Abstract:
An electro-optic modulator includes a substrate, an end-to-end Y-shaped waveguide for optical divergence and convergence, and electrodes. The waveguide is formed in the substrate and the electrodes are formed to substantially sandwich the waveguide in the substrate and voltages applied to the electrodes act to modulate first and second sections of the waveguide such that the optical outputs by the first and second sections are equal or opposite to each other in all necessary respects regarding phase and amplitude, and an improved extinction ratio thus obtained.

Description:
BACKGROUND 
       [0001]    1. Technical Field 
         [0002]    The present disclosure relates to integrated optics and, particularly, to an electro-optic modulator having a high extinction ratio when functioning as a switch. 
         [0003]    2. Description of Related Art 
         [0004]    Electro-optic modulators, such as Mach-Zehner electro-optic modulators, change a refractive index of a branch of a Y-shaped waveguide (hereinafter the first branch) using a modulating electric field, utilizing electro-optic effect. Thus, the modulator can alter a phase of lightwaves traversing the first branch. As a result, the lightwaves traversing the first branch can be given a phase shift and thus interfere with lightwaves traversing another branch of the Y-shaped waveguide (hereinafter the second branch). An output of the Y-shaped waveguide is modulated as the output depends on the phase shift, which in turn depends on the modulating electric field. However, being limited by manufacturing imprecision, all the properties of the lightwaves traversing the first and second branches are not the same. As such, when the modulator is used as a switch, the output is often larger than zero in an off state (i.e., the phase shift is π ) or less than a desired maximum value in an on state (i.e., the phase shift is zero). An extinction ratio of the switch is thus less than satisfactory. 
         [0005]    Therefore, it is desirable to provide an electro-optic modulator that can overcome the above-mentioned problems. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0006]    Many aspects of the present disclosure can be better understood with reference to the following drawings. The components in the drawings are not necessarily drawn to scale, the emphasis instead being placed upon clearly illustrating the principles of the present disclosure. 
           [0007]      FIG. 1  is an isometric view of an electro-optic modulator, according to an embodiment. 
           [0008]      FIG. 2  is a cross-sectional view taken along a line II-II of  FIG. 1 . 
       
    
    
     DETAILED DESCRIPTION 
       [0009]    Embodiments of the present disclosure will be described with reference to the drawings. 
         [0010]      FIGS. 1 and 2  show an electro-optic modulator  10 , according to an embodiment. The modulator  10  includes a substrate  110 , a waveguide  120 , a first ground electrode  131 , a first modulating electrode  132 , a second ground electrode  133 , a second modulating electrode  134 , a third ground electrode  135 , and a third modulating electrode  136 . 
         [0011]    The substrate  110  is made of lithium niobate (LiNbO 3 ) crystal to increase a bandwidth of the modulator  10 , as LiNbO 3  crystal has a high response speed. In this embodiment, the substrate  110  is substantially rectangular and includes a top surface  114 . 
         [0012]    The waveguide  120  is formed by applying a layer of titanium as a coating on a shape corresponding to the waveguide  120  and diffusing the titanium into the substrate  110  by, for example, a high temperature diffusion technology. In this embodiment, the waveguide  120  is formed in the top surface  114 . 
         [0013]    The waveguide  120  is Y-shaped and formed in the substrate  110 . The waveguide  120  includes a first section  121  and a second section  122 . The first section  121  is Y-shaped and includes a first branch  124  and a second branch  125 . The second section  122  is Y-shaped and includes a third branch  127  and a fourth branch  128 . 
         [0014]    The first to fourth branches  124 ,  125 ,  127 ,  128  are substantially parallel with each other and the second and fourth branches  125 ,  128  are located at opposite sides of the first and third branches  124 ,  127 . 
         [0015]    In addition to the first section  121  and the second section  122 , the waveguide  120  includes an input section  129  and an output section  12   a.  The first and second sections  121 ,  122  diverge from the input section  129  and are converged into the output section  12   a.    
         [0016]    In addition to the first branch  124  and the second branch  122 , the first section  121  includes a first input branch  12   b  and a first output branch  12   c.  The first and second branches  124 ,  125  diverge from the first input branch  12   b  and are converged into the first output branch  12   c.    
         [0017]    In addition to the third branch  127  and the fourth branch  128 , the second section  122  includes a second input branch  12   d  and a second output branch  12   e.  The third and fourth branches  127 ,  128  diverge from the second input branch  12   d  and are converged into the second output branch  12   e.    
         [0018]    The substrate  110  defines first to third recesses  111 - 113 , all of which are substantially rectangular and arranged to be parallel with the first to fourth branches  124 ,  125 ,  127 ,  128 , in the top surface  114 . A depth of each of the first to third recesses  111 - 113  is larger than a thickness of the waveguide  120 . The first and second recesses  111 ,  112  are located at two opposite sides of the first section  121 . The second and third recesses  112 ,  113  are located at opposite sides of the second section  122 . The first recess  111  has the same length as and is aligned with the second branch  125 . The third recess  113  has the same length as and is aligned with the fourth branch  128 . Orthogonal projections of the first and third recesses  111 ,  113  on the second recess  112  fall within the second recess  112 . 
         [0019]    The first to third recesses  111 - 113  are completely infilled by the first and second ground electrodes  131 ,  133 , and by the third modulating electrode  136  respectively. 
         [0020]    The first modulating electrode  132 , the second modulating electrode  134 , and the third ground electrode  135  are strip-shaped and parallel with the first to fourth branches  124 ,  125 ,  127 ,  128 . The first modulating electrode  132 , the second modulating electrode  134 , and the third ground electrode  135  are positioned on the top surface  114 . The first modulating electrode  132  is positioned between the first and second branches  124 ,  125 , and has the same length as and is aligned with the second branch  125 . The second modulating electrode  134  and the third ground electrode  135  cover the third and fourth branches  127 ,  128 , and have the same length as and are aligned with the fourth branch  128 . 
         [0021]    The first to third ground electrodes and the modulating electrodes  131 - 136  receive voltages and accordingly modulate the first and second sections  121 ,  122  such that optical outputs of the first and second sections  121 ,  122  are equal to each other. 
         [0022]    The output of the output section  12   a  can be calculated by the following equation: 
         [0000]      α e   i(α-wt) =α 1   e   i(φ-wt) +α 2   e   i(β-wt) ,
 
