Patent Publication Number: US-2007098413-A1

Title: Optical logic element

Description:
BACKGROUND OF THE INVENTION  
      1. Field of the Invention  
      The present invention relates to an optical logic element. More particularly, the present invention relates to an optical logic element using an interferometer realized using a semiconductor optical amplifier (SOA).  
      2. Description of the Related Art  
      Forming an ultrahigh optical communication network may include facilitating networking functions, e.g., switching, signal re-generating, addressing, header identifying, data encoding and encrypting, pattern matching, and the like. Also, an optical logic element, i.e., an all-optical logic gate, may be required to realize optical communication networking functions.  
      SOAs are widely used to realize all-optical logic gates used in optical communications. A non-linear optical phenomenon, e.g., cross gain modulation (XGM), cross phase modulation (XPM), cross polarization modulation (XPoIM), four wave mixing (FWM), or the like, may occur in such an SOA. All-optical logic gates may be realized using the non-linear optical phenomenon occurring in the SOA.  
      As a particular example, SOAs may be used to create a Mach-Zehnder interferometer (MZI) using XPM. Since an SOA-MZI consumes a small amount of power, is simple, easily integrated, stable, has a low extinction ratio, and generates a signal at high speed, the SOA-MZI is very useful for realizing all-optical logic gates. However, when the SOA-MZIs are used, only an exclusive or (XOR) circuit can be realized.  
      A method of realizing XOR circuits using XGM of SOAs has been proposed. However, XGM may result in a low extinction ratio and a low signal quality. Thus, this method may not be appropriate for high speed operation.  
      Further, since logic circuits may be generally realized by NOR circuits or NAND circuits, all-optical NOR circuits or NAND circuits are required to realize efficient optical communication networking.  
     SUMMARY OF THE INVENTION  
      The present invention is therefore directed to all optical logic circuits, which substantially overcome one or more of the problems due to the limitations and disadvantages of the related art.  
      It is therefore a feature of an embodiment of the present invention to provide an all optical logic element that can realize a NOR circuit.  
      It is therefore another feature of an embodiment of the present invention to provide an all optical logic element that can realize a NAND circuit.  
      It is yet another feature of an embodiment of the present invention to provide an all optical logic element that can realize XOR, NOR, OR and NAND circuits.  
      At least one of the above and other features and advantages of the present invention may be realized by providing an optical logic element performing a logic operation on optical signals using an interferometer using a counter-propagation method, including: a first interferometer modulating a continuous optical signal in response to first and second optical signals to output a first modulation signal; and a second interferometer modulating the continuous optical signal in response to a sum signal equal to the sum of the first and second optical signals to output a second modulation signal. The first and second modulation signals and the sum signal may be respectively results of predetermined logic operations performed on the first and second optical signals.  
      The first interferometer may include a first modulator modulating a phase of the continuous optical signal in response to the first optical signal and outputting the continuous optical signal; and a second modulator phase modulating the phase of the continuous optical signal in response to the second optical signal and outputting the continuous optical signal. The first modulation signal may be obtained by summing outputs of the first and second modulators.  
      The first modulator may include a first optical amplifier performing cross phase modulation (XPM) on the continuous optical signal in response to the first optical signal and a first phase shifter shifting the phase of an output of the first optical amplifier by a predetermined amount, and the second modulator may include a second optical amplifier performing XPM on the continuous optical signal in response to the second optical signal.  
      The power of an input signal may be less than a predetermined level, the first and second optical amplifiers output the input signal without delaying the phase of the input signal, and when the power of the input signal is greater than the predetermined level, the first and second optical amplifiers delay the phase of the input signal by a predetermined amount.  
      When the power of the first optical signal is at a high level, the first optical amplifier may delay the phase of the continuous optical signal by π, when the power of the first optical signal is at a low level, the first optical amplifier may not delay the phase of the continuous optical signal, when the power of the second optical signal is at a high level, the second optical amplifier may delay the phase of the continuous optical signal by π, when the power of the second optical signal is at a low level, the second optical amplifier may not delay the phase of the continuous optical signal the first phase shifter shifts the phase of an output of the first optical amplifier by (2n+1)π, where n is an integer, a high level gain of the first optical amplifier may be equal to a high level gain of the second optical amplifier, and a low level gain of the first optical amplifier may be equal to a low level gain of the second optical amplifier.  
      The first phase shifter may include a third optical amplifier performing self-phase modulation (SPM) on the output of the first optical amplifier in response to the output of the first optical amplifier.  
      The second interferometer may include a third modulator phase modulating the continuous optical signal in response to the sum signal and outputting the continuous optical signal; and a fourth modulator amplifying and outputting the continuous optical signal. The second modulation signal may be obtained by summing outputs of the third and fourth modulators with each other.  
      The third modulator may include a fourth optical amplifier performing XPM on the continuous optical signal in response to the sum signal and a second phase shifter shifting the phase of an output of the fourth optical amplifier by a predetermined amount, and the fourth modulator may include a fifth optical amplifier amplifying by a predetermined gain and outputting the continuous optical signal.  
      When the power of the input signal is less than a predetermined level, the fourth optical amplifier may shift the phase of the input signal by a predetermined amount, and when the power of the input signal is greater than the predetermined level, the fourth optical amplifier may shift the phase of the input signal by a predetermined amount.  
      When power of the sum signal is at a high level, the fourth optical amplifier may delay the phase of the continuous optical signal by π, when the power of the sum signal is at a low level, the fourth optical amplifier may not delay the phase of the continuous optical signal, the second phase shifter may shift the phase of an output of the fourth optical amplifier by (2n)π, where n is an integer, high level gains of the first, second, and third optical amplifiers and a gain of the fourth optical amplifier may be equal to one another, and low level gains of the first, second, and third optical amplifiers may be equal to one another. The second modulation signal may be the result of a NOR operation performed on the first and second optical signals, and the sum signal may be the result of a NAND operation performed on the first and second optical signals.  
      When the power of the sum signal is at a high level, the fourth optical amplifier may delay the phase of the continuous optical signal by π, when the power of the sum signal is at a low level, the fourth optical amplifier may not delay the phase of the continuous optical signal, the second phase shifter may shift the phase of the output of the fourth optical amplifier by (2n+1)π, where n is an integer, high level gains of the first, second, and third optical amplifiers may be equal to one another, and low level gains of the first, second, and third optical amplifiers and a gain of the fourth optical amplifier may be equal to one another. The second modulation signal may be the result of an OR performed on the first and second optical signals.  
