The number N dof of the non-radiative modes of a square-law graded-index (GRIN) rod is evaluated using an analysis of the well known solutions of the scalar wave equation in an infinitely extended square-law medium. The number M q of modes that arrive at the plane of the first image in almost the same phase relation as in the object, and which therefore determine the ‘quality of the image’, is also evaluated.
A proposal is made to produce, from a nonlinear diode injection laser, a photon stream with potentially non-classical statistical behaviour. The term ‘quiet photon stream’ is suggested to avoid possible confusion with other types of state such as the two-photon coherent squeezed states that have been described elsewhere. However, it is possible to that the process does give rise to states of phase-sensitive noise. A new interpretation is offered for the production of such non-classical states in that an increased emission is followed by a correlated increase in the probability of absorption and vice versa with the correlation arising through non-linearities within the laser. Thus a feedback mechanism within the diode laser cavity is proposed which certainly leads to saturation of the laser output and may also, as tentatively proposed here, lead to a reduction in the variance of the photon output stream along with possible effects on the phase fluctuations.
A simple method for the rapid determination of the coefficients of a monochromatic wave-aberration polynomial for a given object point and a rotationally symmetric system is discussed. The method is appropriate for optimization programs. Sources of error in the scheme are investigated with emphasis placed on the sine condition error and its reduction. Comparison is also made between two different kinds of the universal coefficients: one provides an exact fit to the polynomial, the other a least-squares fit. Test results for real optical systems are given. The superiority of the scheme over previous methods is demonstrated.
(1986). Thin-film Optical Filters. Optica Acta: International Journal of Optics: Vol. 33, No. 11, pp. 1336-1336.
We investigate the reconstruction of a real and positive spatial pattern or "image" (1) from incomplete phaseless Fourier data Dkwith noise σk, (2) The first step is to define the set of "feasible" images, any of which is consistent with the data. This involves comparing the actualdata Dkwith the simulated data |Fk|2which wouldbe observed (apart from noise) from a trial image f. The simplest comparison measure is chisquared (3) Any trial image f for which χ2>M+3⋅3M (M = number of data) is rejected with 99% confidence: the surviving images are feasible and only these need be considered further. In N-dimensional image-space, the feasible set forms a 2M-dimensional toroid, projected linearly to infinity in any unmeasured Fourier planes. Much of the difficulty encountered with phaseless data stems from the connected topology of this constraint.
Optical and electronic signal-processing schemes for the measurement of circular birefringence using monomode fibre optic techniques are described. Optical mixing of two orthogonal circularly polarized states is utilized to produce a linear state, the azimuth of which is controlled electronically to produce pseudo-heterodyne phase-modulated carriers. The signal-processing techniques are shown to be applicable to the recovery of circular birefringence in the presence of environmental perturbations and over a wide time-scale—from ws to ks. Methods to obtain phase measurement stabilities of -0·05° are presented and the system is demonstrated in a ‘time-varying’ optical-activity measurement.
Passive mode-locking of a c.w. rhodamine 700 dye laser is reported for the first time. Continuous output trains of subpicosecond pulses have been obtained with two saturable absorber dyes, DOTCI and HITCI, in the 727–740 nm and 762–778 nm spectral regions respectively. By the addition of a fast recovery time dye (DCI) to the DOTCI saturable absorber solution, pulses as short as 350 fs at 740 nm have been generated in a linear cavity configuration.
A model of a conditioned Poisson stream of events is proposed in which the intensity is a Markov chain assuming the values f, g, 0 with 0 < f < g. The conditioned Poisson process is specified by assuming that an emission results in the intensity making a transition to the next lower value. In the absence of emissions, the intensity which is a process by itself has a propensity to move up in its state space, the residence time in any state being exponentially distributed with parameter n. It is shown that such a model of emissions possesses antibunching and sub-Poisson properties.
In this paper, the wave theory is adopted to analyse the process of image formation in the electron microscope and to calculate the image intensity distribution. The conditions of transverse and longitudinal coherence are derived based on the Rayleigh criterion. Consequently, the method for selecting the experimental parameters is given.
The imaging properties of a periodic system of phase Fourier holograms on which binary information is recorded depend on the shape of the readout beam propagating through the stack. The readout beam should be of a steady-state type which gives minimum energy losses and assures a uniform and good quality of the reconstructed images. We calculate the resonant modes of the systems composed of linearly and non-linearly recorded holograms by the Prony method. The eigenvalues of a few symmetric and antisymmetric modes with lowest energy losses obtained for Fresnel numbers up to 10 are found. For the low efficiency holograms required in the stack the lowest-order symmetric mode is always of a Gaussian type. The width of the resonant modes is larger in the case of linearly recorded holograms. In both the linear and the non-linear case the width of the resonant modes is smaller than the reference width used during recording.
