Abstract:
An interferometer uses birefringent elements for splitting and combining beams of orthogonal polarization, and for changing the relative phase between the orthogonally polarized beams. A polarization sensitive detector is used to detect a fringe pattern whose periodicity is dependent on the relative optical paths traversed by the orthogonally polarized beams. In an embodiment of the invention, a birefringent beam splitter has an input path and first and second output paths. A birefringent beam combiner has first and second input paths and an output path, the first and second input paths of the birefringent beam combiner aligned respectively with the first and second output paths of the birefringent beam splitter. A polarization sensitive detector is disposed on the output path of the birefringent beam combiner to detect the periodicity of the fringe pattern.

Description:
FIELD OF THE INVENTION  
         [0001]    The present invention is directed generally to optical interferometers, and more particularly to optical interferometers based on the use of birefringent components.  
         BACKGROUND  
         [0002]    Interferometers are useful for measuring optical properties of materials, such as the refractive index. Some interferometers include a large number of reflectors, which can be bulky and difficult to maintain in alignment. For example, a conventional Mach Zehnder interferometer includes a light source, a beamsplitter, two steering mirrors, a second beamsplitter that operates as a beam combiner, and a detector.  
           [0003]    Therefore, there is a need for an interferometer that is easy to maintain in alignment and can be made to be compact.  
         SUMMARY OF THE INVENTION  
         [0004]    Generally, the present invention relates to an interferometer that uses birefringent elements for splitting and combining beams of orthogonal polarization, and for changing the relative phase between the orthogonally polarized beams. A polarization sensitive detector is used to detect a fringe pattern whose periodicity is dependent on the relative optical paths traversed by the orthogonally polarized beams.  
           [0005]    One particular embodiment of the invention is a birefringent interferometer for use with a polarized input light beam. The interferometer includes a first birefringent element oriented to split the polarized input light beam into an ordinary beam and an extraordinary beam and a second birefringent element oriented to combine the ordinary beam and the extraordinary beam into an output beam. A polarization sensitive detector unit is disposed to detect a selected polarization of the output beam.  
           [0006]    Another embodiment of the invention is an interferometer that includes polarization beam splitting means for splitting an incoming polarized light beam into first and second light beams of orthogonal polarization and polarization beam combining means for combining the first and second light beams of orthogonal polarization into an output beam. The interferometer also includes polarization sensitive detection means for detecting polarization of the output beam and wavelength selection means for selecting a wavelength of light detected by the polarization sensitive detection means.  
           [0007]    Another embodiment of the invention is a polarization interferometer that includes a birefringent beam splitter having an input path and first and second output paths and a birefringent beam combiner having first and second input paths and an output path, the first and second input paths of the birefringent beam combiner aligned respectively with the first and second output paths of the birefringent beam splitter. A polarization sensitive detector is disposed on the output path of the birefringent beam combiner.  
           [0008]    The above summary of the present invention is not intended to describe each illustrated embodiment or every implementation of the present invention. The figures and the detailed description which follow more particularly exemplify these embodiments. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0009]    The invention may be more completely understood in consideration of the following detailed description of various embodiments of the invention in connection with the accompanying drawings, in which:  
         [0010]    [0010]FIG. 1 schematically illustrates an operational principle of the polarization interferometer according to the present invention;  
         [0011]    [0011]FIG. 2 schematically illustrates an arrangement for controlling a polarization interferometer according to the present invention;  
         [0012]    [0012]FIG. 3 illustrates a plot of light transmitted through the polarization interferometer of FIG. 1 as a function of frequency;  
         [0013]    [0013]FIG. 4 schematically illustrates an embodiment of a polarization interferometer according to the present invention;  
         [0014]    [0014]FIG. 5 schematically illustrates another embodiment of a polarization interferometer according to the present invention; and  
         [0015]    [0015]FIG. 6 schematically illustrates another embodiment of polarization interferometer according to the present invention. 
     
    
       [0016]    While the invention is amenable to various modifications and alternative forms, specifics thereof have been shown by way of example in the drawings and will be described in detail. It should be understood, however, that the intention is not to limit the invention to the particular embodiments described. On the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the appended claims.  
       DETAILED DESCRIPTION  
       [0017]    In general, the present invention is directed to a polarization interferometer based on the use of birefringent optical crystals. The polarization interferometer is referred to as a polarization Mach-Zehnder interferometer (PMZI). The invention finds application in many index or optical path related components and sub-systems, including, but not limited to, refractive index measurements, thermal effect measurements, electrical/magnetic induced index measurement, frequency locker devices, and distance measurements.  
