Transmission Mode Resonator

The resonator problems that we have discussed are of limited interest until we couple to a source and load in order to examine the response of 

KEITH A. EARLE, DAVID E. BUDIL AND JACK H. FREED 

We may subsume all of the complexity of the full electromagnetic wave description of the Gaussian beam and its coupling to various elements of the resonator into two phenomenological constants the mutual inductances M, and M2 of Fig. 6. This procedure is equivalent to that used to model variable iris coupling into a waveguide cavity, for example. 

Once we have an equivalent circuit, we may manipulate the circuit equations to explore the effect on spectrometer performance of changing the values of circuit elements. It would be useful to have a variable coupling scheme in order to tune the spectrometer for optimum performance, just as in the microwave spectrometer case. Such a scheme is described in Section X. 

We may write a lumped equivalent circuit for the resonator and coupled transmission lines following the prescription in RLS-8 (Montgomery et al., 1948) as shown in Fig. 6. At resonance, the power Pi into the load 

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In a reflection mode spectrometer of high finesse or quality factor Q, the reflected power when matched on resonance is many decibels below the incident power, which reduces the noise floor by many decibels with respect to a transmission mode resonator. When the ESR sample is resonant, the residual resonator mismatch changes, which causes the reflected power to change, and a small signal on a low background is presented to the detector. In order for the signal to be detected, however, it must be discriminated from the radiation incident on the resonator, just as in a conventional reflection mode ESR spectrometer. 

Figure 43. Microwave transmission in a two-mode resonator as a function of the magnetic field strength for measurement of the microwave Hall effect in FeS2 (two measurements with an offset difference).16...

CW) output of microwaves capable of sweeping 10 MHz to 47 GHz. Depending upon the physical dimensions of the resonator and their coupling with the source, this spectrum analyzer can operate to detect the microwave absorption profile of the resonator either in the reflection or in the transmission mode. In this work the frequency range... 

Absorption resonances resulting from excitation of surface modes are accompanied by scattering resonances at approximately the same frequencies this was pointed out following (12.26). In most experiments transmission is measured to determine extinction, which is nearly equal to absorption for sufficiently small particles. However, surface mode resonances have been observed in spectra of light scattered at 90° by very small particles of silver, copper, and gold produced by nucleation of vapor in an inert gas stream (Eversole and Broida, 1977). The scattering resonance peak was at 3670 A, near the expected position of the Frohlich mode, for the smallest silver particles. Although peak positions were predictable, differences in widths and shapes of the bands were concluded to be the result of nonsphericity. 

Most often the transmission mode is found to be the most convenient in Mossbauer spectroscopy, i.e., the y radiation passes from the source through the absorber, and the attenuation of the primary beam is measured at the various Doppler velocities. However, there are a number of cases where a "scattering geometry may be advantageous (SO). The basis for this geometry lies in those processes that take place after resonant absorption of y radiation by the Mossbauer isotope. Specifically, after excitation the Mossbauer isotope may reemit the y ray, or it may decay by emission of internal conversion electrons and X rays [with the probability of internal conversion equal to a/(l + a)]. 

Consider first a Mossbauer isotope with a large associated resonant irradiation energy. The large recoil energy thus results in a small recoil-free fraction, and in the transmission mode the Mossbauer effect is only observed by measuring a small change in the primary beam intensity. The radiation reemitted as a result of these recoil-free events may, however, be superimposed on a weak background if observed for a direction different from the primary beam (SO). Thus, measurement of this radiation intensity versus... 

The other effect operates not through bonds but directly through space or solvent molecules and is called the field effect. Generally, the field effect depends on the molecule geometry, but the inductive effect depends only on the nature of the bonds. In most cases, the two types of effects are considered together more recently, evidence suggests that field effects are a more important mode of transmission than resonance effects (Hansch and... 

We see that reducing the beam waist increases We note that is more weakly dependent on P. We will derive an expression for he field at the sample in a Fabry-Perot resonator in Section VIII after we have developed the appropriate lumped equivalent circuit for a transmission mode spectrometer. 

