Abstract

Spatially parallel analog-to-digital conversion is proposed with a nonlinear Fabry–Perot resonator used as a multifunctional photonic comparator based on the pulse circulation method. The transmissive output of the photonic comparator exhibits a binary signal of either 1 or 0, depending on whether the incident intensity is greater than or less than the switching intensity corresponding to the binary weight, respectively. The photonic comparator complimentarily reflects the incident light, either with or without subtraction of the binary weight, and returns the reflected light to the next-lower digit cycle. Starting at the most significant bit, the recursive circuit successively launches the binary-coded outputs. The analog-to-digital conversion numerically demonstrates up to 6-bit resolution without noticeable errors.

© 2001 Optical Society of America

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1999

J. Cai, G. W. Taylor, “Optoelectronic thyristor-based photonic smart comparator for analog-to-digital conversion,” IEEE Photon. Technol. Lett. 11, 1295–1297 (1999).
[CrossRef]

R. R. Boye, R. W. Ziolkowski, R. K. Kostuk, “Resonant waveguide-grating switching device with nonlinear optical material,” Appl. Opt. 38, 5181–5185 (1999).
[CrossRef]

1998

A. Yariv, R. G. M. P. Koumans, “Time interleaved optical sampling for ultra-high speed A/D conversion,” Electron. Lett. 34, 2012–2013 (1998).
[CrossRef]

Y. Hayasaki, M. Mori, N. Nishida, “Optical image transformations for fully parallel optical analog-to-digital conversion,” Appl. Opt. 37, 3607–3611 (1998).
[CrossRef]

1997

K. T. Jeong, O. Hanaizumi, I. Syuaib, S. Kashiwada, K. Kawase, S. Kawakami, “Analysis and assessment of the gain of optically pumped surface-normal optical amplifiers,” Opt. Commun. 135, 227–232 (1997).
[CrossRef]

M. Y. Frankel, J. U. Kang, R. D. Esman, “High-performance photonic analogue-to-digital converter,” Electron. Lett. 33, 2096–2097 (1997).
[CrossRef]

1996

H. S. Hinton, “Progress in the smart pixel technologies,” IEEE J. Select. Topics Quantum Electron. 2, 14–23 (1996).
[CrossRef]

1995

1994

K. Uchida, S. Kaneko, S. Omi, C. Hata, H. Tanji, Y. Asahara, A. J. Ikushima, T. Tokizaki, A. Nakamura, “Optical nonlinearities of a high concentration of small metal particles dispersed in glass: copper and silver particles,” J. Opt. Soc. Am. B 11, 1236–1243 (1994).
[CrossRef]

T. Tokizaki, A. Nakamura, S. Kaneko, K. Uchida, S. Omi, H. Tanji, Y. Asahara, “Subpicosecond time response of third-order optical nonlinearity of small copper particles in glass,” Appl. Phys. Lett. 65, 941–943 (1994).
[CrossRef]

P. E. Pace, D. Styer, “High-resolution encoding process for an integrated optical analog-to-digital converter,” Opt. Eng. 33, 2638–2645 (1994).
[CrossRef]

1993

K.-K. Law, J. L. Merz, L. A. Coldren, “Superlattice surface-normal asymmetric Fabry–Perot reflection modulators: optical modulation and switching,” IEEE J. Quantum Electron. 29, 727–740 (1993).
[CrossRef]

1992

C. Gu, S. Campbell, J. Hong, Q. B. He, D. Zhang, P. Yeh, “Optical thresholding and maximum operations,” Appl. Opt. 31, 5661–5665 (1992).
[CrossRef] [PubMed]

S. Ohtsuka, T. Koyama, K. Tsunemoto, H. Nagata, S. Tanaka, “Nonlinear optical property of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

A. G. Larsson, J. Maserjian, “Molecular beam epitaxy engineered III–V semiconductor structures for low-power optically addressed spatial light modulators,” Opt. Eng. 31, 1576–1582 (1992).
[CrossRef]

X. Zureng, Z. Guiyan, L. Fucheng, “Application of the CuBr vapor laser as an image-brightness amplifier in high-speed photography and photomicrography,” Appl. Opt. 31, 3395–3397 (1992).
[CrossRef] [PubMed]

1991

1986

1984

B. S. Wherrett, “Fabry–Perot bistable cavity optimization on reflection,” IEEE J. Quantum Electron. QE-20, 646–651 (1984).
[CrossRef]

