Abstract:
A ridge waveguide structure includes a substrate having a top surface; a ridge structure protruding from the top surface; and a waveguide formed in the ridge structure and a shape of the waveguide is corresponding to a shape of the ridge structure; the ridge structure includes a Y-shaped input section and a Y-shaped output section, the Y-shaped input section includes a total input section, a first branch and a second branch, the first branch and the second branch are diverged from the total input section and converged into the Y-shaped output section. The relation also relates to an electro-optic modulator.

Description:
BACKGROUND 
     1. Technical Field 
     The present disclosure relates to an electro-optic modulator having a ridge waveguide structure, wherein the electro-optic modulator can achieve a high extinction ratio when functioning as an optical switch. 
     2. Description of Related Art 
     Electro-optic modulators, such as Mach-Zehner electro-optic modulators, change a refractive index of a branch (hereinafter “the first sub-branch”) of a Y-shaped waveguide by employing a modulating electric field, which utilizes the electro-optic effect. Thus, the modulator can alter a phase of light waves traversing the first sub-branch. As a result, the phase of light waves traversing the first sub-branch can be shifted and thus interfere with light waves traversing another branch (hereinafter “the third sub-branch”) of the Y-shaped waveguide. An output of the Y-shaped waveguide is modulated as the power output depending on the phase shift, which in turn depends on the modulating electric field. However, due to manufacturing imprecision inherent in an electro-optic modulator, the properties of the light waves respectively traversing the first and third sub-branches are not equal to each other. As such, when the electro-optic modulator is used as an optical switch, the power output is often larger than zero in an off state, or is less than a desired maximum value in an on state That is, an extinction ratio of the optical switch may be less than what is considered to be satisfactory. 
     Therefore, it is desirable to provide an electro-optic modulator that can overcome the above-mentioned problems. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an isometric view of a ridge waveguide structure according to a first embodiment of the present invention. 
         FIG. 2  is an isometric view of an electro-optic modulator according to a second embodiment of the present invention. 
         FIG. 3  is a cross-sectional view taken along a line III-III of  FIG. 2 . 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1  shows a ridge waveguide structure  100  according to a first embodiment. The ridge waveguide structure  100  includes a substrate  10  defining a top surface  101 , a ridge structure  12  protruding from the top surface  101 , and a waveguide  13  formed in the ridge structure  12 . The substrate  10  is made of lithium niobate (LiNbO 3 ) or barium niobate (BaNbO 3 ). 
     A top surface of the ridge structure  12  is hollow, thereby defining a series of channels in the ridge structure  12 . The waveguide  13  is filled in the channels. A top surface of the waveguide  13  is substantially coplanar with the top surface of the ridge structure  12 . Thus a shape of the waveguide  13  corresponds to a shape of the ridge structure  12 . A width of the waveguide  13  is less than a width of the ridge structure  12 , and a height of the waveguide  13  is less than a height of the ridge structure  12 . In the illustrated embodiment, a transverse cross-section of any part of the ridge structure  12  defines four sides of a rectangle, with part of a top side of the rectangle recessed where the channel is located. A transverse cross-section of the channel defines a semicircle, or a segment that is smaller than a semicircle. Correspondingly, a transverse cross-section of any part of the waveguide  13  is a semicircle, or a segment that is smaller than a semicircle. In this embodiment, a height of the ridge structure  12  is about 3-4 microns, and a height of the waveguide  13  is about 0.6-0.8 microns. The waveguide  13  is formed in the ridge structure  12  using high temperature diffusion technology. The diffusion temperature is about 1020° C. In a preferred embodiment, the waveguide  13  is made of titanium. 
     The ridge structure  12  includes a Y-shaped input section  120 , a first sub-Y-shaped section  123 , a second sub-Y-shaped section  223 , and a Y-shaped output section  220 . The Y-shaped input section  120  includes a total input section  130 , a first branch  140 , and a second branch  150 . The first branch  140  and the second branch  150  diverge from the total input section  130 , and converge into the Y-shaped output section  220 . The first branch  140  and the second branch  150  have the same length. The length of the first branch  140  is in the range of from about 0.5 centimeters to about 1.0 centimeters. An included angle θ between the first branch  140  and the second branch  150  is not more than 2° . In a preferred embodiment, the included angle θ is about 1°. 
     The first branch  140  includes a first sub-Y-shaped section  123 . The first sub-Y-shaped section  123  includes a first sub-branch  124  and a second sub-branch  125 . The second sub-branch  125  includes a first section  301 , a second section  302  and a third section  303 . The first section  301  and the second sub-branch  125  diverge from the first branch  140 . The second section  302  interconnects the first section  301  and the third section  303 , and the second section  303  is parallel to the first sub-branch  124 . 
     The second sub-Y-shaped section  223  includes a third sub-branch  224  and a fourth sub-branch  225 . The fourth sub-branch  225  includes a fourth section  501 , a fifth section  502  and a sixth section  503 . The fifth section  502  interconnects the fourth section  501  and the sixth section  503 , and the fifth section  503  is parallel to the third sub-branch  224 . In this embodiment, the second sub-branch  125  and the fourth sub-branch  225  are positioned at two opposite sides of the combination of the first sub-branch  124  and the third sub-branch  224 . The first sub-branch  124  and the second sub-branch  125  cooperatively define a first recess  160  therebetween. The third sub-branch  224  and the fourth sub-branch  225  cooperatively define a second recess  260  therebetween. A center  02  of the second section  302 , a center O 1  of the first sub-branch  124 , a center O 3  of the second sub-branch  224 , and a center O 4  of the fifth section  502  all lie on a same straight imaginary line. 
     The Y-shaped output section  220  includes a total output section  230 , a first output section  240 , and a second output section  250 . The third section  303  and the first sub-branch  124  converge into the first output section  240 . The sixth section  503  and the third sub-branch  224  converge into the second output section  250 . The first output section  240  and the second output section  250  converge into the total output section  230 . The third sub-branch  224  extends in a straight line and is coupled to the first branch  140  and the first output section  240 . 
       FIGS. 2-3  show an electro-optic modulator  200  according to a second embodiment. The electro-optic modulator  200  includes the ridge waveguide structure  100 , a first electrode  30 , a second electrode  40 , a third electrode  50 , and a fourth electrode  60 . The first electrode  30 , the second electrode  40 , the third electrode  50  and the fourth electrode  60  are strip-shaped. The first electrode  30  and the third electrode  50  have a same size, and the second electrode  40  and the fourth electrode  60  have a same size. The first, second, third and fourth electrodes  30 ,  40 ,  50 ,  60  are made of metal, and are all formed on the top surface  101  by a vacuum sputtering method. 
     The first electrode  30  is located in the first recess  160 . The second electrode  40  is located beside the second sub-branch  125 . The third electrode  50  is located in the second recess  260 . The fourth electrode  60  is located beside the fourth sub-branch  225 . Centers of the first electrode  30 , the second electrode  40 , the third electrode  50 , and the fourth electrode  60  all lie on a same straight imaginary line. In this embodiment, the first and third electrodes  30 ,  50  are connected with ground, respectively; and the second and fourth electrodes  40 ,  60  are connected with a high potential, respectively. The first electrode  30  and the second electrode  40  are configured for cooperatively modulating the power output of the first output section  230 . The third electrode  50  and the fourth electrode  60  are configured for cooperatively modulating the power output of the second output section  240 . 
     In principle, the light waves traversing in the total output section  230  can be expressed by the following equation:
 
