Abstract:
The present invention provides an EIT-based photonic logic gate, which is constituted by EIT-based stack layers of periodic array of photonic crystal (PCs) layers and EIT (Electromagnetic Induced Transparent) material layers. The input probe signals are incident on the first photonic crystal layer, passing through one or more than one PCs-EIT interfaces and transmitted out from the last EIT material layer. Control filed as the enable signals are incident on each EIT layer to activate the optical logic gate. By varying the detune frequency of probe field and Rabi frequency of control field, its band gap structure can be adjusted. Henceforth, the tunable optical EIT-based photonic logic gate can be achieved as user required.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    1. Technical Field 
         [0002]    The present invention relates to photonic logic gates, and more particularly, to an EIT-based photonic logic gate that is tunable in bandwidth. 
         [0003]    2. Description of Related Art 
         [0004]    Photonic crystals are artificial periodic structures with photonic band gaps, and work by interacting with light. A photonic band gap of a periodic structure refers to a certain frequency range and any waves in the frequency range are not allowed to propagate in the periodic structure. The presence of band gaps promises photonic crystals prospects of extensive applications, because larger band gaps mean a broader band of adjustable light. When a photonic crystal is finished, its band-gap structure is fixed and its refractive index becomes unchangeable. Thus, when a different refractive index is needed, the only way is to make another photonic crystal with the desired refractive index. 
         [0005]    While photonic logic gates have been discussed in some researches as recited below, one with a tunable band is still unknown. 
         [0006]    As disclosed in E. Forsberg, J. She, Optoelectronic Materials and Devices (edited by Y. H. Lee, F. Koyama and Y. Luo, 2006), Proc. of SPIE 6352 (2006), 63520S, a lump of material incorporating therein with a piece of circular dielectric material that contained gaseous EIT (electromagnetically induced transparency) was set in the air for the purposes of research on potential approaches to materials with negative refractive indexes. 
         [0007]    In S. Sangu, K. Kobayashi, A. Shojiguchi and M. Ohtsu, Phys. Rev. B 69 (2004) 115334, the study was directed to the probability of a CuCl-based material among 3 quantum dots being close to a light field, and use of the material after properly configured as an optical AND gate or XOR gate. 
         [0008]    On the other hand, a CuCl-based material in 3 quantasomes (with a particle size ratio thereof being 1:2̂1/2:2) was placed in a NaCl-material array for investigating into the transfer of near-field energy, as described in T. Kawazoe, K. Kobayashi, S. Sangu and M. Ohtsu, Appl. Phys. Lett. 82 (2003), 2957. The paper also proposed the use of the material in a nanoscale photonic switch. 
         [0009]    In view of this, how to modify the internal geometric configuration of photonic crystals so as to change the external optical properties and in turn adjust photonic crystals in band would be an issue for the industry to address. 
       SUMMARY OF THE INVENTION 
       [0010]    For remedying the shortcomings of the prior art, the present invention provides an EIT-based photonic logic gate that includes at least N EIT-based stack layers periodically arranged. Each of the EIT-based stack layers has a photonic crystal layer and an EIT material layer. The photonic crystal layer is made of a material having a positive, zero or negative refractive index, and the photonic crystal layer has binding interfaces. The EIT material layer is made of hydrogen, lithium, sodium, rubidium or cesium, and has binding interfaces. The EIT material layer and the photonic crystal layer are bound mutually at the binding interfaces. The EIT-based stack layers use a probe field incident on the photonic crystal layer as an input probe signal, and uses a control field incident on the EIT material layer as an enable signal. The probe field can thus come out from the last EIT material layer, thereby finishing the signal output of the probe field. 
         [0011]    Therefore, the primary objective of the present invention is to provide an EIT-based photonic logic gate, wherein EIT-based stack layers thereof can be adjusted in bandwidth (including the band-pass width, the band-gap width, and the band-gap band-pass interlacing width) can be adjusted by changing EIT material layer in atom density and thickness, changing the probe field in detune frequency, and changing the control field in Rabi frequency. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0012]    The invention as well as a preferred mode of use, further objectives and advantages thereof will be best understood by reference to the following detailed description of illustrative embodiments when read in conjunction with the accompanying drawings, wherein: 
           [0013]      FIG. 1A  is a schematic drawing according to one preferred embodiment of the present invention illustrating EIT-based stack layers arranged in a limited period to which a probe field and a control field are applied; 
