Abstract:
An apparatus comprising a phase compensator and an optical condenser in communication with the phase compensator. The phase compensator provides for phase shifting a portion of an electromagnetic wave. The optical condenser is shaped to direct the electromagnetic wave to a focal region of the optical condenser.

Description:
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     This invention was made with United States Government support under Agreement No. 70NANB1H3056 awarded by the National Institute of Standards and Technology (NIST). The United States Government has certain rights in the invention. 
    
    
     FIELD OF THE INVENTION 
     The invention relates to a system for confined optical power delivery and enhanced optical transmission efficiency. 
     BACKGROUND INFORMATION 
     In an effort to increase areal density of magnetic storage media, it is desirable to reduce the volume of magnetic material used to store bits of information in magnetic storage media. Superparamagnetic instabilities become an issue as the grain volume is reduced. The superparamagnetic effect is most evident when the grain volume V is sufficiently small that the inequality K u V/k B T&gt;70 can no longer be maintained. K u  is the material&#39;s magnetic anisotropy energy density, k B  is Boltzmann&#39;s constant, and T is the absolute temperature. When this inequality is not satisfied, thermal energy demagnetizes the stored bits. Therefore, as the grain size is decreased in order to increase the areal density, a threshold is reached for a given material K u  and temperature T such that stable data storage is no longer feasible. 
     The thermal stability can be improved by employing a recording medium made of a material with a very high K u . However, with the available materials current recording heads are not able to provide a sufficient or high enough magnetic writing field to write on such a medium. Accordingly, it has been proposed to overcome the recording head field limitations by employing thermal energy to heat a local area on the recording medium before or at about the time of applying the magnetic write field to the medium. By heating the medium, the K u  or the coercivity is reduced such that the magnetic write field is sufficient to write to the medium. Once the medium cools to ambient temperature, the medium has a sufficiently high value of coercivity to assure thermal stability of the recorded information. 
     Heat assisted magnetic recording allows for the use of small grain media, which is desirable for recording at increased areal densities, with a larger magnetic anisotropy at room temperature to assure sufficient thermal stability. Heat assisted magnetic recording can be applied to any type of magnetic storage media, including tilted media, longitudinal media, perpendicular media and patterned media. 
     For heat assisted magnetic recording, an electromagnetic wave of, for example, visible, infrared or ultraviolet light can be directed onto a surface of a data storage medium to raise the temperature of the localized area of the medium to facilitate switching of the magnetization of the area. Well-known solid immersion lenses (SILs) have been proposed for use in reducing the size of a spot on the medium that is subjected to the electromagnetic radiation. In addition, solid immersion mirrors (SIMS) have been proposed to reduce the spot size. SILs and SIMs may be either three-dimensional or two-dimensional. In the latter case they correspond to mode index lenses or mirrors in planar waveguides. A metal pin can be inserted at the focus of a SIM to guide a confined beam of light out of the SIM to the surface of the recording medium. Commonly assigned U.S. Pat. No. 6,795,630, which is hereby incorporated by reference, discloses several waveguides having a metallic pin transducer for concentrating optical energy into a small spot. 
     Data storage systems often incorporate optical components to assist in the recording of information. Such systems may include, for example, optical recording systems, magneto-optical recording systems or other thermal or heat assisted type recording systems, as described herein. An important aspect of such systems utilizing optical components may include the ability to generate small and intense optical spots of energy. The optical spots can be used for various functions in the recording process, such as aiding in the reading or writing of bits of information. 