α e   i(α−wt) =α 1   e   i(φ−wt) +α 2   e   i(β−wt) ,
 
     wherein, α, α 1 , and α 2  are amplitudes of light waves traversing in the total output section  230 , the first output section  240 , and the second output section  250 , respectively; α, φ, and β are phases of light waves traversing in the total output section  230 , the first output section  240 , and the second output section  250 , respectively; e is the base of a natural logarithm exponent; i is an imaginary unit (i 2 =−1); ω is an angular velocity; and t is a time variable. 
     The power output of the total output section  230  can be calculated by the following equation:
 
 S=α   2 =α 1   2 +α 2   2 +2α 1 α 2  cos(φ−β),
 
     wherein S is the power output of the total output section  230 . 
     Similarly, the power outputs of the first and second output sections  240 ,  250  can be calculated by the following equations:
 
α 1   e   i(φ−wt) =α 11   e   i(φ     1     −wt) +α 12   e   i(φ     2     −wt) ,
 
 Q   1 =α 1   2 =α 11   2 α 12   2 +2α 11 α 12 cos(φ 1 −φ 2 ),
 
α 2   e   i(φ−wt) =α 21   e   i(β     1     −wt) +α 22   e   i(β     2     −wt) , and
 
 Q   2 =α 2   2 =α 21   2 +α 22   2 +2α 21 α 22 cos(β 1 −β 2 ),
 
     wherein α 11 , α 12 , α 21 , and α 22  are amplitudes of light waves traversing the first through fourth sub-branches  124 ,  125 ,  224 ,  225 , respectively; φ 1 , φ 2 , β 1 , and β 2 , are phases of light waves traversing the first through fourth sub-branches  124 ,  125 ,  224 ,  225 , respectively; and Q 1  and Q 2  are the respective output powers of the first and second output sections  240 ,  250 . 
     By changing the amplitudes α 11 , α 12 , α 21 , and α 22  and the phases φ 1 , φ 2 , β 1 , and β 2 , the following equations can be realized: Q1=0 (when φ 1 −φ 2 =π and α 11 =α 12 ); and Q2=0 (when β 1−β   2 =π and α 21 =α 22 ). Thus S=0 can be realized. When φ−β=0, a desired maximum value of S can be realized. As such, when the modulator  200  is used as an optical switch, the power output of the waveguide  13  is at zero in an off-state, and substantially reaches a desired maximum value in an on state. Thus an extinction ratio of the modulator  200  is increased. 
     In summary, the waveguide  13  is limited in the ridge structure  12 . Variation of the refractive index is larger than in a conventional planar optical waveguide, and crosstalk of light waves between adjacent sub-branches and/or branches can be avoided. The power output of the first output section  240  is modulated by the first sub-branch  124  and the second sub-branch  125 . The power output of the second output section  250  is modulated by the third sub-branch  224  and the fourth sub-branch  225 . By changing the phases of light waves traversing in the first through fourth sub-branches  124 ,  125 ,  224 ,  225 , the modulator  200  can be used as an optical switch. 
     It is to be understood that even though numerous characteristics and advantages of the present embodiments have been set forth in the foregoing description, together with details of the structures and functions of the embodiments, the disclosure is illustrative only, and changes may be made in detail, especially in the matters of shape, size, and arrangement of parts within the principles of the disclosure to the full extent indicated by the broad general meaning of the terms in which the appended claims are expressed.