied extensively, and the frequency dependence of several of these processes is presented in graphical form. In particular, the introduction of fields at new frequencies and polarization effects are considered. The characteristics of these nonlinear processes peculiar to Doppler broadened lines are discussed, and the processes are interpreted in terms of saturation and coherent modulation of the population inversion density.
Strong nonlinear effects are considered in a more approximate way and are found to consist of saturation of the various linear and nonlinear processes previously considered. These strong nonlinear effects should occur at low enough intensities to be easily observed in practice on a CW basis. With the present formalism, the analytical results of Gordon, White and Rigden regarding gain saturation in laser amplifiers are obtained, and the extension is made to include frequencies away from line center and the effects of multiple spectral components. Again, the introduction of fields at new frequencies is considered in detail. These results are also discussed in terms of saturation and coherent modulation of the populations and "hole burning".https://thesis.library.caltech.edu/id/eprint/3480Modes in spherical-mirror resonators. dominant mode calculations in output-coupled infinite strip mirror resonators
https://resolver.caltech.edu/CaltechETD:etd-01122004-102010
Authors: Specht, Walter Albert
Year: 1965
DOI: 10.7907/P9W2-EX19
PART I
This work is the examination of a cavity mode approach to the mode structure of a laser. Solutions of the vector wave equation for electromagnetic fields in and between perfectly conducting oblate spheroidal cavities are examined for the case of wavelengths much less than cavity dimensions. These solutions are the field modes in Fabry-Perot type resonators with equal-radius concave spherical mirrors, or with concave-convex spherical mirrors, when the parameters of the oblate spheroids are chosen so that the radii of curvature and spacing on the axis of rotation match those of the resonator mirrors. Expressions for the transverse and longitudinal mode structures are derived. The eigenvalue equations are written, and are solved for the case of the two lowest order modes.
Part II
This work is the numerical calculation of the steady state lowest order even and odd symmetry electromagnetic field patterns at the mirrors of the multimode resonator formed by two plane-parallel infinite strip mirrors, modified for output coupling by central strips of zero reflectivity. The equation solved is the scalar Huyghens-Fresnel integral equation (a transverse electromagnetic wave approximation to the vector integral equation, valid when the wavelength is much less than the cavity dimensions) relating the fields at the two mirrors, converted to an eigenvalue equation, and approximated for calculations by a matrix eigenvalue equation. The mode structure, power loss and phase shift per transit, and output coupling are discussed.https://thesis.library.caltech.edu/id/eprint/132Nonlinear and Anisotropic Effects in Magnetically Tuned Laser Amplifiers
https://resolver.caltech.edu/CaltechTHESIS:03302017-091624259
Authors: Dienes, Andrew
Year: 1967
DOI: 10.7907/AF03-T980
<p>Using semiclassical radiation theory and a density matrix
formalism we analyze the nonlinear characteristics of a gas laser
amplifier operating with two optical frequency signals of arbitrary
polarization and having an axial magnetic field. Both perturbational
solutions, valid for relatively weak intensities and solutions valid
for arbitrarily strong fields are obtained for two nonlinear effects:
the saturation interaction of the electromagnetic waves, and the
generation of combination tones. An arbitrary amount of Doppler
broadening is considered throughout.</p>
<p>The detailed treatment of J = 1 to J = 0 model yields the
frequency, magnetic field and polarization dependence of the nonlinear
effects. The results are presented analytically and graphically
and are discussed using physical arguments. It is found that only
saturation but no combination tone generation occurs for two opposite
circularly polarized input signals while both are, in general, present
for two arbitrary linearly or elliptically polarized fields. For
two opposite circular waves the interaction is found to comprise three
parts, each with a different behavior: self saturation, common level
mutual saturation and a coherent double quantum interaction. The
total interaction (coupling) between the two fields is always weak.
The limiting case of a single linearly polarized field is considered
separately, the zero magnetic field "dip" and the nonlinear behavior
of the Faraday rotation is discussed.</p>
<p>For two linearly (or elliptically) polarized waves the three
nonlinear processes listed above take place between opposite circular
components. In addition a modulation of the population inversion
densities occurs due to the presence of two different frequencies with
the same circular polarization. This results in the generation of new
frequencies and also contributes to the coupling between the input
fields. The coupling depends on the magnetic field, and on the frequency
separation and the polarization states of the signals. The
limiting case of zero magnetic field is examined. It is found that the
medium is made effectively anisotropic by the nonlinear interactions.