     Prior to generating the small and intense optical spots of energy, it is usually necessary to couple an electromagnetic wave from an energy source into a desired optical condenser, such as a waveguide. One known structure for coupling the electromagnetic wave into the optical condenser is a diffraction grating. Diffraction gratings are generally known components in an optical system that mutually enhance the effects of diffraction to concentrate the diffracted electromagnetic wave in specific directions determined by the spacing of the lines and by the wavelength of the electromagnetic wave. 
     There is an increased emphasis on improving the areal densities of data storage systems. Thus, all components of a data storage system are being improved to achieve higher areal densities. For example, those systems that incorporate optical components to assist in the recording of information are in need of the ability to efficiently generate even smaller and more intense optical spots of energy to support the data storage systems of the future. 
     Accordingly, there is identified a need for improved devices that overcome limitations, disadvantages, and/or shortcomings of known devices for coupling electromagnetic waves and generating smaller and intense optical spots of energy. 
     SUMMARY OF THE INVENTION 
     The invention meets the identified need, as well as other needs, as will be more fully understood following a review of this specification and drawings. 
     An aspect of the present invention is to provide an apparatus including a phase compensator and an optical condenser in communication with the phase compensator. The phase compensator provides for phase shifting a portion of an electromagnetic wave. The optical condenser is shaped to direct an electromagnetic wave to a focal region of the optical condenser. 
     Another aspect of the invention is to provide an apparatus that includes a phase compensator including a first section having a first wave propagation characteristic and a second section having a second wave propagation characteristic. The apparatus also includes an optical condenser in communication with the phase compensator. 
     Another aspect of the invention is to provide an apparatus that includes a phase compensator and a planar waveguide in optical communication with the phase compensator. 
     These and other aspects of the present invention will be more apparent from the following description. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a pictorial representation of a magnetic disc drive that can include magnetic heads constructed in accordance with this invention. 
         FIG. 2  is a schematic representation of an apparatus constructed in accordance with the invention. 
         FIG. 3  is an isometric view of an optical condenser. 
         FIG. 4  illustrates a planar waveguide in accordance with an aspect of the invention. 
         FIG. 5  illustrates an embodiment of a phase compensator in accordance with the invention. 
         FIG. 6  illustrates an additional embodiment of a phase compensator in accordance with the invention. 
         FIG. 7   a  is an embodiment of an optical condenser in accordance with the invention. 
         FIG. 7   b  is a graphical illustration of intensity versus position for a phase compensated wave in contrast to a non-phase compensated wave. 
         FIG. 8   a  illustrates an embodiment of a phase compensator constructed in accordance with the invention. 
         FIG. 8   b  is a graphical illustration of intensity versus time for a wave passing through the phase compensator illustrated in  FIG. 8   a.    
         FIG. 8   c  is a graphical illustration of signal versus time for a wave passing through the phase compensator illustrated in  FIG. 8   a.    
         FIG. 9  illustrates an additional embodiment of a phase compensator constructed in accordance with the invention. 
         FIG. 10  is a schematic illustration of diffraction gratings and a planar waveguide in accordance with the invention. 
         FIG. 11  is a schematic illustration of diffractions gratings and a planar waveguide constructed in accordance with the invention. 
         FIG. 12  is a graphical illustration of filling factor versus Gaussian FWHM for an embodiment of the invention having a phase compensator in contrast to an embodiment without a phase compensator. 
     
