Abstract:
Techniques and devices for depolaring polarized light by using one or more birefringent optical elements in the optical path of light to scramble the state of polarization of light. Examples of devices for coupling with a fiber or a fiber device, and their applications in various fiber environments are also described.

Description:
FIELD OF INVENTION  
         [0001]    This invention pertains generally to polarization control in fiber optic and free-space optical system. Specifically the present invention relates to an optic apparatus for depolarizing polarized light in optical fibers and in free space.  
         DESCRIPTION OF RELATED ART  
         [0002]    Many components in advanced fiber optic communication (T. Okoshi, “Recent Advances in Coherent Optical Fiber Communication Systems,” J. Lightwave Technology, Vol. LT-5, No. 1, pp 44-52, 1987) and sensing systems, such as interferometers and electro-optic modulators, are polarization sensitive. In order for these polarization sensitive devices to function properly, an input light&#39;s polarization state is precisely aligned with a particular axis of the devices. Unfortunately, the polarization state of light propagating in a length of standard circular fiber varies along, the fiber due to random birefringnece induced by thermal stress, mechanical stress, and irregularities of the fiber core (I. P. Kaminov, “Polarization in Optical Fibers,” IEEE J. Quantum Electronics, Vol. QE-17, No. 1, pp. 15-22, 1981). Thus typically, a standard optic fiber outputs elliptically polarized light with varying degrees of ellipticity, and with the major elliptical axis at an arbitrary angle relative to a reference orientation.  
           [0003]    One prior art method of solving the polarization problem utilizes polarization controllers. Polarization controllers, including, tri-plate controllers, fiber tri-loop controllers, and the Yao controller (see Photonics Spectra, April issue, pp. xxx, 1998), typicaly convert an arbitrary polarization state into a desired polarization state. However, such polarization controllers cannot accommodate rapid polarization fluctuations in the fiber and therefore are unsuitable in systems where the polarization state fluctuates due to time dependent thermal or mechanical stresses on the fiber, or due to polarization fluctuations of the laser light itself.  
           [0004]    Another method of solving the polarization fluctuation problem is to depolarize polarized light One prior art method of depolarizing light utilizes an electro-optic modulator to rapidly modulate the polarization state. However, the electro-optic modulator output is not truly depolarized. The output of the electro-optic modulator depolarizer only appears depolarized to an observer or detector having a response slower than the modulation speed. Another disadvantage of the electro-optic modulator depolarizer is high cost. Typical electro-optic modulator systems utilize a high frequency microwave signal source and an expensive electro-optic modulator. A third disadvantage of such an electro-optic depolarizer is the high loss, resulting from coupling between optical fiber and the waveguide in the electro-optical modulator.  
           [0005]    A second prior art method for depolarizing light uses a recirculating fiber loop which includes a 2×2 fiber coupler with two input ports,  1  and  2 , and two output ports,  3  and  4 . (“Tunable single mode fiber depolarizer” by P. Shen, J. C, Palais, and C. Lin, Electronics Letters, Vol. 33, No. 12, pp.1077-1078). The output port  4  is connected with input port  2  to form a recirculating loop. A first polarization controller is placed at input port  1  and a second polarization controller is placed inside the loop. The loop length is much larger than the coherence length of the input light so that the recirculating beams do not interfere with one another. The to the incoherent addition of the recirculating beams, the output at port  3  is the superposition of different polarization states with different intensities. Depolarization occurs by averaging over the many different polarization states of the recirculating beams. The degree of polarization at output port  3  depends on the input state of polarization, the coupling ratio of the coupler, and the birefringnece of the fiber loop. By properly adjusting the two polarization controllers, polarized light entering input port  1  exits output port  3  unpolarized.  
           [0006]    One disadvantage of using a recirculating fiber loop is that the time coherence of the depolarized beam is degraded and therefore may not be suitable for coherent communication systems. In addition, interference noise may arise when the loop length is not sufficiently longer than the coherence length of the input beam. Furthermore, device performance depends strongly on the input signal&#39;s coherence length and thus the recirculating fiber loop is not suitable for systems where diversified signal sources are present. Finally, the device may be very bulky due to the long, loop length (as long as a few km for DFB lasers).  