      The second phase shifter may include a sixth optical amplifier phase modulating the output of the fourth optical amplifier in response to the output of the fourth optical amplifier.  
      The first and second interferometers may be, for example, Mach-Zehnder interferometers (MZIs), Michelson interferometers, etc. Either interferometer may use the co-propagation method or the counter propagation method. When the co-propagation method is used, the optical logic element may further include a band pass filter for filtering the input optical signals from an output of the co-propagation interferometer to output only the modulation signal. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
      The above and other features and advantages of the present invention will become more apparent to those of ordinary skill in the art by describing in detail exemplary embodiments thereof with reference to the attached drawings in which:  
       FIG. 1  illustrates a schematic diagram of an XOR circuit realized by SOA-MZI;  
       FIGS. 2A and 2B  illustrate graphs of characteristics of the SOAs shown in  FIG. 1 ;  
       FIG. 3  illustrates a schematic diagram of an optical logic element according to an embodiment of the present invention;  
       FIG. 4  illustrates a schematic diagram of an optical logic element according to another embodiment of the present invention;  
       FIG. 5  illustrates a schematic diagram an optical logic element according to another embodiment of the present invention;  
       FIG. 6  illustrates a schematic diagram of an optical logic element according to another embodiment of the present invention; and  
       FIG. 7  illustrates a graph of results of an experiment performed with an optical logic element of an embodiment of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION  
      Korean Patent Application No.10-2005-0099942, filed on Oct. 22, 2005, in the Korean Intellectual Property Office, and entitled: “Optical Logic Element,” is incorporated by reference herein in its entirety.  
      The present invention will now be described more fully hereinafter with reference to the accompanying drawings, in which exemplary embodiments of the invention are illustrated. The invention may, however, be embodied in different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.  
      In accordance with embodiments of the present invention, an optical logic element may be realized using all-optical XOR, NOR, OR, and NAND circuits. As a result, any desired optical logic element may be readily constructed.  
       FIG. 1  illustrates a schematic diagram of an XOR circuit  100  realized by SOA-MZIs. Referring to  FIG. 1 , the XOR circuit  100  may include a first optical amplifier  110 , a phase shifter  130 , and a second optical amplifier  150 . The first optical amplifier  110  may modulate a probe signal PI in response to a first optical signal A. The phase shifter  130  may shift a phase of an output signal of the first optical amplifier  110  by a predetermined value. The second optical amplifier  150  may modulate the probe signal PI in response to a second optical signal B.  
      Optical gains and phases of the first and second optical amplifiers  110  and  150  may vary non-linearly according to the power of an input signal. The first and second optical amplifiers  110  and  150  may perform XPM or XGM on the input signal according to their non-linear characteristics.  
       FIG. 2A  illustrates a graph of a phase shift occurring in an upper arm of an MZI according to the non-linear characteristics of the first optical amplifier  110  of  FIG. 1  with respect to the input power.  FIG. 2B  illustrates a graph of a phase shift occurring in a lower arm of the MZI according to the non-linear characteristics of the second optical amplifier  150  of  FIG. 1  with respect to the input power.  
      As shown in  FIGS. 2A and 2B , if the power of an input signal, i.e., the first optical signal A or the second optical signal B, is less than a predetermined value, the first and second optical amplifiers  110  and  150  have predetermined gains. However, if the power of the input signal is greater than the predetermined value, the gains of the first and second optical amplifiers  110  and  150  decrease with increasing power of the input signal.  
      If the power of the input signal is less than the predetermined value, the first and second optical amplifiers  110  and  150  do not delay the phase, i.e., the optical phase, of the input signal. Thus, the phase shift occurring in the upper arm is π, and the phase shift occurring in the lower arm is 0. However, if the power of the input signal is greater than the predetermined value, the first and second optical amplifiers  110  and  150  delay the phase of the input signal by π. Thus, the phase shift occurring in the upper arm is 2π, i.e., effectively zero, and the phase shift occurring in the lower arm is π.  
      The operation of the XOR circuit  100  will now be described in more detail with reference to  FIGS. 1, 2A , and  2 B.  
      The XOR circuit  100  may modulate a continuous optical signal PI in response to the first and second optical signals A and B, and sums modulated signals to perform an XOR operation on the first and second optical signals A and B.  
      The continuous optical signal PI may be a continuous waveform (CW) probe signal having a first wavelength λ1. The first and second optical signals A and B may be pump signals modulated into pulse wave signals to modulate the continuous optical signal PI, and having a second wavelength λ2.  
      For convenience, it is assumed that the first and second optical signals A and B are modulated to have “LLHH” and “LHLH” patterns, respectively. Here, “L” denotes a low level, and “H” denotes a high level.  
      The XOR circuit  100  may use an SOA-MZI having a counter-propagation method. Thus, the first and second optical signals A and B are input in an opposite direction to a direction along which the continuous optical signal PI is input.  
      As shown in  FIG. 1 , the upper arm may include the first optical amplifier  110  and the phase shifter  130 , and the lower arm may include the second optical amplifier  150 .  
      The phase shifter  130  of the XOR circuit shown in  FIG. 1  may shift the phase of the output signal of the first optical signal  110  by (2n+1)π, i.e., effectively by π. Thus, a phase difference between the signals in the lower and upper arms may be π. This is to set a phase difference between signals at first and second nodes N 1  and N 2  to π on a low level of a pump signal so as to improve an extinction ratio (ER).  
      The first wavelength Al of the continuous optical signal PI is different from the second wavelength λ2 of the first and second optical signals A and B. Thus, the continuous optical signal PI and the first and second optical signals A and B do not affect one another and independently advance, except at the first and second optical amplifiers  110  and  150 .  
      The operation of the XOR circuit  100  according to a detailed logic combination of the first and second optical signals A and B will now be described.  
      In the upper arm, the continuous optical signal PI may be modulated according to the first optical signal A. In other words, if the first optical signal A is at a low level, the first optical amplifier  110  does not delay the phase of the first optical signal A through XPM. Thus, the continuous optical signal PI is phase shifted by the phase shifter  130 . Thus, a continuous optical signal phase shifted by π arrives at the first node N 1 .  
      If the first optical signal A is at a high level, the first optical amplifier  110  delays the phase of the first optical signal A by π through XPM. Thus, the continuous optical signal PI is phase delayed by the first optical amplifier  110  and phase shifted by the phase shifter  130 . As a result, a continuous optical signal that is phase shifted by 2π, i.e., is effectively not phase shifted, arrives at the first node N 1 .  
      In the lower arm, the continuous optical signal PI may be modulated according to the second optical signal B. In other words, if the second optical signal B is at a low level, the second optical amplifier  150  does not delay the phase of the second optical signal B through XPM. Thus, a continuous optical signal that is not phase shifted arrives at the second node N 2 .  