         [0018]    One of the operational principles of the PMZI is described with reference to the optical system  100  schematically illustrated in FIG. 1. A light source  102  generates an output beam  104  that is directed to a birefringent polarization rotation unit  105 . In this particular embodiment, the birefringent polarization unit  105  includes a birefringent crystal  106 . The light source  102  may generate the output beam  104  as a polarized beam or as an unpolarized beam. A polarizer  108  may be placed between the light source  102  and the birefringent crystal  106  to polarize the light beam  104  if it is generated unpolarized, or to clean up the polarization of the light beam if it is generated as a polarized beam.  
         [0019]    The light beam  110  passing into the birefringent crystal  106  is polarized, preferably with its polarization direction at approximately 45° to the fast axis and the slow axis of the birefringent crystal  106 . The birefringent crystal  106  has a length, L, and a birefringence Δn=|n e −n o |, where n e  is the refractive index for an extraordinary ray and n o  is the refractive index for an ordinary ray. In this description, we assume that the crystal  106  displays positive birefringence, with n e  larger than n o , although it will be appreciated that the birefringent crystal  106  may also display negative birefringence, with n o  larger than n e . It will be appreciated that biaxial crystals may also be employed.  
         [0020]    A polarizer  112  is set to polarize the light beam  114  output from the birefringent crystal  106 . The polarizer  112  is preferably oriented parallel to the input polarizer  108 . A detector  116  detects the light passed through the polarizer  112 .  
         [0021]    The transmittance through the optical system  100  is given by the following expression:  
           T=I   out   /I   in =cos 2 [π( n   e   −n   o ) L/λ]   (1)  
         [0022]    where I out  and I in  are the intensities in the analyzed output beam  118  and the input beam  110 , and λ is the wavelength of the light.  
         [0023]    The condition of the maximum transmittance through the optical system  100  is given by the expression:  
           LΔn=mλ, m= 0,1,2,  (2)  
         [0024]    Thus, maximum transmittance through the optical system corresponds to the difference in optical path length between the ordinary and extraordinary rays through the crystal  106  being an integral number of wavelengths.  
         [0025]    The light source  102  is typically capable of emitting light over a broad range of wavelengths. The light source  102  may include, for example, a tunable laser or a broadband light emitter, such as a light emitting diode (LED), halogen lamp, or the like, whose output is collimated through a fiber or through a lens.  
         [0026]    The light may be delivered from the light source  102  to the birefringent polarization rotating unit  105  via an optical fiber terminated with a collimating lens to create a collimated beam that passes through the birefringent polarization rotating unit  105 . Likewise, the light may be delivered from the birefringent polarization rotating unit  105  to the detector  116  via an optical fiber, where a focusing lens focuses the light from the birefringent polarization rotating unit  105  into the fiber.  
         [0027]    The system  100  may include the ability to select the wavelength of light that is detected, in order to obtain a wavelength-dependent signal from the detector  116 , as is further explained in FIG. 2. For example, the light source  102  may generate a single wavelength at any one time, but be tunable over a range of wavelengths. Examples of such a light source include a tunable laser such as a tunable semiconductor laser, or a broadband source whose output is passed through a light disperser, such as a grating or prism, and a narrow band of the broadband light selected, for example using a slit, as the output from the light source. The tunable light source  102  may be controlled by a controller/analyzer  150 , which tunes the wavelength of the output from the light source  102 .  
         [0028]    In another embodiment, the detector  116  may include a wavelength selective element (WSE)  152  that directs light to a photodetector  154  (pd). The WSE  152  may direct only a narrow range of wavelengths to a single channel photodetector  154 . The photodetector  154  may be, for example, a photodiode, an avalanche photodiode, a phototransistor, a charge coupled device (CCD), a photomultiplier or the like. For example, the wavelength selective element may be a diffraction grating, a prism, a filter, or any other suitable optical element that manifests wavelength dispersion so as to separate light of different wavelengths. The WSE  152  may be positioned either before or after the polarizer  112  to provide wavelength separation. The wavelength transmitted by the WSE  152  to the photodetector  154  may be controlled by the controller/analyzer  150 . For example, the controller/analyzer may control the transmission wavelength of the WSE to sweep over a particular wavelength range, and may also control the sweep rate.  
         [0029]    In another embodiment, the WSE  152  may disperse a large portion, if not all, of the light incident thereon from the light source  102  to a multi-channel photodetector  154 , such as a photodiode or CCD array, so that the detector  116  measures the transmittance through the system  100  over multiple wavelengths in a single measurement.  
         [0030]    The output from the photodetector  154  is transmitted to the controller/analyzer  150  for signal amplification and analysis. The controller analyzer may be a computer, such as a PC compatible type computer, or other type of computer, operating with appropriate software to analyze the data received from the photodetector  154  and/or to control the operating wavelength of the light source  102  and/or the WSE  152 . The data analyzed by the controller/analyzer may be transmitted via an interface unit  160  to an external computer or may be displayed on an attached display device  162 , such as a monitor or printer. Furthermore, the controller/analyzer  150  may receive control instructions from an external computer connected via the interface unit  160 .  