1983

H. J. Eichler, “Optical multistability in silicon observed with a cw laser at 1.06 µm,” Opt. Commun. 45, 62–66 (1983).
[CrossRef]

1980

1979

R. Akins, S. Lee, “Coherent optical image amplification by an injection-locked dye amplifier at 632.8 nm,” Appl. Phys. Lett. 35, 660–663 (1979).
[CrossRef]

H. F. Taylor, “An optical analog-to-digital converter—Design and analysis,” IEEE J. Quantum. Electron. QE-15, 210–216 (1979).
[CrossRef]

1978

H. K. Liu, “Coherent optical analog-to-digital conversion using a single halftone photograph,” Appl. Opt. 17, 2181–2185 (1978).
[CrossRef] [PubMed]

B. M. Gordon, “Linear electronic analog/digital conversion architectures, their origins, parameters, limitations, and applications,” IEEE Trans. Circuits Syst. 25, 391–418 (1978).
[CrossRef]

1976

W. Seka, E. Stüssi, “Nonlinear absorber characteristics and their effects on discrimination amplifiers,” J. Appl. Phys. 47, 3538–3541 (1976).
[CrossRef]

Akins, R.

R. Akins, S. Lee, “Coherent optical image amplification by an injection-locked dye amplifier at 632.8 nm,” Appl. Phys. Lett. 35, 660–663 (1979).
[CrossRef]

Armand, A.

Asahara, Y.

K. Uchida, S. Kaneko, S. Omi, C. Hata, H. Tanji, Y. Asahara, A. J. Ikushima, T. Tokizaki, A. Nakamura, “Optical nonlinearities of a high concentration of small metal particles dispersed in glass: copper and silver particles,” J. Opt. Soc. Am. B 11, 1236–1243 (1994).
[CrossRef]

T. Tokizaki, A. Nakamura, S. Kaneko, K. Uchida, S. Omi, H. Tanji, Y. Asahara, “Subpicosecond time response of third-order optical nonlinearity of small copper particles in glass,” Appl. Phys. Lett. 65, 941–943 (1994).
[CrossRef]

Boswell, D.

Boye, R. R.

Cai, J.

J. Cai, G. W. Taylor, “Optoelectronic thyristor-based photonic smart comparator for analog-to-digital conversion,” IEEE Photon. Technol. Lett. 11, 1295–1297 (1999).
[CrossRef]

Campbell, S.

Coldren, L. A.

K.-K. Law, J. L. Merz, L. A. Coldren, “Superlattice surface-normal asymmetric Fabry–Perot reflection modulators: optical modulation and switching,” IEEE J. Quantum Electron. 29, 727–740 (1993).
[CrossRef]

Cunningham, J. E.

de Souza, E. A.

Eichler, H. J.

H. J. Eichler, “Optical multistability in silicon observed with a cw laser at 1.06 µm,” Opt. Commun. 45, 62–66 (1983).
[CrossRef]

Esman, R. D.

M. Y. Frankel, J. U. Kang, R. D. Esman, “High-performance photonic analogue-to-digital converter,” Electron. Lett. 33, 2096–2097 (1997).
[CrossRef]

Frankel, M. Y.

M. Y. Frankel, J. U. Kang, R. D. Esman, “High-performance photonic analogue-to-digital converter,” Electron. Lett. 33, 2096–2097 (1997).
[CrossRef]

Fucheng, L.

Gibbs, H. M.

H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, New York, 1985).

Gordon, B. M.

B. M. Gordon, “Linear electronic analog/digital conversion architectures, their origins, parameters, limitations, and applications,” IEEE Trans. Circuits Syst. 25, 391–418 (1978).
[CrossRef]

Gu, C.

Guiyan, Z.

Hanaizumi, O.

K. T. Jeong, O. Hanaizumi, I. Syuaib, S. Kashiwada, K. Kawase, S. Kawakami, “Analysis and assessment of the gain of optically pumped surface-normal optical amplifiers,” Opt. Commun. 135, 227–232 (1997).
[CrossRef]

Hata, C.

Hayasaki, Y.

He, Q. B.

Hinton, H. S.

H. S. Hinton, “Progress in the smart pixel technologies,” IEEE J. Select. Topics Quantum Electron. 2, 14–23 (1996).
[CrossRef]

Höijer, M.

