Mode matching

FIGURE 34.2 One-dimensional scheme of the free-energy surfaces of the initial and final states. Medium polarization plays the role of the reactive modes. Matching of the electron energy levels corresponds to crossing of the free-energy snrfaces = 17y(P ). 

Key words eigenmode expansion microresonators mode matching mode solvers optical waveguide theory, photonic crystals, waveguide bends. 

The fact that any field in the multilayer structure can be expressed by a superposition of its eigenmodes will be heavily used later as a basic principle of the film mode matching method. 

Sinee PMLs are lossy, the eigenmodes of multilayers with PML are generally eomplex, so that their effective indexes have to be localized in the eomplex plane. The great advantage of PML s is that they can be very easily ineorporated into the modeling software based on mode matching, and their behavior can be easily understood Irom their interpretation in terms of complex coordinate stretching. 

In this section we will discuss the mode matching method applied to vectorial modeling of straight and bent channel waveguides with 2-D cross-... 

Readers may be interested that 2-D and even 3-D modules based on the mode matching method ean be found in several commercial software... 

A.S. Sudbo, Film mode matching a versatile numerical method for vector mode field calculations in dielectric waveguides, Pwre andAppl. Opt. 2, 211-233 (1993). 

L. Prkna, M. Hubalek and J. Ctyroky, Vectorial eigenmode solver for bent waveguides based on mode matching, IEEE Photonics Technol. Lett. 16, 2057-2059 (2004). 

J. Petracek, Modelling of optical waveguide structures by the mode matching method, Assoc. Prof, thesis, (Bmo Technical University, 2004, in Czech). 

A. S. Sudbo, Improved formulation of the film mode matching method for mode field calculations in dielectric waveguides. Pure and Applied Optics 3, 381-388 (1993). 

In addition to a dominant component of one reactant, each EDM also exhibits the matching component of the other reactant. Therefore, the EDM provide a mode-mode matching between reactants as practically independent, with only a small hardness coupling within each subset, they should be useful in an interpretation of the overall B -> A CT providing the mode-to-mode perspective on the accompanying charge reorganization in the reactants. 

The absolute frequency position of the two-photon transition is measured by comparing the infrared dye laser wavelength with an I - stabilized He-Ne reference laser at 633 nm (see Fig.2). The hey of the wavelength comparison is a nonconfocal etalon Fabry-Perot cavity (indicated as FPE in Fig.2) kept under a vacuum better than 10-6 mbar. This optical cavity is built with two silver-coated mirrors, one flat and the other spherical (R = 60 cm), in optical adhesion to a zerodur rod. Its finesse is 60 at 633 nm and 100 at 778 nm. An auxiliary He-Ne laser as well as the dye laser are mode-matched and locked to this Fabry-Perot cavity. Simultaneously the beat frequency between the auxiliary and etalon He-Ne lasers is measured by a frequency counter. 

These features are exploited in an experiment which is taking place in our laboratory. A schematic diagram of this experiment is shown in figure 4. The system consists of an all-lines violet mode-locked Kr+ ion laser operating at a repetition rate of about 250 MHz Which synchronously pumps a C102 dye laser. The dye laser typically produces about 300 mW of average power and pulse durations of about 3 psec. This is frequency doubled to 243 nm in a crystal of p-barium borate to produce in excess of 2 mW average power. The output from the second harmonic crystal is then mode-matched into an ultra-violet enhancement cavity. The free... 

It is important to point out that even at 77 = 0 the observed value V = 0.942 0.006 is far from its ideal value of V = 0. One important source of error is the finite retrieval efficiency, which is limited by two factors. Due to the atomic memory decoherence rate 7C, the finite retrieval time Tr always results in a finite loss probability p 7c Tr. For the correlation measurements we use a relatively weak retrieve laser ( 2 mW) to reduce the number of background photons and to avoid APD dead-time effects. The resulting anti-Stokes pulse width is on the order of the measured decoherence time, so the atomic excitation decays before it is fully retrieved. Moreover, even as 7C —> 0 the retrieval efficiency is limited by the finite optical depth q of the ensemble, which yields an error scaling as p 1/ y/rj. The measured maximum retrieval efficiency at 77 = 0 corresponds to about 0.3. In addition to finite retrieval efficiency, many other factors reduce correlations, including losses in the detection system, background photons, APD afterpulsing effects, and imperfect spatial mode-matching. 

This longest bending mode matches the shortest relaxation time in the Rouse and Zimm models [the relaxation time of a monomer ro, Eq. (8.15)],... 

When thermal mode matches the temperature drop in range of Ar in <... 

Recently, methods have been proposed for solving this model updating problem which avoid mode matching [18,51,52,267]. This is accomplished by employing the concept of system mode shapes that are used to represent the actual mode shapes of the structural system at all degrees of freedom corresponding to those of the dynamical model, but they are distinct from the... 

In this chapter, a Bayesian model updating method using incomplete modal data is presented with applications to structural health monitoring. As reported in the literature [18,51,52,267], the realistic assumption is made that only the modal frequencies and partial mode shapes of some modes are measured system mode shapes are also introduced, which avoid mode matching between the measured modes and those of the dynamical model. The novel feature... 

Fig. 1.3 Spectroscopy in an external enhancement cavity with mode-matching optics...

This sensitivity enhancement in detecting small absorptions has no direct correlation with the gain medium and can be also realized in external passive resonators. If the laser output is mode matched (Vol. 1, Sect. 5.2.3) by lenses or mirrors into the fundamental mode of the passive cavity containing the absorbing sample (Fig. 1.11), the radiation power inside this cavity is q times larger. The enhancement factor q may become larger if the internal losses of the cavity can be kept low. 

If the reflectivity is very high, diffraction losses may become dominant, in particular for cavities with a large separation d of the mirrors. Since the TEMqo mode has the lowest diffraction losses, the incoming laser beam has to be mode-matched by a lens system to excite the fundamental mode of the resonator but not the higher transverse modes. Similar to intracavity absorption, this technique takes advantage of the increased effective absorption length Leff = LUX — R), because the laser pulse traverses the absorbing sample 1/(1 - R) times. 

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