           [0007]    Due to the disadvantages of prior art methods of depolarizing light described above, improved method of depolarizing light is needed.  
         SUMMARY OF THE INVENTION  
         [0008]    The present invention relates to a method and apparatus of depolarizing or randomizing polarization states of an optical beam. One embodiment of the invention uses a wedged birefringent crystal with its wedge formed by many small steps. Another embodiment of the invention contains many randomly oriented birefringent crystal chips. Different parts of the optical beam passing through the apparatus experience different retardations and exit with different polarization states, resulting a spatially depolarized light beam. Focusing the spatially depolarized beam into air optical fiber results in a depolarized guided wave.  
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0009]    The advantages of the present invention will become readily apparent to those ordinarily skilled in the art after reviewing the following detailed description and accompanying drawings wherein:  
         [0010]    [0010]FIG. 1A illustrates a prior art cross section view of a wedged crystal for depolarizing a free space optical beam.  
         [0011]    [0011]FIG. 1B illustrates the orientation of input beam&#39;s polarization with respect to the edges of the wedged crystal.  
         [0012]    [0012]FIG. 2 illustrates a prior art depolarization device with two wedged birefringent crystals cemented together. The beam deviation between two polarization states is also illustrated.  
         [0013]    [0013]FIG. 3 illustrates a fiber optic in-line depolarizer in which the depolarizing element is a wedged birefringent crystal.  
         [0014]    [0014]FIG. 4A illustrates one embodiment of the invention for depolarizing an optical beam using a step-wedged birefringent crystal.  
         [0015]    [0015]FIG. 4B illustrate another embodiment of the invention consisting of two step-wedged birefringent crystals.  
         [0016]    [0016]FIG. 5 illustrates an in-line fiber optic depolarizer using a step-wedged optical depolarizer.  
         [0017]    [0017]FIG. 6A and FIG. 6B illustrate(s) an apparatus for depolarizing an optical beam using a plurality of randomly oriented birefringent crystal chips.  
         [0018]    [0018]FIG. 7A and FIG. 7B illustrate a method for fabricating a depolarizer with randomly oriented birefringent crystal chips.  
         [0019]    [0019]FIG. 8 illustrates a fiber optic in-line depolarizer.  
         [0020]    [0020]FIG. 9A illustrates using a depolarizer in an externally modulated fiber optic link.  
         [0021]    [0021]FIG. 9B illustrates using a depolarizer in a wavelength division multiplexing (WDM) system.  
         [0022]    [0022]FIG. 9C illustrates use of a depolarizer in a coherent communication system.  
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0023]    [0023]FIG. 1A illustrate a side cross section view and FIG. 1B illustrate a front view of using a wedged birefringent material  1018  as a spatial depolarizer. Examples of the birefringent material are quartz, calcite, and YVO 4 . The optical axis (the c axis) of crystal  1080  may be oriented either along x-axis  1002  or along y-axis  1004 . In the embodiment illustrated in FIG. 1A and FIG. 1B, the optical axis is oriented along x-axis  1002 . A light beam  1000  enters birefringent material  1018  on input surface  1019  and exits the birefringent material  1018  from output surface  1020 . Light beam  1000  with a polarization state  1012  propagates along z-axis  1006  and includes an x-polarization component  1014  and a y-polarization component  1016 . x-polarization component  1014  experiences a refractive index n e  and y-polarization component  1016  experiences a refractive index of n o . The phase difference between the two polarization components is:  