    
    
     DETAILED DESCRIPTION 
     This invention encompasses devices that can be used to produce small optical spots and that can be used in magnetic and/or optical recording heads for use with magnetic and/or optical recording media. However, it will be appreciated that the invention may have utility in other technologies such as, for example, high resolution optical microscopy, lithography, integrated opto-electronic devices for telecommunications or other applications. 
     Referring to the drawings,  FIG. 1  is a pictorial representation of a disc drive  10  that can utilize magnetic recording heads, or other type recording heads such as magneto-optical or thermal/heat assisted recording heads constructed in accordance with this invention. The disc drive includes a housing  12  (with the upper portion removed and the lower portion visible in this view) sized and configured to contain the various components of the disc drive. The disc drive includes a spindle motor  14  for rotating at least one data storage medium  16  within the housing, in this case a magnetic disc. At least one arm  18  is contained within the housing  12 , with each arm  18  having a first end  20  with a recording and/or reading head or slider  22 , and a second end  24  pivotally mounted on a shaft by a bearing  26 . An actuator motor  28  is located at the arm&#39;s second end  24 , for pivoting the arm  18  to position the head  22  over a desired sector of the disc  16 . The actuator motor  28  is regulated by a controller that is not shown in this view and is well-known in the art. 
       FIG. 2  schematically illustrates a structure for heating a magnetic recording medium  16  approximate to where the recording head  22  applies a magnetic write field to the recording medium  16  ( FIG. 1 ) in, for example, a heat assisted magnetic recording (HAMR) system. A light source  30  which may be, for example, a laser diode or other suitable laser light source, is used for generating an electromagnetic wave, as represented by arrow  32 . The electromagnetic wave  32  passes through an optical component  34  which in turn directs the electromagnetic wave  32  toward an optical condenser  36 . The optical component  34  may include at least one of, for example, an optical flat, an optical fiber, a laser diode, a lens, a mirror, or a half wave plate. In accordance with an aspect of the invention, a phase compensator for phase shifting a portion of the electromagnetic wave  32  may be positioned along the optical path of the electromagnetic wave  32 . In addition, additional structure for phase shifting the electromagnetic wave may or may not be included within the optical condenser  36 , as will be described in more detail herein. 
       FIG. 3  illustrates a more detailed view of the optical condenser  36 . Specifically, the optical condenser  36  may include a planar waveguide  38  which may be, for example, in the form of a solid immersion mirror (SIM) or a parabolic mirror. The waveguide  38  may have a near field transducer  52  such as, for example, a metallic pin adjacent to an end near the air-bearing surface (ABS) of the recording head  22 . The waveguide  38  includes a dual input grating coupler, generally represented by arrow  40  that is comprised of gratings  42  and  44  separated by a gap  46 . A focus spot or laser spot  33  generated by electromagnetic wave  32  is directed onto the gratings  42  and  44  and coupled to the waveguide  38  by the gratings to produce the electromagnetic waves within the waveguide  38 , as illustrated by arrows  32   a  and  32   b . The electromagnetic waves  32   a  and  32   b  are illustrated as phase shifted by 180° with respect to the wave illustrated by arrow  32   a . Arrows  48  and  50  illustrate the instantaneous electric field of the waves. The waves are reflected off of the parabolic sides of the waveguide  38  and the electric field components of the reflected waves add in the vertical direction at the transducer  52  so that the transducer  52  concentrates the electromagnetic waves near the ABS of the recording head  22  to heat a portion of the magnetic storage medium  16 . The waveguide  38  is shown to be embedded, for example, in a cladding layer  54  and mounted on a slider  56 . 