      If the second optical signal B is at a high level, the second optical amplifier  150  delays the phase of the second optical signal B by π through XPM. Thus, the continuous optical signal PI is phase shifted by the second optical amplifier  150 . As a result, a continuous optical signal phase shifted by π arrives at the second node N 2 .  
      Accordingly, continuous optical signals with different phases depending on the logic combination of the first and second optical signals A and B travel through the upper and lower arms. The continuous optical signals traveling through the upper and lower arms are summed. As a result, a result of performing a logic operation on the first and second optical signals A and B is output.  
      In detail, if the first and second optical signals A and B are both at a low level, the continuous optical signal phase shifted by π arrives at the first node N 1  of the upper arm, but the continuous optical signal that is not phase shifted arrives at the second node N 2  of the lower arm. Thus, the continuous optical signals in the upper and lower arms have a phase difference of π, and, thus, destructively interfere with each other. As a result, an output signal PO is at a low level.  
      If the first optical signal A is at a low level and the second optical signal B is at a high level, a continuous optical signal phase shifted by π arrives at the first node N 1  of the upper arm, and a continuous optical signal phase shifted by π arrives at the second node N 2  of the lower arm. Thus, the continuous optical signals in the upper and lower arms do not have a phase difference, and, thus, constructively interfere with each other. As a result, the output signal PO is at a high level.  
      If the first optical signal is at a high level and the second optical signal B is at a low level, a continuous optical signal phase shifted by 2π, i.e., not phase shifted, arrives at the first node N 1  of the upper arm, and a continuous optical signal that has not been phase shifted arrives at the second node N 2  of the lower arm. Thus, the continuous optical signals in the upper and lower arms do not have a phase difference, and thus constructively interfere with each other. As a result, the output signal PO is at a high level.  
      If the first and second optical signals A and B are both at a high level, a continuous optical signal phase shifted by 2π, i.e., not phase shifted, arrives at the first node N 1  of the upper arm, and a continuous optical signal phase shifted by π arrives at the second node N 2  of the lower arm. Thus, the continuous optical signals of the upper and lower arms have a phase different of π, and, thus, destructively interfere with each other. As a result, the output signal PO is at a low level.  
      As described above, the XOR circuit  100  shown in  FIG. 1  outputs the result of an XOR operation on the first and second optical signals A and B.  
      An optical logic element according to an embodiment of the present invention will now be described with reference to the description of the XOR circuit  100  shown in  FIG. 1 .  
       FIG. 3  illustrates a schematic diagram of an optical logic element  300  according to an embodiment of the present invention. Referring to  FIG. 3 , the optical logic element  300  may include first and second interferometers  310  and  330  using a counter-propagation method. Thus, a direction in which a continuous optical signal PI is input is opposite to a direction in which a first optical signal A, a second optical signal B, and a sum signal C equal to the sum of the first and second optical signals A and B are input.  
      Also, the wavelength λ1 of the continuous optical signal PI is different from the wavelength λ2 of the first and second optical signals A and B. The wavelength λ1 of the continuous optical signal PI is also different from a wavelength λ3 of the sum signal C of the first and second optical signals A and B. The wavelengths λ2 of the first and second optical signals A and B may be different from the wavelength λ3 of the sum signal C as shown in  FIG. 3 . However, although the wavelength λ2 is different than the wavelength λ3 in the present embodiment, the present invention is not limited to this.  
      The first interferometer  310  may modulate the continuous optical signal PI in response to the first and second optical signals A and B to output a first modulation signal M 1 . The second interferometer  330  may modulate the continuous optical signal PI in response to the sum signal C to output a second modulation signal M 2 .  
      The first modulation signal M 1 , the second modulation signal M 2 , and a sum signal MS, equal to the sum of the first and second modulation signals M 1  and M 2 , may each be obtained through a predetermined logic operation performed on the first and second optical signals A and B. In other words, since the first interferometer  310  has the same structure as the XOR circuit  100  shown in  FIG. 1 , the first modulation signal Ml output from the first interferometer  310  may be the result of an XOR operation performed on the first and second optical signals A and B, i.e., M 1 =A XOR B.  
      The first interferometer  310  may include first and second modulators  315  and  325 . The first modulator  315  phase may modulate and output the continuous optical signal PI in response to the first optical signal A. The second modulator  325  phase may modulate and output the continuous optical signal PI in response to the second optical signal B.  
      In other words, the first modulator  315  may output the continuous optical signal PI phase shifted by a predetermined amount to a first node N 1 , and the second modulator  325  may output the continuous optical signal phase PI shifted by a predetermined amount to a second node N 2 .  
      As shown in  FIG. 3 , the output signals of the first and second modulators  315  and  325  may be summed to generate the first modulation signal M 1 , and constructively or destructively interfere with each other according to the shifts in their phases.  
      The first modulator  315  may form an upper arm of the first interferometer  310 , and the second modulator  325  may form a lower arm of the first interferometer  310 . Phase shifts of the output signals of the first and second modulators  315  and  325  may be the same as in the XOR circuit  100  shown in  FIG. 1 .  
      The first modulator  315  may include a first optical amplifier  311  and a first phase shifter  313 . The first optical amplifier  311  may perform XPM on the continuous optical signal PI in response to the first optical signal A. The first phase shifter  313  may shift the phase of an output signal of the first optical amplifier  311  by a predetermined amount.  
      The second modulator  325  may include a second optical amplifier  325  performing XPM on the continuous optical signal PI in response to the second optical signal B.  
      In the present embodiment, the first and second optical amplifiers  311  and  325  may have the characteristics described with reference to  FIGS. 2A and 2B . In other words, if the power of an input signal (hereinafter referred to as “input power”) is less than a predetermined level, the first and second optical amplifiers  311  and  325  may output the input signal without delaying the phase of the input signal. If the input power is greater than the predetermined level, the first and second optical amplifiers  311  and  325  delay and output the phase of the input signal, by a predetermined amount. In the present embodiment, the predetermined amount may be π.  
      Accordingly, if the power of the first optical signal A is at a high level, the first optical amplifier  311  may delay the phase of the continuous optical signal PI by π. If the power of the first optical signal A is at a low level, the first optical amplifier  311  may not delay the phase of the continuous optical signal PI.  
      If the power of the second optical signal B is at a high level, the second optical amplifier  325  in the lower arm of the first interferometer  310  may delay the phase of the continuous optical signal PI by π. If the power of the second optical signal B is at a low level, the second optical amplifier  325  may not delay the phase of the continuous optical signal PI. Here, the first phase shifter  313  may shift the phase of an output signal of the first optical amplifier  311  by (2n+1)π, where n is an integer.  