A. Karlsson, M. Höijer, “Analysis of a VCLAD: vertical-cavity laser amplifier detector,” IEEE Photon. Technol. Lett. 7, 1336–1338 (1995).
[CrossRef]

Hong, J.

Ikushima, A. J.

Jalali, B.

Jan, W. Y.

Jeong, K. T.

K. T. Jeong, O. Hanaizumi, I. Syuaib, S. Kashiwada, K. Kawase, S. Kawakami, “Analysis and assessment of the gain of optically pumped surface-normal optical amplifiers,” Opt. Commun. 135, 227–232 (1997).
[CrossRef]

Kaneko, S.

K. Uchida, S. Kaneko, S. Omi, C. Hata, H. Tanji, Y. Asahara, A. J. Ikushima, T. Tokizaki, A. Nakamura, “Optical nonlinearities of a high concentration of small metal particles dispersed in glass: copper and silver particles,” J. Opt. Soc. Am. B 11, 1236–1243 (1994).
[CrossRef]

T. Tokizaki, A. Nakamura, S. Kaneko, K. Uchida, S. Omi, H. Tanji, Y. Asahara, “Subpicosecond time response of third-order optical nonlinearity of small copper particles in glass,” Appl. Phys. Lett. 65, 941–943 (1994).
[CrossRef]

Kang, J. U.

M. Y. Frankel, J. U. Kang, R. D. Esman, “High-performance photonic analogue-to-digital converter,” Electron. Lett. 33, 2096–2097 (1997).
[CrossRef]

Karlsson, A.

A. Karlsson, M. Höijer, “Analysis of a VCLAD: vertical-cavity laser amplifier detector,” IEEE Photon. Technol. Lett. 7, 1336–1338 (1995).
[CrossRef]

Kashiwada, S.

K. T. Jeong, O. Hanaizumi, I. Syuaib, S. Kashiwada, K. Kawase, S. Kawakami, “Analysis and assessment of the gain of optically pumped surface-normal optical amplifiers,” Opt. Commun. 135, 227–232 (1997).
[CrossRef]

Kawakami, S.

K. T. Jeong, O. Hanaizumi, I. Syuaib, S. Kashiwada, K. Kawase, S. Kawakami, “Analysis and assessment of the gain of optically pumped surface-normal optical amplifiers,” Opt. Commun. 135, 227–232 (1997).
[CrossRef]

Kawase, K.

K. T. Jeong, O. Hanaizumi, I. Syuaib, S. Kashiwada, K. Kawase, S. Kawakami, “Analysis and assessment of the gain of optically pumped surface-normal optical amplifiers,” Opt. Commun. 135, 227–232 (1997).
[CrossRef]

Knox, W. H.

Kostuk, R. K.

Koumans, R. G. M. P.

A. Yariv, R. G. M. P. Koumans, “Time interleaved optical sampling for ultra-high speed A/D conversion,” Electron. Lett. 34, 2012–2013 (1998).
[CrossRef]

Koyama, T.

S. Ohtsuka, T. Koyama, K. Tsunemoto, H. Nagata, S. Tanaka, “Nonlinear optical property of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

Larsson, A. G.

A. G. Larsson, J. Maserjian, “Molecular beam epitaxy engineered III–V semiconductor structures for low-power optically addressed spatial light modulators,” Opt. Eng. 31, 1576–1582 (1992).
[CrossRef]

Law, K.-K.

K.-K. Law, J. L. Merz, L. A. Coldren, “Superlattice surface-normal asymmetric Fabry–Perot reflection modulators: optical modulation and switching,” IEEE J. Quantum Electron. 29, 727–740 (1993).
[CrossRef]

Lee, S.

R. Akins, S. Lee, “Coherent optical image amplification by an injection-locked dye amplifier at 632.8 nm,” Appl. Phys. Lett. 35, 660–663 (1979).
[CrossRef]

Li, Y.

Liu, H. K.

Maserjian, J.

A. G. Larsson, J. Maserjian, “Molecular beam epitaxy engineered III–V semiconductor structures for low-power optically addressed spatial light modulators,” Opt. Eng. 31, 1576–1582 (1992).
[CrossRef]

Merz, J. L.

