**1. Introduction**

urement of low-phase-noise microwave signals. *Journal of the Optical Society of Ameri‐*

[4] Ilchenko, V. S., Yao, X. S., & Maleki, L. (1999). High-Q microsphere cavity for laser stabilization and optoelectronic microwave oscillator. *Proceedings of SPIE*, 3611-190.

[5] Volyanskiy, K., Salzenstein, P., Tavernier, H., Pogurmirskiy, M., Chembo, Y. K., & Larger, L. (2010). Compact Optoelectronic Microwave Oscillators using Ultra-High Q Whispering Gallery Mode Disk-Resonators and Phase Modulation. Optics Express .,

[6] Schliesser, A., & Kippenberg, T. J. (2010). Cavity Optomechanics with Whispering-Gallery Mode Optical Micro-Resonators. *Acta Avances in Atomic Molecular and Optical*

[7] Salzenstein, P., Tavernier, H., Volyanskiy, K., Kim, N. N. T., Larger, L., & Rubiola, E. (2009). Optical Mini-disk resonator integrated into a compact optoelectronic oscilla‐

[8] Tavernier, H., Salzenstein, P., Volyanskiy, K., Chembo, Y. K., & Larger, L. (2010). Magnesium Fluoride Whispering Gallery Mode Disk-Resonators for Microwave Pho‐

[9] Salzenstein, P., Cussey, J., Jouvenceau, X., Tavernier, H., Larger, L., Rubiola, E., & Sauvage, G. (2008). Realization of a Phase Noise Measurement Bench Using Cross Correlation and Double Optical Delay Line. *Acta Physica Polonica A*, 112(5),

[10] Salzenstein, P., Cholley, N., Zarubin, M., Pavlyuchenko, E., Hmima, A., Chembo, Y. K., & Larger, L. (2011). Optoelectronic phase noise system designed for microwaves photonics sources measurements in metrology application. Proceedings of SPIE .,

[11] Anritsu (2000). Typical datasheet Anritsu 69B serie available on page at the following link: http://cem.inrets.fr/private/materiel-labo/images/m\_011\_doc\_gene\_65ghz.pdf

[12] Salzenstein, P., Hmima, A., Zarubin, M., Pavlyuchenko, E., & Cholley, N. (2012). Op‐ toectronic phase noise measurement system with wideband analysis. *Proceedings of*

[13] Salzenstein, P., Pavlyuchenko, E., Hmima, A., Cholley, N., Zarubin, M., Galliou, S., Chembo, Y. K., & Larger, L. (2012). Estimation of the uncertainty for a phase noise optoelectronic metrology system. *Physica Scripta* [T149], 014025, http://dx.doi.org/

[14] GUM: (2008). Guide to the Expression of Uncertainty in Measurement, fundamental reference document. , JCGM 100: (GUM 1995 minor corrections) http://

www.bipm.org/en/publications/guides/gum.html (accessed 5 June 2012).

tonics Applications. *IEEE Photonics Technology Letters*, 22(22), 1629-1631.

*ca B*, 25(12), 2140-2150.

348 Optoelectronics - Advanced Materials and Devices

18(21), 22358-22363.

tor. *Acta Physica Polonica A*, 116(4), 661-663.

*Physica*, 58-207.

1107-1111.

8071-807111.

(accessed 5 June 2012)., 8.

10.1088/00318949 /2012/T149/014025.

*SPIE*, 8439, 84391M.

One of the problems in high speed computing is the limited capabilities of communication links in digital high performance electronic systems. Too slow and too few interconnects be‐ tween VLSI circuits cause a bottleneck in the communication between processor and memo‐ ry or, especially in multiprocessor systems, among the processors. Moreover, the problem is getting worse since the increasing integration density of devices like transistors leads to a higher requirement in the number of necessary channels for the off-chip communication. Hence, we are currently in a situation, which is characterized by too few off-chip links and too slow long on-chip lines, what is described as the interconnect crisis in VLSI technology [1]. More than ten years the use of optical interconnects is discussed as an alternative to solve the mentioned problems on interconnect in VLSI technology [2]. A lot of prototypes and demonstrator systems were built to prove the use of optics or optoelectronics for offchip and on-chip interconnects [3]. The possibilities of current VLSI technology would allow integrating a massively-parallel array processor consisting of a few hundred thousand sim‐ ple processor elements (PEs) on a chip. Unfortunately it would be a huge problem to ar‐ range several of such PE arrays one after the other in order to realize a highly–parallel superscalar and super-pipelined architecture as well as an efficient coupling to a memory chip. The reason for these difficulties is the not sufficient number of external interconnects to move high data volumes from and to the circuits. In optoelectronic VLSI one tries to solve limitation problem by realizing external interconnects not at the edge of a chip but with ar‐