The polarization vectors of two linearly polarized fields rotate apart
unless the angle between them is zero or 90 degrees.</p>
<p>The results are extended to the general J<sub>a</sub> to J<sub>b</sub> transition.
In zero magnetic field the nonlinear effects are found to depend on
ΔJ, while for nonzero magnetic field resonances in the interaction
occur whenever the frequency difference between two opposite circularly
polarized transitions that have common level equals the frequency
separation of the input fields. Combination tone generation takes
place for all but two opposite circularly polarized signals.</p> https://thesis.library.caltech.edu/id/eprint/10120Theory of holography
https://resolver.caltech.edu/CaltechETD:etd-10012002-113521
Authors: Matthews, John Wallace
Year: 1967
DOI: 10.7907/qznw-p178
Computation of the amplitudes of the diffracted fields which are produced when a reflection hologram or a "thick" transmission hologram is illuminated requires that the 3-dimensional nature of the hologram be accounted for. A general analytical method is formulated for computing the diffracted fields in terms of the initial exposing field, the film characteristics, and the illumination field, taking into account the entire emulsion volume. This method, which is applicable to both transmission and reflection holograms, involves characterizing the emulsion volume by the volume density of scattering particles, with the diffracted field being found by coherently summing the scattered waves, neglecting multiple scattering. The initial exposing field and the illumination field are expressed in the form of a sum of plane or quasi-plane waves, and the diffracted field is expressed as a sum of waves, each of which is found by solving a variation of the same basic problem. This problem consists of computing the directions, amplitudes, and phases of the first-order diffracted waves produced when a 3-dimensional array of scattering particles having a sinusoidal density distribution is illuminated by a plane wave. The solution of this problem is considered, with the directions and phases of the diffracted fields being computed for both transmission and reflection holograms. The amplitudes are computed for the case of transmission holograms and the analytical expressions are evaluated numerically for a number of particular cases to determine the effect of varying different parameters on the amplitudes of the diffracted waves. The results are compared with experimental data obtained by making a careful study of different holographic diffraction gratings.
The results of the analytical method described above are compared with the results of the method whereby the hologram is characterized by the transmittance, and it is shown that with respect to the computation of the directions and phases of the diffracted waves, the two methods are equivalent for the case of transmission holograms.
The case where the reference beam is composed of a series of waves (ghost imaging) is considered using both of the above methods, and the translational sensitivity and background noise which arise in this case are investigated. An experiment dealing with translational sensitivity was carried out and the experimental results were found to be in good agreement with the theory.
The duplication of holograms is considered and the duplication process is described in terms of making a hologram of a hologram, rather than in terms of making a contact print. Experimental results are presented to support this point of view and the effects of varying the characteristics of the illumination wave are described. The duplication of both transmission and reflection holograms is dealt with and a simple method for duplicating reflection holograms is proposed and discussed.
https://thesis.library.caltech.edu/id/eprint/3851The Holographic Stereogram
https://resolver.caltech.edu/CaltechTHESIS:04062017-144815513
Authors: McCrickerd, John Thomas
Year: 1969
DOI: 10.7907/gq8t-k869
<p>The holographic stereogram, a hologram synthesized from ordinary
stereoscopic component photographs, is investigated as an alternative to classical
holograms and to previous types of stereograms for three-dimensional perfect
imagery. The process is partly holographic in nature, but it provides images of
naturally illuminated objects, and its application is not limited by the technology
of laser illumination. The pinhole camera stereogram and the fly's eye lens
stereogram are also analyzed, since the principles of their operation are similar.
Pinhole camera stereogram imagery is shown to have several deficiencies, among
which is the necessity for small camera-object distances. The fly's eye lens is
much superior, but is limited in practice by aberrations, a difficulty which the
holographic stereogram overcomes. Also treated are the full-color, the focused type,
and the distortionless-scaled holographic stereogram, and optical spatial
filtering of holographic stereogram images.</p>
<p>The achromatically imaged Fresnel zone plate is analyzed as a technique
of very general applicability which compensates for source incoherency in two-beam
type holographic arrangements. The emphasis is on physical interpretation
rather than mathematical formulation. Two simple graphical mnemonics are
developed for rapid analytical inspection of the effects of, respectively, temporal
and spatial incoherence of the source in any achromatically imaged zone plate
or Gabor in-line type holographic system.</p>
<p>The scalar wave function approximation of physical optics is used
throughout.</p>
https://thesis.library.caltech.edu/id/eprint/10129Holographic Dielectric Gratings: Theory and Practice
https://resolver.caltech.edu/CaltechETD:etd-10072002-134846
Authors: Chang, Milton M.T.