Results on both dispersive optical bistability and bistability by increasing absorption are presented for multiple quantum wells consisting of 120 wells of 63 + thickness GaAs separated by 218 + thick barriers of Al0·4 Ga0·6As. Optical bistability is observed in the wavelength range 845–870nm for incident powers below 10mW. A second absorptive switching feature unique to quantum wells is observed at the n=2 transition. Wavelength bistability is also reported for the first time.
The problem of finding the time development of a three-level atom in interaction with two modulated laser beams is discussed. Formulation of the Hamiltonian in terms of spin-one operators, their squares and their anti-commutators allows exact and approximate analytical solutions for the time evolution operator to be found for a wide variety of interactions involving fields which are amplitude or frequency modulated. A fortuitous set of cyclic commutation relations among the subset of operator combinations Jx, {Jx, Jy} and {Jz, Jx} which allows an exact solution to be found for double photon resonance when the fields are amplitude modulated in quadrature, also allows the possibility of finding approximate solutions for more general modulation phase relations. The use of the formalism for describing population trapping and for finding a method of transient atomic state squeezing is also briefly discussed. The optical-frequency rotating-wave approximation is used throughout.
The standard elementary theory of the Brewster angle generated by a plane interface separating two homogeneous isotropic media, through which incident and transmitted electromagnetic waves are propagating, is well known. We introduce here a more general inhomogeneous medium for which a Brewster wave and a Brewster angle can be defined. The properties of this wave are investigated, together with a model whose field can be expressed in terms of a special degenerate hypergeometric function. Other angles of incidence also yield zero reflectivity, but these are carefully distinguished from the Brewster angle.
In the case of scalar waves and impenetrable material, the coherent scattering cross-section of a nearly spherical particle is calculated, where the surface irregularities are described statistically by a correlation function. The results are valid up to the second order of hk (k is the wavenumber,h2 the mean-square deviation from a smooth sphere), but for any value of the size parameter f = kR0 (RR0 is the radius of the sphere). The limits for small particles (f 1) and for large particles (f d 1) are derived, and it is shown that for f d 1 the scattering pattern outside the diffraction peak coincides with the result obtained by means of the Rayleigh-Rice approach, i.e. by applying scattering results for planar rough areas locally to the curved surface of the scattering body.
The resonance fluorescence spectrum of one and two two-level atoms in an ideal cavity with one resonant mode is investigated as a function of the initial excitation of the system. The analysis is carried out in the Stark representation with respect to the cavity's field and in first-order perturbation theory with respect to the fluorescence field. In the absence of the field of the cavity (n c = 0) and under an initial excitation of one atom only, the spectrum consists of two lines which are symmetrical with respect to ωa. In all other cases the spectrum has a central line at ωa and other lines at ωa ± 2 Ω. The intensity of the higher (ωa ± 4 Ω) harmonics is small and decreases as 1/ 2 c c with increasing n>c. The nonlinearity of the interaction hamiltonian results in the parametric (with respect to the field of the cavity) amplification of the ωa + 2 Ω harmonic and the attenuation of the ωa − 2 Ω harmonic. The stimulated emission of the ωa ± 2 Ω harmonics, vanishing in a strong (n c » 1) field, is shown to exist for two atoms.
The radius of curvature at the top of small liquid drops has been determined both visually and by means of differential interferometry in reflected light (microscope Epival Interphako, Carl Zeiss-Jena). Systematic errors in the interferometric measurements have not been found within the investigated interval of curvatures. A comparison between the data for aqueous and mercury drops showed that there is no pronounced effect of the reflectivity of the surface on the accuracy of the interferometric measurements.
The theory of image formation for an electron microscope is based on the non-relativistic Schrödinger equation, whereas present-day electron microscopes operate with acceleration voltages of the order of one hundred to several hundreds of kilovolts, in which case relativistic effects become important. We present a fully relativistic theory of image formation, based on the appropriate Dirac equation. It is shown that, within certain approximations, always valid for today's electron microscopes, a very simple expression for the current density can still be derived in terms of wave functions that are solutions to the relativistically covariant Klein-Gordon equation. The following paper presents the analysis of the often stated possibility to obtain the relativistically correct current density from the non-relativistic current density just by replacing the values of the non-relativistic momentum by the correct relativistic expression.