         [0000]    wherein, α, α 1 , α 2  are amplitudes of lightwaves traversing the output section  12   a,  the first output branch  12   c,  and the second output branch  12   e  respectively, α, φ, β are phases of lightwaves traversing the output section  12   a,  the first output branch  12   c,  and the second output branch  12   e  respectively, and where e is the natural exponent, i is the imaginary unit, ω is an angular velocity, and t is a time variable. 
         [0023]    The output of the output section  12   a  can be calculated by the following equation: 
         [0000]        S =α 2 =α 1   2 +α 2   2 +2α 1 α 2  cos (φ-β),
 
         [0000]    wherein S is the output of the output section  12   a.    
         [0024]    Similarly, the respective outputs of the first and second output branches  12   c,    12   e  can be calculated by the following equations: 
         [0000]      α 1   e   i(φ-wt) =α 11   e   i(φ     1     -wt) +α 12   e   i(φ     2     -wt) ,
 
         [0000]        Q   1 =α 1   2 =α 11   2 +α 12   2 +2α 11 α 12  cos (φ 1 -φ 2 ),
 
         [0000]      α 2   e   i(φ-wt) =α 21   e   i(β     1     -wt) +α 22   e   i(β     2     -wt) ,
 
         [0000]    and 
         [0000]        Q   2 =α 2   2 =α 21   2 +α 22   2 +2α 21 α 22  cos (β 1 -β 2 ),
 
         [0000]    wherein α 11 , α 12 , α 22 , α 22  are amplitudes of lightwaves traversing the first to fourth branches  124 ,  125 ,  127 ,  128  respectively, φ 1 , φ 2 , β 1 , β 2 , are phases of lightwaves traversing the first to fourth branches  124 ,  125 ,  127 ,  128  respectively, and Q 1 , Q 2  are the respective outputs of the first and second output branches  12   c,    12   e.    
         [0025]    The lightwaves have transverse electric waves (hereinafter the TE mode) and transverse magnetic waves (hereinafter the TM mode). In a coordinate system xyz (see  FIG. 1 ), wherein x axis is a vertical height of the substrate  110  (i.e., perpendicular to the top surface  114 ), the y axis is a horizontal width of substrate  110  (parallel with the top surface  114  and perpendicular to the first to fourth branches  124 ,  125 ,  127 ,  128 ), and the z axis is a length of the substrate  110  (i.e., along a direction that is parallel with the first to fourth branches  124 ,  125 ,  127 ,  128 ), the TE mode has an electric field component {right arrow over (Ey)} vibrating along the y axis only. The TM mode has an electric field component {right arrow over (Ex)} vibrating along the x axis and a {right arrow over (Ez)} vibrating along the z axis. 
         [0026]    By constructing the first to third recesses  111 - 113  and the first to third ground electrodes and the modulating electrodes  131 - 136 , as described above, the modulating electric fields Ē1, Ē2 Ē3 generated by the first to third ground electrodes and the modulating electrodes  131 - 136  traverse the first to fourth branches  124 ,  125 ,  127 ,  128 . A portion of the electric field Ē1 interacting with the first and second branches  124 ,  125  is substantially parallel with the y axis, and thus efficiently modulates the TE mode (i.e. Ey) and alters the phases φ 1 , φ 2 . Portions of the electric fields Ē2, Ē3 interacting with the third and fourth branches  127 ,  128  are substantially parallel with the x axis, and thus efficiently modulate the TM mode (i.e. Ex) and alters the phases β 1 , β 2 . 
         [0027]    By changing the phases φ 1 , φ 2 , β 1 , β 2 , the equations Q 1 =Q 2 , and φ−β=0 (or φ−β=π) can be applied. As such, when the modulator  10  is used as a switch, the output of the waveguide  120  will be exactly zero in an off-state and can be substantially at a desired maximum value in an on state, and thus an extinction ratio of the modulator  10  is increased. 
         [0028]    To avoid lightwaves being absorbed by the second modulating electrode  134  and the third modulating electrode  135 , a buffer layer  140  is formed and sandwiched between the substrate  110  and the second modulating electrode  134  and the third modulating electrode  135 . The buffer layer  140  can be made of silicon dioxide. 
         [0029]    It will be understood that the above particular embodiments are shown and described by way of illustration only. The principles and the features of the present disclosure may be employed in various and numerous embodiments thereof without departing from the scope of the disclosure. The above-described embodiments illustrate the possible scope of the disclosure but do not restrict the scope of the disclosure.