           [0014]      FIG. 1B  is a schematic drawing according to one preferred embodiment of the present invention showing a Lambda-type structure of the EIT&#39;s atomic energy levels; 
           [0015]      FIG. 2A  is a graph of the relative electric permittivity of one preferred example of the present invention versus the detune frequency; 
           [0016]      FIG. 2B  is a graph of the electric permittivity of the preferred example of the present invention versus the Rabi frequency; 
           [0017]      FIG. 3A  is a graph of light-wave bands of limitless layers of the preferred example of the present invention; 
           [0018]      FIG. 3B  is a partial graph of light-wave band gaps of the preferred example of the present invention; 
           [0019]      FIG. 4A  is a graph of the reflection coefficient of a preferred example of the present invention with the number of layers as 1 versus the detune frequency of the probe field; 
           [0020]      FIG. 4B  is a graph of the reflection coefficient of a preferred example of the present invention with the number of layers as 2 versus the detune frequency of the probe field; 
           [0021]      FIG. 4C  is a graph of the reflection coefficient of a preferred example of the present invention with the number of layers as 3 versus the detune frequency of the probe field; 
           [0022]      FIG. 4D  is a graph of the reflection coefficient of a preferred example of the present invention with the number of layers as 4 versus the detune frequency of the probe field; 
           [0023]      FIG. 4E  is a graph of the reflection coefficient of a preferred example of the present invention with the number of layers as 5 versus the detune frequency of the probe field; 
           [0024]      FIG. 4F  is a graph of the reflection coefficient of a preferred example of the present invention with the number of layers as 6 versus the detune frequency of the probe field; 
           [0025]      FIG. 5A  is a graph of the reflectance and transmittance of the preferred example of  FIG. 4A  versus the detune frequency of the probe field; 
           [0026]      FIG. 5B  is a graph of the reflectance and transmittance of the preferred example of  FIG. 4B  versus the detune frequency of the probe field; 
           [0027]      FIG. 5C  is a graph of the reflectance and transmittance of the preferred example of  FIG. 4C  versus the detune frequency of the probe field; 
           [0028]      FIG. 5D  is a graph of the reflectance and transmittance of the preferred example of  FIG. 4D  versus the detune frequency of the probe field; 
           [0029]      FIG. 5E  is a graph of the reflectance and transmittance of the preferred example of  FIG. 4E  versus the detune frequency of the probe field; 
           [0030]      FIG. 5F  is a graph of the reflectance and transmittance of the preferred example of  FIG. 4F  versus the detune frequency of the probe field; and 
           [0031]      FIG. 5G  is a graph of the reflectance and transmittance of the preferred examples of the present invention versus the detune frequency of the probe field. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0032]    While the present invention discloses an EIT-based photonic logic gate, the principles of photonic crystals and electromagnetically induced transparency used therein have been known to people skilled in the art, so are not given in detail in the following description. Meantime, the accompanying drawings to be read in conjunction with the description are intended to structurally express the features of the present invention, so are not and do not need to be made to scale. 
         [0033]    Referring to  FIG. 1A , in a first preferred embodiment of the present invention, a structure with EIT-based stack layers arranged in a limited period is shown. The EIT-based photonic logic gate comprises at least N (N is greater than or equal to 1) EIT-based stack layers  10  periodically arranged. Each of the EIT-based stack layers  10  has a photonic crystal layer  11  as thick as 0.01 μm˜0.15 μm and an EIT material layer  12  as thick as 0.01 μm˜0.15 μm. 
         [0034]    The photonic crystal layer  11  may be made of GaAs, SiO 2  or glass, which has a positive refractive index and can be derived from nature, or may be made of an artificial meta-material of nano scale, which may be a combination of materials of positive, zero or negative refractive indexes, such as periodically arranged metal strips and a split-ring resonator (SRR) formed by periodically arranged rings. The rectangular photonic crystal layer  11  has two opposite surfaces defined herein as a first binding interface  111  and a second binding interface  112 , respectively, for its binding with the electromagnetic induced transparent  12 . 
