Leaky modes

24-3 Leaky modes and space-wave representation of radiation 

Characteristics of leaky modes 24-4 Modal parameters 24-5 Modal fields 24-6 Radiation caustic 24-7 Classification of leaky modes 24-8 Plane-wave decomposition 24-9 Weakly guiding waveguides 24-10 Number of leaky modes 

24-11 Intuitive physical description 24-12 Guided and radiated power 24-13 Fraction of guided power in the core 24-14 Power attenuation coefficient 

24-18 Example Analytical solution for the step-profile fiber 24-19 Example Numerical solution for the step-profile fiber 24-20 Example Step-profile planar waveguide 

We shall mainly be concerned with fibers that propagate only one or a few modes. The spatial transient of multimode fibers was examined in Chapter 8, using the leaky rays of Chapter 7. We recall from Eq. (8-1) that the duration of the spatial transient along the fiber increases exponentially with the fiber parameter V. For example, a step-profile fiber with F = 50 and 6 = (2A) 

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B. MacChesney, D. W. Johnson, P.. Lemaire, L. G. Cohen, and E. M. Rabinovich, "FluorosUicate Substrate Tubes to Eliminate Leaky-Mode Losses in MCVD Single-Mode Fibers with Depressed Index Cladding," paper no. WH2 in Technica/ Digest of Optica/ Fiber Communications Conference, San Diego, Ca/if, Optical Society of America, Washington, D.C., 1985. 

The sensor systems outlined in the present chapter use evanescent electromagnetic radiation to monitor various analytes in aqueous solutions. Therefore, as a beginning, the basic properties of evanescent electromagnetic waves and the so-called TIR phenomena are summarized. Afterwards, two types of waveguide modes will be briefly discussed guided and leaky modes, which both generate evanescent waves at a solid/liquid boundary. 

As mentioned in Sect. 15.2, sometimes a 4th thin layer (M) of metal or die is incorporated between the substrate and waveguide film to decrease the radiation loss into the substrate of the substrate radiation modes. These modes are referred to as leaky modes and the obtained structure is the MCLW. This configuration is also broadly used in evanescent wave sensor systems. 

In actual arrangements typically the reflected light intensity is measured while the incident light angle is varied, resulting in peaks or dips in the reflected light intensity19-21 23-25. These peaks and dips can be connected to the leaky modes... 

A substantial linewidth broadening of the adlayer modes in the whole region near T where they overlap the bulk phonon bands of the substrate the excited adlayer modes may decay by emitting phonons into the substrate they become leaky modes. These anomalies were expected to extend up to trilayers even if more pronounced for bi- and in particular for monolayers. 

Case 3 Operations on the partial leaky mode principles ( ci < mci < co)... 

Fig. 5 Leaky modes of a liquid filled capillary with < 2...

While this longitudinal loss is detrimental for communications or applications involving transport of energy over long distances, this property is potentially very beneficial for sensors utilizing capillaries. Most of the leaky modes will directly excite molecules immobilized on the inner surface of the capillary. The effective attenuation for each of the leaky modes is found to be inversely proportional to the diameter of the capillary and exhibits unacceptable values for all modes with the exception of a few lower order modes, corresponding to almost normal incidence at the proximal end of the capillary, i.e., Oq < 5", ... 

The power attenuation coefficient (2oc) for lower order leaky modes is given by [4] thus. 

The fractional power in the cladding increases with mode number and capillary length. Thus, for sensor application, excitation of higher-order leaky modes leads to direct illumination of the immobilized fluorophores on the surface. 

The products of hybridization are detected through the use of fluorescent labeling. These molecular complexes can either be homogeneously distributed in the liquid core or be bound to the interior surface of the capillary through covalent bonding. In both cases, labeled molecules can be excited either by direct illumination with the leaky modes of the liquid filled core, or by the evanescent waves arising from the guided modes of the capillary wall. Direct excitation is less wasteful of incident photon flux and is the method of choice in conventional fluorometers. Evanescent wave excitation becomes a necessity when direct excitation is either not feasible or results in undesirable sensor performance. Both methods of illumination are possible for the CWBP. 

Fig. 8 Excitation geometry for direct illumination of surface bound molecules. Image on the left shows the modified fiber optic cormector with a fluid port and adjacent optical fiber. Measured nearfield intensity distribution of the distal end confirms propagations of leaky modes...

As discussed in Sect. 2.3, capillary selection may be undertaken by independent consideration of the excitation and emission geometries. Larger ID capillaries are preferred for direct excitation of leaky modes. Capillaries with thinner walls, i.e.. 

D. Smalley, Q. Smithwick, V. Bove, et al.. Anisotropic leaky-mode modulator for holographic video displays. Nature 498, 7454 (2013). 

Luterova K, Skopalova E, Pelant I, Rejman M, Ostatnicky T, Valenta J (2006) Active planar optical waveguides with silicon nanocrystals leaky modes under different ambient conditions. J Appl Phys 100 074307... 

Fig. 5—Prism coupler for exciting (a) guided or (b) leaky modes in liquid-crystal (LC) layers.

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