Abstract:
The present invention proposes a method for modulating refractive indices of optical fiber gratings, wherein the UV exposure on a least one assigned location of an optical fiber grating is divided into to two UV shots, and the intensities or phases of the two UV shots, which expose the location sequentially, are controlled to make the total exposure intensity of one assigned location maintained at a fixed value, whereby the interference fringes, which are created by a superposition of the two UV shots, have fixed phases and adjustable intensities, and whereby the dc index of the optical fiber grating maintains fixed and the ac index independently adjustable.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    1. Field of the Invention 
         [0002]    The present invention relates to an optical fiber grating technology, particularly to a method for modulating refractive indices of optical fiber gratings. 
         [0003]    2. Description of the Related Art 
         [0004]    FBG (Fiber Bragg Grating) is a key element for fiber communication. FBG functions as a filter to reflect the incident light with a wavelength meeting the Bragg condition and permit the light having other wavelengths to pass. FBG is extensively used in WDM (Wavelength Division Multiplexing) systems, DWDM (Dense Wavelength Division Multiplexing) systems, fiber sensor technology and fiber laser technology. 
         [0005]    In FBG fabrication, the cost and quality correlates closely with the variation of the refractive index of the fiber core. Recently, many FBG fabrication technologies have been proposed. A Taiwan patent pending of application No. 200515020 utilizes two polarized light beams, which are vertical to each other, to fabricate FBG, wherein one beam is used to write the fiber and modulate the refractive index, and the other beam is used to maintain the total exposure intensity at a given value. As this method has to control polarization, it needs additional optical elements to work, such as lenses, half-wave plates, and polarizing beam splitters, which will raise the cost. A Taiwan patent pending of application No. 200515021 controls the polarization direction of one light beam in a two beam interference method to maintain the total intensity at a given value, wherein the intensities of the interference fringes are modulated via the relative polarization directions of two light beams. This method can only apply to the two beam interference method. As this method also has to control polarization, it also needs additional optical elements, and the cost thereof also increases. In a paper, by J. B. Jensen, et al., in Optics Letters 2002, p. 1004, the polarization directions are controlled in the phase mask method to maintain the total exposure at a given intensity, and the intensities of the interference fringes are modulated with the intensities of two light beams having different polarization directions. This method can only apply to the phase mask method. As this method also has to control polarization, it also needs additional optical elements, such as half-wave plates and polarizers, and the cost thereof also increases. 
         [0006]    In a U.S. Pat. No. 5,830,622, some specified positions are exposed to UV (Ultra-Violet) light to adjust the refractive index thereof and introduce additional phase shifts. However, this method needs double UV exposures, which is time-consuming. Further, it is hard to obtain the desired phase shifts section by section. In a paper, by J. Albert, et al., in Electronics Letters, 1995, p. 223, an optical fiber is written with a special phase mask. However, the length of the fiber grating will be limited by the length of the phase mask. Further, the special phase mask increases the cost. Besides, the method lacks the flexibility to fabricate other specifications of fiber gratings but can only fabricate a special specification fiber grating. In a paper, by M. J. Cole, et al., in Electronics Letters, 1995, p. 1488, a fuzzy technology is used to modulate the refractive index. In this method, a perturbation error is likely to be introduced into the length of the fiber grating. Further, the dc index does not maintain constant but has a slight perturbation. 
         [0007]    Accordingly, the present invention proposes a novel method for modulating the refractive indices of optical fiber gratings to overcome the abovementioned problems. 
       SUMMARY OF THE INVENTION 
       [0008]    One objective of the present invention is to provide a method for modulating refractive indices of optical fiber gratings, wherein two shots of UV (Ultra-Violet) beams respectively having adjustable phases and different intensities are sequentially projected on an identical location of an optical fiber grating, and whereby the dc index maintains fixed, and the ac index can be independently modulated with the cost reduced and without using additional optical elements. 
         [0009]    Another objective of the present invention is to provide a method for modulating refractive indices of optical fiber gratings, whereby the ac index of an optical fiber grating can has an arbitrary profile. 
         [0010]    Further objective of the present invention is to provide a method for modulating refractive indices of optical fiber gratings, which can modulate the refractive index at any position of an optical fiber grating. 
         [0011]    In the method for modulating refractive indices of optical fiber gratings of the present invention, two shots of UV beams are sequentially projected on at least one location of an optical fiber grating; the total exposure intensity at one location is maintained constant; the intensities and phases of the two UV beams are controlled to maintain the dc index of the optical fiber grating fixed with the ac index adjustable. The present invention can also make the ac index of an optical fiber grating have an arbitrary profile. The two UV beams are sequentially and section by section projected on a plurality of locations of an optical fiber grating. In the entire exposure process, the two UV beams are equidistantly-spaced and partially-overlapped to expose the plurality of locations section by section, and the intensities and phases of the two UV beams are controlled to maintain the dc index fixed along the optical fiber grating and modulate the profiles of the ac index into an arbitrary shape. 
         [0012]    Below, the embodiments of the present invention will be described in detail in cooperation with the attached drawings to make easily understood the objectives, technical contents, characteristics and accomplishments of the present invention. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0013]      FIG. 1  and  FIG. 2  are diagrams schematically showing the process of a method for modulating refractive indices of optical fiber gratings according to the present invention; 
           [0014]      FIG. 3(   a ) is a diagram schematically showing a resultant amplitude of the a superposition of two UV beams with the phase differences thereof varied according to the present invention; 
           [0015]      FIG. 3(   b ) is a diagram schematically showing a resultant amplitude of a superposition of two UV beams with the intensities thereof varied according to the present invention; 
           [0016]      FIG. 4  is a diagram schematically showing amplitudes and phases of UV beam  1  and UV beam  2 ; 
           [0017]      FIG. 5(   a ) is a diagram schematically showing a profile of the normalized ac index in the case of symmetric phase shifts according to the present invention; 
