Abstract:
Beam splitter designs for interferometers provide a phase difference between the two resulting interference beams that are independent of the polarization status of the incident beam. The polarization independent phase coating is achieved by making the internal beam splitting coating of an unpolarized beam splitter to be symmetrical. A symmetrical coating will produce the phase matching condition, Ψ S   R −Ψ S   R′ =Ψ PR −Ψ PR′ =0.

Description:
[0001]    This application claims priority to U.S. Provisional Patent Application Ser. No. 60/452,647, filed Mar. 7, 2003 titled: “Unpolarized Beam Splitter Of Polarization-Independent Phase Difference While Using As An Interferometer,” incorporated herein by reference.  
         [0002]    This application claims priority to U.S. Provisional Patent Application Ser. No. 60/456,295, filed Mar. 20, 2003 titled: “Thermal Tuning Optical Tuning Filter,” incorporated herein by reference.  
         [0003]    This application claims priority to U.S. Provisional Patent Application Ser. No. 60/456,300, filed Mar. 20, 2003 titled: “Hitless Optical Tunable Filter,” incorporated herein by reference.  
         [0004]    This application claims priority to U.S. Provisional Patent Application Ser. No. 60/456,356, filed Mar. 21, 2003 titled: “Sharp-Edge Step Phase Interferometer And Its Applications,” incorporated herein by reference.  
         [0005]    This application claims priority to U.S. Provisional Patent Application Ser. No. 60/459,124, filed Mar. 30, 2003 titled: “Optical Channel Analyzer Utilizing Tunable Filter Technology,” incorporated herein by reference. 
     
    
     
       BACKGROUND OF THE INVENTION  
         [0006]    1. Field of the Invention  
           [0007]    The present invention relates to optical communication, and more specifically, it relates to a beam splitter designed such that the phase difference between the two interference beams is independent of the polarization status of the incident beam.  
           [0008]    2. Description of Related Art  
           [0009]    An un-polarized beam splitter (UBS) is popularly used in interferometers such as the Michelson (FIG. 1) and the Mach-Zehnder (FIG. 2). In the conventional Michelson interferometer of FIG. 1, the incident light  10  from the left-hand side of beam-splitter  12  is separated into two beams; part of the power is reflected ( 14 ) from the beam splitter and the rest of light is transmitted ( 16 ). After those two beams ( 16 , 14 ) are reflected from mirrors M 1  and M 2  respectively, beam  16  is reflected by, and beam  14  is transmitted through, beam-splitter  12  again. The interference takes place at both the bottom  18  and the left  20  of the beam-splitter. Constructive interference takes place when the optical path length difference (OPD) is an integer multiplication of wavelength. Since the total energy is conserved, the summation of optical power at the bottom arm and the left arm should be equal to the optical power delivered from the light source. In other words, when constructive interference occurs at the bottom arm, destructive interference occurs at the left arm.  
           [0010]    It would be advantageous if a beam splitter for use in an interferometer were available such that the phase difference between the two interference beams were polarization independent  
         SUMMARY OF THE INVENTION  
         [0011]    It is an object of the present invention to provide beam splitter designs where the phase difference between the two resulting interference beams in an interferometer are independent of the polarization status of the incident beam.  
           [0012]    It is another object of the invention to provide optical interleaver designs that incorporate a beam splitters designed such that the phase difference between the two beams produced by the beam splitters is independent of the polarization status of the incident beam.  
           [0013]    These and other objects will be apparent to those skilled in the art based on the disclosure herein.  
           [0014]    A polarization independent phase coating is achieved by making the internal beam splitting coating of an unpolarized beam splitter to be symmetrical. A symmetric coating, for purposes of this application, is achieved when the coating structure looks the same to a beam propagating through it from either the front side or from rear side. For instance, in Equation (2.1) and (2,2), the phase difference of the two interference beams at the bottom arm does not depend on the polarization when the phase of the reflected beam incident with the front side is equal to that a beam incident with the rear side. A symmetrical coating will produce the phase matching condition, Ψ S   R −Ψ S   R′ =Ψ PR −Ψ PR′ =0. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0015]    The accompanying drawings, which are incorporated into and form a part of the disclosure, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention.  
         [0016]    [0016]FIG. 1 shows a conventional Michelson interferometer.  
         [0017]    [0017]FIG. 2 shows a Mach-Zehnder interferometer  
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0018]    This invention proposes a coating design for a beam splitter such that the phase difference between the two interference beams is polarization independent, when the beam splitter is used to separate and combine the light beam for an interferometer.  
         [0019]    An explanation of the relevant formulas is provided in the exemplary embodiments discussed below.  
         [0020]    Referring again to FIG. 1, the various phase functions are:  
         [0021]    ψ RMT : reflected by BS         reflected by mirror         transmit through BS.  
         [0022]    ψ TMR : transmitted through BS         reflected by mirror         reflected by BS.  
         [0023]    ψ RMR : reflected by BS         reflected by mirror         reflected by BS.  
         [0024]    ψ TMT : transmitted by BS         reflected by mirror         transmit through BS.  
         [0025]    ψ ST : phase introduced by the BS for S-polarized light, transmitted beam with front side incidence.  
         [0026]    ψ ST : phase introduced by the BS for S-polarized light, transmitted beam with rear side incidence.  
         [0027]    ψ SR : phase introduced by the BS for S-polarized light, reflected beam with front side incidence.  
         [0028]    ψ SR′ : phase introduced by the BS for S-polarized light, reflected beam with rear side incidence.  
         [0029]    ψ PT : phase introduced by the BS for P-polarized light, transmitted beam with front side incidence.  
         [0030]    ψ PT : phase introduced by the BS for P-polarized light, transmitted beam with rear side incidence.  
         [0031]    ψ PR : phase introduced by the BS for P-polarized light, reflected beam with front side incidence.  
         [0032]    ψ PR′ : phase introduced by the BS for P-polarized light, reflected beam with rear side incidence.  
         [0033]    ψ B =ψ TMR′ −ψ RMT  (phase difference in the bottom arm).  
         [0034]    ψ L =ψ TMT′ −ψ RMR  (phase difference in the left arm).  
         [0035]    Power is defined as:  
         [0036]    P B : optical power in the bottom arm.  
         [0037]    P L : optical power in the left arm.  
         [0038]    Assuming that the incident polarization is S-polarized, the two electric fields at the bottom arm can be expressed as:  
             E   →       TMR   ′       =         s   ^     2          exp        (     i                   Ψ     TMR   ′         )           ,   and               E   →     RMT     =         s   ^     2            exp        (     i                   Ψ   RMT       )       .                             
 