Year: 1969
DOI: 10.7907/CWA9-QS54
<p>A holographic dielectric grating is a diffraction grating comprised of a periodic variation of the refractive index of a medium, and is produced by the interference pattern of two monochromatic waves. Emphasis is placed upon photographic emulsion as the medium for recording the pattern, but the treatment is general and includes any material that can have an internal modulation of the refractive index. Three topics are treated: the effective dielectric constant of the emulsion, the diffraction of light by dielectric gratings, and the techniques for producing gratings with high efficiency and good resolution.</p>
<p>The photographic emulsion is treated as an artificially loaded material, i.e. as a suspension of grains in a gelatin base. A Mie scattering theory analysis is used and the effect of adjacent scatterers on the local field is accounted for by the Lorentz-Lorenz relation. The optical density of the emulsion is shown to be proportional to the number of grains present. The effective index variation after bleaching is proportional to the pre-bleached optical density, which implies that the emulsion should have a linear density vs. exposure curve to effect a sinusoidally modulated index of refraction. A relation between the modulation transfer function (MTF) of bleached and unbleached emulsion is derived. Means for improvement of the MTF is also obtained analytically.</p>
<p>The diffraction of light by a dielectric grating is analyzed using the Raman-Nath formalism which is generalized to include loss. Graphs are presented showing the diffraction efficiency versus the index modulation for a wide range of thicknesses and loss. The peak efficiency for arbitrary emulsion thickness can be obtained from measurements at a specific thickness. The conclusion is reached that presently available emulsion should be made thicker, preferably in the 20-30 micron range.</p>
<p>The basic physical processes of various holographic materials are described. The processing techniques of photographic emulsion are emphasized and the merits of various bleaches are evaluated. It is found that resolution can be increased by using a reversal process. The dielectric grains in an emulsion processed this way are round in shape. A desensitizing dye can be used to stabilize the grains. A method of extending the dynamic range of the photographic emulsion using a pre-flashing exposure technique is also described.</p>
<p>Several experiments are proposed, and recommendations are made which may serve as guide-lines for the development of more suitable materials for holographic recording.</p>https://thesis.library.caltech.edu/id/eprint/3952Gas Laser Discharge Noise and its Effect on the Laser Output
https://resolver.caltech.edu/CaltechTHESIS:03212016-082302712
Authors: Yoh, James
Year: 1969
DOI: 10.7907/ysmv-qp80
<p>A large portion of the noise in the light output of a laser oscillator is associated with the noise in the laser discharge. The effect of the discharge noise on the laser output has been studied.
