Reflection wavelength

An important point is that and F2 lie on a circle, the focal circle/ of radius R/2. Foci for other reflected wavelengths will lie on the same circle, as can be shown graphically. Another important point is that the virtual sources of Ai, X2 and of other reflected wavelengths (the S s in the figure) also lie on the same circle. 

In the thermochromic liquid crystal (TLC) the dominant reflected wavelength is temperature-dependent and it has been employed for full-field mapping of temperature fields for over three decades. Although it is non-intrusive and cost effective, there are some problems in applying it to micro-scale measurements, because of size (typically tens of micrometers) and time response (from a few milliseconds to several hundred milliseconds depending on the material and the form). Examples of application are micro-fabricated systems (Chaudhari et al. 1998 Liu et al. 2002) and electronic components (Azar et al. 1991). 

Dichroic mirror (or so called chromatic beam-splitter) reflects wavelengths of light below the transition wavelength value and transmits wavelengths above this value. 

The CD reflection spectra are quite sharp at all temperatures, and the reflection wavelength, corresponding to the optical pitch of the TChLC phase, increased progressively with temperature from 500 nm at 70 °C to 1,000 nm at 140 °C. It was considered that the positive sign of the CD reflection band indicated M screw sense helicity of the cholesteric phase. Very recently, a smectic A-cholesteric phase transition was also observed for PDMBS.348... 

Fig. 14. Preliminary infrared absorption spectra of the metal-molecule stretch mode for C Oand C Ointhec(4 x 2) structure on Pt(l 11) at 100 K recorded by a reflection wavelength modulation spectrometer. The recorded first derivative spectrum has been numerically integrated. Both spectra are reproduced in the figure.

Fig. 4 Selective reflection wavelength (optical pitch) as a function of temperature for three samples host material showing SmC and SmCA without dopant, with 1% and 3% dopant The chemical structures of the rod-shaped host and the bent-shaped dopant molecules are also shown. As shown in inset, inverse pitch increases almost linearly with dopant content [4]...

The complementary color particles will absorb some of the same wavelengths as the original color reflected thereby decreasing the number of originally reflected wavelengths and thus the color intensity. 

SRU Biosystems (Woburn, MA) applied the principle of the colorimetric resonant grating reflection in the so-called BIND (Biomolecular Interaction Detection) system that allows parallel readout in 96- and 384-well microplate format (http //www.srubiosystems.com). A grating with a period shorter than the reflected wavelength range (550 nm) and a depth in the range of 170 nm is structured by... 

Thus, LC siloxanes with reflection wavelengths in the UV, in the visible, and IR regions can be obtained by variation of the concentration of the chiral compound. Additionally, structural properties like the ring size influence the wavelength of reflection. 

By substituting the cholesterol moiety by dihydrocholesterol, the range of reflection wavelengths can be extended to the IR. Right handed materials were obtained by using doristerol derivatives instead of cholesterol compounds [16]. 

Fig. 13. Influence of curing temperature on A,- The reflection wavelength of the cured material was measmed at 20°C. A linear relationship holds for the examined temperature range 65-85 C with a gradient of about -2 nm/K. The open symbols show X before crosslinking.

Fig. 14. Temperature dependence of the reflection wavelength for cured layers of LC siloxanes. The slope of the linear behavior correlates well with that determined from thermal expansion. For comparison the temperature dependence before curing is also shown for a red reflecting LC siloxane.

Lyotropic liquid crystalline cellulose derivatives exhibit unique optical properties because of their helicoidal supramolecular structure.The chiro-optical properties of the helicoidal structure can be described by a pitch p (or its inverse, the twist p ) p = 2o/fi, where is the reflection wavelength and h is the mean refractive index of a sheet, and the corresponding handedness of the twist right-handed helicoidal structure being assigned to a positive pitch p > 0) and left-handed helicoidal structures to a negative pitch p < The nematic mesophase can be... 

Cowie, J.M.G. Rodden, G.I. Blending as a method of tuning reflection wavelength and helical twisting sense in films and composites of liquid crystalline cellulose derivatives. Polymer 2002, 43 (12), 3415-3419. 

While the above process is irreversible, trans - cis conversion of azobenzene in the mixtures of cholesteryl chloride and its nonanoate causes reversible shift of the cholesteric reflection wavelength (21). When azobenzene is chemically bonded to cholesteryl moiety, the same phenomenon was observed (22). 

The reflective wavelength of cholesteric liquid crystals varies according to temperature. Such an effect has been made useful in thermography. It has been applied in the diagnosis of cancers by displaying the skin temperature distribution. It has also been applied to test faults in integrated circuits. The applications also include thermometers and temperature warning indicators and non-destructive detection. 

For L=0.6m and R=1800 m, 6y=25 m. The natural deflection of such a segment of, say, 3-4 cm thickness is 5,wm. Even with such a small deflection as 25/tm, an accurately curved surface can still be achieved over the full length of the mirror. Accurate focussing in this way becomes more difficult at shorter wavelengths if we wish to reflect wavelengths greater than, say, 0.5 A, then, for platinum, 0C=3 mrad, R is then 3600 m and <3V is only 19,um (for a segment of 0.75m and p=llm). 

At the selective reflection wavelength, a component of linearly polarized light, e.g., right-handed or left-handed circularly polarized light, is totally reflected without a phase reversal by a twisted helicoidal structure at a wavelength correlated to the pitch P. An oblique incident of light is presumed onto the substrate plane or nematic sheet (see Fig. 3)... 

Figure 3. Schematic representation of the cholesteric liquid-crystalline structure of cellulosics P=Xjn where P represents the pitch, A the reflection wavelength, and n the mean refractive index of a sheet. P>0 for a right-handed twist, and P<0 for a left-handed twist.

Equations (1) and (2) contain the pitch P besides experimentally available quantities, i.e., the selective reflection wavelength A , the optical rotation 0, and the refractive indices Mo and of a nematic sheet. The usually determined cholesteric birefringence can be converted to the nematic one by A nem= 2Awci,. By fitting Eq. (2) to the actual measured data, the pitch is obtained and the validity of Eq. (2) tested. In the limit of A Eq. (2) leads to... 

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