Guided mode

An essentially identical situation exists for the multiple reflection in optical fibers. In this case, the boundary conditions for the multiple reflections and the considerations governing the existence and number of guided modes are formulated in cylindrical coordinates. For a noncoherent source, the light propagated by a fiber again appears as a continuum of intensity. The number of modes M in the fiber of radius r (both r and X are in pm) is characterized by the V-number, which is a practical figure of merit for the fiber. 

For a fiber in which the interface forms a sharp step between the media of refractive indices m and m, the number of supported modes is M = V2/2. For fibers with a Graduated Refractive INdex (GRIN) it is M V2/4 (Fig. 9.13). Thus, for a step cylindrical fiber 

a 1pm diameter fiber would support one mode of green (X = 500 nm) light. Obviously, optical throughput (energy) of such a fiber is very low. A typical fiber of d 10pm supports thousands of modes. 

Flat optical waveguides offer the possibility of increasing the optical throughput but maintaining the monomode internal reflection. This is achieved in the 

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Figure 10-11. The sample is a 290 nm thin film of LPPP deposited on a BK7 substrate. A planar waveguide glass/polymer/air is formed since the polymer film has the highest index of refraction. The resulting intensity profile of the guided TE waveguide mode for the sample is shown on the right hand side. Only one guided mode is supported.

Figure 7. Concept of optical sensor based on spectroscopy of guided modes. A change in the refractive index alters propagation constant of a guided mode.

Main types of biomolecular recognition elements used in affinity biosensors based on spectroscopy of guided modes include antibodies, nucleic acids and biomimetic materials. Antibodies are used most frequently because of their high affinity, versatility, and commercial availability. 

Affinity biosensors based on spectroscopy of guided modes have been used for detection of small analytes such as pesticides and herbicides... 

Representatives of medium-size analytes detected by affinity biosensors based on spectroscopy of guided modes include food-safety related analytes such as staphylococcal enterotoxin B , botulinum toxin, and E. coli... 

Of course in defining application fields of certain types of 10 sensors they have to be compared with competitors in the terms of the market. Strong points of optical sensors are no EMI, potential of high sensitivity and spectral discrimination. The guided mode character adds to these no need of... 

The mechanism that induces such a change in the resonance wavelength behavior is the transition of the lowest order cladding mode into an overlay guided mode and the consequent mode redistribution. Here, the attention is focused on the analysis of the transition curves to determine the novel sensitivity characteristics of HRI-coated LPGs and to outline the dominant role of the overlay thickness and the mode order. 

Therefore Z)opt provides a convenient single parameter that can be used to estimate the response of guided modes to very thin adsorbed layers. To assess and compare surface sensitivity, in this chapter, we will use the differential change of mode effective index with the optical thickness ... 

Unlike the dependence of Aeff on film thickness alone (dNc /dd) that is sometimes used as a figure of merit for guided mode molecular sensors, 5m0d captures both the index and thickness dependence of the sensor response in a single parameter. While Dopt does not uniquely determine the film response for other optical techniques such as ellipsometry and reflectance difference, once d and n of the film are known, the optical thickness can be evaluated and comparisons are made between guided mode sensors and other techniques. 

Guided mode calculations were also carried out to compare the sensor response of several waveguide systems. In these simulations a model molecular monolayer is represented by a 2-nm thick layer with a refractive index of n 1.5. The optical properties of this model layer are typical of a dense layer of organic molecules on a substrate1 41, and are a reasonable approximation for a streptavidin protein layer bound to a biotinylated surface, the experimental model system we use to characterize our sensors. The ambient upper cladding was assumed to be water with a refractive index of n 1.32. For all examples, the lower cladding was assumed to be Si02 with an index of n 1.44. In the simulations, the effective index of... 

Fig. 10.1 Binding event between analyte and receptor molecules occurring at the core cover interface of a three layer waveguide structure within the evanescent region of a guided mode. NeS indicates the effective refractive index of the fundamental guided mode...

Under conditions of total internal reflection, guided modes are obtained due to the constructive interference between the light rays propagating through the waveguide30... 

In order to achieve guiding in the deposited polyelectrolyte adlayer, the effective refractive index of the guided mode N must be lower than the RI of the adlayer, A. 

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