Abstract:
A method and apparatus for rotating through a selected angle the polarization vector of a substantially linearly polarized electromagnetic beam by using three or four reflections with the output electromagnetic beam being substantially free of ellipticity. By selecting the second and third angles of incidence such that the ellipticity introduced by the second reflection is cancelled by the third reflection and the first and fourth angles of incidence which introduce substantially no ellipticity, the polarization vector of the incident electromagnetic beam need not be restricted to being parallel or perpendicular to the incident plane.

Description:
BACKGROUND OF THE INVENTION 
     A polarization rotator is a device that rotates the polarization vector (E-vector) of an electromagnetic wave through a selected angle. The rotation of the E-vector, usually by 90°, is a frequent requirement in numerous applications, especially those using a laser. 
     In the visible region of the spectrum, retardation plates are often used to produce the desired rotation. However, in the infrared portion of the spectrum, retardation plates are of limited value since the known birefringent materials having a high threshold for laser damage are not easily obtainable. Moreover, retardation plates produce the desired rotation only at a single wavelength. 
     To overcome the problems inherent in retardation plates in the infrared range, the seven and five reflection polarization rotators of the prior art were developed. The seven reflection polarization rotator was introduced by F. Keilmann in an article in Optics Communications, Vol. 14, p. 236 (1974) entitled How To Flip The Polarization Of Infrared Laser Beams, and the five reflection polarization flipper was introduced by A. R. Chraplyvy in an article in Applied Optics, Vol. 15, p. 2022 (1976) entitled Polarization Flipper For Infrared Laser Beams. 
     Each of the polarization rotators of the prior art requires that the E-vector of the electromagnetic wave remain either perpendicular or parallel to the plane defined by the incident and reflected electromagnetic waves to and from that surface. The seven reflection polarization rotator of the prior art also limits every reflection angle to 45°. 
     These limitations on the prior art polarization rotators have been selected to prevent the introduction of ellipticity at any point in the electromagnetic wave. Thus, the prior art devices must be properly oriented relative to the incident wave E-vector in order to have a 90° rotation of the output polarization. If the incident orientation includes a deviation of x, there will be a 2x error in the rotation angle, in addition to the introduction of ellipticity in the output polarization. 
     It would be advantageous to have a polarization rotator that uses fewer than five reflections to increase the throughput and to simplify the construction of the device. It would be a greater advantage if the E-vector of the incident electromagnetic wave were not constrained to being either perpendicular or parallel to the plane defined by the incident and reflected electromagnetic waves to and from the first reflective surface. By removing the perpendicular or parallel orientation restraint, the device would permit the rotation of the E-vector through the desired angle regardless of its orientation to the incident wave. The present invention represents such a polarization rotator. 
     SUMMARY OF THE INVENTION 
     In accordance with the illustrated embodiment, the present invention provides a polarization rotator including three or four reflective surfaces which overcome the limitations of the prior art rotators discussed above. With the present invention, the polarization vector of an incident substantially linearly polarized electromagnetic beam can be rotated through a selected angle with the output beam being substantially free of ellipticity. To accomplish this, without requiring that the polarization vector of the incident beam be either perpendicular or parallel to the incident plane, the incident beam is reflected through a first selected angle of incidence with the resultant first reflected beam being substantially free of ellipticity. This first reflected beam is next reflected through a second selected angle of incidence and the resulting second reflected beam is then reflected through a third selected angle of incidence with the second and third angles being selected such that the ellipticity introduced at the second reflection is substantially cancelled at the third reflection. The resultant third reflected beam is thus substantially free of ellipticity. 
     One way to achieve the ellipticity cancellation discussed above is to orient the second and third reflective surfaces such that the plane defined by the first and second reflected beams is substantially perpendicular to the plane defined by the second and third reflected beams, in addition to the second reflective surface being oriented such that the plane defined by the first and second reflected beams forms an enclosed angle of substantially 135° with the plane defined by the incident and the first reflected beam, i.e., the incident plane. 
     In the three reflection configuration where the third reflected beam is the output beam, the second and third reflective surfaces are oriented such that the third reflected beam is coplanar with the incident beam. 
     By adding a fourth reflective surface that is oriented to reflect the third reflected beam through a fourth selected angle of incidence, a fourth reflected beam is produced that is substantially free from ellipticity. With the addition of the fourth surface, it is possible to orient the output beam, i.e., the fourth reflected beam, so that it is either coplanar or colinear with the incident beam. 
    
