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DOI: 10.22184/1993-7296.FRos.2020.14.8.696.707
The implementation of interference logical elements (LE) is proposed, based on the functioning of which the difference in the intensity values of coherent light waves arising as a result of their interaction with each other and with the waveguides of the logical elements.
The elements form a functionally complete basis.
The requirements for the identity of the intensity values corresponding to the logical constants “0” and “1”, generated by different elements at given fixed time intervals, are fulfilled.
Means for scaling the intensity values of logical constants are proposed. The estimates of the parameters of the elements – speed, power consumption, physical dimensions – are obtained, showing their advantages over electronic counterparts.
Fields of application of interference LEs are digital devices of control systems and computer technology.
The implementation of interference logical elements (LE) is proposed, based on the functioning of which the difference in the intensity values of coherent light waves arising as a result of their interaction with each other and with the waveguides of the logical elements.
The elements form a functionally complete basis.
The requirements for the identity of the intensity values corresponding to the logical constants “0” and “1”, generated by different elements at given fixed time intervals, are fulfilled.
Means for scaling the intensity values of logical constants are proposed. The estimates of the parameters of the elements – speed, power consumption, physical dimensions – are obtained, showing their advantages over electronic counterparts.
Fields of application of interference LEs are digital devices of control systems and computer technology.
Теги: functionally complete basis intensity scaling interference interference logic element интерференционный логический элемент интерференция масштабирование интенсивности функционально полный базис
Photonic computer. Element base
S. A. Stepanenko
Russian Federal nuclear center-all-Russian research Institute of experimental physics, Sarov, Nizhny Novgorod region, Russia
The implementation of interference logical elements (LE) is proposed, based on the functioning of which the difference in the intensity values of coherent light waves arising as a result of their interaction with each other and with the waveguides of the logical elements.
The elements form a functionally complete basis.
The requirements for the identity of the intensity values corresponding to the logical constants “0” and “1”, generated by different elements at given fixed time intervals, are fulfilled.
Means for scaling the intensity values of logical constants are proposed. The estimates of the parameters of the elements – speed, power consumption, physical dimensions – are obtained, showing their advantages over electronic counterparts.
Fields of application of interference LEs are digital devices of control systems and computer technology.
Key words: interference logic element, interference, functionally complete basis, intensity scaling
Received on: 04.09.2020
Accepted on: 24.09.2020
INTRODUCTION
The development of science and technology gives rise to problems that require computing systems with maximum performance – supercomputers. The electronic technologies on which modern supercomputers are based are close to their physical limits. Alternative means of increasing productivity are relevant, in particular, based on previously unused physical principles.
Over the past 30 years, quantum computing has been actively studied [1]. However, the prospects for their implementation are still uncertain. Moreover, in the modern view, quantum computers allow solving a limited special class of problems.
Another option for increasing productivity provides for the creation of a universal digital photonic computer (DPC) [2], the functioning of which is based on the effects of interaction of coherent systems of light waves generated by laser radiation. The class of problems for the solution of which the DPC is intended coincides with the class of problems solved on a computer.
One of the fundamental aspects that determine the possibility and feasibility of implementing a DPC is the element base – logical elements (LE) that perform operations on light pulses.
Active LEs that involve nonlinear effects are inferior in performance and energy efficiency to modern electronic elements [3].
Known passive LEs [4–8] have short durations of the operation, however, they are characterized either by technological drawbacks – the difference in the sizes of LEs that implement different functions is only 0.4 nm [5], or by the same intensity values for various logical constants [4, 7, 8], or the need to use a low temperature – T ≈ 3° K and prolonged relaxation [6].
The LEs proposed below use the difference in light intensity values arising from the interference of coherent light waves and their interaction with waveguides. Estimates of the parameters of these LEs show their competitiveness with electronic analogs and the possibility of using them for the implementation of digital devices.