     As described herein, the optical condenser  36  can provide for phase shifting a portion of the electromagnetic wave  32 . For example,  FIG. 4  makes use of a diffraction grating arrangement for providing the phase shifting. Specifically,  FIG. 4  illustrates a two dimensional planar waveguide  58  in the form of, for example, a SIM and including first and second diffraction gratings  60  and  62 . Diffraction gratings are commonly used to inject light into a planar waveguide. To generate split linear polarization, the two diffraction gratings  60  and  62  are used with a longitudinal offset X between them as illustrated. The purpose of the dual grating is to introduce a relative phase shift of about 180° between the two halves of the light beam. Arrows  64  and  66  illustrate an incident electromagnetic wave having an electric field represented by arrows  68  and  70 , respectively, and a transverse electric waveguide mode having an electric field represented by arrows  72 ,  74 ,  76  and  78 . As shown by arrows  68  and  70 , the electric field of the incident wave is initially linearly polarized in the plane of the waveguide for TE modes. Grating  60  is used to launch the wave into half of the waveguide  58 . Grating  62  is used to launch the wave into the other half of the waveguide  58 . The longitudinal offset and the position of the two gratings causes a 180° phase shift to occur between the two waveguide modes as shown by arrows  72  and  74 . After reflection from the edges  80  and  82  of the waveguide  58 , the reflected waves as illustrated by arrows  84  and  86  have electric fields that include both longitudinal and transverse components in the case of a TE polarization. When the reflected waves meet at the focal point, the transverse components of the fields cancel and the longitudinal components of the electric fields add. This excites surface plasmons on the near field transducer  88 , which may be, for example, a metallic pin. 
     In contrast to providing for phase shifting the electromagnetic wave within the optical condenser  36 , such as providing the offset gratings  60  and  62  as described herein and illustrated in  FIG. 4 , an aspect of the invention includes providing for the phase shifting of the electromagnetic wave to occur prior to the electromagnetic wave reaching the diffraction gratings. It will be appreciated that in accordance with the invention, phase shifting may occur prior to the electromagnetic wave reaching the diffraction gratings and/or phase shifting may occur once the electromagnetic wave reaches the diffraction gratings as well. 
       FIG. 5  illustrates an embodiment of the invention for phase shifting the electromagnetic wave  32 . Specifically,  FIG. 5  illustrates a phase compensator  90  which in this embodiment includes an optical flat  92  with a thickness t and a refractive index n f  and having a thin film  94  with a thickness d 1  and a refractive index n d  deposited on the optical flat  92 . As used herein, “optical flat” generally refers to an optical component formed of a transparent material and having opposing surfaces wherein each surface has a flatness less than about one-tenth the wavelength of an electromagnetic wave that would propagate or pass through the optical flat. The film  94  provides a split line  96  for the optical flat  92  such that a portion of the electromagnetic wave  32   a  that passes through the film  94  and the optical flat  92  on one side of the split line  96  is phase shifted relative to the remaining portion of the electromagnetic wave  32   b  that passes only through the optical flat  92  on the other side of the split line  96 . Thus, it will be appreciated that the split line  96  acts as a dividing line for determining which portion of the wave  32  is phase shifted and which portion of the wave  32  is not phase shifted. The thicknesses and material choices for the optical flat  92  and the film  94  are selected to provide the desired amount of phase shifting, which in one embodiment of the invention is about 180°. To generate split linear light, the optical path difference between the part of the electromagnetic wave  32   a  that passes through both the film  94  and the optical flat  92  and the part of the electromagnetic wave  32   b  that passes just through the optical flat  92  must satisfy the following equation: 
                         (       2   ⁢   m     +   1     )     ⁢   λ     2     =       (       n   d     -   1     )     ⁢     d   1               (     Equation   ⁢           ⁢   1     )               
In this equation, m is an integer ≦0 and λ equals the wavelength of the electromagnetic wave  32 .
 