      Under these conditions, the first interferometer  310  according to the present embodiment may perform the same operation as the XOR circuit  100  shown in  FIG. 1 . Thus, the first modulation signal M 1  may be the result of an XOR operation performed on the first and second optical signals A and B.  
      Since the first interferometer  310  has the same structure as the XOR circuit  100  shown in  FIG. 1  as described above, the detailed operation of the first interferometer  310  will not be described herein.  
      The second interferometer  330  may include third and fourth modulators  335  and  345 . The third modulator  335  may phase modulate and output the continuous optical signal PI in response to the sum signal C. In other words, the third modulator  335  may output the continuous optical signal PI phase shifted by a predetermined amount to a third node N 3 . The fourth modulator  345  may amplify P 1  by a predetermined gain and output the continuous optical signal PI.  
      As shown in  FIG. 3 , output signals of the third and fourth modulators  335  and  345  may be summed to generate a second modulation signal M 2 , and may constructively or destructively interfere with each other according to the shift in their phases. The third modulator  335  may form an upper arm of the second interferometer  330 , and the fourth modulator  345  may form a lower arm of the second interferometer  330 . The phase shifts of the output signals of the third and fourth modulators  335  and  345  may be the same as the phase shifts of the output signals of the first and second modulators  315  and  325 .  
      The third modulator  335  may include a third optical amplifier  331  and a second phase shifter  333 . The third optical amplifier  331  may phase modulate the continuous optical signal PI in response to the sum signal C. The second phase sifter  333  may phase shift an output signal of the third optical amplifier  331  by a predetermined value.  
      In the present embodiment, the second interferometer  330  may perform different logic operations according to a phase shift amount of the second phase shifter  333  in a similar manner to the first interferometer  310 .  
      The fourth modulator  345  may be a fourth optical amplifier  345  amplifying by a predetermined gain and outputting the continuous optical signal PI. The fourth optical amplifier  345  may perform self-phase modulation (SPM) on the continuous optical signal PI. In the present embodiment, the fourth optical amplifier  345  does not shift the phase of the continuous optical signal PI.  
      As in the description of the XOR circuit  100  shown in  FIG. 1 , the first and second optical signals A and B may be optical pulse signals modulated into “LLHH” and “LHLH” signals, respectively. Thus, the sum signal C may have three levels, i.e., a low level (AB=“LL”), a first high level (AB=“LH” or AB=“HL”), and a second high level (AB=“HH”). Here, the first high level is less than the second high level.  
      In the present embodiment, the third optical amplifier  331  may have the characteristics described with reference to  FIGS. 2A and 2B . In other words, if the input power is less than a predetermined level, the third optical amplifier  331  may output the input signal without delaying the phase of the input signal. If the input power is greater than the predetermined level, the third optical amplifier  331  may delay the phase of the input signal by a predetermined amount. In the present embodiment, the predetermined value may be π.  
      Thus, if the power of the sum signal C is at the low level, the third optical amplifier  331  may not delay the phase of the continuous optical signal PI. If the power of the sum signal C is at the first or second high level, the third optical amplifier  331  may delay the phase of the continuous optical signal PI by π.  
      The optical logic element  300  may perform a logic operation in accordance with the phase shift implemented by the second phase shifter  333 . In detail, if the second phase shifter  333  shifts the phase of the output signal of the third optical amplifier  331  by π, the second interferometer  330  may perform an OR operation. If the second phase sifter  333  does not shift the phase of the output signal of the third optical amplifier  331 , the second interferometer may perform a NOR operation. Another logic operation of the optical logic element  300  will now be described.  
      If the first and second optical signals A and B are both at a low level, the third optical amplifier  331  may not delay the phase of the continuous optical signal PI. However, the first optical signal A and/or the second optical signal B are at a high level, the third optical amplifier  331  may delay the phase of the continuous optical signal PI by π.  
      The fourth optical amplifier  345  may amplify the continuous optical signal PI by a predetermined gain and may output the amplified continuous optical signal PI regardless of the levels of the first and second optical signals A and B, and may not delay the phase of the continuous optical signal PI.  
      If the second phase shifter  333  shifts the phase of the output signal of the third optical amplifier  331  by (2n)π, i.e., effectively does not shift the phase of the output signal of the third optical amplifier  331 , the optical logic element  300  will perform the following operation.  
      If the first and second optical signals A and B are both at a low level, a continuous optical signal that is not phase shifted is output to a third node N 3 . Thus, continuous optical signals in the upper and lower arms of the second interferometer  330  do not have a phase difference, and thus constructively interfere with each other. As a result, the second modulation signal M 2  is at a high level.  
      If the first optical signal A and/or the second optical signal B are at a high level, a continuous optical signal phase shifted by π is output to the third node N 3 . The continuous optical signals in the upper and lower arms of the second interferometer  330  have a phase difference of π, and, thus, destructively interfere with each other. As a result, the second modulation signal M 2  is at a low level.  
      If the second phase shifter  333  shifts the phase of the output signal of the third optical amplifier  331  by (2n)π, the second modulation signal M 2  is the result of an NOR operation performed on the first and second optical signals A and B.  
      The result of the NOR operation can be added to the result of an XOR operation to obtain a result of an NAND operation. Thus, the sum signal MS equal to the sum of the first and second modulation signals Ml and M 2  is the result of an NAND operation.  
      If the second phase shifter  333  shifts the phase of the output signal of the third optical amplifier  331  by (2n)π, the optical logic element  300  according to the present embodiment may perform an XOR operation (the first modulation signal M 1 ), a NOR operation (the second modulation signal M 2 ), and a NAND operation (the sum signal MS of the first and second modulation signals M 1  and M 2 ) on the first and second optical signals A and B.  
      If the second phase shifter  333  shifts the phase of an output of the fourth optical amplifier by (2n+1)π, i.e., effectively by π, the optical logic element  300  may perform the following operation.  
      If the first and second optical signals A and B are both at a low level, a continuous optical signal phase shifted by π is output to the third node N 3 . Thus, the continuous optical signals in the upper and lower arms of the second interferometer  330  have a phase difference of π, and thus destructively interfere with each other. As a result, the second modulation signal M 2  is at a low level.  
      If the first optical signal A and/or the second optical signal B are at a high level, a continuous optical signal that is not phase shifted is output to the third node N 3 . Thus, the continuous optical signals in the upper and lower arms of the second interferometer  330  do not have a phase difference, and, thus, constructively interfere with each other. As a result, the second modulation signal M 2  is at a high level.  