    
     DESCRIPTION OF THE DRAWINGS 
     FIG. 1 represents the electromagnetic wave path through a polarization rotator of the present invention with the locations of the reflective surfaces at A, B, C, and D being selected to provide a 90° clockwise rotation between the E-vectors of the input and output waves. 
     FIG. 2 represents the electromagnetic wave path through a polarization rotator of the present invention with the locations of the reflective surfaces at A, B, C, and D being selected to provide a 75° clockwise rotation between the E-vectors of the input and output waves. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The polarization rotator of the present invention geometrically manipulates the E-vector of the incident electromagnetic wave through the selected rotational angle by reflections from three or four surfaces 10, 12, 14, and 16. Through the proper selection of the coordinates of each of the reflection vertices and the reflection angles, any selected rotation of the E-vector of the input wave can be obtained, using either three or four reflections. Additionally, by the proper selection of the geometry of the device and the placement of the reflective surfaces, a polarization converter can be constructed wherein the linear polarization of a beam can be converted to an elliptic/circular polarization or vice versa. 
     To perform polarization rotation by means of three or four reflective surfaces, the input beam must be substantially linearly polarized, and the reflective surfaces so placed that any ellipticity introduced by third reflective surface 14 substantially cancels the ellipticity introduced by second reflective surface 12, with the ellipticity introduced at first reflective surface 10 and fourth reflective surface 16 being kept to a minimum. These guidelines serve to assure that the output beam is substantially linearly polarized with the E-vector rotated by the desired angle from the E-vector of the input beam. 
     In FIG. 1 there is shown one orientation of the three or four reflection vertices at points A, B, and C, or A, B, C, and D, respectively. With these configurations of the reflection vertices, the polarization vector, E i , of the input linearly polarized beam is rotated clockwise by 270° or 90° forming the E 3  -vector or the E 0  -vector, respectively, in the output beam. When three reflective surfaces 10, 12, and 14 are used, the output beam, CD, is coplanar with the input beam, IA. By adding fourth reflective surface 16 at D, the output beam, DO, is made colinear with the input beam, IA. 
     While the E i  -vector of the input beam is shown in FIG. 1 as being perpendicular to the plane IAB for ease of visualizing the operation of the device, this is not a necessary restriction on the orientation of the E i  -vector. To achieve proper operation of the present device it is only necessary that the input beam be linearly polarized, i.e., that the E i  -vector be perpendicular to the input beam depicted by the line IA. 
     To further help visualize the orientation and placement of the reflection vertices for the desired 270° or 90° rotation of E i , a dimensioned rectangular block (dimensional in any selected units) is shown enclosing those vertices. As defined by the dimensions on this block, the angles of incidence at each of the reflection vertices are as follows: A i  45°; B i  22.5°; C i  45°; and D i  67.5° with reflective surface 16 at D being omitted in the three reflection case. On each segment of the beam, the orientation of its E-vector is shown based on the initial orientation of E i  for this configuration of the reflective vertices. Additionally, the normal and tangential components of vectors E 1  and E 2  are shown. These normal and tangential components are defined with respect to the surfaces ABC and BCD, respectively. 
     In the above discussion we have assumed that each of reflective surfaces 10, 12, 14 and 16 were of a material having infinite conductivity. However, when real materials are used, ellipticity is introduced at any reflective surface where the incident E-vector is neither parallel nor perpendicular to the plane of incidence (i.e., the plane formed by the incident and reflected beams). Thus, in FIG. 1 where E i  is perpendicular to the incident plane IAB and E 3  is perpendicular to the incident plane CDO, the reflections at A and D are free of ellipticity, whereas the reflections at B and C are not. However, since the planes ABC and BCD are mutually perpendicular, the tangential component, E 1t  (the normal component, E 1n ) for the reflection at B becomes the normal component, E 2n  (the tangential component, E 2t ) for the reflection at C; hence the ellipticities introduced at B and C substantially cancel each other. This cancelling effect would be complete if the angles of incidence at B and C were equal. Since these angles are 22.5° and 45° respectively in the embodiment shown in FIG. 1, a small amount of ellipticity remains in the E-vector of the output beam, DC or DO. 
     Tracing the E-vectors through each of the reflections in FIG. 1, it can be seen when starting with the E i  -vector in the positive x direction that the E 1  -vector will be in the negative x direction after reflection at A. Since plane ABC is at 135° with plane IAB, it can be seen that: 
     