The discharge noise has been explained through an ac equivalent circuit of the laser discharge tube.</p>
<p>The discharge noise corresponds to time-varying spatial fluctuations in the electron density, the inverted population density and the dielectric permittivity of the laser medium from their equilibrium values. These fluctuations cause a shift in the resonant frequencies of the laser cavity. When the fluctuation in the dielectric permittivity of the laser medium is a longitudinally traveling wave (corresponding to the case in which moving striations exist in the positive column of the laser discharge), the laser output is frequency modulated.</p>
<p>The discharge noise has been analyzed by representing the laser discharge by an equivalent circuit. An appropriate ac equivalent circuit of a laser discharge tube has been obtained by considering the frequency spectrum of the current response of the discharge tube to an ac voltage modulation. It consist of a series ρLC circuit, which represents the discharge region, in parallel with a capacitance C', which comes mainly from the stray wiring. The equivalent inductance and capacitance of the discharge region have been calculated from the values of the resonant frequencies measured on discharge currents, gas pressures and lengths of the positive column. The experimental data provide for a set of typical values and dependencies on the discharge parameters for the equivalent inductance and capacitance of a discharge under laser
operating conditions. It has been concluded from the experimental data that the equivalent inductance originates mainly from the positive column while the equivalent capacitance is due to the discharge region other than the positive column.</p>
<p>The ac equivalent circuit of the laser discharge has been shown analytically and experimentally to be applicable to analyzing the internal discharge noise. Experimental measurements have been made on the frequency of moving striations in a laser discharge. Its experimental dependence on the discharge current agrees very well with the expected dependence obtained from an analysis of the circuit and the experimental data on the equivalent circuit elements. The agreement confirms the validity of representing a laser discharge tube by its ac equivalent circuit in analyzing the striation phenomenon and other low frequency noises. Data have also been obtained for the variation of the striation frequency with an externally-applied longitudinal magnetic field and the increase in frequency has been attributed to a decrease in the equivalent inductance of the laser discharge.</p>
https://thesis.library.caltech.edu/id/eprint/9628Magnetic field and pressure effects in a saturated gas laser amplifier
https://resolver.caltech.edu/CaltechTHESIS:08112015-153553907
Authors: Menzies, Robert Thomas
Year: 1970
DOI: 10.7907/3h9r-da77
<p>Theoretical and experimental studies of a gas laser amplifier are presented, assuming the amplifier is operating with a saturating optical frequency signal. The analysis is primarily concerned with the effects of the gas pressure and the presence of an axial magnetic field on the characteristics of the amplifying medium. Semiclassical radiation theory is used, along with a density matrix description of the atomic medium which relates the motion of single atoms to the macroscopic observables. A two-level description of the atom, using phenomenological source rates and decay rates, forms the basis of our analysis of the gas laser medium. Pressure effects are taken into account to a large extent through suitable choices of decay rate parameters.</p>
<p>Two methods for calculating the induced polarization of the atomic medium are used. The first method utilizes a perturbation expansion which is valid for signal intensities which barely reach saturation strength, and it is quite general in applicability. The second method is valid for arbitrarily strong signals, but it yields tractable solutions only for zero magnetic field or for axial magnetic fields large enough such that the Zeeman splitting is much larger than the power broadened homogeneous linewidth of the laser transition. The effects of pressure broadening of the homogeneous spectral linewidth are included in both the weak-signal and strong-signal theories; however the effects of Zeeman sublevel-mixing collisions are taken into account only in the weak-signal theory.</p>
<p>The behavior of a He-Ne gas laser amplifier in the presence of an axial magnetic field has been studied experimentally by measuring gain and Faraday rotation of linearly polarized resonant laser signals for various values of input signal intensity, and by measuring nonlinearity - induced anisotropy for elliptically polarized resonant laser signals of various input intensities. Two high-gain transitions in the 3.39-μ region were used for study: a J = 1 to J = 2 (3s<sub>2</sub> → 3p<sub>4</sub>) transition and a J = 1 to J = 1 (3s<sub>2</sub> → 3p<sub>2</sub>) transition. The input signals were tuned to the centers of their respective resonant gain lines.</p>