      If the second phase shifter  333  shifts the phase of the output signals of the third optical amplifier  331  by (2n+1)π, the second modulation signal M 2  is a result of an OR operation performed on the first and second optical signals A and B. In other words, the optical logic element  300  according to the present embodiment may perform an XOR operation (the first modulation signal M 1 ) and an OR operation (the second modulation signal M 2 ) on the first and second optical signals A and B.  
       FIG. 4  illustrates a schematic diagram of an optical logic element  400  according to another embodiment of the present invention. Referring to  FIG. 4 , the optical logic element  400  may be the same as the optical logic element  300  shown in  FIG. 3 , except that the optical logic element  400  may include fifth and sixth optical amplifiers  413  and  433  serving as the first and second phase shifters. Like reference numerals in  FIG. 4  are the same as those in  FIG. 3 .  
      In detail, the fifth optical amplifier  413  may perform SPM on an output signal of a first optical amplifier  411  in response to the output signal of the first optical amplifier  411 . The sixth optical amplifier  433  may perform SPM on an output signal of a third optical amplifier  431  in response to the output signal of the third optical amplifier  431 .  
      In the present embodiment, the fifth optical amplifier  413  may delay the phase of the output signal of the first optical amplifier  411  by a predetermined amount, e.g., by (2n+1)π, i.e., effectively by π. The sixth optical amplifier  433  may delay a phase of the output signal of the fourth optical amplifier  431  by a predetermined amount, e.g., by (2n+1)π or (2n)π, i.e., effectively by π or 0.  
      The optical logic element  400  shown in  FIG. 4  may have the same structure and performs the same operations as the optical logic element  300  shown in  FIG. 3 , except that the fifth and sixth optical amplifiers are used in place of the first and second phase shifters  313  and  333  of the optical logic element  300 . Thus, the structure and detailed operation of the optical logic element  400  will not be described herein.  
      In the optical logic element  400  shown in  FIG. 4 , a first optical signal A, a second optical signal B, and a sum signal C equal to the sum of the first and second optical signals A and B, may be directly input to the first optical amplifier  411 , a second optical amplifier  425 , and to the third optical amplifier  431 , respectively, so as to prevent the first and second optical signals A and B and the sum signal C from being distorted by the fifth and sixth optical amplifiers  413  and  433 .  
       FIG. 5  illustrates a schematic diagram of an optical logic element  500  according to another embodiment of the present invention.  
      The optical logic element  500  shown in  FIG. 5  may have the same structure as the optical logic element  300  shown in  FIG. 3 , except that the first optical amplifier  311  and the first phase shifter  313  may be integrated into a first modulator  515 , and the third optical amplifier  331  and the second phase shifter  333  may be integrated into a third modulator  535 .  
      In detail, a first interferometer  510  of the optical logic element  500  may include first and second modulators  515  and  525 , which may be optical amplifiers, and a second interferometer may include third and fourth modulators  535  and  545 , which may be optical amplifiers. Thus, the first modulator  515  may include a first optical amplifier, and the third modulator  535  may include a second optical amplifier.  
      The first optical amplifier in the first modulator  515  may perform XPM on a continuous optical signal PI in response to a first optical signal A, and then may delay the phase of the continuous optical signal PI by a predetermined amount. The third modulator  535  may perform XPM on the continuous optical signal PI in response to a sum signal C equal to the sum of the first optical signal A and a second optical signal B, and then may delay the phase of the continuous optical signal PI by a predetermined amount.  
      The operation of the optical logic element  500  is the same as that of the optical logic element  300  shown in  FIG. 3 , except that both XPM and phase shifting are performed by modulators  515  and  535 , and thus will not be described herein.  
       FIG. 6  illustrates a schematic diagram of an optical logic element  600  according to another embodiment of the present invention. The optical logic elements  300 ,  400 , and  500  shown in  FIGS. 3, 4 , and  5  use interferometers using a counter-propagation method, while the optical logic element  600  uses an interferometer using a co-propagation method.  
      In other words, as shown in  FIG. 6 , first and second optical signals A and B, a sum signal C equal to the sum of the first and second optical signals A and B, and a continuous optical signal PI may be input to the logic element  600  in the same direction.  
      In the optical logic element  600 , continuous optical signals modulated by first and second modulators  615  and  625  interfere with each other to generate a first modulation signal M 1 , and continuous optical signals modulated by third and fourth modulators  635  and  645  interfere with each other to generate a second modulation signal M 2 . Thus, the optical logic element  600  needs to filter the first and second optical signals A and B, and the sum signal C, from the signals output from a first interferometer  610  and a second interferometer  630 .  
      Accordingly, unlike the optical logic elements  300 ,  400 , and  500  shown in  FIGS. 3, 4 , and  5 , the optical logic element  600  further includes first and second band pass filters  650  and  670 . The first band pass filter  650  filters the first and second optical signals A and B outputs from the first interferometer  610  to output a first modulation signal M 1 . The second band pass filter  670  filters the sum signal C output from the second interferometer  630  to output a second modulation M 2 .  
      The optical logic element  600  has the same structure and performs the same operations as the optical logic element  300  shown in  FIG. 3  except that the optical logic element  600  further includes the first and second band pass filters  650  and  670 . Thus, the detailed operation of the optical logic element  600  will not be described herein.  
      As described above, an optical logic element according to an embodiment of the present invention uses an MZI. However, the present invention may be realized using an interferometer having the same characteristics as a Michelson interferometer or the like by those of ordinary skill in the art.  
      Optimal operating conditions for an optical logic element according to an embodiment of the present invention will now be described based on the optical logic element  300  shown in  FIG. 3 . The following description is related to optimal operating conditions of an optical logic element according to an embodiment of the present invention, and the operation of the optical logic element is not limited to the optimal operation conditions.  
      In the first interferometer  310 , the power of the continuous optical signal PI is defined as PIN, high and low levels of power of the first optical signal A are respectively defined as PAL and PAH, and high and low levels of power of the second optical signal B are respectively defined as PBL and PBH. Optical gains of the first optical signal A and the continuous optical signal PI, i.e., PIN+PAL and PIN+PAH, obtained through the first optical amplifier  311  are respectively defined as G 1 L and G 1 H, and optical gains the second optical signal B and the continuous optical signal PI, i.e., PIN+PBL and PIN+PBH, obtained through the first optical amplifier  311  are respectively defined as G 2 L and G 2 H.  
      Thus, the first modulation signal M 1  is obtained by combining signals with powers of PING 1 L and PING 1 H with signals with powers of PING 2 L and PING 2 H. XPM performed by optical amplifiers is mainly performed on an input signal at a high level. Thus, a power PO 1 -AB of the first modulation signal Ml can be represented by Equation 1:  
               P     01   -   AB       =       P   in     (       G     1   ⁢   A       +     G     2   ⁢   B       +           G     1   ⁢   A       ·     G     2   ⁢   B         2     ⁢     cos   ⁡     (       ϕ   1     +     Δ   ⁢           ⁢     ϕ   XPM         )           )             (   1   )             
 