© 2013 Krasilenko et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Krasilenko et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

rays of optical detectors and light emitters which send and receive data directly out from the chip area. Honeywell has developed such devices with VCSEL diodes (vertical surface emit‐ ting laser diodes) and metal – semiconductor – metal photo-detectors in research project [4].

Taking into consideration the above-described approach, consisting in universality, let us recollect some known facts regarding the number of functions. The number of Boolean func‐ tions of *n* variables in algebra of two-valued logic (TVL), which is also Boolean algebra,

Design and Modeling of Optoelectronic Photocurrent Reconfigurable (OPR) Multifunctional Logic Devices (MFLD) as

*k*–valued logic (*k*>2) are reflections*A<sup>n</sup>* → *A*, where *A*={0, 1,... *k*-1}, and the number of func‐

∧

CL algebra can be infinite or finite (the set of reflections is always infinite). CL functions are called only those functions of the set*N*∧, which are realized by formulas. The number *N*<sup>∧</sup> of CL functions in the most developed CL algebra – quasi-Boolean Cleenee algebra (*Δ* =(*Cu*,∧,∨,-)), in which any function on any set of arguments takes the value of one of the arguments or its negation, is finite. In this case the number *N*∧(*n*) of functions of *n* argu‐ ments increases with increase of *n* very rapidly [4]:*N*∧(0)=2 ;*N*∧(1)=6;*N*∧(2)=84;*N*∧(3)=43918.

We would like to draw the attention to the fact, that both natural neurons and their more complex physical and mathematical models suggest discrete-analog and purely analog means for information processing with different level of accuracy, with the possibility of re‐ arrangement of chosen coding system. This, in its turn, requires corresponding image neu‐ ron circuit engineering with programmable logic operations, with transition from analog to

Thus, the search of means aimed at construction of elements, especially universal (at least quasi-universal or multifunctional) with programmable tuning, able to perform not only op‐ erations of two-valued logic, but other matrix (multi-valued, continuous, neural-fuzzy, etc.) logic operations is very actual problem [15]. One of promising directions of research in this sphere is the application of time-pulse-coded architectures (TPCA) that were considered in works [18-20]. These architectures were generalized in [11], taking into account basic possi‐ ble approaches as well as system and mathematical requirements. The time-pulse represen‐ tation of matrix continuous-logic variables by two-level optic signals not only permits to increase functional possibilities (up to universality), stability to noise, stability and decrease requirements regarding alignment and optical system, but also simplify control circuits and adjustment circuits to required function, operation, and keep untouched the whole meth‐ odological basis of such universal elements construction, irrespective of valuedness of a log‐

But there is another approach based on the use of universal logic elements with the structure of multiple-input multiple-output (MIMO) and time-pulse coding. We call such elements the elements of picture type (PT). At increase of number of input operands and valuedness of logic (up to continuous) the number of executable functions also increases by the expo‐ nential law. This property allows simplifying operation algorithms of such universal optoe‐ lectronic logical elements and hence to raise information processing speed. Most general conceptual approaches to construction of universal picture neural elements and their mathe‐ matical rationales were presented in paper [11]. But those were only system and structural

. Algebra, formed by set *C*

logic (CL) algebra, and the number of CL functions, as reflections *Cu*

. In this TVL there are *N*<sup>2</sup> =2*n* atoms, which are minterms. Functions of *<sup>n</sup>* variables

*<sup>u</sup>* <sup>=</sup> 0, 1 or *<sup>C</sup>*

∧ *b*

the Universal Circuitry Basis for Advanced Parallel High-Performance Processing

= −1, 1 is called continuous

http://dx.doi.org/10.5772/54540

351

*<sup>n</sup>* <sup>→</sup>*Cu* depending on the

equals22*<sup>n</sup>*

tions equals*Nk* <sup>=</sup>*<sup>k</sup> <sup>k</sup> <sup>n</sup>*

discrete processing, to storing etc.

ic and type of a logic.