<p>The experimental results agree quite well with corresponding theoretical expressions which have been developed to include the nonlinear effects of saturation strength signals. The experimental results clearly show saturation of Faraday rotation, and for the J = 1 t o J = 1 transition a Faraday rotation reversal and a traveling wave gain dip are seen for small values of axial magnetic field. The nonlinearity induced anisotropy shows a marked dependence on the gas pressure in the amplifier tube for the J = 1 to J = 2 transition; this dependence agrees with the predictions of the general perturbational or weak signal theory when allowances are made for the effects of Zeeman sublevel-mixing collisions. The results provide a method for measuring the upper (neon 3s<sub>2</sub>) level quadrupole moment decay rate, the dipole moment decay rates for the 3s<sub>2</sub> → 3p<sub>4</sub> and 3s<sub>2</sub> → 3p<sub>2</sub> transitions, and the effects of various types of collision processes on these decay rates.</p>
https://thesis.library.caltech.edu/id/eprint/9097The origins of the nonlinear refractive indices of liquids and glasses
https://resolver.caltech.edu/CaltechTHESIS:06132016-142455107
Authors: Owyoung, Adelbert
Year: 1972
DOI: 10.7907/E9HM-AK76
<p>Nonlinear refractive index changes in isotropic media are a consequence of two distinct types of mechanisms. An "electronic" mechanism arises from the nonlinear distortion of the electron orbits about the nuclei and a "nuclear" mechanism arises from an electric-field-induced change in the motions of nuclei. </p>
<p>A general treatment of nonlinear optical phenomena involving a polarization cubic in the electric field strength is given with the topic of nonlinear index changes treated as a special case. A central result of this theory is the following expression for the nonlinear polarization <u>P</u><sub>3</sub>(t) in terms of the electric field <u>E</u>(t), the "electronic" parameter σ and the "nuclear response functions" a(t) and b(t): </p>
<p><u>P</u><sub>3</sub>(t) = σ-2 <u>E</u>(t)▪ <u>E</u>(t) <u>E</u>(t) + ∫ a(t-τ)<u>E</u>(τ)▪<u>E</u>(τ)dτ <u>E</u>(t) </p>
<p>+ ∫ b(t-τ)<u>E</u>(τ)▪<u>E</u>(t)<u>E</u>(τ)dτ </p>
<p>In the theory the relationship between these parameters and the nonlinear susceptibility tensor <u>X</u><sub>3</sub>, is established. Several experiments in nonlinear optics are analyzed; in particular, it is shown that Kerr effect measurements lead to a determination of the quantity σ + β (where β = ʃ b(t)dt) whereas measurements of the intensity dependent rotation of the polarization ellipse of a monochromatic optical beam yield the quantity σ + 2β. Hence together these two techniques offer a means of uniquely determining both the "electronic" parameter a and the "nuclear" parameter β in any isotropic medium. </p>
<p>The nonlinear susceptibility element X<sub>3</sub><sup>1221</sup> (-ω,ω,ω,-ω) = σ+2β/24 is calculated from ellipse rotation measurements in fused quartz, BK-7 borosilicate crown glass, and SF-7 dense flint glass giving values of 1.5, 2.3, and 9.9 x 10<sup>-15</sup> esu at λ = 6943Å, respectively. These measurements constitute the first observations of ellipse rotation in any solid and (with an absolute accuracy of 11%) are the most accurately known of any nonlinear optical parameter in glasses. </p>
<p>Although the interpretation of these results along with Kerr, three-wave mixing, and third harmonic generation data nominally indicate that σ ˃˃ β for glasses, we hesitate to conclude that the nonlinear refractive indices in glasses are purely "electronic" in origin until the uncertainties in the latter measurements are reduced. If it is assumed however that electronic contributions are dominant, these experimental data would indicate that the nonlinear refractive index n<sub>2</sub> for a linearly polarized beam in fused quartz, BK-7 glass, and SF-7 glass is 1.2, 1.7, and 6.9 x 10<sup>-13</sup> esu respectively. </p>
<p>Parallel investigations of "ellipse rotation" in the symmetric molecule liquid CC1<sub>4</sub> show that X<sub>3</sub><sup>1221</sup> (-ω,ω,ω,-ω) = 6.1 x 10<sup>-15</sup> esu. This value when interpreted along with very accurate Kerr measurements indicate that the fractional electronic contribution to the Kerr constant of CC1<sub>4</sub> is given by σ/σ+β = 0.54 ± 0.17. Hence both electronic and nuclear contributions are significant to nonlinear refractive index changes in CC1<sub>4</sub>.</p>
https://thesis.library.caltech.edu/id/eprint/9873Detection of Mode-Locked Laser Signals
https://resolver.caltech.edu/CaltechTHESIS:11122019-160113596
Authors: D'Orazio, Robert Joseph
Year: 1973
DOI: 10.7907/26D2-8776
<p>In this work we describe our approach to matched-filtering for mode-locked laser signals. Our optical receiver consists of a passive laser cavity controlled in length and a photodetector with its associated electronics. The length of the passive Fabry-Perot cavity is chosen roughly equal to the cavity length of the transmitting laser, but with provision for fine fractional wavelength control of its length. In addition to the selective filtering characteristics of the passive cavity (passbands of unity transmission matching the frequencies of the multi-mode laser), a readout of the vernier length control, peaking the output, provides for an extremely wide range of velocity measurements with either an active or passive vehicle moving relative to the receiver.</p>
