The Imaginary Refractive Index

The absorbance spectrum, of a sample with an effective optical path length through the sample, /, and the absorption index, a, are related by 

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Additional functionality that could be incorporated into an instrument is to perform measurements at different wavelengths. The optical size of the particle would thereby change, but the imaginary refractive index would change too, providing access to the imaginary part of the refractive index. 

Like the real refractive index, the imaginary refractive index is also a dimensionless quantity. For pure materials, is given by... 

In order to calculate particle size distributions in the adsorption regime and also to determine the relative effects of wavelength on the extinction cross section and imaginary refractive index of the particles, a series of turbidity meas irements were made on the polystyrene standards using a variable wavelength UV detector. More detailed discussions are presented elsewhere (23) > shown here is a brief summary of some of the major results and conclusions. 

The real part of this nnmber is the normal refractive index n = c/v(c and v being the speed of light in vacnnm and in the medium, respectively). The imaginary part of the complex refractive index, k, is called the extinction coefficient. It is necessary to recall here that both magnitndes, n and k, are dependent on the frequency (wavelength) of the propagating wave co,N = N(co). 

It is known that measnring the absorption coefficient (and thns the extinction coefficient) over the whole freqnency range, 0 < real part of N(co) - that is, the normal refractive index ( >) - can be obtained by nsing the Kramers-Kronig relationships (Fox, 2001). This is an important fact, because it allows us to obtain the frequency dependence of the real and imaginary dielectric constants from an optical absorption experiment. 

Allen et a/. (1991) performed these computations for 1-octadecene droplets, and they measured the evaporation rate of the droplets as a function of laser power. To determine the absolute irradiance /, of the laser beam, they also measured the force on the particle exerted by the laser beam using the techniques discussed above. The photon pressure force is given by Eq. (87), which involves the complex refractive index. The real component of the refractive index n was determined from optical resonance measurements, and the imaginary component was obtained iteratively. That is, they assumed a... 

Table III shows that the experimental and predicted evaporation rates are in good agreement at all beam intensities. There is some inconsistency at the highest power levels. It was difficult to maintain the droplet in the center of the laser beam at the highest power level, and the measured evaporation rate is somewhat low as a result of that problem. Additional computations demonstrate that the predicted evaporation rate is quite sensitive to the choice of the imaginary component of N, so the results suggest that this evaporation method is suitable for the determination of the complex refractive index of weakly absorbing liquids. For strong absorbers, the linearizations of the Clausius-Clapeyron equation and of the radiation energy loss term in the interfacial boundary condition may not be valid. In this event, a numerical solution of the governing equations is required. The structure of the source function, however, makes this a rather tedious task.

The real and imaginary parts of the complex refractive index satisfy Kramers-Kronig relations sometimes this can be used to assess the reliability of measured optical constants. N(oj) satisfies the same crossing condition as X(w) N (u) = N( — u). However, it does not vanish in the limit of indefinitely large frequency lim JV(co) = 1. But this is a small hurdle, which can be surmounted readily enough by minor fiddling with JV(co) the quantity jV(co) — 1 has the desired asymptotic behavior. If we now assume that 7V( ) is analytic in the top half of the complex [Pg.28]

The rate at which electromagnetic energy is removed from the wave as it propagates through the medium is determined by the imaginary part of the complex refractive index. If the irradiances I0 and lt (or rather their ratio) are measured at two different positions z = 0 and z = h, then a, and hence k, can be obtained in principle from the relation... 

There are two sets of quantities that are often used to describe optical properties the real and imaginary parts of the complex refractive index N = n + ik and the real and imaginary parts of the complex dielectric function (or relative permittivity) e = c + ie". These two sets of quantities are not independent either may be thought of as describing the intrinsic optical properties of matter. The relations between the two are, from (2.47) and (2.48),... 

We must reemphasize that the real and imaginary parts of the complex dielectric function (and the complex refractive index) are not independent. Arbitrary choices of c and <" (or n and k) do not necessarily correspond to... 

FIG. 5.14 The real and imaginary parts of the complex refractive index of gold versus wavelength in air and in water. (Data from Van de Hulst 1957.)... 

Looking at the phenomenon of optical absorption by the medium from the viewpoint of classical wave mechanics, we see that the attenuation of electromagnetic radiation can be attributed to the interaction of the oscillating electric vector with the medium. Any phenomenon involving periodic oscillations can be decomposed to real and imaginary components. Thus, the ordinary refractive index n is the real part of the index of refraction n, which can be written as... 

Figure 29. Imaginary (a) and real (b) parts of the complex refraction index at 22.2°C. Ordinary water is represented by solid lines and circles, heavy water is represented by dashed lines and boxes. In the low-frequency region (for v < 20 cm-1), calculation is performed using approximation 17 modified as described in Appendix 3.2 in the rest region, it is performed using the recorded data [51] given in Table XI.

For size quantification of these particle systems, the underlying LII model has to be extended taking into consideration the optical metal particle properties (Vander Wal et al., 1999 Kreibig and Vollmer, 1995) on the one hand side and the contact surface area, on the other hand. The optical metal properties, which are in particular determined by the high imaginary part of the complex refraction index, show low absorption coefficients. 

In optics, the complex refractive index is defined as N = n + ik = ( r(co))l/1, where the real index of refraction, n, and extinction coefficient, k, are related to the real and imaginary parts of the complex dielectric constant by ... 

No external parameter occurs in the two-photon figure of merit T. It is a function of the material only without any possibility to tune the figure of merit by external means. With the nonlinear refractive index n2 and the two-photon absorption coefficient a2 proportional to the real and imaginary part of the complex third-order susceptibility 3 >= 3 > -et<>>< 3 1 the two-photon figure of merit T 1 can be rewritten as a function of the nonlinearity phase (p< VK... 

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