         [0035]    The EIT (Electromagnetically Induced Transparency) material layer  12  is made of a monovalent alkaline metal selected from I-A group, such as hydrogen, lithium, sodium (Na), rubidium (Rb) and cesium (Cs). Since the EIT material layer  12  is made from an atomic gas, the atomic gas has to be contained in a container that is transparent to laser, and does not affect the progress of laser. Thus, glass is an ideal material for such a container. The EIT material layer  12 , corresponding to the photonic crystal layer  11 , is also rectangular, and also has its opposite surfaces defined as a first binding interface  121  and second binding interface  122 . The photonic crystal layer  11  and the EIT material layer  12  are bound to each other with the facing second and first binding interfaces  112 ,  121 , so as to construct an EIT-based stack layer  10 . Binding between the layers can be achieved by a high-temperature adhesive or laminating process. Generally, the adhesive or laminating process is performed at 300° K˜500° K. 
         [0036]    Still referring to  FIG. 1A , the EIT-based stack layers  10  made of the photonic crystal layers  11  and the EIT material layers  12  receive a probe field A and a control field B, for changing the bandwidth of the photonic crystal layer  11  and the electric permittivity of the EIT material layer  12 . 
         [0037]    For applying the fields, more than one beam of the probe field A is prepared. In the present preferred embodiment, two beams of the probe field A with different frequencies are used and denoted by A 1  and A 2 , respectively. A beam of the control field B is also used. The probe field A and the control field B are both lasers at resonance frequency. The probe field A must has its luminous intensity far smaller than that of the control field B. Preferably, the luminous intensity of the control field B is 10 to 200 times as much as the luminous intensity of the probe field A. 
         [0038]    Then the probe field A is casted into the first binding interface  111  of the photonic crystal layer  11  as the input probe signal, which passes through the second binding interface  112  of the photonic crystal layer  11  and the first binding interface  121  of the EIT material layer  12 , and goes through the photonic crystal layers and the EIT material layers of the N EIT-based stack layers  10  successively, before coming out from the second binding interface  122  of the Nth EIT-based stack layer  10  as the output signal Y. Meantime, the control field B is casted into the EIT material layer  12  as the enable signal. In the EIT material layer  12 , the probe field A is not absorbed by a medium, so the medium is transparent to the probe field A. Such transparency is caused by the two-photon resonance put of the control field B. 
         [0039]    As to resonance laser, external parameters such as the wavelength, the luminous intensity, the detune frequency and the de-phased rate have to be controlled because they influence the photonic crystal layer  11  (in, for example, bandwidth, including the width of the band-pass structure, the width of the band-gap structure, and the width of the band-gap band-pass interlacing structure) and the EIT material layer  12  (in, for example, electric permittivity). Therefore, in the present preferred embodiment, the probe field A and the control field B are such selected that their parameters are as below. The probe field A has a wavelength between 380 nm and 800 nm, a luminous intensity between 1 cd and 10 cd, and a detune frequency between −10 8  s −1  and +10 8  s −1 , while the control field B has wavelength between 380 nm and 800 nm, a luminous intensity between 50 cd and 200 cd, and a de-phased rate between −10 5  s −1  and +10 5  s −1 . 
         [0040]    Now referring to  FIG. 1B , it shows a Gamma-type structure of the EIT&#39;s atomic energy levels. The EIT material layer  12  is a three-energy-level system having a first energy level | 1 &gt;, a second energy level | 2 &gt; and a third energy level | 3 &gt;. Generally, the first energy level | 1 &gt; and the second energy level | 2 &gt; act as ground-state energy levels, and the third energy level | 3 &gt; acts as an excited-state energy level. The third energy level | 3 &gt; has a radiative natural decay rate Γ 3 , while the second energy level | 2 &gt; has a different non-radiative decay rate  72 . 
         [0041]    After repeated tests, the atomic and optical parameters selected for the present preferred embodiment are as below. The EIT-based stack layer  10  has an atomic number density between 10 9  m −3  and 10 23  m −3 , an electrical dipole moment between 10 −28  C·m and 10 −30  C·m, a spontaneous emission decay rate between 0.1×10 7  s −1  and 5×10 7  s −1 , and a Rabi frequency c between 0.5×10 7  s −1  and 5×10 7  s −1 . The disclosed parameters are subject to practical needs in manufacturing. The parameters will be further discussed below. 
         [0042]    The atomic number density and the electrical dipole moment are respectively in direct proportion to the polarization coefficient, and the entire electric permittivity is equal to 1+the polarization coefficient. When transiting from the first energy level | 1 &gt; or the second energy level | 2 &gt; to the third energy level | 3 &gt;, electrons form an electrical dipole, with the electrically positive properties in the atomic nucleus. The foregoing electrical dipole moment is one of the parameters of electrical dipole, and makes charged particles aggregate at the surface of substance. This phenomenon is known as polarization, and the level of polarization per unit volume is the polarization coefficient. 