<p>In studying the mode-locked laser we use the matched-filter criterion resulting from the optimization of the signal-to-noise ratio. This criterion specifies that the amplitude transmission function be T<sub>m</sub>(ω) = AE*(ω)/S<sub>n</sub>(ω); where E(ω) is the Fourier transform of the laser signal E<sub>1</sub>(t); S<sub>n</sub>(ω) is the power spectral density of the additive input noise; the asterisk denotes the complex conjugate; and A is any nonzero complex constant. For an actual laser signal, writing E(ω) for the multi-tone laser with finite linewidths Δω<sub>ℓ</sub> yields an expression which is comparable on a mode by mode basis to the transmission function for a Fabry-Perot cavity. The resulting matching conditions are that Δω<sub>p</sub> = Δω<sub>ℓ</sub> and h<sub>o</sub> = h in which Δω<sub>p</sub> is the linewidth of the receiver cavity of length h<sub>o</sub>, and h is the length of the transmitter cavity.</p>
<p>The Fabry-Perot cavity is probably as close a physical realization to a matched-filter for the multi-toned laser as can be attained in a passive system. Even so, gain narrowing invariably results in Δω<sub>ℓ</sub> < Δω<sub>p</sub>, thereby limiting the observed improvement in signal-to-noise ratio from its optimal value. For high gain lasers with cavities of low finesse, the receiver can be made closer to the ideal, while greater departures are to be expected in the case of low gain.</p>
<p>Further study of the use of the passive cavity in contrast to no cavity shows that the signal-to-noise ratio improves approximately by the finesse of the cavity which is typically 150. Considering the improvement in signal-to-noise ratio as a function of the number of oscillating modes N we find that the peak value of the temporally varying detected output has a signal-to-noise ratio proportional to N<sup>2</sup>, i.e., it varies as the peak power of the mode-locked laser.</p>
<p>Now, suppose that the mode-locked laser is moving toward our receiver with a velocity v. For TEM waves, an emitted frequency ω' will be observed shifted to ω given by ω = γ(1 + v/c)ω' in which γ = [1 - (v/c)<sup>2</sup>]<sup>-l/2</sup> and c is the speed of light. In this case where there is relative motion, we find that optimal detection of the mode-locked laser signal requires a receiver with a cavity length h<sub>o</sub> given by h<sub>o</sub> = h/[γ(1 + v/c)]. Similarly, if the mode-locked laser and the passive cavity were on a common platform, then the echo from a vehicle moving toward this platform with velocity v would be shifted to ω = (1 + 2v/c)ω', where we have set γ = 1. So by vernier adjustments of the passive cavity length we can read a large range of approach velocities with a resolution independent of the velocity.</p>https://thesis.library.caltech.edu/id/eprint/13571A wavelength diversity technique for smoothing of speckle
https://resolver.caltech.edu/CaltechTHESIS:08312011-132624162
Authors: Jain, Atul
Year: 1974
DOI: 10.7907/02VQ-6128
Theoretical and experimental results are given for the
wavelength dependence of speckle, thus establishing a method for the reduction of speckle noise in holographic microscopy with the use of multitoned illumination and a panchromatic viewing system. A model is presented for a partially diffuse phase type of object and the statistical behavior of t he speckle produced in the image of this
object is studied. A calculation is made for the spectral autocorrelation function which gives a wavelength spacing required to decouple the speckle patterns produced by two tones, this spacing being found to be inversely proportional to the standard deviation of the heights of the scatterers on the object. A criteria is defined for the degradation of an image due to speckle and the resultant improvement is found to depend on the square root of the
number of independent tones used.
The wavelength dependence of speckle is verified in a
series of experiments where we illuminate the object by both laser and bandlimited light. We first demonstrate the averaging of speckle in the image of a pap smear when we use four tones of an argon laser (5145, 4965, 4880 and 4765 Å). We then show that the image of a rough object is speckly even for bandwidths up to 5Å; and then we demonstrate the smoothing of speckle when both a scotch
tape diffuser and a section of an optic nerve is illuminated by six equally spaced bandlimited tones scanning 1,500Å.
Thus, in this study, we demonstrate the feasibility of
eliminating objective speckle in holographic microscopy using a multimonochromatic source and also provide a theoretical basis for studying the properties of rough surfaces by studying the wavelength diversity of the speckle produced by them.
https://thesis.library.caltech.edu/id/eprint/6640The modulated grating hologram
https://resolver.caltech.edu/CaltechTHESIS:07212014-154218408
Authors: MacQuigg, David R.