               Δφ        (   x   )       =         2        π   ·     (       n   e     -     n   o       )     ·   x   ·   tan                   α     λ     =       2        π   ·   Δ                     n   ·   x   ·   tan                   α     λ               (   1   )                               
 
         [0024]    where x is the position of an optical ray on the x-coordinate, α is the wedge angle, λ is the optical wavelength of the incident light, and Δn is the birefringnece of the crystal. When an input polarization is oriented θ degree from x-axis  1002 , as shown in FIG. 1B, the output light field can be expressed as: 
           {right arrow over (E)}E   0   e   iφ     0   ( {circumflex over (x)} cos θ+ ŷ sin θ −e   iΔφ(x) )  (2) 
         [0025]    where Δφ(x) is given in Eq. (1), E 0  is the amplitude of the input field, φ 0  is a constant phase, {circumflex over (x)} and ŷ are the unit vectors of the x-axis and y-axis respectively. When θ=45°, Eq. (2) becomes: 
           {right arrow over (E)}=E   0   e   iφ     0   ( {circumflex over (x)}+ŷe   iΔφ(x) )/{square root}{square root over (2)}  (3) 
         [0026]    It is evident from Eq. (3) that optical rays incident at different location along the x axis have different polarization states. For example, for two optical rays with Δφ=2 mπ and Δφ=(2m+1)π(where m is an integer), the corresponding outputs from the depolarizer of FIG. 1A are orthogonally polarized linear polarization states. For two optical rays with Δφ=(2m±¼)π, the corresponding outputs are circularly polarized with opposite sense of rotation. Therefore, birefringent crystal wedge  1018  imparts different polarization states to different portions of an optical beam, resulting in a spatially depolarized beam. By focusing the spatially depolarized light beam into a single mode fiber, we obtain a depolarized guided signal.  
         [0027]    For an optical beam with a diameter D, the maximum difference in phase angle Δφ between two rays within the beam is  
               δ   max     =       max        [       Δφ        (     x   1     )       -     Δφ        (     x   2     )         ]       =       2        π   ·   Δ                     n   ·   D   ·   tan                   α     λ               (   4   )                               
 
         [0028]    In order to completely depolarize light, δ max  preferably equal to or greater than 2π or 
           Δn ·tan α≈Δ n·α≧λ/D   (5) 
         [0029]    In an alternative arrangement, two wedged birefringent crystals are coupled together to form a composite wedge, as shown in FIG. 2. In the example of FIG. 2, the output surface  2020  of the first birefringent crystal  2004  is coupled to an input surface  2001  of the second wedged birefringent crystal  2008 . In FIG. 2, an optical axis  2002  of a first wedge crystal  2004  is oriented 90° from optical axis  2006  of the second wedged crystal  2008 . The optical phase difference between a x-polarization component and a y-polarization component of a light ray passing through the composite wedge is computed using:  
               Δφ        (   x   )       =         2        π   ·   Δ                   n     λ          (     d   -     2        x   ·   tan                   α       )               (   6   )                               
 
         [0030]    where d is the thickness  2014  of the polarization depolarizer. For an optical beam with a diameter of D, the maximum Δφ difference between two rays within the beam is  
                 δ   max     =       max        [       Δφ        (     x   1     )       -     Δφ        (     x   2     )         ]       =       2        π   ·   Δ                     n   ·   2          D   ·   tan                   α     λ         ,           (   7   )                               
 
         [0031]    which is twice as that of a single wedge. The condition for complete polarization randomization across the beam is 
           Δn·α≧λ/ 2 D   (8) 
         [0032]    Thus, in one example, to depolarize an optical beam with a wavelength of 1550 nm and a diameter of 0.5 mm using quartz crystal wedge having a Δn of 0.009, the wedge angle α should be larger than 5°.  