           [0018]      FIG. 5(   b ) is a diagram schematically showing a relationship between the phase difference and the normalized ac index in the case of symmetric phase shifts according to the present invention; 
           [0019]      FIG. 6(   a ) is a diagram schematically showing a profile of the normalized ac index when the phase difference is π according to the present invention; and 
           [0020]      FIG. 6(   b ) is a diagram schematically showing a relationship between the intensity ratio and the normalized ac index when the phase difference is π according to the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0021]    Refer to  FIG. 1  and  FIG. 2  diagrams schematically showing the process of a method for modulating refractive indices of optical fiber gratings according to the present invention. As shown in  FIG. 1 , the present invention provides an optical fiber grating  10 . A plurality of locations X 1 , . . . , Xn is equidistantly assigned in the optical fiber grating  10  and divides the optical fiber grating  10  into a plurality of grating sections. The total exposure intensity at each location is written by two beams—UV beam  1  and UV beam  2 . UV beam  1  and UV beam  2  have a Gaussian shape, and the phases and intensities of them are adjustable. UV beam  1  and UV shot  2  are sequentially projected on locations X 1 , . . . , and Xn section by section. In other words, UV beam  1  and UV beam  2  are sequentially projected on location X 1 ; then, UV beam  1  and UV beam  2  are sequentially projected on locations X 2 , . . . , and Xn respectively. The total exposure intensity at each location is identical. UV beam  1  and UV beam  2  are equidistantly-spaced and partially-overlapped in exposing locations X 1 , . . . , and Xn, as shown in  FIG. 2 . UV beam  1  and UV beam  2  have continuous phases in the grating sections so as to form the fiber Bragg grating having the predetermined index profile by generating a constructive superposition. As UV beam  1  and UV beam  2  are equidistantly-spaced in exposing locations X 1 , . . . , and Xn, the dc index maintains fixed along the optical fiber grating  10 , and the ac index can be modulated via changing the intensities and phases of UV beam  1  and UV beam  2 . 
         [0022]    Below are disclosed two approaches of controlling the intensities and phases of UV beam  1  and UV beam  2  to modulate the ac index according to the present invention. In Approach I of the present invention, it is supposed that the total exposure intensity at each location is 2I 0 , and that the Gaussian-shaped UV beam  1  and UV beam  2  have an identical intensity I 0 . The phase differences between one location (X 2 , . . . , or Xn) and the positions where UV beam  1  and UV beam  2  for the location are projected on the optical fiber grating  10  are respectively Δθ and −Δθ. In other words, UV beam  1  and UV beam  2  have symmetric phase shifts. Thus, the phase difference between the fringe distribution created by a superposition of UV beam  1  and UV beam  2  and the corresponding grating section will be zero. Then, the ac index can be modulated via modulating the phase difference Δθ and −Δθ. As the ac index n ac  of the optical fiber grating varies linearly with the intensities of UV light, the ac index is proportional to the fringe distribution created by a superposition of UV beam  1  and UV beam  2 . Refer to  FIG. 3(   a ) a diagram schematically showing the ac indices at one location for different Δθ&#39;s when UV beam  1  and UV beam  2  has an identical intensity I 0 . When Δθ=π/2, complete destructive interference occurs, and the amplitudes thereof mutually cancel out, and n ac  is minimum. When Δθ=π/3, the amplitudes thereof partially cancel out. When Δθ=0, complete constructive interference occurs and generates the greatest amplitude, and n ac  is maximum. Refer to  FIG. 4  a diagram schematically showing the amplitudes and phases of UV beam  1  and UV beam  2 . UV beam  1  and UV beam  2  can be respectively expressed by Equation (1) and Equation (2): 
         [0000]        I ( x )= I   1   e   i(kx+θ     1     )    (1) 
         [0000]        I ( x )= I   2   e   i(kx+θ     2     )    (2) 
         [0000]    wherein I 1  and I 2  are respectively the intensities of UV beam  1  and UV beam  2 , and θ 1  and θ 2  are respectively the phase differences with respect to one location. The phase and amplitude of the interference fringe distribution created by a superposition of UV beam  1  and UV beam  2  can be expressed by Equation (3): 
         [0000]        I ( x )= I   1   e   i(kx+θ     1     )   +I   2   e   i(kx+θ     2     )    (3) 
         [0000]    As UV beam  1  and UV beam  2  have an identical intensity I 0  and respectively have phase differences Δθ and −Δθ, Equation (4) can be derived from Equation (3) and expressed by 
         [0000]        I ( x )=2 I   0   e   ikx  cos(Δθ) ∝  n   ac    (4) 
         [0000]    wherein the ac index is proportional to the interference fringe distribution. Refer to Table 1 and  FIG. 3(   a ) for the normalized ac indices with respect to several phase differences Δθ (0, π/3, π/2). Refer to  FIG. 5(   a ) and  FIG. 5(   b ) for the profiles of the normalized ac indices and the relationship between the phase difference and the normalized ac index. 
         [0023]    In Approach II of the present invention, it is supposed that the total exposure intensity at each location is 2I 0 , and that UV beam  1  and UV beam  2  have different intensities. In other words, UV beam  1  and UV beam  2  sequentially expose one location respectively with an intensity mI 0  and an intensity (2 31  m)I 0 . Further, the phase differences between one location and the positions where UV beam  1  and UV beam  2  for the location are projected on the optical fiber grating  10  are respectively 0 and π. Thus, the phase difference between the fringe distribution created by a superposition of UV beam  1  and UV beam  2  and the corresponding grating section will be zero. Then, the ac index can be modulated via modulating the intensities of UV beam  1  and UV beam  2 . Refer to  FIG. 3(   b ) a diagram showing the ac indices at one location for different intensities of UV beam  1  and UV beam  2  when the phase differences of UV beam  1  and UV beam  2  with respect to the location are respectively 0 and π. When UV beam  1  and UV beam  2  have an identical intensity I 0 , complete destructive interference occurs, and the amplitudes thereof mutually cancel out, and n ac  is minimum. When UV beam  1  has an intensity 1.5I 0  and UV beam has an intensity 0.5I 0 , the amplitudes thereof partially cancel out. When UV beam  1  has an intensity 2I 0  and UV beam has an intensity 0, the resultant amplitude is completely contributed by UV beam  1 , and n ac  is maximum. The phase and amplitude of the interference fringe distribution created by a superposition of UV beam  1  and UV beam  2  can be expressed by Equation (5): 
         [0000]        I ( x )=2 I   0   e   ikx ( m −1) ∝  n   ac    (5) 
         [0000]    Refer to Table 1 and  FIG. 3(   b ) for the ac indices with respect to different intensities in Approach II. Refer to  FIG. 6(   a ) and  FIG. 6(   b ) for the profiles of the normalized ac indices when the phase difference is π in Approach II and the relationship between the intensity ratio and the normalized ac index. 
         [0000]    
       