Year: 1975
DOI: 10.7907/VZN5-MT65
<p>A phase and amplitude, off-axis hologram has been synthesized
from three computer-generated transmission masks, using a multiple-exposure
holographic recording method. Each of the masks controls one
fixed-phase component of the complex hologram transmittance. The basic
grating is generated optically, relieving the computer of the burden of
drawing details the size of each fringe. The maximum information
capacity of the computer plotting device can then be applied to the
generation of the grating modulation function. By this method large
digital holograms (25 mm by 25 mm) have been synthesized in dichromated
gelatin. The recording method is applicable to virtually any holographic
medium. </p>
<p>The modulated grating hologram was designed primarily for the
application of spatial filtering, in which the requirement is a hologram
with large dynamic range and large free spectral range. Choice of a
low-noise, high-efficiency medium such as dichromated gelatin will allow
exceptionally large dynamic range. Independence of the optically-generated
carrier grating from the computer-generated modulation functions
allows arbitrarily large free spectral range. </p>
<p>The performance of a holographic spatial filter will be limited
ultimately by noise originating from imperfections in the holographic
medium. The characteristics of this noise are analyzed, and in the
case of a high diffraction efficiency hologram are shown to differ significantly
from previous analyses. The dominant noise source in holograms
of high diffraction efficiency will be scattering of the first order
or imaging wave by deformations in the hologram surface or other
effects of low spatial frequency. Experimental measurements in various
low-noise holographic media verify these predictions. </p>
https://thesis.library.caltech.edu/id/eprint/8578Edge diffraction of a convergent wave. Diffraction of Lagguerre Gaussian beams by a circular aperture
https://resolver.caltech.edu/CaltechETD:etd-11112003-093137
Authors: Livanos, Alexander Constantine R.
Year: 1975
DOI: 10.7907/KDAN-7033
PART I.
Closed form solutions have been derived for the focal plane diffraction patterns of (a) a convergent spherical wave illuminating a segment of a circular aperture and (b) a convergent Gaussian beam diffracted by an infinite edge. The theoretical results agree with the experiments showing that the edge produces a spike of light with intensity variation inversely proportional to the squared distance from the center, that the pattern is symmetric in the focal plane, and that in the case of the uniform illumination the intensity has high spatial frequency components while for the Gaussian case the pattern does not ring when the edge is positioned symmetrically in the beam.
In addition, the near focus intensity distribution for a convergent uniform amplitude wave illuminating a semicircular aperture is presented, and it is shown that the fact that the radiation pattern is symmetric only at the focal plane can be used very effectively to determine the exact location of that plane.
PART II.
The diffraction of a Laguerre Gaussian beam (TEM[subscript p,l] mode of a laser resonator) by a circular aperture is presented here. We calculate the electric field for the Fresnel region, and study the loss of power as a function of relative aperture size and mode index, showing that the conventional rule of thumb in selecting apertures by "going out a few times w[subscript o]" is not accurate for large mode indices.https://thesis.library.caltech.edu/id/eprint/4502Spatial and spectral behavior of speckle in an imaging system
https://resolver.caltech.edu/CaltechETD:etd-02182005-111421
Authors: Melville, Richard Devern Samuels
Year: 1975
DOI: 10.7907/2KP8-CT79
When coherent illumination is reflected from or transmitted through a medium which causes random phase changes in the illumination, a random interference pattern termed speckle results.
We have studied speckle in an imaging system and have described and measured the effect of polarization of the illumination, the first order statistics of speckle intensity, and the autocorrelation of speckle intensity as a function of space and wavelength variables.
We have measured the relationship between the amount of depolarization of a plane polarized input in transmission through opal glass diffusers of various thicknesses and the effect of this phenomenon on the first and second order statistics of speckle intensity. A relationship between diffuser thickness and the probability density function for speckle intensities has been calculated and measured. The autocorrelation of speckle intensities has been calculated and measured as a function of both the spatial dimension of the speckle pattern and the wavelength of the illumination. We find that the spatial behavior of the autocorrelation depends upon the limiting aperture of the optical system, while the wavelength dependence is a function of the roughness of the diffuser and is only very slightly influenced by the imaging system.https://thesis.library.caltech.edu/id/eprint/672