       FIG. 6  illustrates another embodiment of the invention that includes a phase compensator  90   a  which comprises an optical flat  92   a  having a thickness t and a refractive index of and a portion of the optical flat that is etched to create a void, generally represented by arrow  98  wherein the void has a depth or thickness illustrated by arrow d 2 . Once the electromagnetic wave  32  passes through the phase compensator  90   a , then one side of the beam  32   a  will be phase shifted relative to the beam  32   b  due to the void  98 . The void  98  further defines the split line  96   a  for determining how much of the electromagnetic wave will be phase shifted. The amount of material that must be removed to form the void  98  must satisfy the following relationship: 
     
       
         
           
             
               
                 
                   
                     
                       
                         ( 
                         
                           
                             2 
                             ⁢ 
                             m 
                           
                           + 
                           1 
                         
                         ) 
                       
                       ⁢ 
                       λ 
                     
                     2 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           n 
                           f 
                         
                         - 
                         1 
                       
                       ) 
                     
                     ⁢ 
                     
                       d 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
     As illustrated in  FIGS. 5 and 6 , the phase compensators  90  and  90   a  may be integrally combined with, for example, the optical component  34 , or the phase compensators  90  and  90   a  may be formed separate from or without the optical component  34 . The phase compensator  90  or  90   a , or other phase compensators constructed in accordance with the invention, may be advantageously positioned at any point along the optical path from the light source  30  to the optical component  34  to the optical condenser  36  as long as the placement of the phase compensator allows for phase shifting of the electromagnetic wave prior to the electromagnetic wave  32  being coupled into the optical condenser  36 . 
     The optical flat  92  and  92   a  illustrated in  FIGS. 5 and 6 , respectively, may be formed of glass or any other common transparent material. In addition, the optical flat  92  and  92   a  thicknesses t may be in the range of about 0.1 mm to about 1 cm. Furthermore, the film  94  may be formed of silicon nitride, aluminum oxide or any other transparent film. In addition, the film  94  may have a thickness d 1  in the range of about 100 nm to about 1000 nm. The void  98  illustrated in  FIG. 6  may have a depth or thickness d 2  in the range of about 350 nm to about 1000 nm. 
     The phase compensators  90  and  90   a  may be positioned anywhere along the optical path from the light source  30  to the optical component  34  to the optical condenser  36 , such as placing the phase compensator  90  or  90   a  on the slider  56  portion thereof. The phase compensators  90  and  90   a  need to be generally centered on the wave  32  (made up of  32   a  and  32   b ) so that the wave intersects the respective split lines  96  and  96   a , i.e., in one embodiment preferably about half of the wave  32  is phase shifted and about half of the wave  32  is not phase shifted. 
     Electromagnetic modeling of the electromagnetic waves  32   a  and  32   b  that pass through the phase compensator  90 , as illustrated in  FIG. 5  indicate that the focus spot will have two maxima with one maxima phase shifted relative to the other. This is illustrated in  FIGS. 7   a  and  7   b . Specifically,  FIG. 7   a  illustrates an optical condenser  36   a  that is similar to the optical condenser  36  illustrated in  FIG. 3  and described herein except that as described the phase shifting of the electromagnetic wave occurs prior to the wave reaching the condenser  36   a  and results in focus spots  33   a  and  33   b  on the gratings  42   a  and  44   a .  FIG. 7   b  illustrates the intensity versus position across the width of the gratings for the phase compensated wave (shown in dotted line) as opposed to the non-phase compensated wave that is incident upon the gratings without any prior phase shifting (shown in solid line). It will be apparent that one advantage of the invention is that due to the gap  46   a  being formed between the gratings  42   a  and  44   a , the portion of the electromagnetic wave in the center portion of the structure that would otherwise not be coupled into the waveguide is now being efficiently coupled into the gratings  42   a  and  44   a  as a result of the focus spots  33   a  and  33   b  and the intensity profile as illustrated. This results in the efficient coupling of the electromagnetic wave into the optical condenser  36   a  in order that a smaller and a more intense optical spot may be generated. 
       FIG. 8   a  illustrates a phase compensator  190  constructed in accordance with the invention. Specifically, the phase compensator  190  was fabricated using electron beam evaporation of, for example, a thin film  194  of alumina onto an optical flat  192 . A shadow mask was used so that the thin film  194  of alumina was only deposited on one-half of the optical flat  192 . The phase compensator  190  was fabricated for a wavelength of 830 nm, so the target thickness was 638 nm [(830 nm)/2/(1.65−1)]. In the direction perpendicular to the split line  196 , the focused spot has two maxima  195  and  197  (see  FIG. 8   b ) while in the direction parallel to the split line  196 , there is one maximum 199 (see  FIG. 8   c ). An advantage to using this technique is that the two maxima  195  and  197  are better suited for coupling light into the waveguide since no energy is lost in the gap between the gratings. It will be appreciated that the thin film coating should not be limited to optical flats only and can be deposited, for example, on the end of an optical fiber, on the facet of a laser diode, on a focusing lens or on a slider. 