Fig. 6. Lumped equivalent circuit for a transmission mode spectrometer near a resonance. Kj is the output voltage of the millimeter wave source, Rj is the source resistance, and Cf are the equivalent inductance and capacitance of the resonator, is the resonator resistance, and the load resistance of the detector. The mutual inductances M, and M2 model the coupling into and out of the resonator.

For small particles, and in many other cases, one will use fluorescence instead of transmission. However, saturation effects such as we saw for transmission mode also occur in fluorescence as well (Troger et al. 1992 Castaner and Prieto 1997). The classic case here is that of a thick piece of pure metal such as Cu. In this material, the ratio of the resonant to non-resonant absorption is about 85 15. This means that for every 100 incident photons, 85 of them create -holes and thus could stimulate fluorescence. Now, suppose the resonant absorption goes up by 10% due to EXAFS. Now the ratio is 93.5 15, or about 86.1 13.9. Thus, the resonant process accounts for 86.1% of the total, which means the fluorescence intensity only goes up by 1.3% instead of 10%. This example shows that, again, the response saturates as a function of the absorption one wants to measure. 

Mossbauer experiments in the transmission mode (as shown in Fig. 1) usually use recoilless y-rays emitted from a radioactive source followed by resonant recoilless reabsorption by a non-radioactive absorber. If the probability of recoilless emission from a source is/ and the y-photon has width Fj at half-height then the number of transitions N(E) with energies between E -E) and (Ey-E+dE) is given by ... 

Surface Plasmon Resonance Sensors, Hgure 3 (a) Schematic of a typical optical configuration and the fluidic connections empioyed with a transmission mode LSPR device, (b) Schematic and images iiiustrating the architecture of the microfluidic chip with embedded nanohoie arrays at relevant centimeter-, micrometer-, and nanometer-length scales. Figure and caption reprinted from De Leebeeck et al. [8]... 

According to Colomban et al., within the broad band assigned to the hydrogen-bond mode there are several transmission windows, so-called Evans holes [355, 356], These holes are caused by the coupling of a narrow band with a very broad band. Principally, this is a phenomenon similar to the Fermi resonance. The interaction of two or more modes results in new modes and bands of different energies with corresponding transmission modes in the infrared spectrum and emissions in the Raman spectrum, which actually have been observed by Colomban et al. [350]. As a consequence, ex situ spectra have to be checked for unexpected transmissions. In the spectra recorded in situ and shown in Figure 25, band shifts as compared to band positions found in spectra... 

A typical device for accumulating the Mossbauer spectrum is the multichannel analyser, where the count rate is a function of a definite value of the Doppler velocity. The count rate is normalized relative to the off-resonance count rate. Hence, for transmission-mode Mossbauer spectroscopy relative intensities are always less than unity (or 100%). In Mossbauer scattering experiments relative intensities always exceed 100% and can reach several hundred percent in the case of electron detection from samples with a high abundance of the resonant isotope. It is most often that the -y ,ax value corresponds to the first channel and the +y ,ax value to the last channel. The quality of a Mossbauer spectrometer is determined by how accurately the modulation of the y-quanta energy follows the chosen mode of movement. 

Waveguides are coimnonly used to transmit microwaves from the source to the resonator and subsequently to the receiver. For not-too-high-frequency radiation (<10 GHz) low-loss MW transmission can also be achieved usmg strip-lines and coaxial cables. At the output of a klystron an isolator is often used to prevent back-reflected microwaves to perturb the on-resonant klystron mode. An isolator is a microwave-ferrite device that pemiits the transmission of microwaves in one direction and strongly attenuates their propagation in the other direction. The prmciple of this device involves the Faraday effect, that is, the rotation of the polarization... 

In summary, it has been demonstrated that plasmon-mode wavefunctions of gold nanoparticles resonant with the incident light can be visualized by near-field transmission imaging. 

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