1. IDENTIFICATION OF LOGICAL CONSTANTS
LEs perform operations on coherent electromagnetic waves. The operands and results of operations are logical constants – zero (“0”) and one (“1”). They are identified by the intensity I of an electromagnetic wave [9] propagated in the waveguide [10].
Electromagnetic wave – linearly polarized monochromatic [9], hereinafter – traveling wave, is represented by a light pulse of duration , where m is an integer, λ is the wavelength [9], υ is the speed of light in the waveguide. The quantity is called the pulse size.
The value of the intensity of the output signal of the LE is generated either in the absence of input pulses – no effects are involved in the LE, or in the case of one input pulse – the effects generated by the traveling wave are involved, or in the case of two input counter impulses – the effects generated by the standing wave are used [9].
To perform logical operations, it is necessary to redistribute the intensity in the waveguides. For this, slots are used. A slit [9] is a part of the waveguide surface through which radiation is transmitted to another waveguide or to the environment. To remove energy from the slot, a unidirectional type (1 × 2) coupler [10] is used with a given branching ratio , which means the fraction of the intensity diverted through the slot into the branching waveguide.
The remainder of the energy in a waveguide with m-slots after the passage of a traveling wave is proportional to the value , where is the wave intensity at the entrance to the waveguide. The amount of energy released from the waveguide through the slits is proportional to the value .
In the process of collision of coherent pulses of duration τ, antinodes and nodes of a standing wave are formed [9]. Distance between antinodes (and between nodes) λ / 2. If the slits of the waveguide are located above the antinodes (there are 2m of them), then the total intensity at both outputs of the waveguide will be ; in this case, the total intensity released in 2m slots of the waveguide is equal to . If the slots of the waveguide are located above the nodes, then ; and .
Elements in the waveguides of which the slits are located above the antinodes or above the nodes of the standing wave are called the LE of the first and, accordingly, the LE of the second type, and we denote it as LE1 and LE2.
2. FUNCTIONALLY COMPLETE BASIS
Let us apply the considered effects to create a functionally complete basis of the elements “AND”, “exclusive OR” and “NOT”, which implement the functions &, and [11].
The LEs proposed below use the waveguide structure shown in Figure 1. Let us characterize in terms of [12] its elements and the operations they perform.
A pulse with a polarization of 0° entering the waveguide at the input 1 changes after the left-side rotator the polarization plane by 45° according to the rule of the left screw and enters the waveguide through the polarization mirror Μ11. After the Faraday rotator it restores the plane of polarization and interacts with the slots and (if any) with the counter pulse that came after similar operations from input 2. Both pulses are coherent and equally polarized. As a result of their collision, antinodes and nodes are formed. Above the antinodes (or above the nodes), in the same plane, there are slots and bidirectional branching waveguides. The design of such a waveguide is shown in inset A to Fig. 1.
After interacting with the slots, the residual part of the pulse from input 1 enters the Faraday rotator , changes the plane of polarization and is reflected by polarizing mirrors М12 to the right-handed rotator , which restores the original polarization. Further, the pulse reflected by the mirror M2 is fed to the output Ο1, where it is combined (if any) with the pulse from input 2, on which the same operations were performed.
The output Ο2 receives energy from the branching waveguides obtained by the interaction of pulses with the slots.
2.1. Elements of the first type
Element “AND”. Let a pulse of size mλ propagate in one of the directions indicated in Fig. 1 by symbols and (this means , or , ). At the output of the element, we have ; this corresponds to .
If the pulses propagate in both directions (this means , ), then antinodes and nodes of a standing wave are formed. The cracks above the antinodes. At the output , we have ; this corresponds to .
Element “Exclusive OR”. In the case of one pulse, we have at the output the intensity , which corresponds to. For two opposite pulses, we have on the intensity , which corresponds to .
Element “NOT”. Here and below, the implementation of the function (“NOT”) is achieved by supplying “1” to one of the inputs of the element that implements .