         E.sub.1t =E.sub.1n =E.sub.1 /√2                     (1) 
    
     where E 1  represents the magnitude of the E 1  vector 
     E 1n  is the magnitude of the normal component of E 1  to the plane ABC 
     E 1t  is the magnitude of the tangential component of E 1  to the plane ABC. 
     After reflection at B, since planes ABC and BCD are perpendicular, 
     
         E.sub.2t =E.sub.1n.sup.γ =γ.sub.B.sbsb.n E.sub.1n =γ.sub.B.sbsb.n E.sub.1 /√2                  (2a) and 
    
     
         E.sub.2n =E.sub.1t.sup.γ =γ.sub.B.sbsb.t E.sub.1t =γ.sub.B.sbsb.t E.sub.1 /√2                  (2b) 
    
     where γ B .sbsb.n is the reflection coefficient at B to the incident normal component of the polarization vector E 1   
     γ B .sbsb.t is the reflection coefficient at B to the incident tangential component of the polarization vector E 1   
     E 1n .sup.γ and E 1t .sup.γ are the magnitudes of E 1n  and E 1t  respectively, after reflection at B. 
    
     After the next reflection at C, we get 
     
         E.sub.2n.sup.γ =.sup.γ C.sub.n.sup.γ B.sub.t E.sub.1 /√2                                                (3a) and 
    
     
         E.sub.2t.sup.γ =.sup.γ C.sub.t.sup.γ B.sub.n E.sub.1 /√2                                                (3b) 
    
     where 
     .sup.γ C n  and .sup.γ C t  are defined similarly to .sup.γ B n  and .sup.γ B t  at C 
     E 2n .sup.γ and E 2t .sup.γ  have similar definitions to E 1n .sup.γ and E 1t .sup.γ after reflection at C. 
     Hence, since planes BCD and CDO are at 45° to each other, the normal and tangential components of E 3  to plane CDO can be expressed as follows: 
     
         E.sub.3n =(.sup.γ C.sub.n.sup.γ B.sub.t +.sup.γ C.sub.t.sup.γ B.sub.n)E.sub.1 /2                    (4a) 
    
     
         E.sub.3t =(.sup.γ C.sub.n.sup.γ B.sub.t -.sup.γ C.sub.t.sup.γ B.sub.n)E.sub.1 /2                    (4b) 
    
     If a high conductivity reflective surface, such as aluminum, is used for each of the reflective surfaces, each of the reflective coefficients will be very close to unity, thus: 
     
         .sup.γ C.sub.n.sup.γ B.sub.t ≃.sup.γ C.sub.t.sup.γ B.sub.n                               (5) and 
    
     
         E.sub.3n ≃E.sub.1 and E.sub.3t ≃0 (6) 
    
     therefore, 
     
         E.sub.3 ≃E.sub.3n ≃E.sub.1 since E.sub.3n &gt;&gt;E.sub.3t                                                (7) 
    
     with E 3n  being rotated clockwise through 270° from E i . 
     Finally, 
     
         E.sub.on ≃.sup.γ D.sub.n (.sup.γ C.sub.n.sup.γ B.sub.t +.sup.γ C.sub.t .sup.γ B.sub.n) E.sub.1 /2                                                (8a) 
    