      where φ1 is a phase difference between the signals in the upper and lower arms of the first interferometer  310 , i.e., a phase difference produced by the first phase shifter  313 , ΔφXPM is a phase difference between the signals in the upper and lower arms due to XPM, i.e., a difference between a phase shift ΔφXPM 1  occurring due to XPM performed by the first optical amplifier  311  and a phase shift ΔφXPM 2  due to XPM performed by the second optical amplifier  325 , and G 1 A and G 1 B are optical gains provided by the first and second optical amplifiers  311  and  325 , respectively.  
      If AB=“LL,” G 1 L and G 2 L both may have large values, and A(PXPM may have a value approximately equal to “0.” If AB=“LH” or AB=“HL,” one of G 1 A and G 2 B may have a large value, the other one may have a small value, and ΔφXPM may have a value approximately equal to “π.” If AB=“HH,” G 1 H and G 2 H may both have small values, and ΔφXPM may have a value approximately equal to “0.” 
      Four levels exist at φ1=0. The four levels are a PO 1 -LL((φ1=0) level having a maximum value due to ΔφXPM approximately equal to “0” on a curve of PO 1 -LL, i.e., if AB=“LL,” with respect to (φ1, a PO 1 -LH((φ1=0) level inside a curve of PO 1 -LH, i.e., if AB=“LH” with respect to φ1, a PO 1 -HL(φ1=0) level inside a curve of PO 1 -HL, i.e., if AB=“HL” with respect to φ1, and a PO 1 -HH((φ1=0) level inside a curve of PO 1 -HH, i.e., if AB=“HH” with respect to φ1. Four levels exist at φ1=π. The four levels are a PO 1 -LL((φ1=π) level having a minimum value due to ΔφXPM approximately equal to “0” on a curve of PO 1 -LL with respect to φ1, a PO 1 -LH(φ1=π) level inside a curve of PO 1 -LH with respect to φ1, a PO 1 -HL(φ1=π) level inside a curve of PO 1 -HL with respect to φ1, and a PO 1 -HH(φ1=π) level inside a curve of PO 1 -HH with respect to φ1.  
      Here, if six values of PO 1 -LL(φ1=0), PO 1 -LL(φ1=π), PO 1 -LH(φ1=0), PO 1 -LH(φ1=π), PO 1 -HL(φ1=0), and PO 1 -HL(φ1=π) inside curves PO 1 -AB(φ1=0) and PO 1 -AB(φ1=π) are checked, the six values are substituted for Equation 1 so as to obtain values of PING 1 L, PING 2 L, PING 1 H, PING 2 H, ΔφXPM 1 , and ΔφXPM 2  that can be expressed as in Equations 2 through 5:  
                         P   in     ⁢     G     1   ⁢           ⁢   L         =         (           P       O   ⁢           ⁢   1     -   II       ⁡     (     ϕ   =   0     )         ±         P       O   ⁢           ⁢   1     -   LL       ⁡     (     ϕ   =   π     )           )     2     /   4       ,     
     ⁢         P   in     ⁢     G     2   ⁢   L         =         (           P       O   ⁢           ⁢   1     -   LL       (     ϕ   =   0         ∓         P       O   ⁢           ⁢   1     -   LL       ⁡     (     ϕ   =   π     )           )     2     /   4         ⁢     
     ⁢           *     ⁢   upper     ⁢           ⁢   sign   ⁢     :     ⁢           ⁢               ⁢     G             ⁢     1   ⁢           ⁢   L               ≥               ⁢     G             ⁢     2   ⁢           ⁢   L               ,     
     ⁢       lower   ⁢           ⁢   sign   ⁢     :     ⁢           ⁢       G     1   ⁢   L           ≤       G     2   ⁢   L                   (   2   )                     P   in     ⁢     G     1   ⁢   H         =         -     P   in       ⁢     G     2   ⁢   L         +       (         P       O   ⁢           ⁢   1     -   HL       ⁡     (     ϕ   =   0     )       +       P       O   ⁢           ⁢   1     -   HL       ⁡     (       ϕ   1     =   π     )         )     /   2         ,     
     ⁢         P   in     ⁢     G     2   ⁢   H         =         -     P   in       ⁢     G     1   ⁢   L         +       (         P       O   ⁢           ⁢   1     -   LH       ⁡     (       ϕ   1     =   0     )       +       P       O   ⁢           ⁢   1     -   LH       ⁡     (     ϕ   =   π     )         )     /   2                 (   3   )                       Δ   ⁢           ⁢     ϕ     XPM   ⁢           ⁢   1         =       cos     -   1       ⁡     [           P       O   ⁢           ⁢   1     -   HL       ⁡     (     ϕ   =   0     )       -       P   in     ⁢     G     1   ⁢   H         -       P   in     ⁢     G     2   ⁢   L             2   ⁢     P   in     ⁢         G     1   ⁢   H       ·     G     2   ⁢   L               ]                   =     cos   ⁡     [           p       O   ⁢           ⁢   1     -   HL       ⁡     (     ϕ   =   π     )       -       P   in     ⁢     G     1   ⁢   H         -       P   in     ⁢     G     2   ⁢   L               -   2     ⁢     P   in     ⁢         G     1   ⁢   H       ·     G     2   ⁢   L               ]                     (   4   )                       Δ   ⁢           ⁢     ϕ     XPM   ⁢           ⁢   2         =       cos     -   1       ⁡     [           P       O   ⁢           ⁢   1     -   LH       ⁡     (     ϕ   =   0     )       -       P   in     ⁢     G     1   ⁢   L         -       P   in     ⁢     G     2   ⁢   H             2   ⁢     P   in     ⁢         G     1   ⁢   L       ·     G     2   ⁢   H               ]                   =     cos   ⁡     [           p       O   ⁢           ⁢   1     -   LH       ⁡     (     ϕ   =   π     )       -       P   in     ⁢     G     1   ⁢   L         -       P   in     ⁢     G     2   ⁢   H               -   2     ⁢     P   in     ⁢         G     1   ⁢   L       ·     G     2   ⁢   H               ]                     (   5   )             
 