The values of the functions , and the corresponding values of , , are presented in Table 1.
Identity of intensity values. For the correct functioning of devices made of LEs, it is necessary that the same intensities correspond to the same logical constants obtained at the same time intervals at the outputs of the LEs realizing &, and . In particular, for LE1 the following must be fulfilled
The solution to this system of equations
and .
The m values are specified by the required duration of the operation.
A functionally complete basis of interference LE1 is obtained.
2.2. TYPE SECOND ELEMENTS
Various structures can be used to implement LE2; consider the first. It is the same as shown in Figure 1. Outputs are designated and . The slots are located above the nodes.
Element “AND”. A single pulse, meaning , , or , , interacts with 2m slots. At the output of , we have .
Let the impulses propagate in both directions, i. e. , . In the process of their interaction, which occurs upon reaching the middle of the waveguide (after m slots), the intensity in the slot is not released. At the output of we have .
Element “Exclusive OR”. The element structure contains one slit. For one pulse on , we have , which corresponds to . For two counter impulses, we have , where ∆ is arbitrarily close to 0, which corresponds to .
The values of the functions , , and the corresponding values of , are presented in Table 2.
Identity of intensity values. Required execution
whence, specifying m, we find the requireed q1 and q2.
For example, for we have and . The values and correspond to and .
Other options for the implementation of LE2 are obtained by using the structure shown in Figure 2 and solving the corresponding systems of equations. An example of such a system is the following
On the left side of the equations, the values of the intensities at the output O1 of the “AND” element are indicated. the traveling wave interacts with 2m slots and . If there are two pulses, then before the collision of pulses and the formation of nodes, the intensity in each direction is equal to . After the collision, no intensity is released in the gap. At the output, we have .
On the right side of the equations, the values of intensities at the O2 output of the “exclusive OR” element are indicated. The branching waveguides of the slots between the rotators are connected in pairs, the first branching waveguide from the side of the pulse x1 is connected oppositely to the first branching waveguide from the side of the pulse x2. A slit and a branching waveguide with a branching coefficient are arranged over the node formed by the collision of these pulses.
The branching waveguides located above the other i-slots, , are connected in a similar way.
The output of the “exclusive OR” element is obtained by combining the outputs of the branching waveguides located on both sides in front of the rotators, and the outputs of pairwise (oppositely) connected branching waveguides from the slots between the rotators.
In the case of two pulses (this corresponds to and ), we have at the output of the element the value . In the case of one pulse, for example, coming from the left (which corresponds to and ), the intensity at the output of the “exclusive OR” element is .
The first term is due to the interaction of the momentum with с slots located before the rotator. The second one is the interaction of the pulse with the slot arranged in each of the branching waveguides.
The values of the functions and and the corresponding values of , are presented in Table 3.
The feasibility of using the considered options is determined by the technological parameters.
A functionally complete basis of interference LE2 is obtained.
3. ZOOM INTENSITY
Let us evaluate the possibilities of increasing the difference in intensity values corresponding to logical “0” and logical “1”.
3.1. J-level element structures
The waveguide into which the input pulses come from outside the element is called the first level waveguide. The waveguide into which the input pulses come from the k-th level waveguide, where is called the level waveguide.
A two-level LE1 is shown in Fig. 3.
Designations and designations of structural elements coincide with those specified in 2.1.
Each LE1 waveguide has 2m slots at the antinodes. The element outputs are designated O1 and O2.
Element “AND”. For , or , , we have a single pulse, the intensity of which after the waveguide of the first level is equal to . As a result of interaction with 2m slots of the second-level waveguide, its intensity at the output of will be .
In the case , , we have two counter pulses at the inputs of the second-level waveguide; the intensity of each . As a result of their interaction, the total value of the intensity at the output , corresponding to a logical unit, is equal to .
Element “Exclusive OR”. The output is designated . The values are obtained similarly to the above.
