Optical frequency divider

A much more general and appealing scheme would be a true optical frequency divider, as could be realized by synchronizing the cyclotron motion of an electron with a laser field [33,34],... 

Figure 1. Block diagram of an optical frequency divider showing two servo loops where the laser is locked to a reference cavity and the cavity to a radio frequency standard. The LiTa03 modulator is driven at

Fig. 5. Principle of an optical frequency interval divider. An arbitrary large frequency interval fi — fe is phase coherently divided by two by locking a third laser (/a) precisely in the center of the interval. This is achieved by phase locking the sum frequency /i +/2 to the second harmonic 2/3. Then /3 — (/1 + /2)/2 holds...

The next big advance towards higher precision was the 1997 phase-coherent measurement of the frequency gap with an optical frequency interval divider chain [27]. The 2.1 THz gap was no longer measured by counting cavity fringes, but divided down to the radio frequency domain by a phase-locked chain of five optical frequency interval dividers [56] (see Fig. 5). The accuracy of this approach was limited by the secondary frequency standard to 3.4 parts in 1013, exceeding the accuracy of the best previous measurements by almost two orders of magnitude. 

Fig. 4. The first self-referenced frequency chain that has been used in Refs. [16,19,31] uses an optical frequency interval divider (oval symbol) [34] that fixes the relation between the frequencies /, 4/ and 7/ by locking f + 7f to 2 x 4/. The 3.39 /Am laser at / is locked through the divider after the frequency comb locked the difference between 3.5/ and 4/...

In extension to this frequency chain we installed an optical frequency interval divider [23] to extrapolate to 1064 nm (see Fig. 3). The center frequency of the optical divider stage is given by the Nd YAG laser at 946 nm laser with its frequency determined via the beat note with the comb locked laser diode at 946 nm. The higher input frequency of the divider stage is set by a diode laser at 852 nm which is heterodyned with another diode laser at 852 nm, also phase locked to the frequency comb. The lower input frequency of the divider stage is determined by the iodine stabilized Nd YAG laser at 1064 nm. While scanning the frequency doubled 1064 nm Nd YAG laser over the iodine line the two beat notes at 852 nm and 946 nm are measured with a rf-counter. They are then used to determine the absolute frequency of the 1064 nm Nd YAG laser. 

Fig. 5. Optical difference frequency divider and synthesizer of hydrogen transition frequencies [35].

The quality factor, or Q-factor, is a general dimensionless parameter, used in mechanical, electrical, electromagnetic, and optical contexts. Given some signal intensity S(co) as a function of frequency m, the Q-factor is defined as the resonance frequency divided by the bandwidth A (see Fig. 9.4) ... 

Deformation polarization It can be divided into two independent types Electron polarization—the displacement of nuclei and electrons in the atom under the influence of an external electric field. Because electrons are very light, they have a rapid response to the field changes they may even follow the field at optical frequencies. 

Th. Udem, A. Huber, B. Gross, J. Reichert, M. Prevedelli, M. Weitz, and T. W. Hansch, Phase-Coherent Measurement of the Hydrogen 15-2 5 Transition Frequency with an Optical Frequency Interval Divider Chain, Physical Review Letters 79, 2646-2649 (1997). 

In an FTIR instrument, the Fourier transform converts the intensity versus optical path difference to the intensity versus wavenumber. The optical path difference can be considered to be in the time domain because it is obtained by multiplying time with the speed of a moving mirror. The wavenumber can be considered in the frequency domain because it is equal to frequency divided by the light speed. 

Primary length measurements are these days based on optical frequency standards. If one needs a unit of length, for example, a wave-length for interferometric measurement, then one divides the optical frequency by the value of the speed of light (299 792 458 m.s ) as defined in the SI metre. The mise en pratique of the metre [44] lists a number of frequency-stabilised lasers at various wavelengths in the visible and near infrared spectral regions. 

Equation (3) is the key equation that describes the most important characteristics of the SOA, including the gain and carrier dynamics. In this equation, / is the injected current, q is the charge on the electron (i.e., 1.6 x 10 C), V = wdL is the volume of the active region, A r is a coefficient describing the rate of non-radiative recombination, B is the radiative recombination coefficient, C is the Auger recombination coefficient, h is Planck s constant (i.e., 6.63 X Js), v is the optical frequency, and P is the optical irradiance (i.e., the optical power divided by the cross-sectional area of the active region). 

The OLED emits a certain number of photons per second. The energy of one photon is E=hv. The energy of N photons is EN=Nhv, with units of joules. Therefore, by knowing how many optical watts are generated by the OLED, one can calculate the number of photons per second, as long as the frequency (or wavelength) is known. The number of photons per second equals the light output in watts divided by hv. N( , = W/hv. 

There is one important idea, the raison d etre of this book, that we should like to implant firmly in the minds of our readers scattering theory divorced from the optical properties of bulk matter is incomplete. Solving boundary-value problems in electromagnetic theory may be great fun and often requires considerable skill but the full physical ramifications of mathematical solutions are hidden to those with little knowledge of how refractive indices of various solids and liquids depend on frequency, the values they take, and the constraints imposed on them. Accordingly, this book is divided into three parts. 

In order to test the measurements of the 2S — 8S and 2S — 8D transitions, the frequencies of the 2S — 12D intervals have also been measured in Paris [49]. This transition yields complementary information, because the 12D levels are very sensitive to stray electric fields (the quadratic Stark shift varies as n7), and thus such a measurement provides a stringent test of Stark corrections to the Rydberg levels. The frequency difference between the 2S — Y2D transitions (A 750 nm, u 399.5 THz) and the LD/Rb standard laser is about 14.2 THz, i.e. half of the frequency of the CO2/OSO4 standard. This frequency difference is bisected with an optical divider [56] (see Fig. 5). The frequency chain (see Fig. 11) is split between the LPTF and the LKB the two optical fibers are used to transfer the CO2/OSO4 standard from the LPTF to the LKB, where the hydrogen transitions are observed. This chain includes an auxiliary source at 809 nm (u 370.5 THz) such that the laser frequencies satisfy the equations ... 

Electrophoretic instruments for analysis of colloidal suspensions can be divided into two basic classes optical instruments for which the operator observes the migration of particles in a field using a microscope and laser-based instruments that measure the Doppler shift in the frequency of the scattered light from particles... 

We turn now to a matter of more direct physical relevance, the local electric dipole moment induced when a particular ion is displaced by some vector u. The transverse charge is defined to be the magnitude of that dipole moment divided by the displacement (and by the magnitude of the electronic charge). We saw in Eq. (9-22) that is directly related to an observable splitting between the longitudinal and transverse optical-mode frequencies, so that this is a quantity that can be compared with experiment. 

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