         [0043]    The foregoing spontaneous emission decay rate Γ 3  does not vary with any parameters because it represents an estimated probability of natural radiation for the electrons of the third energy level | 3 &gt; transiting to the first energy level | 1 &gt;. Once the material is selected, and the distance between the third energy level | 3 &gt; and the first energy level | 1 &gt; is fixed, the spontaneous emission decay rate Γ 3  is maintained at 0.1×10 7  s −1 ˜5×10 7  s −1 . Spontaneous emission decay rate Γ 3 =2×10 7  s −1  is one of the possible fixed values, so this value is taken as the benchmark for frequency. 
         [0044]    The different non-radiative decay rate γ 2  does not vary with any parameters because it represents an estimated probability of natural radiation for the electrons of second energy level | 2 &gt; transiting to the first energy level | 1 &gt;. Once the material is selected, and the distance between the second energy level | 2 &gt; and the first energy level | 1 &gt; is fixed, the non-radiative decay rate γ 2  is maintained at 10 4  s −1 ˜5×10 5  s −1 . Non-radiative decay rate γ 2 =10 5  s −1  is one of the possible fixed values, approximately equal to 1/20˜1/500 of the spontaneous emission decay rate Γ 3 . 
         [0045]    The Rabi frequency Ω c  of the control field B and the Rabi frequency Ω p  of the probe field A represent fixed parameters for the electrons of the third energy level | 3 &gt; transiting to the second energy level | 2 &gt;, and for the electrons of the third energy level | 3 &gt; transiting to the first energy level | 1 &gt;, respectively. Once the materials are selected, the Rabi frequency Ω c  of the control field B and the Rabi frequency Ω p  of the probe field A are fixed. The detune frequency Δ c  of the control field B and the detune frequency Δ p  of the probe field A represent a value obtained by subtracting a frequency difference between the third energy level | 3 &gt; and the first energy level | 2 &gt; from the control field&#39;s frequency, and a value obtained by subtracting a frequency difference between the third energy level | 3 &gt; and the first energy level | 1 &gt; from the probe field&#39;s frequency. 
         [0046]    Some examples will be given below to further explain the features of the present invention.  FIG. 1A  is a structure with said EIT-based stack layers  10  arranged in a limited period. 
         [0047]    Through the numerical analysis conducted to the EIT-based stack layers  10 , it is proven that changing the detune frequency Δ p  of the probe field A and changing the Rabi frequency Ω c  of the control field B can bring about significant change to the relative electric permittivity, Bloch wave number, reflection coefficient and reflectance. The following explanation will be clear when read in conjunction with the particular drawings. 
         [0048]      FIG. 2A  is a graphic of the relative electric permittivity versus the detune frequency. The relative electric permittivity refers to the permittivity of the EIT-based stack layers  10  with limited layers relative to the electric permittivity of free space, and the standardized detune frequency Δ p  of the probe field A is taken as a variable to see variation. The real component is between a negative real number and a positive real number, with one or more extreme values, and the imaginary component is between zero and a positive real number, with one or more extreme values. There is only one point where the real component is 1 and the imaginary component is 0. It is learned from  FIG. 2A  that the real component and the imaginary component both significantly vary in the interval between −0.5Γ 3  and 2Γ 3 . 
         [0049]      FIG. 2B  is a graphic of the relative electric permittivity versus the Rabi frequency. The relative electric permittivity refers to the permittivity of the EIT-based stack layers  10  with limited layers relative to the electric permittivity of free space, and the standardized Rabi frequency Ω c  of the control field B is taken as a variable to see variation. The real component is between a negative real number and a positive real number, with two extreme values, and the imaginary component is between zero and a positive real number, with one maximum value. There is only one point where the real component is 1 and the imaginary component is 0. It is learned from  FIG. 2B  that the real component and the imaginary component both significantly vary in the interval between −0.5Γ 3  and 2Γ 3 . 
         [0050]      FIG. 3A  is a graph of light-wave bands of limitless layers. When the light-wave frequency on the vertical axis is (1.3˜1.8)×10 8 ×Γ 3 , the Bloch wave number is a pure imaginary number (at this time, light is blocked from passing through this area, which is referred to as a band gap). When the light-wave frequency on the vertical axis is (1.8˜2.5)×10 8 ×Γ 3 , the Bloch wave number is a pure real number (at this time, light is allowed to pass through this area, which is referred to as a band pass). 
