Abstract:
A right-angle bending waveguide includes a circular-hole-type square-lattice photonic crystal (PhC) and a single compensation scattering rod having a low refractive index. The right-angle bending waveguide is a PhC formed from first dielectric rods having a low refractive index arranged in a background dielectric having a low refractive index according to a square lattice. In the PhC, one row and one column of the first dielectric rods having a high refractive index are removed to form the right-angle bending waveguide. A second dielectric rod having a high refractive index is arranged at a corner of the right-angle bending waveguide. The second dielectric rod is the compensation scattering rod or an air hole. The first dielectric rods are circular rods having the low refractive index or air holes. The right-angle bending waveguide having the circular-hole-type square-lattice PhC and the single compensation scattering rod having the low refractive index has extremely low reflectance and a very high transmission rate, facilitates large-scale optical path integration, and provides a broader space for PhC application.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a non-provisional application of an International Patent Application No. PCT/CN2015/090877 with a filing date of Sep. 28, 2015, designates the United States, now pending, and further claims priority to Chinese Patent Application No. 201410515261.7 with a filing date of Sep. 29, 2014. The content of the aforementioned applications, including any intervening amendments thereto, are incorporated herein by reference 
     
    
     NOTICE OF COPYRIGHT 
       [0002]    A portion of the disclosure of this patent document contains material which is subject to copyright protection. The copyright owner has no objection to any reproduction by anyone of the patent disclosure, as it appears in the United States Patent and Trademark Office patent files or records, but otherwise reserves all copyright rights whatsoever. 
       BACKGROUND OF THE PRESENT INVENTION 
     Field of Invention 
       [0003]    The present invention relates to a photonic-crystal bending waveguide, and more particularly to right-angle bending waveguide having a circular-hole-type dielectric rod with low refractive index, and a single compensation having low refractive index and arranged on a square-lattice photonic crystal (PhC) having high refractive index dielectric background. 
       Description of Related Arts 
       [0004]    In 1987, E. Yablonovitch of Bell laboratory of the United States and S. John of 
         [0005]    Princeton University independently put forward the concept of PhC respectively in discussion about suppressions of spontaneous radiations and in discussion about localizations of photons. The PhC has a substance structure formed by periodically arranging dielectric materials in a space, and is usually an artificial crystal composed of two or more materials with different dielectric constants. 
         [0006]    A PhC has strong and flexible control ability for the light propagation, and has high conduction efficiency for both of the linear transmission and sharp right-angle bending transmissions. If a line effect is introduced in the PhC architecture for creating a light-guiding channel, called a photonic crystal waveguide (PCW), the waveguide passed through this PhC architecture only has a small loss even at the corner of the right angle (90 degrees). The above mentioned PhC architecture is totally different from the traditional basic optical waveguide having the completely internal reflection, and the effect of the defect-type waveguide is adapted for guiding the photon within the photonic bandgap (PBG) to form a new state, and the density of the new state of photon adjacent to transmission mode in the defect-type waveguide is zero. Therefore, the defect-type waveguide is used as a PCW to achieve the transmission mode without the leakage of light, and the PCW is the basic device to form a photonic integrated circuit. The bending PCW can improve the integration of optical circuit, so the associated research with respect to the bending PCW is very important. 
       SUMMARY OF THE PRESENT INVENTION 
       [0007]    The invention is advantageous in that it provides a right-angle bending waveguide having a circular-hole-type square-lattice PhC and a single compensation scattering rod having a low refractive index, wherein the right-angle bending waveguide has an extremely low reflective index and a very high transmission index. 
         [0008]    In order to achieve the above mentioned advantage, the foregoing and other objects and advantages are attained by the following design: 
         [0009]    The right-angle bending waveguide having a circular-hole-type square-lattice PhC and a single compensation scattering rod having a low refractive index comprises a first dielectric rod having a low refractive index arranged in a high refractive index dielectric background to form a PhC having a square lattice, a corner position, a second dielectric rod having a low refractive index arranged on the corner position; the second dielectric rod is a/an compensation scattering rod or air hole, and the first dielectric rod is a/an circular-type and low refractive rod or air hole. 
         [0010]    The second dielectric rod can be a/an semicircular low refractive index rod or air hole, a/an bow-shape low refractive index rod or air hole, a/an circular low refractive index rod or air hole, a/an triangular low refractive index rod or air hole, a/an triangle low refractive index rod or air hole, a/an polygon low refractive index rod or air hole, or a/an low refractive rod or air hole having a smooth closed curve cross-sectional contour. 