The values of the functions , and the corresponding values , , obtained at the outputs of two-level LE1, are presented in Table 4.
Here, the ratio of the intensities of logical “1” and logical “0” is 2 times greater than in single-level LE1.
Identical logical constants must correspond to the same intensities at the outputs of LE1. It is necessary
We find: and .
In the general case, for J-level LE1:
Similarly, for J-level LE2, considered in Section 2, it is necessary:
The duration of the operation J by level elements is at least τJ, where τ is the duration of the operation execution by a single-level element, the “pipeline” mode is possible.
3.2. Dynamics of Intensity Values
The above estimates of the intensities at the outputs of the LE are valid for the first, single execution of the operation. As a result of successive operations, the intensity values corresponding to different logical constants can approach each other. This is due to the difference in the values of the output intensity when performing operations on the same or different operands.
Let from the output of the i-th element the pulse arrives at the input (i + 1) of the element, where i = 1,2,…, h. Let us denote the values of the intensities “1” and “0” after h operations at the output of the h-th element by the symbols and . The initial input values corresponding to logical “1” and logical “0” will be denoted by and, accordingly, . For J level element “AND” of the first type we have
Substituting the values of the intensities, we get
.
For the J-level element “AND” of the second type, we have
,
.
The intensity values satisfy the condition:
.
These relations are also valid for LE “exclusive OR” and “NOT” of both types.
4. EXAMPLE OF IMPLEMENTATION AND APPLICATION
To implement interference LEs, fiber-optic [11] or planar-integral [10] waveguides, photonic crystals (PC) [13], graphene structures [6] can be used.
To localize the intensity at the antinodes (and at the nodes), it is necessary that the size of the slit be ~0,1λ. For , silicon photonic crystals [5] are known that satisfy this condition. Let us estimate the parameters of LE1 from this PC.
Let and satisfy the requirements for speed and intensity difference. We calculate and .
The slits are realized by linear defects in the PC [5], and are achieved at nm and nm, where is the radius of the defect rod; the condition is met. The diameter of the waveguide for the self-collimation regime is 6p, where p = 0.418 μm is the silicon grating constant [5].
For the mutual isolation of the branching waveguides, the distance between the centers of the slits is chosen 8p = 3.3 μm [5]. A Faraday rotator in a PC takes 1.5 μm, any other structural element is about 1.0 μm [14]. We take the length of the waveguide L = 75 μm. The duration of the operation is s, where m / s is the speed of light in the waveguide.
The limiting amount of energy in an LE made of silicon at λ = 1.55 μm and s will be J, where W / cm2 is the threshold value of intensity, J / cm 2 radiation resistance of silicon s [14], m 2 is the area of the light spot. The number of photons in a pulse pcs. For reliable identification of a pulse at T = 300K, 103 photons are sufficient [13]. Power budget [11] ≈62.7 dB.
Performing one operation with and reduces the signal power by dB. Without regeneration, 10 operations can be performed within s. The subsequent application of nonlinear optical switches of the picosecond range for regeneration [16] will “hardly” affect the performance and power consumption of devices.
In the process of performing operations, pulses are transmitted only in waveguides, coherence is preserved. From the values of the intensity at the outputs of the elements (provided that the direction of the pulse movement is taken into account), it is possible to set the values of the intensities at the inputs, i. e. the proposed LEs are reversible [17]. The energy remains in the LE and is used to amplify and regenerate the signal. The total energy losses are determined by the losses in the waveguides (this value is γ = 0.1 dB / cm), and the efficiency of radiation input into the waveguide is (μ ≥ 0.9) [3].
It was shown in [2] that, at λ = 1.55 µm, a DPC made of elements with identical values of γ, μ, and L has, in comparison with a computer, at the same power consumption, about 104 times higher productivity.
CONCLUSION
Structures of interference logic elements that form a complete functional basis are proposed.