         [0051]      FIG. 3B  is a partial graph of light-wave band gaps of the preferred example of the limitless layers. The EIT-based stack layers  10  with limitless layers, when taking the wave frequency of the probe field A as the variable, has one or more band-gap band-pass interlacing structures having the Bloch wave number as a complex number, representing a propagating mode wave decaying with the distance. The band-gap band-pass interlacing happens around 8.0×10 6 ˜8.5×10 6  on the vertical axis. For converting this into an actual frequency band, it has to be multiplied by the spontaneous emission decay rate Γ 3 =2×10 7 , the frequency being ω p =(8.0×10 6 ˜8.5×10 6 )×(2×10 7 )=(1.6×10 14 ˜1.7×10 14  s −1 ). At this time, the Bloch wave number on the corresponding horizontal axis may be a pure real number, a pure imaginary number or a complex number, expressed as K=Kr+(j×Ki). The band-pass structure is K=Kr+(j×0), where Kr is not zero, and Ki is zero. The band-gap structure is K=0+(j×Ki), where Kr is zero, and Ki is not zero. The band-gap band-pass interlacing structure is K=Kr+(j×Ki), where neither Kr nor Ki is zero. Referring to  FIG. 3B , when the light-wave frequency on the vertical axis is (8.0˜8.5)×10 6 ×Γ 3 , the Bloch wave number is a complex number (at this time, the light passes while decaying with the distance, and here is known as the band-gap band-pass interlacing area). The above description demonstrates that the preferred embodiment is tuneable in terms of frequency bandwidth, wherein the frequency bandwidth may be the width of the band-gap structure, the width of the band-pass structure, or even the width of the band-gap band-pass interlacing structure. 
         [0052]    Referring to  FIGS. 4A ,  4 B,  4 C,  4 D,  4 E and  4 F together, graphics of the reflection coefficient versus the detune frequency of the probe field are given for the cases where the layer number N is 1, 2, 3, 4, 5 and 6, respectively. As to the reflection coefficient of the EIT-based stack layer(s)  10  having one or N layers, when the incident medium for the first binding interface  111  of the photonic crystal layer  11  is air, the penetrant medium of the second binding interface  122  of the EIT material layer  12  of the Nth EIT-based stack layer  10  is air. Given that the electric permittivity is 8.85×10 −12  F/m and the permeability is 4π×10 7  H/m, when the standardized detune frequency Δ p  of the probe field A is taken as a variable (with a varying range of −1˜2), there are 2N+1 extreme values. The fact that the reflection coefficient significantly varies in the range of 0.2˜0.8 on the horizontal axis suggests that the reflection coefficient significantly varies in the range of (0.2˜0.8)×2×10 7 =0.4×10 7 ˜1.6×10 7  s −1 , namely in the range equal to 1/10 10  of the light-wave frequency of (10 17  s −1 ). 
         [0053]    Referring to  FIGS. 5A ,  5 B,  5 C,  5 D,  5 E and  5 F together, graphics of the reflectance and transmittance versus the detune frequency of the probe field are given for the cases where the layer number N is 1, 2, 3, 4, 5 and 6, respectively. As to the reflectance and transmittance of one or more (or N) EIT-based stack layers  10 , when the incident medium of the first binding interface  111  of the photonic crystal layer  11  is air, the penetrant medium of the second binding interface  122  of the EIT material layer  12  is air. Given that the electric permittivity is 8.85×10 −12  F/m and the permeability is 4π×10 7  H/m, when the standardized detune frequency Δ p  of the probe field A is taken as a variable (with a varying range of −1˜2), there are 2N extreme values. As the reflectance is the squared absolute value of the reflection coefficient, it is similar to the reflection coefficient by having the significant variation confined in the range of 0.35˜0.55 on the horizontal axis. This means the reflection coefficient significantly varies in the range of (0.35˜0.55)×2×10 7 =0.7×10 7 ˜1.1×10 7  s −1 , namely in the range equal to 1/10 10  of the light-wave frequency of (10 17  s −1 ). 
         [0054]    Also refer to  FIG. 5G  for the graphic of the reflectance (reflectance=1−transmissivity) versus the detune frequency of the probe field when N is 3, 4, 5 and 6. 
         [0055]    In the case where the layer number N is 4 (N=4), when the detune frequency Δ p  of the probe field A is 0.46Γ 3 , the transmissivity is at the minimum, and when the detune frequency Δ p  is 0.53Γ 3 , the transmissivity is at the maximum. 
         [0056]    In the case where the layer number N is 6 (N=6), the fact is opposite. That is, when the detune frequency Δ p  of the probe field A is 0.46Γ 3 , the transmissivity is at the maximum, and when the detune frequency Δ p  is 0.53Γ 3 , the transmissivity is at the minimum. 
         [0057]    The examples show that different numbers of layers cause significant change in terms of reflectance and transmissivity with the variation of the detune frequency Δ p  of the probe field A. Such significant change is useful for the design of photonic logic gates (such as OR gates and NAND gates). The truth table for OR gates and NAND gates is given below (Only when all inputs for an OR gate are logic 0 will the output be logic 0; only when all inputs for an NAND gate are logic 1 will the output be logic 0). The present preferred embodiment uses two beams of the probe field A having different frequencies. The present preferred embodiment determines the different usable frequencies according to the maximum of the transmissivity with respect to the detune frequency Δ p  of the probe field A: 
         [0000]    
       