         [0031]    It will be appreciated that the detector  116  need only produce signals that correspond to different wavelengths, and need not include all the features just described for controlling the detected wavelength. For example, if the light source  102  directs broadband light through the birefringent polarization rotation unit  105 , then the controller/analyzer  150  need not control either the light source  112  or the WSE  152  if the photodetector  154  is a multiple channel detector, although such control need not be excluded. Furthermore, if the light source  102  is a tunable light source, then the WSE  152  need not be present, although it may be included for increased wavelength sensitivity. Likewise, where the light source  102  is a tunable light source, the photodetector  154  may be a single channel detector if there is no WSE  152  present, or may be a multiple channel detector if a WSE  152  is present. It will be appreciated that several different configurations of light source  102  and detector  116  may be used.  
         [0032]    A typical transmission signal detected by the detector is illustrated in FIG. 3. The signal  302  includes a series of uniformly spaced peaks  304 . The frequency separation between the peaks, Δν, is given by the expression:  
         Δν= c /( LΔn )  (3)  
         [0033]    where c is the speed of light in vacuum.  
         [0034]    It will be appreciated that the valleys in the recorded signal may not reach zero intensity if the optical intensity in the ordinary and extraordinary rays is not equal. Thus, it is advantageous for maximum signal contrast that the polarization of the beam  100  input to the crystal  106  be at around  450  in order to excite the ordinary and extraordinary rays equally.  
         [0035]    The frequency spacing of the PMZI output signal reflects the path difference between the e-ray and the o-ray. An important issue is how the o-ray and e-ray are dealt with in the birefringent polarization rotation unit  105 . Another embodiment  400  of the PMZI is illustrated in FIG. 4. A light source  402  directs light through a polarizer  404  to a birefringent polarization rotation unit  405 . The light from the birefringent polarization rotation unit  405  is directed through an analyzing polarizer  412  to a detector  416 .  
         [0036]    The birefringent polarization rotation unit  405  includes two birefringent optical crystals  406   a  and  406   b  separated by a certain distance. The optical axes of the first and second crystals  406   a  and  406   b  are in the y-z plane. In this embodiment, the optical axis of the first crystal  406   a  is also set at +θ relative to the z-direction in the y-z plane. Conversely, the optical axis of the second crystal  406   b  set at −θ relative to the z-direction in the y-z plane. The transmittance through the PMZI  400  may be expressed as:  
             T   =         I     o                 u                 t         I     i                 n         =       cos   2          [       π        (           n   e          (   θ   )         cos                 α       -     n   o       )            L   /   λ       ]                 (   4   )                               
 
         [0037]    where each crystal  406   a  and  406   b  has a length of L/2, the extraordinary refractive index is n e (θ), and the birefringent walk-off angle is α.  
         [0038]    The frequency spacing, Δν, of the detected spectrum is given by the following expression;  
               Δ                 v     =     c     L        (           n   e          (   θ   )         cos                 α       -     n   o       )                 (   5   )                               
 
         [0039]    It will be appreciated that the optical axis of the first crystal  406   a  may be oriented at −θ relative to the z-direction while the optical axis of the second crystal  406   b  is oriented at +θ relative to the z-direction. It will also be appreciated that the two crystals need not be formed of the same material, in which case expressions (4) and (5) would need to be modified to account for the different refractive indices of the two materials. The following description assumes that the two crystals  406   a  and  406   b  are formed of the same material.  
         [0040]    The input beam  403  is split into two beams, first and second polarized beams  470  and  472  in the first crystal  406   a . The polarization state of the first polarized beam  470  is orthogonal to the polarization state of the second polarized beam  472 . The two polarized beams  470  and  472  are recombined in the second crystal  406   b . The splitting and combining of the two beams  470  and  472  is a result of tilting the optical axes of the crystals relative to the z-direction.  
         [0041]    In the first crystal  406   a , the first polarized beam  470  is an extraordinary beam  420  that walks off from the second polarized beam  472 . In the first crystal  406   a , the second polarized beam  472  is an ordinary beam  422 . The extraordinary beam  420  is preferably spatially separated from the ordinary beam  422  upon exiting the first crystal  406   a  so that the first and second polarized beams  470  and  472  have no spatial overlap in the gap between the two crystals  406   a  and  406   b . This requires the designer to select the length of the first crystal  406   a  based on the required walk-off distance and the walk-off-angle of the crystal  406   a.    
         [0042]    The first polarized beam  470  enters the second crystal  406   b  as an extraordinary ray  424  and the second polarized beam  472  enters the second crystal  406   b  as an ordinary ray  425 . The length of the second crystal  406   b  is selected so that the first and second polarized beams  470  and  472  combine at the output face of the second crystal  406   b  to produce a single output beam  426 .  