         [0033]    The single-wedge and composite-wedge depolarizers described above yield an optical beam with spatially randomized polarization states, however, as illustrated in FIG. 1A and FIG. 2, the x-polarization component and the y-polarization component exit the crystal wedge  1018  or  2008  at different angles. The different exit angles result from the different refractive indexes experienced by each polarization component. For example, the angle differences between two polarization components for the cases of FIG. 1A and FIG. 2 respectively are: 
         Δθ A   ≈Δn·α/n   (9A) 
         Δθ R ≈2 Δn·α/n   (9B) 
         [0034]    Where α is the wedge angle, n is the index of refraction of the medium after the crystal, and Δn is the difference in refractive index experienced by the x-polarization component and the y-polarization component. Substitutions of Eq. (9A) in Eq. (7) and Eq. (9B) in Eq. (8) yield an angle deviation of:  
               Δ                   θ   A       =       Δθ   B     ≥       1   n          λ   D                 (   10   )                               
 
         [0035]    The slightly different exit angles may not be a problem for a free space beam with a sufficiently large beam diameter D. However, the different exit angles make it difficult to couple equal quantities of the x- and y-components exiting from the crystal wedge into an optical fiber. Equal quantities of the x and the y polarization components in the fiber produce a truly depolarized beam of light.  
         [0036]    [0036]FIG. 3 illustrates one method of coupling a depolarizer with an input optical fiber  3002  and an output optical fiber  3018 . A collimating lens  3020  collimates a light beam from input fiber  3002 . The collimated beam passes through a depolarizer  3004 . The output of depolarizer  3004  is focused into output fiber  3018  by a focusing lens  3014 . Depolarizer  3004  can either be a simple wedge shown in FIG. 1A or a composite wedge shown in FIG. 2. Input fiber  3002  can either be a non-polarization maintaining fiber, a polarization maintaining (PM) fiber, a polarizing (PZ) fiber, or another light source. When a non-polarization maintaining input fiber  3002  is used, a polarization controller may be incorporated to adjust the state of polarization incident on crystal wedge  3005  so that the incident beam polarization is approximately 45° from c-axes  3000 ,  3006  of crystal wedges  3005 ,  3007 . When input fiber  3002  is a PM fiber, the slow or fast axis of the PM fiber is oriented approximately 45° from the orientation of crystal c-axes  3000  and  3006 . An optional polarizer  3008  may be positioned at input side of depolarizer  3004  with its passing axis oriented 45° from c-axes  3000  and  3006 . The incorporation of optional polarizer  3008  facilitates alignment of the input polarization to depolarizer  3004  by maximizing power output from depolarizer  3004 .  
         [0037]    Because the x-polarization component and the y-polarization component exit depolarizer  3004  with slightly different angles, as described in Eq. (9) and Eq. (10), focusing lens  3014  focuses each polarization component to a slightly different location. The resulting lateral difference Δd between two polarization components is illustrated in FIG. 3 and may be expressed as:  
               Δ                 d     =       Δθ   ·   f     ≥       1   n          λ   D        f               (   11   )                               
 
         [0038]    where f is the back focal length of the lens. For an output fiber with a numerical aperture of NA, the focal length f satisfies the following relationship for maximum power coupling: 
           D/f≦NA   (12) 
         [0039]    Substitution of Eq. (12) in Eq. (11) yields:  
               Δ                 d     ≥       1   n          λ   NA               (   13   )                               
 
         [0040]    For optimum polarization randomization, both polarization components are focused into fiber  3018 . To focus both polarization components into the fiber with minimum loss, Δd is preferably less than the fiber core diameter d. For a standard single mode fiber with NA=0.12 at λ=1.55 um and n=1.5, we obtain from Eq. (13) that Δd≧8.33 um, close to a typical fiber core diameter of 9 um. Therefore, it is possible to focus both polarization components into a single mode fiber, although the insertion loss may be high.  
         [0041]    [0041]FIG. 4A illustrates a depolarizer which eliminates the angle difference Δθ. In the depolarizer of FIG. 4, a birefringent crystal wedge  4000  is formed by many small steps, e.g. steps  4008 ,  4010 , and  4012 . Each step includes a subsurface, such as  409 ,  411 ,  413 , oriented approximately parallel to the input surface  4001  of the birefringent wedge  4000 . The normal incidence of each collimated beam portions  4002 ,  4004 ,  4006  results in no beam deviation for either the x- or y-polarization components. Within each step, optical rays experience the same amount of birefringent phase difference and thus have the same output polarization state. However, a beam portion  4002 ,  4004 ,  4006  in a different step experiences a different amount of birefringent phase difference between the x- and the y-polarization components, resulting in a different output polarization state. Thus each step corresponds to an output polarization state. Because the optical beam covers a sufficient number of steps, the states of polarization are randomized across the beam.  