         
               
               
               
               
             
           
               
                   
               
               
                   
                   
                 Y = A 1  + A 2   
                 
                   Y = A 1  · A 2   
                 
               
               
                 IN A1   
                 IN A2   
                 (4 OR Gates) 
                 (6 NAND Gates) 
               
               
                   
               
             
             
               
                 0 (0.46 Γ 3 ) 
                 0 (0.46 Γ 3 ) 
                 0 
                 1 
               
               
                 0 (0.46 Γ 3 ) 
                 1 (0.53 Γ 3 ) 
                 1 
                 1 
               
               
                 1 (0.53 Γ 3 ) 
                 0 (0.46 Γ 3 ) 
                 1 
                 1 
               
               
                 1 (0.53 Γ 3 ) 
                 1 (0.53 Γ 3 ) 
                 1 
                 0 
               
               
                   
               
             
          
         
       
     
         [0058]    To sum up, by merely adjusting the photonic crystals and the photonic crystal layer  11  in thickness and the EIT material layer  12  in atom density and thickness, while controlling the probe field A and control field B, the EIT-based stack layers  10  can be changed in terms of band (including the band-pass width, the band-gap width, and the band-gap band-pass interlacing width), so as to use different levels of transmissivity to design all-optical devices such as optical switches, photonic crystals and photonic logic gate. 
         [0059]    The present invention has been described with reference to the preferred embodiments and it is understood that the embodiments are not intended to limit the scope of the present invention. Moreover, as the contents disclosed herein should be readily understood and can be implemented by a person skilled in the art, all equivalent changes or modifications which do not depart from the concept of the present invention should be encompassed by the appended claims.