Free Trial

Safari Books Online is a digital library providing on-demand subscription access to thousands of learning resources.

  • Create BookmarkCreate Bookmark
  • Create Note or TagCreate Note or Tag
  • PrintPrint

G.2 Filter Design

Although the power transfer function of any given stack of dielectrics can be determined using the preceding procedure, designing a filter of this type to meet a given filter requirement is a more typical problem encountered in practice. The multiple dielectric slab structure exemplified by Figure G.1(c) is quite versatile, and a number of well-known filter transfer functions, such as the Butterworth and the Chebyshev, may be synthesized using it [Kni76]. However, the synthesis of these filters calls for a variety of dielectric materials with different refractive indices. This may be a difficult requirement to meet in practice.

It turns out, however, that very useful filter transfer functions can be synthesized using just two different dielectric materials, a low-index dielectric with refractive index nL and a high-index dielectric with refractive index nH [Kni76]. Assume we want to synthesize a bandpass filter with center wavelength λ0. Then, a general structure for doing this is to use alternate layers of high-index and low-index dielectrics with thicknesses equivalent to a quarter or a half wavelength at λ0. (A quarter-wavelength slab of the dielectric with refractive index nL would have a thickness λ0/4nL.) Since these thicknesses at optical wavelengths are quite small, the term thin film is more appropriately used instead of slab. The dielectric thin films that are a half-wavelength thick at λ0 are called the cavities of the filter. A particularly useful filter structure consists of a few cavities separated by several quarter-wavelength films. If H and L denote quarter-wavelength films (at λ0) of the high- and low-index dielectrics, respectively, then we can represent any such filter by a sequence of Hs and Ls. Two Ls or two Hs in succession would represent a half-wavelength film. For example, if the lightly shaded dielectrics are of low index and the darker shaded are of high index, the filter consisting of the multiple dielectric films 2-8 shown in Figure G.1(c) can be represented by the sequence HLHLLHLH. If the surrounding dielectrics, 1 and 9, are denoted by G (for glass), the entire structure in Figure G.1(c) can be represented by the sequence GHLHLLHLHG. If we know the refractive indices nG, nL, and nH of the G, L, and H dielectrics, respectively, the transfer function of the filter can be calculated using the procedure outlined. For nG = 1.52, a typical value for the cover glass, nL = 1.46, which is the refractive index of SiO2 (a low-index dielectric), and nH = 2.3, which is the refractive index of TiO2 (a high-index dielectric), this transfer function is plotted in Figure G.3. From this figure, we see that the main lobe is quite wide compared to the center wavelength, and the side lobe suppression is less than 10 dB. Clearly, a better transfer function is needed if the filter is to be useful.


  

You are currently reading a PREVIEW of this book.

                                                                                                                    

Get instant access to over $1 million worth of books and videos.

  

Start a Free 10-Day Trial


  
  • Safari Books Online
  • Create BookmarkCreate Bookmark
  • Create Note or TagCreate Note or Tag
  • PrintPrint