TE modes

The propagation of the ie TE mode, the TEj -mode through a slabguide can be described mathematically by the equation ... 

Figure 6. Reflectivity vs. incident angle 6 at wavelength 7500 A for TEpolarized light. Two TE modes (n - I and 2) were observed, as designated.

For a given m, there are a series of ko satisfying (8.7), which are referred to as the vth (v = 1,2,3,...) order resonant mode. The radial and tangential components of the electric field for TE modes can be obtained with ... 

Using the Mie scattering method, the resonant wavelength shift due to the adsorbed lipid membrane onto the tube wall is simulated with the microtube dimensions identical to the previous simulations. The refractive index of lipid bilayer is assumed to be 1.46. When the inner surface of a tube is coated with lipid membrane, the magnetic field for TE mode can be described in the following form ... 

Fig. 9.4 The calculated TM and TE modes for X 1550 nm light propagating in the 220 nm x 450 nm photonic wire waveguide shown in Fig.9.3. The mode electric field profiles are shown as line plots along the center axis of the waveguide (indicated by the dashed lines), as well as in full cross section by gray scale contour plots...

Calculations for TE polarized light give similar results42, but the maximum induced 8/Vell in the PWEF waveguide is about three times smaller than for the TM mode. This difference is largely due to the absence of the surface field enhancement factor of (9.5), since the electric field of the TE mode is parallel to the waveguide surface and hence there is no electric field discontinuity. 

Fig. 9.8 Cross section of a silicon slot waveguide consisting of two 180 nm x 250 nm silicon channels, separated by a 50 nm gap. The solid line represents a line plot of the electric field amplitude of the horizontally polarized TE mode, taken along the horizontal midline of the waveguide...

Fig. 16.2 Nanoscale optofluidic sensor arrays (NOSA). (a) 3D illustration of a NOSA sensing element. It consists of a ID photonic crystal microcavity, which is evanescently coupled to a Si waveguide, (b) The electric field profile for the fundamental TE mode propagating through an air clad Si waveguide on SiOi. (c) SEM of a NOSA device array. It illustrates how this architecture is capable of two dimensional multiplexing, thus affording a large degree of parallelism, (d) Actual NOSA chip with an aligned PDMS fluidic layer on top. Reprinted from Ref. 37 with permission. 2008 Optical Society of America...

It should be possible in principle to determine the orientation of chromophores in a single monolayer on an OWG by the absorption of transverse electric (TE, s-polarized) and transverse magnetic (TM, p-polarized) modes laser. Swalen et al. [109] reported that much stronger absorption was observed for a thin evaporated film of 4-dimethylamino-4 -nitrostilbene with the TM mode and for seven monolayers of cyanine dyes with the TE mode. These results corresponded... 

The pyrazine LB films was expected to show uniaxial birefringence because the LB film possess uniaxial molecular orientation. Accordingly, the refractive index in the film plane no and film thickness W was determined by the analysis of TE modes. Then, the refractive index perpendicular to the film plane ne was obtained form the analysis of the TM modes. 

Figure 3.22. Optical mode intensity profile for the first two TE modes of the film in Figure 3.6 at a film thickness of 250 nm. 

The term immittanee is used for the sake of generality for TE modes, the physical meaning of the matrix U is namely the transversal admittance (it mutually relates the field components and ) while for TM modes it is impedanee (the field components and Ely are related). It ean be derived from Eq. (13) by algebraic manipulations that upon translation from C to C + AC, the immittance matrix is transformed as follows ... 

INFICON has developed a new technology for overcoming these constraints on the active oscillator. The new system constantly analyzes Ihe response of the crystal fo an applied frequency not only fo determine the (series) resonance frequency, but also fo ensure that the quartz oscillates in the desired mode. The new system is insensitive te mode hopping and the resultant inaccuracy. It is fast and precise. The crystal frequency is determined 10 times a second w/ith an accuracy to less than 0.0005 Hz. 

Figure 6. The guided mode dispersion curves for a birefringent film and an optically isotropic substrate. Both the fundamental and harmonic curves are shown. The TE mode utilizes the ordinary refractive index and TM primarily the extraordinary index. Note the change in horizontal axis needed to plot both the fundamental and harmonic dispersion curves. Phase-matching of the TEq(co) to the TMo(2o>) is obtained at the intersection of the appropriate fundamental and harmonic curves.

In Fig. 18b the center of mass of the peaks are monitored versus time. It is seen that the rates of change in peak position are not identical for the TE and TM modes. This may be due to the higher cover index sensitivity of the TM mode (approximately a factor of 2 larger than for the TE mode), but also the fact that the probing depths are different for the two modes (approxi-... 

In anisotropic materials, the electronic bonds may have different polarizabilities for different directions (you may think of different, orientation-dependent spring constants for the electronic harmonic oscillator). Remembering that only the E-vector of the light interacts with the electrons, we may use polarized light to test the polarizability of the material in different directions, lno is one of the most important electro-optic materials and we use it as an example. The common notations are shown in Figure 4.7. If the E-vector is in plane with the surface of the crystal, the wave is called a te wave. In this example, the te wave would experience the ordinary index na of LiNbOs (nG 2.20). If we rotate the polarization by 90°, the E-ve ctor will be vertical to the surface and the wave is called tm. In lno, it will experience the extraordinary index ne 2.29. Therefore these two differently polarized waves will propagate with different phase velocities v c/n. In the example of Figure 4.7, the te mode is faster than the tm mode. 

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