This allows the realization of stacked 3-D chip architecture in principle. The main problems are not the manufacturing and operating of single devices but the combination of different passive optical elements with active optoelectronic and electronic circuits in one system. This requires sophisticated mounting and alignment techniques which allow low mechani‐ cal tolerances and the handling of thermal problems. At present the situation for smart de‐ tector circuits is much easier. They can be regarded as a subset of OE-VLSI circuits because they consist only of arrays of photo-detectors with corresponding evaluation circuit for ana‐ logue to digital converting. Optical detectors based on PN or PIN photodiodes can be mono‐ lithically integrated with digital electronics in silicon what simplifies the design enormously compared with OE-VLSI circuits that in addition contain sender devices realized in GaAs technologies. Furthermore smart detector circuits can be manufactured in nearly every semi‐ conductor fabric. Smart detectors or smart optical sensors show a great application field and market potential. Therefore our approach favors a smart pixel like architecture combining parallel signal detection with parallel signal processing in one circuit. Each pixel has its own PE what guarantees the fastest processing.

The strategic direction of solution of various scientific problems, including the problem of creation of artificial intelligence (AI) systems, human brain simulators, robotics systems, monitoring and control systems, decision-making systems, as well as systems based on arti‐ ficial neural networks, etc., becomes fast-acting and parallel processing of large2-D arrays of data (up to 1024x1024 and higher) using non-conventional computational systems, corre‐ sponding matrix logics (multi-valued, signed-digit, fuzzy logics, continuous, neural-fuzzy and others) and corresponding mathematical apparatus [5-11]. For numerous perspective re‐ alizations of optical learning neural networks (NN) with two dimensional structure [5], of recurrent optical NN [6], of the continuous logic equivalency models (CLEM) NN [7-10], the elements of matrix logic are required, and not only of two-valued property, threshold, hy‐ brid but also continuous, neural-fuzzy logics and adequate structure of vector-matrix com‐ putational procedures with basic operations of above-mentioned logics. Optic and optoelectronic technologies, methods and principles as well as corresponding element base provide attractive alternative for 2D data processing. These technologies and methods suc‐ cessfully decide problems of parallelism, input-output and interconnections. Advanced nontraditional parallel computing structures and systems, including neural networks, require both parallel processing and parallel information input/output. At the same time there are many new approaches that are based on new logics (neural-fuzzy, multi-valued, continuous etc.). The using of the standard sequential algorithms based on a few operations makes the approaches long-running. But only a few of them [12] can be used for processing of 2D data and perform wide range of needed arithmetic and logic operations). Generalization of scalar two-valued logic on matrix case has led to intensive development of binary images algebra (BIA) [13] and 2D Boolean elements for optic and optoelectronic processors [12-17].

Design and Modeling of Optoelectronic Photocurrent Reconfigurable (OPR) Multifunctional Logic Devices (MFLD) as the Universal Circuitry Basis for Advanced Parallel High-Performance Processing http://dx.doi.org/10.5772/54540 351

rays of optical detectors and light emitters which send and receive data directly out from the chip area. Honeywell has developed such devices with VCSEL diodes (vertical surface emit‐ ting laser diodes) and metal – semiconductor – metal photo-detectors in research project [4].

This allows the realization of stacked 3-D chip architecture in principle. The main problems are not the manufacturing and operating of single devices but the combination of different passive optical elements with active optoelectronic and electronic circuits in one system. This requires sophisticated mounting and alignment techniques which allow low mechani‐ cal tolerances and the handling of thermal problems. At present the situation for smart de‐ tector circuits is much easier. They can be regarded as a subset of OE-VLSI circuits because they consist only of arrays of photo-detectors with corresponding evaluation circuit for ana‐ logue to digital converting. Optical detectors based on PN or PIN photodiodes can be mono‐ lithically integrated with digital electronics in silicon what simplifies the design enormously compared with OE-VLSI circuits that in addition contain sender devices realized in GaAs technologies. Furthermore smart detector circuits can be manufactured in nearly every semi‐ conductor fabric. Smart detectors or smart optical sensors show a great application field and market potential. Therefore our approach favors a smart pixel like architecture combining parallel signal detection with parallel signal processing in one circuit. Each pixel has its own