K.-K. Law, J. L. Merz, L. A. Coldren, “Superlattice surface-normal asymmetric Fabry–Perot reflection modulators: optical modulation and switching,” IEEE J. Quantum Electron. 29, 727–740 (1993).
[CrossRef]

Mori, M.

Nagata, H.

S. Ohtsuka, T. Koyama, K. Tsunemoto, H. Nagata, S. Tanaka, “Nonlinear optical property of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

Nakamura, A.

T. Tokizaki, A. Nakamura, S. Kaneko, K. Uchida, S. Omi, H. Tanji, Y. Asahara, “Subpicosecond time response of third-order optical nonlinearity of small copper particles in glass,” Appl. Phys. Lett. 65, 941–943 (1994).
[CrossRef]

K. Uchida, S. Kaneko, S. Omi, C. Hata, H. Tanji, Y. Asahara, A. J. Ikushima, T. Tokizaki, A. Nakamura, “Optical nonlinearities of a high concentration of small metal particles dispersed in glass: copper and silver particles,” J. Opt. Soc. Am. B 11, 1236–1243 (1994).
[CrossRef]

Nishida, N.

Ohtsuka, S.

S. Ohtsuka, T. Koyama, K. Tsunemoto, H. Nagata, S. Tanaka, “Nonlinear optical property of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

Omi, S.

K. Uchida, S. Kaneko, S. Omi, C. Hata, H. Tanji, Y. Asahara, A. J. Ikushima, T. Tokizaki, A. Nakamura, “Optical nonlinearities of a high concentration of small metal particles dispersed in glass: copper and silver particles,” J. Opt. Soc. Am. B 11, 1236–1243 (1994).
[CrossRef]

T. Tokizaki, A. Nakamura, S. Kaneko, K. Uchida, S. Omi, H. Tanji, Y. Asahara, “Subpicosecond time response of third-order optical nonlinearity of small copper particles in glass,” Appl. Phys. Lett. 65, 941–943 (1994).
[CrossRef]

Pace, P. E.

P. E. Pace, D. Styer, “High-resolution encoding process for an integrated optical analog-to-digital converter,” Opt. Eng. 33, 2638–2645 (1994).
[CrossRef]

Sawchuk, A. A.

Seka, W.

W. Seka, E. Stüssi, “Nonlinear absorber characteristics and their effects on discrimination amplifiers,” J. Appl. Phys. 47, 3538–3541 (1976).
[CrossRef]

Smith, S. D.

Soffer, B. H.

Strand, T. C.

Stüssi, E.

W. Seka, E. Stüssi, “Nonlinear absorber characteristics and their effects on discrimination amplifiers,” J. Appl. Phys. 47, 3538–3541 (1976).
[CrossRef]

Styer, D.

P. E. Pace, D. Styer, “High-resolution encoding process for an integrated optical analog-to-digital converter,” Opt. Eng. 33, 2638–2645 (1994).
[CrossRef]

Syuaib, I.

K. T. Jeong, O. Hanaizumi, I. Syuaib, S. Kashiwada, K. Kawase, S. Kawakami, “Analysis and assessment of the gain of optically pumped surface-normal optical amplifiers,” Opt. Commun. 135, 227–232 (1997).
[CrossRef]

Tanaka, S.

S. Ohtsuka, T. Koyama, K. Tsunemoto, H. Nagata, S. Tanaka, “Nonlinear optical property of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

Tanji, H.

T. Tokizaki, A. Nakamura, S. Kaneko, K. Uchida, S. Omi, H. Tanji, Y. Asahara, “Subpicosecond time response of third-order optical nonlinearity of small copper particles in glass,” Appl. Phys. Lett. 65, 941–943 (1994).
[CrossRef]

K. Uchida, S. Kaneko, S. Omi, C. Hata, H. Tanji, Y. Asahara, A. J. Ikushima, T. Tokizaki, A. Nakamura, “Optical nonlinearities of a high concentration of small metal particles dispersed in glass: copper and silver particles,” J. Opt. Soc. Am. B 11, 1236–1243 (1994).
[CrossRef]

Taylor, G. W.

J. Cai, G. W. Taylor, “Optoelectronic thyristor-based photonic smart comparator for analog-to-digital conversion,” IEEE Photon. Technol. Lett. 11, 1295–1297 (1999).
[CrossRef]

Taylor, H. F.

H. F. Taylor, “An optical analog-to-digital converter—Design and analysis,” IEEE J. Quantum. Electron. QE-15, 210–216 (1979).
[CrossRef]

Tokizaki, T.