The duration of the logical operation is equal to the interval for which the light pulse travels the distance from the input to the output of the element.
The requirements for the identity of the intensity values corresponding to the same logical constants produced by different elements are met.
Scaling the values of the intensity of the logical constants is achieved by increasing the number of waveguide levels and is accompanied by a proportional increase in the duration of the operations.
On the example of a digital photonic computer, the expediency and prospects of using the proposed elements are shown.
The content of this article is an extended presentation of work [18].
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ABOUT AUTHOR
Stepanenko Sergey Alexandrovich, Dr. of Sc.(Phys.and Math),
e-mail: SAStepanenko@vniief.ru, Russian Federal nuclear center-all-Russian research Institute of experimental physics, Sarov, Nizhny Novgorod region, Russia
S. A. Stepanenko
Russian Federal nuclear center-all-Russian research Institute of experimental physics, Sarov, Nizhny Novgorod region, Russia
The implementation of interference logical elements (LE) is proposed, based on the functioning of which the difference in the intensity values of coherent light waves arising as a result of their interaction with each other and with the waveguides of the logical elements.
The elements form a functionally complete basis.
The requirements for the identity of the intensity values corresponding to the logical constants “0” and “1”, generated by different elements at given fixed time intervals, are fulfilled.
Means for scaling the intensity values of logical constants are proposed. The estimates of the parameters of the elements – speed, power consumption, physical dimensions – are obtained, showing their advantages over electronic counterparts.
Fields of application of interference LEs are digital devices of control systems and computer technology.
Key words: interference logic element, interference, functionally complete basis, intensity scaling
Received on: 04.09.2020
Accepted on: 24.09.2020
INTRODUCTION
The development of science and technology gives rise to problems that require computing systems with maximum performance – supercomputers. The electronic technologies on which modern supercomputers are based are close to their physical limits. Alternative means of increasing productivity are relevant, in particular, based on previously unused physical principles.
Over the past 30 years, quantum computing has been actively studied [1]. However, the prospects for their implementation are still uncertain. Moreover, in the modern view, quantum computers allow solving a limited special class of problems.
Another option for increasing productivity provides for the creation of a universal digital photonic computer (DPC) [2], the functioning of which is based on the effects of interaction of coherent systems of light waves generated by laser radiation. The class of problems for the solution of which the DPC is intended coincides with the class of problems solved on a computer.
One of the fundamental aspects that determine the possibility and feasibility of implementing a DPC is the element base – logical elements (LE) that perform operations on light pulses.
Active LEs that involve nonlinear effects are inferior in performance and energy efficiency to modern electronic elements [3].
Known passive LEs [4–8] have short durations of the operation, however, they are characterized either by technological drawbacks – the difference in the sizes of LEs that implement different functions is only 0.4 nm [5], or by the same intensity values for various logical constants [4, 7, 8], or the need to use a low temperature – T ≈ 3° K and prolonged relaxation [6].
The LEs proposed below use the difference in light intensity values arising from the interference of coherent light waves and their interaction with waveguides. Estimates of the parameters of these LEs show their competitiveness with electronic analogs and the possibility of using them for the implementation of digital devices.
1. IDENTIFICATION OF LOGICAL CONSTANTS
LEs perform operations on coherent electromagnetic waves. The operands and results of operations are logical constants – zero (“0”) and one (“1”). They are identified by the intensity I of an electromagnetic wave [9] propagated in the waveguide [10].
Electromagnetic wave – linearly polarized monochromatic [9], hereinafter – traveling wave, is represented by a light pulse of duration , where m is an integer, λ is the wavelength [9], υ is the speed of light in the waveguide. The quantity is called the pulse size.
The value of the intensity of the output signal of the LE is generated either in the absence of input pulses – no effects are involved in the LE, or in the case of one input pulse – the effects generated by the traveling wave are involved, or in the case of two input counter impulses – the effects generated by the standing wave are used [9].