      An optimal optical gain and optical phase difference for operating an optimal operation of the first interferometer  310  may be obtained using Equations 2 through 5. The results of the optimal optical gain and phase difference are shown in Tables 1 and 2.  
      In the second interferometer  330 , optical gains the first optical signal A and the continuous optical signal PI, i.e., PIN+PAL+PBL, PIN+PAL+PBH or PIN+PAH+PBL, and PIN+PAH+PBH, experienced in the third optical amplifier  331  may be defined as G 3 LL, G 3 LH or G 3 HL, and G 3 HH, and an optical gain the continuous optical signal PI, i.e., PIN, experienced in the fourth optical amplifier  345 , may be defined as G 4 .  
      Thus, the second modulation signal M 2  is a signal obtained by combining and interfering level signals of PING 3 LL, PING 3 LH or PING 3 HL, and PING 3 HH with a level signal of PING 4 . Since XPM performed by the third optical amplifier  311  vary with each level, a power PO 2 -AB of the second modulation signal M 2  can be induced as in Equation 6: 
 
 P   02-AB   P   in ( G   3AB   +G   4   +2√{square root over ( G   3AB   ·G   4 )} cos(φ   2 +Δφ XPM )   (6) 
 
      where φ 2  is a phase difference between the upper and lower arms of the second interferometer  330 , i.e., a phase difference by the second phase shifter  333 , Δφ XPM  is a difference between a phase shift between the upper and lower arms due to XPM, i.e., a phase shift Δφ XPM3  due to XPM performed by the third optical amplifier  331 , a phase shift Δφ XPM4  due to XPM performed by the fourth optical amplifier  345 , and G 3AB  and G 4  respectively are optical gains in the third and fourth optical amplifiers  331  and  345 . As described above, in the present embodiment, Δφ XPM4 =0, particularly, G 4  may be controlled so as to control a gain difference between the third and fourth optical amplifiers.  
      If AB=“LL”, G 3LL  (hereinafter referred to as G 3L ) may have a large value, and Δφ XPM  may have a value approximately equal to 0. If AB=“LH” or “HL,” G 3LH  and G 3HL  may be expressed as G 3H  having a small value, and Δφ XPM  may have a value approximately equal to π. If AB=“HH,” G 3HH  may have a very small value, and Δφ XPM  may have a value approximately equal to π.  
      Four levels exist at φ 2 =0. The four levels are a P O2-LL (φ2=0) level having a maximum value on a curve of P O2-LL  with respect to φ 2  due to Δφ XPM  being approximately equal to 0, a P O2-LH (φ2=0) level inside a curve of P O2-LH  with respect to φ2, a P O2-HL (φ2=0) level inside a curve of PO 2 -HL with respect to φ2 and a P O2-HH (φ2=0) level inside a curve of PO 2 -HH with respect to φ 2 .  
      Also, four levels exist at φ 2 =π. The four levels are a P O2-LL (φ 2 =π) level having a minimum value on a curve of P O2-LL  with respect to φ 2  due to Δφ XPM  being approximately equal to 0, a P O2-LH (φ2=π) level inside a curve of P O2-LH  with respect to φ 2 , a P O2-HL (φ 2 =π) inside a curve of P O2-HL  with respect to φ 2 , and a P O2-HH (φ 2 =π) level inside a curve of P O2-HH  with respect to φ 2 .  
      Here, if the P O2-LL (φ 2 =0), P O2-LL (φ 2 =π), P O2-LH (φ 2 =0) or P O2-HL (φ 2 =0), P O2-LH (φ 2 =π) or P O2-HL (φ 2 =π), P O2-HH (φ 2 =0), and P O2-HH (φ 2 =π) levels are checked inside curves of P O2-AB (φ 2 =0) and P O2-AB (φ 2 =π), the six levels may be substituted into Equation 6 to obtain values of PING 3L , PING 3H , PING 3HH , PING 4 , Δφ XPM3H , and Δφ XPM3HH , which may be given by Equations 7 through 10:  
                         P   in     ⁢     G     3   ⁢           ⁢   L         =         (           P       O   ⁢           ⁢   2     -   LL       ⁡     (       ϕ   2     =   0     )         ±         P       O   ⁢           ⁢   2     -   LL       ⁡     (       ϕ   2     =   π     )           )     2     /   4       ,     
     ⁢         P   in     ⁢     G   4       =         (           P       O   ⁢           ⁢   2     -   LL       (       ϕ   2     =   0         ∓         P       O   ⁢           ⁢   2     -   LL       ⁡     (       ϕ   2     =   π     )           )     2     /   4         ⁢     
     ⁢           *     ⁢   upper     ⁢           ⁢   sign   ⁢     :     ⁢           ⁢               ⁢     G             ⁢     3   ⁢           ⁢   L               ≥               ⁢     G             ⁢   4             ,     
     ⁢       lower   ⁢           ⁢   sign   ⁢     :     ⁢           ⁢       G     3   ⁢   L           ≤       G   4                 (   7   )                     P   in     ⁢     G     3   ⁢   H         =         -     P   in       ⁢     G   4       +       (       P       O   ⁢           ⁢   2     -   LH       ⁡     (       ϕ   2     =   π     )       )     /   2         ,     
     ⁢         P   in     ⁢     G     3   ⁢   HH         =         -     P   in       ⁢     G   4       +       (         P       O   ⁢           ⁢   2     -   HH       ⁡     (       ϕ   2     =   0     )       +       P       O   ⁢           ⁢   2     -   HH       ⁡     (       ϕ   2     =   π     )         )     /   2                 (   8   )                       Δ   ⁢           ⁢     ϕ     XPM   ⁢           ⁢   3   ⁢   H         =       cos     -   1       ⁡     [           P       O   ⁢           ⁢   2     -   LH       ⁡     (       ϕ   2     =   0     )       -       P   in     ⁢     G     3   ⁢   H         -       P   in     ⁢     G   4           2   ⁢     P   in     ⁢         G     3   ⁢   H       ·     G   4             ]                   =       cos     -   1       ⁡     [           P       O   ⁢           ⁢   2     -   LH       ⁡     (       ϕ   2     =   π     )       -       P   in     ⁢     G     3   ⁢   H         -       P   in     ⁢     G   4             -   2     ⁢     P   in     ⁢         G     3   ⁢   H       ·     G   4             ]                     (   9   )                       Δ   ⁢           ⁢     ϕ     XPM   ⁢           ⁢   3   ⁢   HH         =       cos     -   1       ⁡     [           P       O   ⁢           ⁢   2     -   HH       ⁡     (       ϕ   2     =   0     )       -       P   in     ⁢     G     3   ⁢   HH         -       P   in     ⁢     G   4           2   ⁢     P   in     ⁢         G     3   ⁢           ⁢   HH       ·     G   4             ]                   =       cos     -   1       ⁡     [           P       O   ⁢           ⁢   2     -   HH       ⁡     (       ϕ   2     =   π     )       -       P   in     ⁢     G     3   ⁢   HH         -       P   in     ⁢     G   4             -   2     ⁢     P   in     ⁢         G     3   ⁢           ⁢   HH       ·     G   4             ]                     (   10   )             
 
      Optimal optical gains and phase differences for the optimal operation of the second interferometer  330  can be obtained from Equations 7 through 10 and are shown in Tables 1 and 2.  
                                   TABLE 1                                      XOR(φ 1  = π)   NOR(φ 2  = 0)   OR(φ 2  = π)   NAND(=XOR + NOR)                                                     A   B   O   P O1 (φ 1  = π)   O   P O2 (φ 2  = 0)   O   P 02 (φ 2  = π)   O   P 03  = P O1 (φ 1  = π) + p 02 ((φ 1  = π)               L   L   L   0   H   c + f + 2{square root over ((cf))}   L   c + f − 2{square root over ((cf))}   H   c + f − 2{square root over ((cf))}       L   H   H   a + b + 2{square root over ((ab))}   L   d + f − 2{square root over ((df))}   H   d + f + 2{square root over ((df))}   H   a + b + 2{square root over ((ab))} + d + f − 2{square root over ((df))}       H   L   H   a + b + 2{square root over ((ab))}   L   d + f − 2{square root over ((df))}   H   d + f + 2{square root over ((df))}   H   a + b + 2{square root over ((ab))} + d + f − 2{square root over ((df))}       H   H   L   0   L   e + f − 2{square root over ((ef))}   H   e + f + 2{square root over ((ef))}   L   e + f − 2{square root over ((ef))}                  
 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 2 
               
             
            
               
                   
                   
               
               
                   
                   
               
               
                   
                 XOR(φ  2  = π) 
                 XOR(φ 2  = 0) 
                 OR(φ 2  = π) c = f, 
                 NAND 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Δφ XPM   
                 Δφ XPM   
                 a = c, b = d 
                 d = f ≈ e 
                 d ≈ e 
                 (=XOR + NOR) 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 A 
                 B 
                 (XOR) 
                 (NOR/OR) 
                 O 
                 P O1 (φ 1  = π) 
                 O 
                 P O2 (φ 2  = 0) 
                 O 
                 P O2 (φ 2  = π) 
                 O 
                 P 03   
               