The strategic direction of solution of various scientific problems, including the problem of creation of artificial intelligence (AI) systems, human brain simulators, robotics systems, monitoring and control systems, decision-making systems, as well as systems based on arti‐ ficial neural networks, etc., becomes fast-acting and parallel processing of large2-D arrays of data (up to 1024x1024 and higher) using non-conventional computational systems, corre‐ sponding matrix logics (multi-valued, signed-digit, fuzzy logics, continuous, neural-fuzzy and others) and corresponding mathematical apparatus [5-11]. For numerous perspective re‐ alizations of optical learning neural networks (NN) with two dimensional structure [5], of recurrent optical NN [6], of the continuous logic equivalency models (CLEM) NN [7-10], the elements of matrix logic are required, and not only of two-valued property, threshold, hy‐ brid but also continuous, neural-fuzzy logics and adequate structure of vector-matrix com‐ putational procedures with basic operations of above-mentioned logics. Optic and optoelectronic technologies, methods and principles as well as corresponding element base provide attractive alternative for 2D data processing. These technologies and methods suc‐ cessfully decide problems of parallelism, input-output and interconnections. Advanced nontraditional parallel computing structures and systems, including neural networks, require both parallel processing and parallel information input/output. At the same time there are many new approaches that are based on new logics (neural-fuzzy, multi-valued, continuous etc.). The using of the standard sequential algorithms based on a few operations makes the approaches long-running. But only a few of them [12] can be used for processing of 2D data and perform wide range of needed arithmetic and logic operations). Generalization of scalar two-valued logic on matrix case has led to intensive development of binary images algebra

(BIA) [13] and 2D Boolean elements for optic and optoelectronic processors [12-17].

PE what guarantees the fastest processing.

350 Optoelectronics - Advanced Materials and Devices

Taking into consideration the above-described approach, consisting in universality, let us recollect some known facts regarding the number of functions. The number of Boolean func‐ tions of *n* variables in algebra of two-valued logic (TVL), which is also Boolean algebra, equals22*<sup>n</sup>* . In this TVL there are *N*<sup>2</sup> =2*n* atoms, which are minterms. Functions of *<sup>n</sup>* variables *k*–valued logic (*k*>2) are reflections*A<sup>n</sup>* → *A*, where *A*={0, 1,... *k*-1}, and the number of func‐ tions equals*Nk* <sup>=</sup>*<sup>k</sup> <sup>k</sup> <sup>n</sup>* . Algebra, formed by set *C* ∧ *<sup>u</sup>* <sup>=</sup> 0, 1 or *<sup>C</sup>* ∧ *b* = −1, 1 is called continuous logic (CL) algebra, and the number of CL functions, as reflections *Cu <sup>n</sup>* <sup>→</sup>*Cu* depending on the CL algebra can be infinite or finite (the set of reflections is always infinite). CL functions are called only those functions of the set*N*∧, which are realized by formulas. The number *N*<sup>∧</sup> of CL functions in the most developed CL algebra – quasi-Boolean Cleenee algebra (*Δ* =(*Cu*,∧,∨,-)), in which any function on any set of arguments takes the value of one of the arguments or its negation, is finite. In this case the number *N*∧(*n*) of functions of *n* argu‐ ments increases with increase of *n* very rapidly [4]:*N*∧(0)=2 ;*N*∧(1)=6;*N*∧(2)=84;*N*∧(3)=43918.

We would like to draw the attention to the fact, that both natural neurons and their more complex physical and mathematical models suggest discrete-analog and purely analog means for information processing with different level of accuracy, with the possibility of re‐ arrangement of chosen coding system. This, in its turn, requires corresponding image neu‐ ron circuit engineering with programmable logic operations, with transition from analog to discrete processing, to storing etc.