To perform logical operations, it is necessary to redistribute the intensity in the waveguides. For this, slots are used. A slit [9] is a part of the waveguide surface through which radiation is transmitted to another waveguide or to the environment. To remove energy from the slot, a unidirectional type (1 × 2) coupler [10] is used with a given branching ratio , which means the fraction of the intensity diverted through the slot into the branching waveguide.
The remainder of the energy in a waveguide with m-slots after the passage of a traveling wave is proportional to the value , where is the wave intensity at the entrance to the waveguide. The amount of energy released from the waveguide through the slits is proportional to the value .
In the process of collision of coherent pulses of duration τ, antinodes and nodes of a standing wave are formed [9]. Distance between antinodes (and between nodes) λ / 2. If the slits of the waveguide are located above the antinodes (there are 2m of them), then the total intensity at both outputs of the waveguide will be ; in this case, the total intensity released in 2m slots of the waveguide is equal to . If the slots of the waveguide are located above the nodes, then ; and .
Elements in the waveguides of which the slits are located above the antinodes or above the nodes of the standing wave are called the LE of the first and, accordingly, the LE of the second type, and we denote it as LE1 and LE2.
2. FUNCTIONALLY COMPLETE BASIS
Let us apply the considered effects to create a functionally complete basis of the elements “AND”, “exclusive OR” and “NOT”, which implement the functions &, and [11].
The LEs proposed below use the waveguide structure shown in Figure 1. Let us characterize in terms of [12] its elements and the operations they perform.
A pulse with a polarization of 0° entering the waveguide at the input 1 changes after the left-side rotator the polarization plane by 45° according to the rule of the left screw and enters the waveguide through the polarization mirror Μ11. After the Faraday rotator it restores the plane of polarization and interacts with the slots and (if any) with the counter pulse that came after similar operations from input 2. Both pulses are coherent and equally polarized. As a result of their collision, antinodes and nodes are formed. Above the antinodes (or above the nodes), in the same plane, there are slots and bidirectional branching waveguides. The design of such a waveguide is shown in inset A to Fig. 1.
After interacting with the slots, the residual part of the pulse from input 1 enters the Faraday rotator , changes the plane of polarization and is reflected by polarizing mirrors М12 to the right-handed rotator , which restores the original polarization. Further, the pulse reflected by the mirror M2 is fed to the output Ο1, where it is combined (if any) with the pulse from input 2, on which the same operations were performed.
The output Ο2 receives energy from the branching waveguides obtained by the interaction of pulses with the slots.
2.1. Elements of the first type
Element “AND”. Let a pulse of size mλ propagate in one of the directions indicated in Fig. 1 by symbols and (this means , or , ). At the output of the element, we have ; this corresponds to .
If the pulses propagate in both directions (this means , ), then antinodes and nodes of a standing wave are formed. The cracks above the antinodes. At the output , we have ; this corresponds to .
Element “Exclusive OR”. In the case of one pulse, we have at the output the intensity , which corresponds to. For two opposite pulses, we have on the intensity , which corresponds to .
Element “NOT”. Here and below, the implementation of the function (“NOT”) is achieved by supplying “1” to one of the inputs of the element that implements .
The values of the functions , and the corresponding values of , , are presented in Table 1.
Identity of intensity values. For the correct functioning of devices made of LEs, it is necessary that the same intensities correspond to the same logical constants obtained at the same time intervals at the outputs of the LEs realizing &, and . In particular, for LE1 the following must be fulfilled
The solution to this system of equations
and .
The m values are specified by the required duration of the operation.
A functionally complete basis of interference LE1 is obtained.
2.2. TYPE SECOND ELEMENTS
Various structures can be used to implement LE2; consider the first. It is the same as shown in Figure 1. Outputs are designated and . The slots are located above the nodes.
Element “AND”. A single pulse, meaning , , or , , interacts with 2m slots. At the output of , we have .