         [0042]    [0042]FIG. 4B illustrates another embodiment of the invention in which two stepped birefringent crystal wedges  4016  and  4020  with orthogonal crystal axis orientations  4014  and  4022  are positioned such that an incident beam of light propagates in a direction substantially orthogonal to crystal axis orientations  4014 ,  4022 . One method of maintaining the position of the two crystal wedges  4016  and  4020  is to cement the crystal wedges together with an optical cement having a refractive index close to that of the crystal.  
         [0043]    [0043]FIG. 4C illustrates that a preferred polarization state  4024  of an input beam into an input surface of the crystal wedges  4016  and  4020  is linear and oriented 45° from crystal axes  4014  and  4022 .  
         [0044]    [0044]FIG. 5 illustrates a fiber optic depolarizer using step crystal wedges in a system described in FIG. 3. The system of FIG. 5 includes all input optical fiber  5002 , a collimating lens  5004 , a step crystal wedge  5006  (either a single wedge in FIG. 4A or a double wedge shown in FIG. 4B), a focusing lens  5008 , and a receiving fiber  5010 . An optional polarizer  5012  may be placed at input side of the crystal wedge for aligning polarization state incident onto the wedge. In the illustrated embodiment, the passing axis of polarizer  5012  is oriented 45° from the crystal axes of first crystal wedge  5006  to ensure that the input optical beam is polarized 45° from the crystal optical axes.  
         [0045]    The previously described embodiments are polarization sensitive, thus the performance of the device depends on an input beam&#39;s polarization state. However, in some fiber optic applications, polarization insensitive devices are preferred. FIG. 6A illustrates a front view and FIG. 6B illustrates a side view of a polarization insensitive depolarizer  6000 . The polarization insensitive depolarizer  6000  includes many randomly oriented micro birefringent crystal chips, e.g.  6002 ,  6004 ,  6006 . The cross section of the chips can be of arbitrary shape, including circular, square, rectangular, triangular, or a combination thereof. The cross sectional area of each chip is significantly smaller than the beam size (however, not too small to cause scattering). Typically the crystal chips have a cross sectional dimension of approximately 0.1 mm×0.1 mm to depolarize a light beam having a cross sectional dimension of 1 mm×1 mm. The optical axis of each chip is preferably in a plane that is perpendicular to the beam propagation direction.  
         [0046]    It can be shown that a quarter wave plate is capable of converting a linear polarization state into any desired polarization state if the relative orientation between the linear polarization state and the optical axis of the plate can be arbitrarily rotated (see Yariv and Yeh, Optical Waves in Crystals, John Wiley &amp; Sons). Therefore in one embodiment, the thickness and birefringnece of each birefringent chip is selected to be a quarter wave plate (either single order or multi-order). As illustrated in FIG. 6B, when a light beam of linear polarization passes through the depolarizer, different beam portions  6008 ,  6012 ,  6016  of beam  6007  experience corresponding quarter wave plates  6010 ,  6014 , and  6018 , each quarter wave plate oriented in different directions. Consequently, the output polarization states of different parts of the beam are different and are approximately randomized.  
         [0047]    One method of fabricating depolarizer  6000  is to sandwich a plurality of mica chips between two glass plates. Optical cement may be used to hold the mica chips and the glass plates together. The refractive index of the optical cement is preferably close to that of the glass and that of the mica chips. The optical axes of the mica chips may either be randomly oriented or be arranged in such a way that their orientation angles are evenly distributed from 0 to 180 degree.  