         [0011]    The second dielectric rod is a/an semi-circular low refractive index rod or air hole. 
         [0012]    The high refractive index dielectric background is made of a dielectric having a refractive index greater than two. 
         [0013]    The high refractive index dielectric background is made of silicon, gallium arsenide, or titanium dioxide. 
         [0014]    The high refractive index background dielectric is made of silicon, which has a refractive index of 3.4. 
         [0015]    The low refractive index background dielectric is a medium having refractive index less than 1.6. 
         [0016]    The low refractive index background dielectric is air, vacuum, magnesium fluoride, or silicon dioxide. 
         [0017]    The background dielectric having low refractive index is air. 
         [0018]    The right-angle bending waveguide is a TE-mode waveguide. 
         [0019]    The area of the structure of the right-angle bending waveguide is equal or larger than 7a×7a, and here “a” is the lattice constant of the PhC. 
         [0020]    The PhC optical waveguide device of the present invention can be widely applied to various integrated photonic devices. Compared with the prior art, it has the following positive effects. 
         [0021]    1. The right-angle bending waveguide having circular-hole-type square-lattice PhC and single compensation rod with low refractive index has a very low reflection and a very high transmission index, which can provide a better application for PhCs; 
         [0022]    2. The structure of the present invention is based on the multiple scattering theory, wherein the light waves transmitted through the compensation scattering rod with low refractive index is able to achieve the compensation for the phase and amplitude, so as to reduce the reflection index, and enhance the transmission index; 
         [0023]    3. The right-angle bending waveguide having circular-hole-type square-lattice PhC and single compensation rod with low refractive index is based on a square-lattice structure, which can be used for large-scale integrated optical circuit designs, wherein the optical circuit of the present invention is simple and easy to be designed, so as to apply to large-scale optical integration devices; 
         [0024]    4. The right-angle bending waveguide having circular-hole-type square-lattice PhC and single compensation rod with low refractive index is based on a square-lattice structure, so that different light circuits and different optical elements are easy to be connected and coupled with each other, and the cost thereof is efficiently reduced. 
         [0025]    Still further objects and advantages will become apparent from a consideration of the ensuing description and drawings. 
         [0026]    These and other objectives, features, and advantages of the present invention will become apparent from the following detailed description, the accompanying drawings, and the appended claims. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0027]      FIG. 1  is a core region of a circular-hole type square-lattice PhC and a single compensation scattering right-angle bending waveguide having low refractive index according to a preferred embodiment of the present invention. 
           [0028]      FIG. 2  is a diagram of transmission characteristic vs. normalized frequency for the circular-hole square-lattice PhC and a single compensation scattering right-angle bending waveguide having a low refractive index according to the above mentioned preferred embodiment of the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       [0029]    The following description is disclosed to enable any person skilled in the art to make and use the present invention. Preferred embodiments are provided in the following description only as examples and modifications will be apparent to those skilled in the art. The general principles defined in the following description would be applied to other embodiments, alternatives, modifications, equivalents, and applications without departing from the spirit and scope of the present invention. 
         [0030]    Referring to  FIG. 1  of the drawings, a right-angle bending waveguide having a circular-hole-type square-lattice PhC and a single compensation scattering rod with a low refractive index according to a preferred embodiment of the present invention is illustrated, wherein the right-angle bending waveguide comprises a plurality of first dielectric rods having a low refractive index arranged in a high refractive index dielectric background to form a PhC having a square lattice. In the right-angle bending waveguide, one row or one column of the first dielectric rods with low refractive index is removed to form the right-angle bending waveguide; the right-angle bending waveguide further comprises a corner position, at least one second dielectric rod arranged on the corner position, wherein the second dielectric rod is a compensation scattering rod or an air hole, which can generate compensation reflection waves for offsetting with reflective waves from the right-angle bending waveguide; the compensation scattering rods can be a variety of shapes, such as semicircular low refractive index rods or air holes, bow-shape low refractive index rods, circular low refractive index rods or air holes, triangular low refractive index rods or air holes, triangle low refractive index rods or air holes, polygon low refractive index rods or air holes, or low refractive rods or air holes having smooth closed curve cross-sectional contours; The high refractive index background is made of a medium having refractive indexes greater than two; The high refractive index background is made of silicon, gallium arsenide, or titanium dioxide. The low refractive index background is a medium having refractive index less than 1.6; the low refractive index background can be used as air, vacuum, magnesium fluoride, or silicon dioxide; the low refractive index background can be used is air. 