     
         E.sub.ot ≃.sup.γ D.sub.t (.sup.γ C.sub.n.sup.γ.sub.B.sub.t - γC.sub.t.sup.γ B.sub.n) E.sub.1 /2                                                (8b) 
    
     yielding 
     
         E.sub.o ≃E.sub.1 since E.sub.on &gt;&gt;E.sub.ot   (9) 
    
     where E o  is rotated clockwise by 90° from E i . 
     The ellipticity of E o  can be calculated from equations 8a and 8b. Using the American Institute of Physics Handbook standard (n-ik=28-i70) for aluminum mirrors with an incident infrared beam having a wavelength of 10.6 μm, the ellipticity, E, equals 0.0065 which is sufficiently low for most applications. In the visible light range, however, E ot  becomes appreciable and a significant amount of ellipticity will be experienced. For example, for light with a 6328 A wavelength, n-ik=1.21-i7 yielding an ellipticity of E=0.05. 
     Through experimentation, by using a He-Ne laser (visible light) with a polarization ratio of greater than 1000:1 and a calcite polarizer with an extinction coefficient greater than 40 dB to produce an input beam with a polarization ratio of greater than 10 7  :1 resulted in an output beam having an ellipticity of E=0.06. From the calculation results presented in the last paragraph, it can be seen that with an incident beam having a wavelength in the 10 μm region, the ellipticity will be an order of magnitude smaller. 
     A second orientation of the three or four reflection vertices at points A, B, and C, or A, B, C, and D is shown in FIG. 2. This orientation provides a 285° or 75° clockwise rotation between the input and output polarization vectors, E i  and E 3  or E 0 , respectively. 
     To obtain the 285° or 75° of rotation between E i  and E 3  or E 0 , the reflection vertices are located at the points shown in FIG. 2 in a rectangular block outline that is dimensioned as shown (any selected units). As defined by the dimensions on this block, the angles of incidence at each of the reflection vertices are as follows: A i  45°; B i  30°; C i  45°; and D i  67.5° with the reflection surface at D omitted in the three reflection configuration. 
     Tracing the E-vectors through each of the reflections in FIG. 2 as we did for FIG. 1 above, it can again be seen that when the E i  -vector is in the positive x direction that the E 1  vector will be in the negative x direction after reflection at A. Then, for the reasons as stated above with equation (1): 
     
         E.sub.1t =E.sub.1n =E.sub.1 /√2                     (10) 
    
     Then, after reflection at B, we have 
     
         E.sub.2t =E.sub.1n.sup.γ =.sup.γ B.sub.n 1n =.sup.γ B.sub.n E.sub.1 /√2                                (11a) 
    
     and 
     
         E.sub.2n =E.sub.1t.sup.γ =.sup.γ B.sub.t E.sub.1t =.sup.γ B.sub.t E.sub.1 /√2                                (11b) 
    
     After the next reflection at C, we get, as in equations (3a) and (3b), 
     
         E.sub.2n.sup.γ =.sup.γ C.sub.n .sup.γ B.sub.t E.sub.1 /√2                                                (12a) 
    
     
         E.sub.2t.sup.γ =.sup.γ C.sub.t.sup.γ B.sub.n i E.sub.1 /√2                                                (12b) 
    
     Now, with reference to plane CDO, the normal and tangential components of E 3  are ##EQU1## 6 Note that E 3  is the output polarization direction. When the reflection at D is employed to make the output beam colinear with the input beam, the normal and tangential components of E o  are given by 
     
         E.sub.on =E.sub.3n.sup.γ =.sup.γ D.sub.n (√3.sup.γ C.sub.n.sup.γ B.sub.t = γC.sub.t .sup.γ B.sub.n)E.sub.1 /√8                                                (14a) 
    
     and 
     
         E.sub.ot =E.sub.3t.sup.γ =.sup.γ D.sub.t (√3.sup.γ C.sub.t.sup.γ B.sub.n -.sup.γ C.sub.n .sup.γ B.sub.t)E.sub.1 /√8                                (14b) 
    
     The ellipticity can be calculated as before. At 10.6μ with aluminum mirrors, we find that the ellipticity produced in the output beam in the 3-mirror case is 0.0052 and that in the 4-mirror case 0.0085.