         
               
               
               
             
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
             
             
               
                   
                   
               
               
                   
                 Parameters 
                   
               
             
          
           
               
                   
                   
                 Approach I 
                 Approach II 
               
               
                   
                   
                 θ 1  = −θ 2  = Δθ 
                 θ 1  = 0, θ 2  = π 
               
               
                   
                 Normalized n ac   
                 I 1  = I 2  = I 0   
                 I 1  = mI 0 , I 1  + I 2  = 2I 0   
               
               
                   
                   
               
               
                   
                 n ac  = 1 
                 Δθ = 0 
                 m = 2 
               
               
                   
                 n ac  = 0.5 
                 Δθ = π/3 
                 m = 1.5 
               
               
                   
                 n ac  = 0 
                 Δθ = π/2 
                 m = 1 
               
               
                   
                   
               
             
          
         
       
     
         [0024]    From  FIG. 5(   a ) and  FIG. 6(   a ), it is known that an optical fiber grating with a bell-shaped ac index distribution is obtained via controlling the intensities or phases of two UV beams. The method for modulating refractive indices of optical fiber gratings of the present invention can apply to an optical fiber grating in any location where a refractive index modulation is intended. For example, when the refractive index modulation is only needed in one grating section, a location is assigned to the grating section, and two beams of UV beams are projected on the location with the phases or intensities of UV beams being varied according to one of the approaches of the present invention. Thus, the refractive index modulation is realized in the grating section. Therefore, the present invention can indeed modulate the profile of the ac index into an arbitrary shape. 
         [0025]    In conclusion, the method for modulating refractive indices of optical fiber gratings of the present invention controls the phases and intensities to maintain the dc index fixed with the ac index independently adjustable without using additional optical elements. The method of the present invention is simple and cost-efficient. Further, the present invention can apply to the phase-mask and double beam interference technologies. 
         [0026]    The embodiments described above are only to exemplify the technical thoughts and characteristics of the present invention to enable the persons skilled in the art to understand, make, and use the present invention. However, it is not intended to limit the scope of the present invention. Any equivalent modification or variation according to the spirit of the present invention is to be also included within the scope of the present invention.