T. Tokizaki, A. Nakamura, S. Kaneko, K. Uchida, S. Omi, H. Tanji, Y. Asahara, “Subpicosecond time response of third-order optical nonlinearity of small copper particles in glass,” Appl. Phys. Lett. 65, 941–943 (1994).
[CrossRef]

K. Uchida, S. Kaneko, S. Omi, C. Hata, H. Tanji, Y. Asahara, A. J. Ikushima, T. Tokizaki, A. Nakamura, “Optical nonlinearities of a high concentration of small metal particles dispersed in glass: copper and silver particles,” J. Opt. Soc. Am. B 11, 1236–1243 (1994).
[CrossRef]

Tsuda, S.

Tsunemoto, K.

S. Ohtsuka, T. Koyama, K. Tsunemoto, H. Nagata, S. Tanaka, “Nonlinear optical property of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

Uchida, K.

K. Uchida, S. Kaneko, S. Omi, C. Hata, H. Tanji, Y. Asahara, A. J. Ikushima, T. Tokizaki, A. Nakamura, “Optical nonlinearities of a high concentration of small metal particles dispersed in glass: copper and silver particles,” J. Opt. Soc. Am. B 11, 1236–1243 (1994).
[CrossRef]

T. Tokizaki, A. Nakamura, S. Kaneko, K. Uchida, S. Omi, H. Tanji, Y. Asahara, “Subpicosecond time response of third-order optical nonlinearity of small copper particles in glass,” Appl. Phys. Lett. 65, 941–943 (1994).
[CrossRef]

Walden, R. H.

R. H. Walden, “Analog-to-digital converter technology comparison,” in Gallium Arsenide Integrated Circuit (GaAs IC) Symposium 1994. Technical Digest 1994, 16th Annual (Institute of Electrical and Electronics Engineers, New York, 1994), pp. 217–219.

Wherrett, B. S.

B. S. Wherrett, “Fabry–Perot bistable cavity optimization on reflection,” IEEE J. Quantum Electron. QE-20, 646–651 (1984).
[CrossRef]

Xie, Y. M.

Yariv, A.

A. Yariv, R. G. M. P. Koumans, “Time interleaved optical sampling for ultra-high speed A/D conversion,” Electron. Lett. 34, 2012–2013 (1998).
[CrossRef]

Yeh, P.

Zhang, D.

Zhang, Y.

Ziolkowski, R. W.

Zureng, X.

Appl. Opt.

Appl. Phys. Lett.

R. Akins, S. Lee, “Coherent optical image amplification by an injection-locked dye amplifier at 632.8 nm,” Appl. Phys. Lett. 35, 660–663 (1979).
[CrossRef]

S. Ohtsuka, T. Koyama, K. Tsunemoto, H. Nagata, S. Tanaka, “Nonlinear optical property of CdTe microcrystallites doped glasses fabricated by laser evaporation method,” Appl. Phys. Lett. 61, 2953–2954 (1992).
[CrossRef]

T. Tokizaki, A. Nakamura, S. Kaneko, K. Uchida, S. Omi, H. Tanji, Y. Asahara, “Subpicosecond time response of third-order optical nonlinearity of small copper particles in glass,” Appl. Phys. Lett. 65, 941–943 (1994).
[CrossRef]

Electron. Lett.

M. Y. Frankel, J. U. Kang, R. D. Esman, “High-performance photonic analogue-to-digital converter,” Electron. Lett. 33, 2096–2097 (1997).
[CrossRef]

A. Yariv, R. G. M. P. Koumans, “Time interleaved optical sampling for ultra-high speed A/D conversion,” Electron. Lett. 34, 2012–2013 (1998).
[CrossRef]

IEEE J. Quantum Electron.

K.-K. Law, J. L. Merz, L. A. Coldren, “Superlattice surface-normal asymmetric Fabry–Perot reflection modulators: optical modulation and switching,” IEEE J. Quantum Electron. 29, 727–740 (1993).
[CrossRef]

B. S. Wherrett, “Fabry–Perot bistable cavity optimization on reflection,” IEEE J. Quantum Electron. QE-20, 646–651 (1984).
[CrossRef]

IEEE J. Quantum. Electron.