Thus, the search of means aimed at construction of elements, especially universal (at least quasi-universal or multifunctional) with programmable tuning, able to perform not only op‐ erations of two-valued logic, but other matrix (multi-valued, continuous, neural-fuzzy, etc.) logic operations is very actual problem [15]. One of promising directions of research in this sphere is the application of time-pulse-coded architectures (TPCA) that were considered in works [18-20]. These architectures were generalized in [11], taking into account basic possi‐ ble approaches as well as system and mathematical requirements. The time-pulse represen‐ tation of matrix continuous-logic variables by two-level optic signals not only permits to increase functional possibilities (up to universality), stability to noise, stability and decrease requirements regarding alignment and optical system, but also simplify control circuits and adjustment circuits to required function, operation, and keep untouched the whole meth‐ odological basis of such universal elements construction, irrespective of valuedness of a log‐ ic and type of a logic.

But there is another approach based on the use of universal logic elements with the structure of multiple-input multiple-output (MIMO) and time-pulse coding. We call such elements the elements of picture type (PT). At increase of number of input operands and valuedness of logic (up to continuous) the number of executable functions also increases by the expo‐ nential law. This property allows simplifying operation algorithms of such universal optoe‐ lectronic logical elements and hence to raise information processing speed. Most general conceptual approaches to construction of universal picture neural elements and their mathe‐ matical rationales were presented in paper [11]. But those were only system and structural solutions that is why they require further development and perfection. Mathematical and other theoretical fundamentals of design of matrix multi-functional logical devices with fast acting programmable tuning were considered in paper[19], where expediency of functional basis unification, that is promising for optoelectronic parallel-pipeline systems (OEPS) with command-flow 2D-page (picture) organization [20], necessity in arrays of optic or optoelec‐ tronic triggers (memory elements) of picture type for storage of information and controlling adjusting operands as well as perspective principles of presentation and coding of multi-val‐ ued matrix data (spatial, time-pulse and spectral) were shown. Besides, the analysis of vari‐ ous algebra logics [11, 19, 21-24] for functional systems of switching functions, in spite of their diversity allows us to suggest a very useful idea, in our opinion, that lies in following.

form contrast-conversion (complementary operand) image for analog picture optic inputs if

Design and Modeling of Optoelectronic Photocurrent Reconfigurable (OPR) Multifunctional Logic Devices (MFLD) as

the Universal Circuitry Basis for Advanced Parallel High-Performance Processing

http://dx.doi.org/10.5772/54540

353

Thus, becomes obvious that for time – pulse coding realization of PNE of matrix-continuous -logic (MCL) with programmable tuning is necessary UPE of TVL or picture MFLD, by means of which continuously – logic operations over time – pulse signals can be realized. In Figure 1 selection of picture logic functions is carried out by electric adjusting signals and all array cells will realize the same function at the same time. For many appendices it is expedi‐ ent to choose a logic function at each point of the matrix processor, and therefore there is a desire to make management and tuning also in the form of optical matrix operands. It essen‐ tially expands functionality of such processors and MFLD on which basis they are realized.

In work [25] MFLD of two-valued logic (TVL) on current mirrors, photodiodes and LEDs with schemes of their drivers are described and simulated. They are relatively difficult as contain four current mirrors (CM), four schemes ХОR, four elements АND and one logic ele‐ ment OR. In the same work different optoelectronic circuitry were offered on base of 2-4 CM and one photo diode, realizing the Boolean operations AND, NOT, OR, NOR, et al with po‐ tential and current outputs. They are based on threshold elements, comparators of currents (photocurrents) on current mirrors and circuitry of limited subtraction (CLS). Such base ele‐ ments also were used for realization of other elements of continuous logic, including opera‐ tions equivalence (nonequivalence) and etc. [21, 26, 27]. Therefore developing further this

PWMs PT have complementary outputs.

**Figure 1.** The PNE of matrix-continuous-logic (MCL) with programmable tuning

approach we use for design of the OPR MFLD.

It is possible to create more sophisticated problem-oriented processors, in which the specific time-pulse operands encoding and only elements of two-valued logic are used, which will realize functions of different logics, continuous etc. Taking into account the universality, parallel information processing of the universal elements and the use of only two-valued logic elements for implementation of all other operations the approach is a very promising.

That is why the aim of the given work is to consider the results of design and investigation of optoelectronic smart time-pulse coded photocurrent reconfigurable MFLD as basic com‐ ponents for 2D-array logic devices for advanced neural networks and optical computers.