         [0031]    A preferred embodiment are provided base on the above mentioned information: 
         [0032]    The lattice constant of the square-lattice PhC is a first dielectric rod having a low refractive index is a circular air rod (or air hole), and a radius of the air hole is 0.495a; light waves transmitted within the waveguide are polarized to form TE waves; the compensation scattering rod having low refractive index is air rod, which also can be called as a scattering hole or scattered air hole, so the second dielectric rod which is defined as compensation scattering rod is an air hole or an air rod. The second dielectric rod also can be a semi-circular air hole; The second dielectric rod is a semicircular scattering compensation air hole having a radius of 0.39538a; the coordinate of the second dielectric rod is defined by the displacement from the origin to X and Z-direction at distance of 0.18961a and 0.82705a respectively, and the angle of rotation is 124.722799 degrees; the light source is located at a coordinate of (−5.3a, 0) having a displacement according to X direction and the Z-direction respectively; an initial angle of an incident light is 160 degrees. The high-refractive-index second refractive dielectric background is silicon (Si) having a refractive index of 3.4; the low refractive index dielectric is air. The area of the structure of the PhC having the rectangular waveguide is 15a×15a, and a return loss spectrum and an insertion loss spectrum of the PhC having right-angle bending waveguides are shown in  FIG. 2 . As shown in  FIG. 2 , a horizontal axis of the spectrum is defined as working frequency, and the vertical axis of the spectrum is defined as transmission, wherein dotted lines are shown as the return loss (defined as L R =−10 log (P R /P I )), and solid lines are shown as the insertion loss (defined as L I =−10 log (P T /P I )), wherein P I  is the incident power, and P r  is the refractive power, and P T  is the transmission power. The highest value of the normalized frequency is 0.3 (ωa/2πc), and at the same time, the maximum value of the return loss and the insertion loss for the right-angle bending waveguide of the PhC is 34.07 dB and 0.0016 dB respectively. 
         [0033]    A first alternative mode of the above mentioned preferred embodiment is: The lattice constant of the square-lattice PhC is a, which is defined as 0.465 μm; so the optimum normalized wavelength is 1.542 μm; the first dielectric rod having the low refractive index is a circular air rod (or air hole), and a radius of the air hole is 0.230175 μm; light waves transmitted within the waveguide are polarized to form TE waves; the second dielectric rod which is defined as compensation scattering rod is a semi-circular air hole or an air rod; The second dielectric rod is a semicircular scattering compensation air hole having a radius of 0.183855 μm; the coordinate of the second dielectric rod is defined by the displacement from the origin to X and Z-direction at distance of 0.088169 μm and 0.384581 μm respectively, and the angle of rotation is 124.722799 degrees; the light source is located at a coordinate of (−2.4645 μm, 0) having a displacement according to X direction and the Z-direction respectively; the initial angle of the incident light is 160 degrees. The second refractive dielectric background having high refractive index is silicon (Si) having a refractive index of 3.4; the low refractive index dielectric is air. The area of the structure of the PhC having rectangular waveguide is 15a×15a, and the maximum value of the return loss and the insertion loss for the right-angle bending waveguide of the PhC is 20.542796 dB and 0.038303 dB respectively. 
         [0034]    A second alternative mode of the above mentioned preferred embodiment is: The lattice constant of the square-lattice PhC is a, which is defined as 0.465 μm, so the optimum normalized wavelength is 1.55 μm; the first dielectric rod having the low refractive index is a circular air rod (or air hole), and a radius of the air hole is 0.230175 μm; light waves transmitted within the waveguide are polarized to form TE waves; the second dielectric rod which is defined as compensation scattering rod is a semi-circular air hole or an air rod; The second dielectric rod is a semicircular scattering compensation air hole having a radius of 0.183855 μm; the coordinate of the second dielectric rod is defined by displacing from the origin to X and Z-direction at distance of 0.088169 μm and 0.384581 μm respectively, and the angle of rotation is 124.722799 degrees; the light source is located at a coordinate of (−2.4645 μm, 0) having a displacement according to X direction and the Z-direction respectively; an initial angle of an incident light is 160 degrees. The high refractive index second dielectric background is silicon (Si) having a refractive index of 3.4; the low refractive index dielectric is air. The area of the structure of the PhC having rectangular waveguide is 15a×15a, and the maximum value of the return loss and the insertion loss for the right-angle bending waveguide of the PhC is 34.07 dB and 0.0016 dB respectively. 