Let the impulses propagate in both directions, i. e. , . In the process of their interaction, which occurs upon reaching the middle of the waveguide (after m slots), the intensity in the slot is not released. At the output of we have .
Element “Exclusive OR”. The element structure contains one slit. For one pulse on , we have , which corresponds to . For two counter impulses, we have , where ∆ is arbitrarily close to 0, which corresponds to .
The values of the functions , , and the corresponding values of , are presented in Table 2.
Identity of intensity values. Required execution
whence, specifying m, we find the requireed q1 and q2.
For example, for we have and . The values and correspond to and .
Other options for the implementation of LE2 are obtained by using the structure shown in Figure 2 and solving the corresponding systems of equations. An example of such a system is the following
On the left side of the equations, the values of the intensities at the output O1 of the “AND” element are indicated. the traveling wave interacts with 2m slots and . If there are two pulses, then before the collision of pulses and the formation of nodes, the intensity in each direction is equal to . After the collision, no intensity is released in the gap. At the output, we have .
On the right side of the equations, the values of intensities at the O2 output of the “exclusive OR” element are indicated. The branching waveguides of the slots between the rotators are connected in pairs, the first branching waveguide from the side of the pulse x1 is connected oppositely to the first branching waveguide from the side of the pulse x2. A slit and a branching waveguide with a branching coefficient are arranged over the node formed by the collision of these pulses.
The branching waveguides located above the other i-slots, , are connected in a similar way.
The output of the “exclusive OR” element is obtained by combining the outputs of the branching waveguides located on both sides in front of the rotators, and the outputs of pairwise (oppositely) connected branching waveguides from the slots between the rotators.
In the case of two pulses (this corresponds to and ), we have at the output of the element the value . In the case of one pulse, for example, coming from the left (which corresponds to and ), the intensity at the output of the “exclusive OR” element is .
The first term is due to the interaction of the momentum with с slots located before the rotator. The second one is the interaction of the pulse with the slot arranged in each of the branching waveguides.
The values of the functions and and the corresponding values of , are presented in Table 3.
The feasibility of using the considered options is determined by the technological parameters.
A functionally complete basis of interference LE2 is obtained.
3. ZOOM INTENSITY
Let us evaluate the possibilities of increasing the difference in intensity values corresponding to logical “0” and logical “1”.
3.1. J-level element structures
The waveguide into which the input pulses come from outside the element is called the first level waveguide. The waveguide into which the input pulses come from the k-th level waveguide, where is called the level waveguide.
A two-level LE1 is shown in Fig. 3.
Designations and designations of structural elements coincide with those specified in 2.1.
Each LE1 waveguide has 2m slots at the antinodes. The element outputs are designated O1 and O2.
Element “AND”. For , or , , we have a single pulse, the intensity of which after the waveguide of the first level is equal to . As a result of interaction with 2m slots of the second-level waveguide, its intensity at the output of will be .
In the case , , we have two counter pulses at the inputs of the second-level waveguide; the intensity of each . As a result of their interaction, the total value of the intensity at the output , corresponding to a logical unit, is equal to .
Element “Exclusive OR”. The output is designated . The values are obtained similarly to the above.
The values of the functions , and the corresponding values , , obtained at the outputs of two-level LE1, are presented in Table 4.
Here, the ratio of the intensities of logical “1” and logical “0” is 2 times greater than in single-level LE1.
Identical logical constants must correspond to the same intensities at the outputs of LE1. It is necessary
We find: and .
In the general case, for J-level LE1:
Similarly, for J-level LE2, considered in Section 2, it is necessary:
The duration of the operation J by level elements is at least τJ, where τ is the duration of the operation execution by a single-level element, the “pipeline” mode is possible.
3.2. Dynamics of Intensity Values
The above estimates of the intensities at the outputs of the LE are valid for the first, single execution of the operation. As a result of successive operations, the intensity values corresponding to different logical constants can approach each other. This is due to the difference in the values of the output intensity when performing operations on the same or different operands.
