Abstract:
A stepped etalon having a top surface and two bottom surfaces that are parallel to the top surface and are each positioned at different distances from the top surface. Each bottom surface has an edge, wherein the edges face one another and a sloping step is positioned between the two edges so that rays from a beam of light projected onto the top surface of the etalon strike the step at the Brewster angle and pass through the etalon without any light being reflected back therein.

Description:
FIELD OF THE INVENTION  
   The present invention relates to etalons, and more particularly to an improvement in the design of a stepped Fabry-Perot etalon that eliminates reflection. 
   BACKGROUND OF THE INVENTION  
   Stepped Fabry-Perot etalons are typically comprised of a body of transparent material having a top planar surface and two bottom planar surfaces that are parallel to the top surface but are positioned at different distances from the top surface so that there is a step between the two bottom surfaces. The bottom surface that is closer to the top surface is commonly referred to as the thin side and the bottom surface that is farther from the top surface is commonly referred to as the thick side. In determining the frequency of a beam of light projected onto the top surface, use is made of the transmittance functions of the top and bottom surfaces of the etalon. 
   In conventional etalons, the step between the two bottom surfaces is perpendicular to the surfaces, and reflections from the step back into the etalon are at a different angle than that of the original beam of light. Since the transmittance function of the etalon depends on the angle at which light impinges on the top and bottom surfaces of the etalon, the transmittance function for the original beam of light and the transmittance function for the light reflected from the step are different. Thus, the overall transmittance function is defined by the uncontrolled interference of the original and reflected light. The etalon characteristic of the stepped etalon becomes irregular. This effect occurs in the proximity of the step so as to make the area near the step unusable. This is an obstacle to the miniaturization of the etalon. 
   In an attempt to reduce this deleterious effect, random features have been formed on the step to scatter the light. Doing so helps to a degree because the more light scattered, the less light is reflected, but it does not solve the problem completely. 
   SUMMARY  
   In accordance with the present invention, reflections from the step of a Fabry-Perot stepped etalon are eliminated by forming the step at an angle with respect to the top and bottom surfaces such that light from the original beam passes through the step rather than being reflected back. The step is formed at an angle so that a beam of light strikes the step at the Brewster angle. To avoid any reflection, the light beam must be linearly polarized and collimated and the electric component vector of the light beam must be in the plane of incidence. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  shows a cross sectional view of a conventional etalon having a vertical step. 
       FIG. 2  shows a graph of the transmittance of light plotted as a function of the frequency of light in TerraHertz (THz) for both the thick and thin sides of the etalon shown in  FIG. 1 . 
       FIG. 3  shows a cross-sectional view of an exemplary embodiment of an etalon fabricated according to the present invention. 
       FIG. 4  shows a perspective view of the etalon shown in  FIG. 3 . 
       FIG. 5  shows a graph of the transmittance of light plotted as a function of the frequency of light in TerraHertz (THz) for both the thick and thin sides of the etalon fabricated according to the present invention and shown in  FIGS. 3 and 4 . 
   

   DETAILED DESCRIPTION OF THE INVENTION  
     FIG. 1  shows a cross sectional view of a conventional etalon  10 . Since the present invention incorporates elements in etalon  10 , a detailed review of its operation will aid in understanding the teachings of the present invention. Etalon  10  is comprised of a top surface  12 , a first bottom surface  14 , the thick side, and a second bottom surface  16 , the thin side. Top surface  12  and first and second bottom surfaces  14  and  16  are all parallel to one another. First bottom surface  14  is positioned at a distance t 1 , herein shown by way of example to be 1.0 millimeter (mm) from top surface  12 , and second bottom surface  16  is positioned at a distance t 2 , herein shown by way of example to be 0.999910 mm from top surface  12 . First and second bottom surfaces  14  and  16  each have an edge  18  and  20 , respectively, that face one another. A step  22  lies between edges  18  and  20  and is perpendicular to both of them. Etalon  10  may be fabricated from glass, silicon or any other optical material. 
   A line  24  represents the path of the central ray of a beam of collimated linearly polarized light that is projected onto top surface  12  at an angle of incidence of θ with respect to a line  26  that is perpendicular to top surface  12 . As a result of the difference in the speed of light in air outside of etalon  10  and the speed of light in etalon  10 , the beam of light represented by line  24  is refracted so that it enters etalon  10  at an angle θ′. The beam of light then proceeds along a path  28  so as to strike step  22  at an angle of incidence i with respect to a line  30  that is perpendicular to step  22 , and is then totally reflected at an angle of reflection r=i along path  32 . 