         [0035]    A third alternative mode of the above mentioned preferred embodiment is: The lattice constant of the square-lattice PhC is a, which is defined as 0.3 μm, so the optimum normalized wavelength is 1.00 μm; the first dielectric rod having a low refractive index is a circular air rod (or air hole), and a radius of the air hole is 0.1485 μm; light waves transmitted within the waveguide are polarized to form TE waves; the second dielectric rod which is defined as compensation scattering rod is a semi-circular air hole or an air rod; The second dielectric rod is a semicircular scattering compensation air hole having a radius of 0.118614 μm; the coordinate of the second dielectric rod is defined by the displacement from the origin to X and Z-direction at distance of 0.056883 μm and 0.248115 μm respectively, and the angle of rotation is 124.722799 degrees; the light source is located at a coordinate of (−1.59 μm, 0) having a displacement according to X direction and the Z-direction respectively; an initial angle of an incident light is 160 degrees. The high refractive index second dielectric background is silicon (Si) having a refractive index of 3.4; the low refractive index dielectric is air. The area of the structure of the PhC having the right-angle bending waveguide is 15a×15a, and the maximum value of the return loss and the insertion loss for the right-angle bending waveguide in the PhC is 34.07 dB and 0.0016 dB respectively. 
         [0036]    A fourth alternative mode of the above mentioned preferred embodiment is: 
         [0037]    The lattice constant of the square-lattice PhC is a, which is defined as 0.444 μm, so the optimum normalized wavelength is  1 . 48  ii m; a first dielectric rod having a low refractive index is a circular air rod (or air hole), and a radius of the air hole is 0.21978 μm; light waves transmitted within the waveguide are polarized to form TE waves; the second dielectric rod which is defined as compensation scattering rod is a semi-circular air hole or an air rod; The second dielectric rod is a semicircular scattering compensation air hole having a radius of 0.175549 μm; the coordinate of the second dielectric rod is defined by the displacement from the origin to X and Z-direction at distance of 0.084187 μm and 0.36721 μm respectively, and the angle of rotation is 124.722799 degrees; the light source is located at a coordinate of (−2.3532 μm, 0) having a displacement according to X direction and the Z-direction respectively; an initial angle of an incident light is 160 degrees. The high refractive-index second dielectric background is silicon (Si) having a refractive index of 3.4; the low refractive index dielectric is air. The area of the structure of the PhC having the rectangular waveguide is 15a×15a, and the maximum value of the return loss and the insertion loss for the right-angle bending waveguide of the PhC is 34.07 dB and 0.0016 dB respectively. 
         [0038]    A fifth alternative mode of the above mentioned preferred embodiment is: The lattice constant of the square-lattice PhC is a, which is defined as 150 μm, so the optimum normalized wavelength is 500 μm; the first dielectric rod having a low refractive index is a circular air rod (or air hole), and a radius of the air hole is 74.25 μm; light waves transmitted within the waveguide are polarized to form TE waves; the second dielectric rod which is defined as the compensation scattering rod is a semi-circular air hole or an air rod; The second dielectric rod is a semicircular scattering compensation air hole having a radius of 59.307 μm; the coordinate of the second dielectric rod is defined by the displacement from the origin to X and Z-direction at distance of 28.4415 μm and 124.0575 μm respectively, and the angle of rotation is 124.722799 degrees; the light source is located at a coordinate of (−795 μm, 0) having a displacement according to X direction and the Z-direction respectively; the initial angle of the incident light is 160 degrees. The high refractive-index second dielectric background is silicon (Si) having a refractive index of 3.4; the low refractive index dielectric is air. The area of the structure of the PhC having the right-angle bending waveguide is 15a×15a, and the maximum value of the return loss and the insertion loss for the right-angle bending waveguide of the PhC is 34.07 dB and 0.0016 dB respectively. 
         [0039]    One skilled in the art will understand that the embodiment of the present invention as shown in the drawings and described above is exemplary only and not intended to be limiting. 
         [0040]    It will thus be seen that the objects of the present invention have been fully and effectively accomplished. The embodiments have been shown and described for the purposes of illustrating the functional and structural principles of the present invention and is subject to change without departure from such principles. Therefore, this invention includes all modifications encompassed within the spirit and scope of the following claims.