               
                   
               
               
                 L 
                 L 
                 0 
                 0 
                 L 
                 0 
                 H 
                 c + d + 2{square root over ((cd))} 
                 L 
                 0 
                 H 
                 c + d + 2{square root over ((cd))} 
               
               
                 L 
                 H 
                 π 
                 π 
                 H 
                 c + d + 2{square root over ((cd))} 
                 L 
                 0 
                 H 
                 d + f + 2{square root over ((df))} 
                 H 
                 c + d + 2{square root over ((cd))} 
               
               
                 H 
                 L 
                 π 
                 π 
                 H 
                 c + d + 2{square root over ((cd))} 
                 L 
                 0 
                 H 
                 d + f + 2{square root over ((df))} 
                 H 
                 c + d + 2{square root over ((cd))} 
               
               
                 H 
                 H 
                 0 
                 π 
                 L 
                 0 
                 L 
                 ≈0 
                 H 
                 ≈d + f + 2{square root over ((df))} 
                 L 
                 ≈e 
               
               
                   
               
            
           
         
       
     
      For convenience, PING 1L =PING 2L =a, PING 1H =PING 2H =b, PING 3L =c, PING 3H =d, PING 3HH =e, and PING 4 =f. Also, it is assumed that a phase shift caused by XPM is π at a high level and 0 at a low level.  
      In the present embodiment, gains and phase differences between upper and lower arms of first and second interferometers can be adjusted so as to optimally operate an optical logic element.  
      In other words, a gain and a phase difference may be optimized so as to realize an optical logic element capable of performing XOR, NOR, OR, and NAND operations.  
      Bias currents of optical amplifiers and control voltages of phase shifters can be adjusted by those of ordinary skill in the art so as to easily adjust a gain and phase difference.  
      Also, an extinction ratio (ER) may be expressed as in Equation 11: 
 
 ER= 10 log(high state level/low state level)   (11) 
 
      In the present embodiment, a maximum ER can be obtained through the following process.  
      Combinations of bias currents of the first, second, third, and fourth optical amplifiers  311 ,  325 ,  331 , and  345  are set at appropriate resolutions below a maximum value.  
      If all combinations of bias currents are applied to the first and second optical amplifiers  311  and  325  of the first interferometer  310 , P O1-LL (φ 1 =0), P O1-LL (φ 1 =π), P O1-LH (φ 1 =0), P O1-LH (φ 1 =π), P O1-HL (φ 1 =0), and P O1-HL (φ 1 =π) levels may be measured. If all combinations of bias currents are applied to the third and fourth optical amplifiers  331  and  345  of the second interferometer  330 , P O2-LL (φ 2 =0), P O2-LL (φ 2 =π), P O2-LH (φ 2 =0) or P O2-HL (φ 2 =0), P O2-LH (φ 2 =π) or P O2-HL (φ 2 =π), P O2-HH (φ 2 =0), and P O2-HH (φ 2 =π) levels may be measured.  
      Values of PING 1L , PING 2L , PING 1H , PING 2H , Δφ XPM1 , and Δφ XPM2  are calculated with respect to the first interferometer  310 , and combinations of optical bias currents satisfying gain conditions of PING 1L =PING 2L =PING 3L  and PING 1H =PING 2H =PING 3H  may be obtained. Values of PING 3L , PING 3H , PING 3HH , PING 4 , Δφ XPM3H , and Δφ XPM3HH  of the second interferometer  310  may be calculated, and combinations of optimal bias currents satisfying PING 3H =PING 4 ≈. PING 3HH  and conditions of PING 3L =PING 4  and PING 3H ≈PING 3HH  with respect to XOR and OR operations may be obtained.  
      As described above, combinations of optical bias currents may be obtained so as to obtain an optimal ER.  
       FIG. 7  illustrates a timing diagram of results of an experiment performed on an optical logic element according to an embodiment of the present invention, i.e., FIGS.  7 ( c ),  7 ( d ),  7 ( e ), and  7 ( f ) respectively illustrate the results of XOR, NOR, OR, and NAND operations on first and second optical signals A and B shown in FIGS.  7 ( a ) and  7 ( b ).  
      In the experiment, a continuous optical signal PI was generated using a tunable laser diode (LD) having a wavelength of 1549.79 nm. Also, a distributed feedback (DFB) LD 1  having a wavelength of 1551.47 nm was used to generate the first and second optical signals A and B input to a first interferometer, and a DFB LD 2  having a wavelength of 1553.79 nm was used to generate a sum signal C equal to the sum of the first and second optical signals A and B.  
      In the experiment, a pulse pattern generator (PPG) was used to program the first and second optical signals A and B and the sum signal C with a repeating pattern of “00001111” at a speed of 2.5 Gbps so as to directly modulate the first and second signals A and B and the sum signal C with the DFB LD 1  and DFB LD 2 .  
      To generate the first and second optical signals A and B in the first interferometer, an optical divider was used to divide an optical signal modulated in a repeated pattern into two signals and transmit one of the two signals through a time delay line corresponding to a half period of a total signal pattern so that combinations of the first and second optical signals A and B were repeated as “LL,” “LH,” “HL,” and “HH.” 
      In the second interferometer, an output of the DFB LD 2  passed through an additional MZI, and a time delay line corresponding to a half period of a total signal pattern was inserted in the middle of an arm of the additional MZI so as to output a sum signal equal to the sum of first and second optical signals having combinations of “LL,” “LH,” “HL,” and “HH.” 
      As shown in  FIG. 7 ( c ), when a phase shift of a first phase shifter was π, the output of the first interferometer was an XOR operation on the first and second optical signals A and B.  
      As shown in  FIG. 7 ( d ), when a phase shift of a second phase shifter was 0, the output of the second interferometer was an XOR operation on the first and second optical signals A and B.  
      As shown in  FIG. 7 ( e ), when the phase shift of the second phase shifter was π, the output of the second interferometer was an OR operation on first and second optical signals.  
      As shown in  FIG. 7 ( f ), when the phase shifter value of the first phase shifter was π and the phase shift of the second phase shifter was 0, the outputs of the first and second interferometers were NAND operations on the first and second optical signals.  
      As described above, an optical logic element according to the present invention can realize all-optical XOR, NOR, OR, and NAND circuits. As a result, the optical logic element can be easily realized by realizing the all-optical NOR or NAND circuit. Also, optimal operation conditions can be obtained for the optical logic element so as to maximize an ER and minimize a bit error rate.  
      Exemplary embodiments of the present invention have been disclosed herein, and although specific terms are employed, they are used and are to be interpreted in a generic and descriptive sense only and not for purpose of limitation. Accordingly, it will be understood by those of ordinary skill in the art that various changes in form and details may be made without departing from the spirit and scope of the present invention as set forth in the following claims.