Let from the output of the i-th element the pulse arrives at the input (i + 1) of the element, where i = 1,2,…, h. Let us denote the values of the intensities “1” and “0” after h operations at the output of the h-th element by the symbols and . The initial input values corresponding to logical “1” and logical “0” will be denoted by and, accordingly, . For J level element “AND” of the first type we have
Substituting the values of the intensities, we get
.
For the J-level element “AND” of the second type, we have
,
.
The intensity values satisfy the condition:
.
These relations are also valid for LE “exclusive OR” and “NOT” of both types.
4. EXAMPLE OF IMPLEMENTATION AND APPLICATION
To implement interference LEs, fiber-optic [11] or planar-integral [10] waveguides, photonic crystals (PC) [13], graphene structures [6] can be used.
To localize the intensity at the antinodes (and at the nodes), it is necessary that the size of the slit be ~0,1λ. For , silicon photonic crystals [5] are known that satisfy this condition. Let us estimate the parameters of LE1 from this PC.
Let and satisfy the requirements for speed and intensity difference. We calculate and .
The slits are realized by linear defects in the PC [5], and are achieved at nm and nm, where is the radius of the defect rod; the condition is met. The diameter of the waveguide for the self-collimation regime is 6p, where p = 0.418 μm is the silicon grating constant [5].
For the mutual isolation of the branching waveguides, the distance between the centers of the slits is chosen 8p = 3.3 μm [5]. A Faraday rotator in a PC takes 1.5 μm, any other structural element is about 1.0 μm [14]. We take the length of the waveguide L = 75 μm. The duration of the operation is s, where m / s is the speed of light in the waveguide.
The limiting amount of energy in an LE made of silicon at λ = 1.55 μm and s will be J, where W / cm2 is the threshold value of intensity, J / cm 2 radiation resistance of silicon s [14], m 2 is the area of the light spot. The number of photons in a pulse pcs. For reliable identification of a pulse at T = 300K, 103 photons are sufficient [13]. Power budget [11] ≈62.7 dB.
Performing one operation with and reduces the signal power by dB. Without regeneration, 10 operations can be performed within s. The subsequent application of nonlinear optical switches of the picosecond range for regeneration [16] will “hardly” affect the performance and power consumption of devices.
In the process of performing operations, pulses are transmitted only in waveguides, coherence is preserved. From the values of the intensity at the outputs of the elements (provided that the direction of the pulse movement is taken into account), it is possible to set the values of the intensities at the inputs, i. e. the proposed LEs are reversible [17]. The energy remains in the LE and is used to amplify and regenerate the signal. The total energy losses are determined by the losses in the waveguides (this value is γ = 0.1 dB / cm), and the efficiency of radiation input into the waveguide is (μ ≥ 0.9) [3].
It was shown in [2] that, at λ = 1.55 µm, a DPC made of elements with identical values of γ, μ, and L has, in comparison with a computer, at the same power consumption, about 104 times higher productivity.
CONCLUSION
Structures of interference logic elements that form a complete functional basis are proposed.
The duration of the logical operation is equal to the interval for which the light pulse travels the distance from the input to the output of the element.
The requirements for the identity of the intensity values corresponding to the same logical constants produced by different elements are met.
Scaling the values of the intensity of the logical constants is achieved by increasing the number of waveguide levels and is accompanied by a proportional increase in the duration of the operations.
On the example of a digital photonic computer, the expediency and prospects of using the proposed elements are shown.
The content of this article is an extended presentation of work [18].
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ABOUT AUTHOR
Stepanenko Sergey Alexandrovich, Dr. of Sc.(Phys.and Math),
e-mail: SAStepanenko@vniief.ru, Russian Federal nuclear center-all-Russian research Institute of experimental physics, Sarov, Nizhny Novgorod region, Russia
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