H. F. Taylor, “An optical analog-to-digital converter—Design and analysis,” IEEE J. Quantum. Electron. QE-15, 210–216 (1979).
[CrossRef]

IEEE J. Select. Topics Quantum Electron.

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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of photonic A/D conversion system. The four insets represent the spatial intensity distribution of the optical flow signals.

Fig. 2
Fig. 2

Schematic representation of the intensity-dependent characteristics of the ideal photonic comparator: (a) transmission and (b) reflection characteristics.

Fig. 3
Fig. 3

Stacked version of the photonic A/D conversion system using the back-and-forth optical circuit mechanism.

Fig. 4
Fig. 4

Schematic arrangement of the asymmetric nonlinear Fabry–Perot resonator with input and output signals. R F and R B , reflectivity at the front and the back mirrors, respectively.

Fig. 5
Fig. 5

Light intensity (a) transmitted and (b) reflected by the NFP resonator in dependence on the incident light intensity. Output–input curves are calculated with four different values of cavity detuning (δ) from the Fabry–Perot resonance.

Fig. 6
Fig. 6

Reflection characteristics of the NFP resonator for four different mirror reflectivity couples: (i) R F = 0.48, R B = 0.99, δ = -0.2π; (ii) R F = 0.43, R B = 0.96, δ = -0.23π; (iii) R F = 0.39, R B = 0.93, δ = -0.25π; (iv) R F = 0.34, R B = 0.9, δ = -0.28π. Two envelope lines indicate the off-resonance reflectivity R off and the on-resonance reflectivity R on.

Fig. 7
Fig. 7

Reflective output–input characteristics of the NFP resonator with mirror reflectivity of the same relation R F /R B =exp(-αd): (i) R F = 0.81, R B = 0.99; (ii) R F = 0.78, R B = 0.95; (iii) R F = 0.74, R B = 0.9; (iv) R F = 0.7, R B = 0.85. Cavity detuning δ is designed for (a) zero reflection at downward switching, (i) -0.07π, (ii) -0.08π, (iii) -0.1π, (iv) -0.12π, and for (b) enhancement of the hysteresis loop, (i) -0.1π, (ii) -0.12π, (iii) -0.14π, (iv) -0.16π.

Fig. 8
Fig. 8

Switching intensity for the NFP resonator as a function of absorption length αd with α fixed at 1 × 103 cm-1.

Fig. 9
Fig. 9

Transfer functions for (a) 3-bit, (b) 4-bit, and (c) 5-bit A/D conversions. The analog input values are normalized by quantization width, and the digital output numbers are translated into decimal.

Fig. 10
Fig. 10

Schematic representation of the associated output–input characteristics of (a) the photonic comparator and (b) the optical amplifier with a shiftable threshold. (I) and (II) indicate the cases for the binary outputs 0 and 1, respectively.

Fig. 11
Fig. 11

Transfer functions for (a) 5-bit, (b) 6-bit, and (c) 7-bit A/D conversions for the optical thresholding amplifier associated with the photonic comparator. The analog input values are normalized by quantization width, and the digital output numbers are translated into decimal.

Equations (11)

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θ=2πdn2Icλ+δ,
n2=4π2 Reχ3cn02,
It=αd1-RBexp-αd1-exp-αd1+RB exp-αd Ic,
Ir=I0-αd1-RB exp-2αd1-exp-αd1+RB exp-αd Ic,
Ic=1-RF1+RB exp-αd1-exp-αdαd1-RFRB1/2 exp-αd2+4αdRFRB1/2 exp-αdsin2 θ I0,
It1+4RFRB1/2 exp-αd1-RFRB1/2 exp-αd2×sin22πn2expαd-11+RB exp-αdλα1-RB It+δ-1-RB1-RFexp-αd1-RFRB1/2 exp-αd2 I0=0.
I0-Ir1+4RFRB1/2 exp-αd1-RFRB1/2 exp-αd2×sin22πn21-exp-αd1+RB exp-αdλα1-RB exp-2αd×I0-Ir+δ-1-RF1-RB exp-2αd1-RFRB1/2 exp-αd2 I0=0.
Roff=1-1-RF1-RB exp-2αd1+RFRB1/2 exp-αd2,
Ron=1-1-RF1-RB exp-2αd1-RFRB1/2 exp-αd2.
RF/RB=exp-2αd.
Ed=|Pn-Pq|maxPFS×100 %.

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