   The beam of light is reflected from first bottom surface  14  along path  34  to top surface  12  so as to be reflected back and forth between top surface  12  and first bottom surface  14  as indicated by paths  36 ,  38  and  40 . Other rays in the beam of light also strike step  22  and are reflected in a manner corresponding to that of the central ray just described. As a result of the reflections from step  22 , light striking the bottom surfaces  14  or  16  within a region defined by the lines  42  and  44 , herein shown by way of example to be 0.8 mm apart, introduces loss into the overall transmittance function of etalon  10 . 
     FIG. 2  shows a graph of the transmittance function of light plotted as a function of the frequency of light in THz for both first bottom surface  14  and second bottom surface  16  of etalon  10 , wherein the transmittance function is represented by a scale of numbers from 0.0, denoting no transmittance of light through etalon  10 , to 1.0, representing 100% transmittance of light through etalon  10 . Curve  46  represents the transmittance function of first bottom surface  14 , the thick side of etalon  10 , and curve  48  represents the transmittance function of second bottom surface  16 , the thin side, of etalon  10 . 
     FIG. 3  shows a cross sectional view of an exemplary embodiment of an etalon  50  fabricated according to the present invention. Etalon  50  is comprised of a top surface  52 , a first bottom surface  54 , the thick side, and a second bottom surface  56 , the thin side. Top surface  52  and first and second bottom surfaces  54  and  56  are all parallel to one another. First bottom surface  54  is positioned at a distance t 1 , herein shown by way of example to be 1.0 mm, from top surface  52 , and second bottom surface  56  is positioned at a distance t 2 , herein shown by way of example to be 0.999910 mm, from top surface  52 . First and second bottom surfaces  54  and  56  each have an edge  58  and  60 , respectively, that face one another. In accordance with the present invention, a sloping step  62  is positioned between edges  58  and  60  so as to be at an angle other than 90° with respect to first and second bottom surfaces  54  and  56 . 
   A line  64  represents the path of the central ray of a beam of collimated linearly polarized light that is projected onto top surface  52  at an angle of incidence θ with respect to a line  66  that is perpendicular to top surface  52 . The beam of light represented by line  64  is refracted and enters etalon  50  at an angle θ′ and then proceeds along a path  68  so as to strike sloping step  62  at an angle of incidence i′ that is approximately equal to the Brewster angle with respect to a line  70  that is perpendicular to sloping step  62 . The central ray of the beam of light then passes through sloping step  62  along a path  72 . 
   Since the beam of light is collimated, all rays of light striking sloping step  62  will also pass through step  62  and will not be reflected back into etalon  50 . The useless region of etalon  50  where reflections occur is positioned between lines  74  and  76 , and given the particular dimensions of etalon  50 , is approximately 300 nanometer (nm). Thus, the useless region of etalon  50  is 2600 times smaller than the useless region of conventional etalon  10  shown in  FIG. 1  and described above. 
   The electric component vector of the collimated and linearly polarized beam of light represented by line  64  must be in the plane of incidence because only for such an orientation of the electric component vector will there no reflection at the Brewster angle of light back into etalon  50 . Accordingly, an etalon designed according to the present invention can be fabricated to be smaller than conventional etalons. 
     FIG. 4  shows a perspective view of etalon  50  shown in  FIG. 3 . Elements corresponding to those shown in  FIG. 5  are numbered the same. As shown in  FIG. 4 , etalon  50  includes sides  78 ,  80 ,  82  and  84 , and ends  86  and  88 . Sides  78 ,  80 ,  82  and  84  are all coplanar. 
   Any suitable directing means, e.g.,  90 , can be used to project a linearly polarized beam of light within the dashed lines  92 ,  94 ,  96  and  98  onto top surface  52  with an angle of incidence of θ, wherein the electric component vector of the beam of light is in the plane of incidence. Although it is preferable to fabricate etalon  50  in the form of a solid block of material such as glass or silicon, it is possible to substitute air for certain sections of the material in which case top surface  52  and first and second bottom surfaces  54  and  56  would be mirrors that may be kept in position by attachment to suitable spacers  100  and  102 . 
     FIG. 5  shows a graph of the transmittance function of light plotted as a function of the frequency of light in THz for both first bottom surface  54  and second bottom surface  56  of etalon  50 . Curve  104  represents the transmittance function of first bottom surface  54 , the thick side of etalon  50 , and curve  106  represents the transmittance function of second bottom surface  56 , the thin side, of etalon  50 . 
   Numerous modifications to and alternative embodiments of the present invention will be apparent to those skilled in the art in view of the foregoing description. Accordingly, this description is to be construed as illustrative only and is for the purpose of teaching those skilled in the art the best mode of carrying out the invention. Details of the embodiment may be varied without departing from the spirit of the invention, and the exclusive use of all modifications which come within the scope of the appended claims is reserved.