         [0039]    The total electric field at the bottom will be:  
                     E   →     =         E   →       TMR   ′       +       E   →     RMT                   =         s   ^     2          [       exp        (                        φ     TMR   ′         )       +     exp        (                        φ   RMT       )         ]                   =       s   ^                     cos        [         φ     TMR   ′       -     φ   RMT       2     ]            exp        [             (         φ     TMR   ′       +     φ   RMT       2     )       ]                     =       s   ^                     cos        (       ψ   B     2     )              exp        (                        ψ        (   v   )         )       .                     Equation                   (   1   )                                 
 
         [0040]    The first term in Equation (1) is the amplitude of the total electric field in the bottom arm and the second term is the corresponding phase. The amplitude is dependant upon the phase difference between the two interference beams, and the phase is the average of the two beams, where  
           ψ   B     =       φ     TMR   ′       -     φ   RMT         ,       and                 ψ     =           φ     TMR   ′       +     φ   RMT       2     .                             
 
         [0041]    Note that  
                       ψ     TMR   ′       =              2        π        (     v     v   1       )         +     ψ   ST     +     ψ     SR   ′           ,                   ψ   RMT     =              2      π        (     v     v   2       )       +     ψ   SR     +     ψ   ST         ,                     ψ   B     (   s   )       ≡              ψ     TMR   ′       -     ψ   RMT         =       2        π        (     v     v   0       )         +     (       ψ     SR   ′       -     ψ   SR       )         ,              and                   ψ     (   s   )       ≡                ψ     TMR   ′       +     ψ   RMT       2       =       π        (       v     v   1       +     v     v   2         )       +     ψ   ST     +       (         ψ     SR   ′       +     ψ   SR       2     )     .                     Equation                   (   2.1   )                                 
 
         [0042]    When the incident polarization is P-polarized,  
                         ψ   B     (   p   )       ≡       ψ     TMR   ′       -     ψ   RMT         =       2        π        (     v     v   0       )         +     (       ψ     PR   ′       -     ψ   PR       )         ,   and                   ψ     (   p   )       ≡         ψ     TMR   ′       -     ψ   RMT       2       =       π        (       v     v   1       +     v     v   2         )       +     ψ   PT     +       (         ψ     PR   ′       +     ψ   PR       2     )     .                     Equation                   (   2.2   )                                 
 
         [0043]    Notice that in the derivation of Equation (2.1) and (2.2), the phases introduced from the AR-coated surface of the cube and the two reflection mirrors are neglected. Those phases do not have polarization dependence since the incident angles at those surfaces are dose to normal.  
         [0044]    The polarization dependent feature of Ψ B  and Ψ in Equation (2.1) and (2.2) can result in certain problems. When the phase difference Ψ B  has polarization dependence, the interference fringe will peak at a different frequency. Therefore, when the incident polarization includes both P and S, the fringe contrast will be degraded. Further, since the phase of the total electric field, Ψ, has polarization dependence, it can cause group velocity delay (GVD) between the P- and S-polarized light for a short pulse incidence from the left side of the cube, which is called polarization mode dispersion (PMD).  
         [0045]    To make Ψ B  polarization independent, one has to design the coating of the beam splitter (e.g., 12) such that Ψ S   R −Ψ S   R ′=Ψ PR −Ψ PR′ . One of the choices is to make the coating symmetric, which means the beam will see the same layer structure whether it is incident from the front side or the rear side. Such conditions will assure that Ψ S   R =Ψ S   R′  and Ψ PR =Ψ PR′ .  
         [0046]    With a symmetric coating on the beam splitter, in Equ. ( 2 . 1 ) and ( 2 . 2 ), Ψ S   R −Ψ S   R′ =Ψ PR −Ψ PR′ =0. The optical power at the bottom arm is as follows.  
         P   B     =              E   →          2     =                cos        (       ψ   B     2     )            exp        (     ψ        (   v   )       )              2     =         cos   2          (       π                 v       v   0       )       .                               
 
         [0047]    The optical power at the left arm,  
         P   L     =       1   -     P   B       =         sin   2          (       π                 v       v   0       )       .                             
 
         [0048]    Both P B  and P L  are independent of the incident polarization.  
         [0049]    The unpolarized beam splitter of the present invention can be used in an optical interleaver. Examples of optical interleavers in which the present invention may be used are provided in U.S. Pat. No. 6,587,204, titled “The Application Of A Step-Phase Interferometer In Optical Communication,” issued Jul. 1, 2003, and incorporated herein by reference.  
         [0050]    The foregoing description of the invention has been presented for purposes of illustration and description and is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of the above teaching. The embodiments disclosed were meant only to explain the principles of the invention and its practical application to thereby enable others skilled in the art to best use the invention in various embodiments and with various modifications suited to the particular use contemplated. The scope of the invention is to be defined by the following claims.