         [0043]    A sample of optical material  450  may be inserted into the path of one of the polarized beams  470  and  472 , at the gap between the two crystals  406   a  and  406   b . FIG. 5 illustrates the sample  450  inserted in the path of the extraordinary ray from the first crystal  406   a . The sample  450  changes the path length difference between the optical paths of the two polarized beams  470  and  472  before they are recombined in the second crystal  406   b . This results in a change in the frequency spacing of the transmission spectrum. Hence, the frequency spacing of the transmission spectrum when the sample  450  is inserted between the crystals  406   a  and  406   b , Δν a , is given by the expression:  
               Δ                   v   a       =     c       L        (           n   e          (   θ   )         cos                 α       -     n   o       )       +       L   a          (       n   a     -   1     )                   (   6   )                               
 
         [0044]    where n a  is the refractive index of the optical material  450  for the polarization of the light passing through the sample  450 , and L a  is the physical length of the sample  450  through which the first polarized beam  470  passes. It will be appreciated that this expression assumes that the region between the crystals  406   a  and  406   b  contains a vacuum, air, or other gas having a refractive index close to 1. If the region between the crystals contains some other material having, for example, a refractive index of n m , then the term (n a -1) in expression (6) would be replaced by (n a -n m ).  
         [0045]    Subtracting expression (6) from expression (5) yields an expression for the refractive index of the optical material  450 :  
           n   a =1 −c [1/Δν−1/Δν a   ]/L   a   (7)  
         [0046]    Thus, the refractive index of a piece of material may be determined by measuring the frequency spacing of the transmission spectrum before and after insertion of the piece of optical material. The optical material used to form the sample  450  measured may be a transparent solid, such as a glass or crystal, a liquid or a gas. Liquids and gases are preferably measured in a calibrated cell. The cell may be calibrated by first measuring the path length difference introduced as by the empty cell empty, before filling the cell with the material to be measured in the PMZI.  
         [0047]    An advantage of the polarization interferometer over other types of interferometer is that each beam contains polarized light, so the refractive indices of birefringent materials may be measured directly. The PMZI may also be used to measure refractive index changes induced by external effects, such as electrical, magnetic, radiation, thermal, acoustic or pressure effects. The transmission spectrum through the PMZI may be recorded before and after the change in the external effect. The index change, Ana, is given by the expression:  
         Δ n   a   =c [1/Δν 1 −1/Δν 2   ]/L   a   (8)  
         [0048]    where Δν 1  is the frequency spacing before the effect change and Δν 2  is the frequency spacing measured after the effect change.  
         [0049]    It will be appreciated that the second crystal  406   b  may have its optic axis directed at the same angle, θ, towards the z-direction in the y-z plane as the first crystal  406   a , for example as illustrated in FIG. 6. The second crystal is also oriented so that the first interferometer beam  470 , which is an extraordinary beam  420  in the first crystal  406   a  enters the second crystal  406   b  as an ordinary beam  460 . Also, the second interferometer beam  472 , which is an ordinary beam  422  in the first crystal  406   a , enters the second crystal  406   b  as an extraordinary beam  462 . The extraordinary beam  462  is deviated by the walk-off effect towards the ordinary beam  460 . Therefore, the first and second interferometer beams  470  and  472  are combined at the exit face  466  of the second crystal  406   b.    
         [0050]    In such an embodiment, the optical path difference between the two interferometer beams  470  and  472  is zero, or close to zero, when there is no material  450  positioned between the crystals, in which case the frequency separation of the transmission peaks is infinite, if not extremely large. However, the introduction of the sample of optical material  450  into one of the beams introduces a path length difference between the two beams  470  and  472 , producing a measurable peak separation. Since the frequency separation of the peaks without the optical material present is known to be infinite, in other words 1/Δν is zero, this arrangement permits the refractive index of the optical material  450  to be determined from expression (7) using only a single measurement, that is a measurement of Δν a .  
         [0051]    Any suitable birefringent material may be used for the birefringent crystals  406   a  and  406   b . Yttrium orthovanadate, YVO 4 , is a particularly useful material, since its large birefringence permits the crystals  406   a  and  406   b  to have a large walk-off angle, and so the two beams  420  and  422  are spatially separated in a relatively small length of material. However, other materials may also be used, including, for example, lithium niobate, barium borate, rutile and calcite.  
         [0052]    As noted above, the present invention is applicable to optical systems and is believed to be particularly useful for providing a compact polarization interferometer that may be used for measuring refractive indices and changes in refractive index. The present invention should not be considered limited to the particular examples described above, but rather should be understood to cover all aspects of the invention as fairly set out in the attached claims. Various modifications, equivalent processes, as well as numerous structures to which the present invention may be applicable will be readily apparent to those of skill in the art to which the present invention is directed upon review of the present specification. The claims are intended to cover such modifications and devices.