     Although any transparent dielectric material can be used for the thin film that is deposited, for example, on an optical flat as described herein, ideally the dielectric materials are made of the same material as the optical flat. If this is done, then the reflection losses from the dielectric/air interface will be the same as at the optical flat/air interface for the remainder of the optical flat and there will be no reflection losses at the dielectric/optical flat interface thereby maintaining equal amplitudes for the transmitted electric fields which correspond to the best interference between the two beams and the focal plane in the lowest minimum at the center of the spot. Furthermore, a dielectric anti-reflection coating may be applied uniformly over the phase compensator  90 ,  90   a  or  190 . 
       FIG. 9  illustrates an additional embodiment of a phase compensator  200  constructed in accordance with the invention. In this embodiment, the phase compensator  200  includes a half wave plate. In an optical wave plate, there is a fast and slow axis and they are designed so that a beam traveling on the fast axis will be shifted by a half wavelength relative to the slow axis. To adjust the phase of the incident beam, a half wave plate is cut in half and assembled together as shown in  FIG. 9 . It should be noted that two separate half wave plates cannot be used because they will not have the same total optical path link along their fast or slow axes. The arrows  202  and  204  refer to the fast axis of the film once assembled. The slow axes are at a right angle to the fast axes. A beam of light or wave  32   b  passing through the phase compensator  200  is polarized along the fast axis  204  while the other half of the beam or wave  32   a  travels along the slow axis that is at a right angle to fast axis  202 . By definition a beam traveling on the slow axis experiences a 180 degree phase shift. 
     It will be appreciated that a phase compensator constructed in accordance with the invention (such as, for example, phase compensator  90  illustrated in  FIG. 5 , phase compensator  90   a  illustrated in  FIG. 6 , and phase compensator  190  illustrated in  FIG. 8   a ) provide for the phase compensator to include a first section or portion having different wave propagation characteristics than a second section or portion of the phase compensator. For example, phase compensator  90  illustrated in  FIG. 5  includes a first section that includes the thin film  94  and the optical flat  92  on one side of the split line  96  that provides for the wave  32   a  to propagate through this section in a different manner than how the wave  32   b  propagates through the optical flat  92  section. Thus, the differing wave propagation characteristics of the phase compensator  90  allow for the desired phase shifting. Phase compensator  90   a  includes a first section having the void  98  on one side of the split line  96   a  which results in different wave propagation characteristics than the second section that only includes the optical flat  92   a  on the other side of the split line  96   a . Also, the phase compensator  190  has different wave propagation characteristics for the optical flat  192  section in comparison to the section on the other side of the split line  196  that includes a thin film  194  deposited on the optical flat  192 . Advantageously, by providing a phase compensator having first and second sections or portions that have differing wave propagation characteristics, an incoming wave  32  may be phase shifted as desired depending upon the particular wave propagation characteristics, e.g., refractive index differences, thickness differences, material differences or other optical property differences, that are selected. 
     The overall coupling efficiency of a device is the product of the grating efficiency and the amount of light that hits the grating. Because of finite size of the grating in the incident spot, not all the light hits the grating and there is an optimal spot size for a given grating. This is referred to as the “filling factor” for the SIM opening.  FIG. 10  illustrates this concept wherein there is provided gratings  242  and  244  with a gap  246  therebetween for coupling light into a planar waveguide  238  constructed in the form a SIM. The total power in the cross track direction (i.e., the filling factor) that couples into the waveguide  238  is given by the integral expression as follows: 
                           P   av     =       ⁢         ∫     -   W       -   a       ⁢       1     σ   ⁢       2   ⁢   π           ⁢     ⅇ     -       x   2       2   ⁢     σ   2             ⁢           ⁢     ⅆ   x         +       ∫   a   W     ⁢       1     σ   ⁢       2   ⁢   π           ⁢     ⅇ     -       x   2       2   ⁢     σ   2             ⁢           ⁢     ⅆ   x                       =       ⁢       erf   ⁡     (     W       2     ⁢   σ       )       -     erf   ⁡     (     a       2     ⁢   σ       )                       (     Equation   ⁢           ⁢   3     )               
wherein x equals a variable unit of length in the same direction as “a” and “W”, erf equals an error function, and the remaining parameters are as illustrated in  FIG. 10 .
 