         [0048]    [0048]FIG. 7 illustrates a different method of manufacturing a polarization independent depolarizer. First, many birefringent rods, such as rods  7000 ,  7002 ,  7004 , are made. The optical axis of each rod is oriented to include a substantial component perpendicular to the rod&#39;s longitudinal axis  7008 . The birefringent rods are bundled together. The rods are distributed such that the optical axes in a bundle are randomly oriented in a plane or are arranged in such a way that their orientation angles are evenly distributed from 0 to 180 degree. Optical cement may be used to hold the bundle together. In one embodiment, the refractive index of the cement is close to that of the rods. In an alternative embodiment, the optical cement is opaque to prevent light from passing between rods. Prevention of light passing between rods helps preventing the slight bias towards the original input polarization. In an alternative embodiment, when maximum transmittance is desired without having a bias towards the original input polarization, square rods may be bundled together, as illustrated in FIG. 7C. An optional enclosure may be used to confine the bundle and hold the rods together. The bundle of rods illustrated in FIG. 7A is cut into thin slices  7006 ,  7010 ,  7012  etc. When the slices are polished, each slice forms a depolarizer with a cross section such as cross sections  7014  or  7016 . In one embodiment of the invention, the birefringent rods are birefringent fibers (or polarization maintaining fibers). In an alternative embodiment, the birefringent rods are made of quartz or other birefringent crystals.  
         [0049]    [0049]FIG. 8 illustrates the polarization independent depolarizer as used in a fiber optic system. A collimating lens  8002  collimates light from an input fiber  8000 . A wave plate  8004  containing many birefringent chips with randomly or evenly distributed crystal axis orientations. A focusing lens  8008  focuses light output by wave plate  8004  into a fiber  8010 . Enclosure  8012  holds all the parts together.  
         [0050]    [0050]FIG. 9A illustrates using a depolarizer  9000  in a optical fiber communication system. Polarized light from laser  9006  is depolarized by depolarizer  9000  before entering a length of fiber  9010  An optional polarizer  9002  properly polarizes the light output of fiber  1910  before the light enters a polarization sensitive electro-optic modulator  9004 . The modulated light from the electro-optic modulator propagates through fiber  9012  before entering receiver  9008 . Depolarizing light before fiber  9010  is to prevent polarization fluctuation caused by the fiber. Polarization fluctuation may be converted to amplitude fluctuation by the electro-optic modulator or other polarization sensitive devices in the system and causes transmission error.  
         [0051]    [0051]FIG. 9B illustrates using depolarizers  9028 ,  9030 ,  9032 ,  9034  in a wavelength division multiplexing (WDM) system. Depolarizers  9028 ,  9030 ,  9032 ,  9034  depolarize light beams with different wavelengths from lasers  9020 ,  9022 ,  9024 ,  9026  respectively. The depolarized light beams are then combined by a wavelength division multiplexer  9036  for input into fiber  9038 . A polarization sensitive electro-optic modulator  9042  modulates the received light beams. Light beams with different wavelengths are separated by a wavelength division demultiplexer  9044  and transmitted to a corresponding receiver  9046 . An optional polarizer  9040  may be used before electro-optic modulator to convert the depolarized light beams into linearly polarized beams with a proper polarization orientation.  
         [0052]    [0052]FIG. 9C illustrates using a depolarizer  9052  in a coherent heterodyne communication system. Light beam from laser  9048  is modulated by a phase modulator and is then depolarized by depolarizer  9052  before entering a fiber  9062 . At the receiver end, the light beam is polarized by an optional polarizer  9054 . Coupler  9056  combines the output of polarizer  9054  with a local oscillator light from laser  9058 . The optional polarizer  9054  is oriented such that the polarized output light has the same polarization state at coupler  9056  as the light from local oscillator laser  9058 . The combined beam is detected by a photodetector  9060 .  
         [0053]    In the preceding detailed description, various details have been included to facilitate understanding of the invention. However, it is to be understand that the invention is not limited to such details because many alterations, modifications, and variations are within the scope of the teachings contained herein. Accordingly, the invention should not be limited by the preceding examples, but only by the scope of the claims which follow.