The behavior of the field of a Gaussian beam as it propagates is described by a few parameters such as the spot size, the radius of curvature, and the Gouy phase.

: is the Gouy phase shift, an extra contribution to the phase that is seen in Gaussian beams.

The longitudinal phase delay or Gouy phase of the beam is

is the Gouy phase.

where,,, and are the waist, spot size, radius of curvature, and Gouy phase shift as given for a Gaussian beam ; is a normalization constant ; and is the k < sup > th </ sup > physicist's Hermite polynomial.

Four kilometres to the south of Aubencheul, at Gouy which used to be called Gouy en Arrouaise, ( Click on Pienne on this map ) the Michelin 1: 200 000 map shows an abbey ruin, at the source of the Escaut.

The headwaters of the Scheldt are in Gouy, in the Aisne department of northern France.

Early measurements were made using the Gouy balance where a sample is hung between the poles of an electromagnet.

All and all, according to historical documents, the western part of the Urmia Lake has been a center of attention of the prehistoric nations, the evidence of which are the numerous ancient hills in the area, such as Gouy Tapeh, 6 kilometers southeast of the lake which competes with the oldest hills of Mesopotamia, Asia the Minor, and the Iranian Plateau.

* Jacques de Gouy ( c. 1610 – after 1650 )

Eugene Müller, with the aid of a Gouy balance, established for the first time that these compounds are paramagnetic with a triplet ground state.

Other members of the Curies ' circle of scientist friends — including William Crookes ; future Nobel laureate Jean Perrin and his wife Henriette ; Louis Georges Gouy ; and Paul Langevin — were also exploring spiritualism, as was Pierre Curie's brother Jacques, a fervent believer.

On July 24, 1905, Pierre Curie reported to his friend Gouy: " We have had a series of séances with Eusapia Palladino at the for Psychical Research.

Pierre was eager to enlist Gouy.

On April 14, 1906, just five days before his accidental death, Pierre Curie wrote Gouy about his last séance with Palladino: " There is here, in my opinion, a whole domain of entirely new facts and physical states in space of which we have no conception.

where the proportionality sign indicates that there might be a phase on the right hand side.

Interestingly, experimental evidence indicates that this phase forms by a first-order transition.

One of the more recent citations in the Oxford English Dictionary indicates that, while today honeymoon has a positive meaning, the word was originally a reference to the inevitable waning of love like a phase of the moon.

In this definition, increase in ( or ) indicates retardation ( delay ) in phase, while decrease indicates advance in phase.

A lunisolar calendar is a calendar in many cultures whose date indicates both the moon phase and the time of the solar year.

A phase transition indicates a change in structure and can be recognized by an abrupt change in properties.

The degree of nonlinearity of the phase indicates the deviation of the group delay from a constant.

According to Kotowski, this episode indicates that even the most minor activities of the German minority were closely scrutinized by the Polish authorities beginning with the earliest phase of Polish policy towards the German minority.

Other research indicates that losses unquestionably affected the build-up for Operation Neptune, the actual landing phase of the invasion of Europe.

) A quick way to determine if the stepper motor is working is to short circuit every two pairs and try turning the shaft, whenever a higher than normal resistance is felt, it indicates that the circuit to the particular winding is closed and that the phase is working.

A recent final publication of the French excavations by Jean-Baptist Humbert outlining evidence of a decorated frieze, opus sectile, fine columns etc., indicates a phase of a wealthier occupation, " une grande maison ", at Qumran.

Current knowledge of coronal mass ejection kinematics indicates that the ejection starts with an initial pre-acceleration phase characterized by a slow rising motion, followed by a period of rapid acceleration away from the Sun until a near-constant velocity is reached.

indicates the strength of the phase fluctuations as it

The absence of speleothem decorations which can only form in air filled caves, indicates that the flooded Florida caves have a single genetic phase origin, having remained water filled even during past low sea levels.

This phase difference is the Berry phase, and its occurrence typically indicates that the system's parameter dependence is singular ( undefined ) for some combination of parameters.

A large body of evidence, which is consider either direct or indirect that small ions are liberated into the gas phase through the ion evaporation mechanism, de la Mora, Electrospray ionization of large multiply charged species proceeds via Dole ’ s charged residue mechanism, Analytica Chimica Acta 406: 93 – 104, 2000 at page 104, " An evaluation of the electric field on the drop surface at the point when it just ceases to be spherical ( yet carries the total ion charge z ) indicates that small PEG ions may be formed by ion evaporation.

The phase of the output voltage determines the direction of the displacement ( up or down ) and amplitude indicates the amount of displacement.

If the straight line ( or deviation from it ) appears with a slope of negative one, this indicates that the left and right channels are 180 ° out of phase.

* Lattice AN6017 application note comparing and contrasting filters ( in order of damping coefficient, from lower to higher values ): Gaussian, Bessel, linear phase, Butterworth, Chebyshev, Legendre, elliptic.

In addition to Gaussian minimum-shift keying ( GMSK ), EDGE uses higher-order PSK / 8 phase shift keying ( 8PSK ) for the upper five of its nine modulation and coding schemes.

where is the optical phase error introduced by atmospheric turbulence, R ( k ) is a 2 dimensional square array of independent random complex numbers which have a Gaussian

At each phase of the light field, the distribution is a Normal distribution | Gaussian of constant width.

In here, S transform is derived as the phase correction of the continuous wavelet transform with window being the Gaussian function.

In this figure, the amplitude and intensity are Gaussian function s. The phase function is quadratic, resulting in an instantaneous frequency sweep sometimes called a chirp, in analogy to the sound of some bird s.

The following image demonstrates the usage of phase correlation to determine relative translative movement between two images corrupted by independent Gaussian noise.

In this equation, represents the wavelength of the sinusoidal factor, represents the orientation of the normal to the parallel stripes of a Gabor function, is the phase offset, is the sigma of the Gaussian envelope and is the spatial aspect ratio, and specifies the ellipticity of the support of the Gabor function.

Upon reception of the signal, the demodulator examines the received symbol, which may have been corrupted by the channel or the receiver ( e. g. additive white Gaussian noise, distortion, phase noise or interference ).

For an ultrashort pulse with a Gaussian shape and constant phase, the intensity at time t is given by I ( t ):