The optimal spot size is given by the following equation:
 
     
       
         
           
             
               
                 
                   
                     σ 
                     optimal 
                   
                   = 
                   
                     
                       
                         
                           W 
                           2 
                         
                         - 
                         
                           a 
                           2 
                         
                       
                       
                         2 
                         ⁢ 
                         
                           ln 
                           ⁡ 
                           
                             ( 
                             
                               W 
                               a 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                   ) 
                 
               
             
           
         
       
     
       FIG. 11  illustrates a similar configuration as set forth in  FIG. 10  wherein there is provided gratings  242  and  244  with a gap  246  therebetween for coupling an electromagnetic wave into a planar waveguide  238 . In the embodiment illustrated in  FIG. 11 , the wave that is coupled into the gratings  242  and  244  is provided by, for example, the phase compensator  190  set forth in  FIG. 8   a  having the two maxima separated by a distance  2   u  as opposed to the single maximum. For this embodiment, the total power in the cross track direction (i.e., the filling factor) that couples into the waveguide  238  is given by the following integral expression: 
                           P   av     =       ⁢         1   2     ⁢       ∫     -   W       -   a       ⁢       1     σ   ⁢       2   ⁢   π           ⁢     ⅇ     -         (     x   +   u     )     2       2   ⁢     σ   2             ⁢           ⁢     ⅆ   x           +       1   2     ⁢       ∫   a   W     ⁢       1     σ   ⁢       2   ⁢   π           ⁢     ⅇ     -         (     x   -   u     )     2       2   ⁢     σ   2             ⁢           ⁢     ⅆ   x                         =       ⁢         1   2     ⁢     erf   ⁡     (       W   -   u         2     ⁢   σ       )         -       1   2     ⁢     erf   ⁡     (       a   -   u         2     ⁢   σ       )                         (     Equation   ⁢           ⁢   5     )               
wherein x equals a variable unit of length in the same direction as “a” and “W”, erf equals an error function, and the remaining parameters are as illustrated in  FIG. 11 .
 
The optimal spot size is provided by the following equation:
 
                     σ   optimal     =             (     W   -   u     )     2     -       (     a   -   u     )     2         2   ⁢     ln   ⁡     (       W   -   u       a   -   u       )                     (     Equation   ⁢           ⁢   6     )               
In one embodiment of the invention set forth in  FIG. 11 , 2 W=50 μm and 2a=6 μm.
 
       FIG. 12  illustrates the filling factor for the embodiments set forth in  FIG. 10  (without phase compensator) and  FIG. 11  (with phase compensator).  FIG. 12  clearly illustrates that with the use of a phase compensator one can choose the FWHM of the incident spots and the separation between them in order to achieve a filling factor of about 1.0. This is not possible for coupling with a traditional Gaussian profile which  FIG. 12  illustrates a filling factor of approximately 0.75 is achievable. 
     Although the phase compensator described herein can be used in any coupling application where split linear light is required, it is better suited for a situation where a coupling grating is not used. For example, some of the light delivery options contemplated for heat assisted magnetic recording use an end fire coupling scheme where a phase compensator would be required to generate split linear light. In addition, the phase compensator might be useful in other as yet unforeseen applications where, for example, a prism coupler is used and split linear light is required. This may occur if the solid immersion mirror is ever used, for example, in a microscopy application. 
     Whereas particular embodiments have been described herein for the purpose of illustrating the invention and not for the purpose of limiting the same, it will be appreciated by those of ordinary skill in the art that numerous variations of the details, materials, and arrangement of parts may be made within the principle and scope of the invention without departing from the invention as described in the appended claims.