Capacity to generate random signals by semi-nonlinear coupler



  • Bui Xuan Kien (Corresponding Author) Electric Power University
  • Dinh Van Chau Electric Power University
  • Nguyen Manh Thang Academy of Military Science and Technology
  • Pham Thanh Quang Academy of Military Science and Technology



Nonlinear optics; Nonlinear coupler; Optical wireless communication; Free-space communication; Information security.


The semi-nonlinear coupler (SNC) is used to split an optical signal into two different amplitude signals, and to reshape a series of signals. The mentioned applications are based on the monotonical dependence of the transmission coefficients on the input intensity, which changes in an interval. In this paper, we show that there is a certain interval of input intensity, in which the transmission coefficients overlap one to other. This behaviors of SNC can be used to generate random signals. Using the expression described the output-input power relation, the expression of the optical merge signal, carrier signal and coded-carrier signal, the overlapping region of the input intensity is numerically observed. Consequence, the random signals are simulated. The obtained signals are discussed to show the opportunity to use them for the information security of the wireless or free-space optical communication in the future.


[1]. C. W. Therrien, M. Tummala, “Probability and random process for electrical and computer engineers”, CRC Pres, p.249, (2012).

[2]. E. Garmire, “Signal Processing With A Nonlinear Fabry-Perot”, Proc. SPIE 0269, 69-74 (1981).

[3]. I. S. Varnosfadenani, M. F. Sabahi, M. Atael, “Joint equalization and detection in chaotic communication systems using simulation-based methods”, Communications 69, 1445-1452 (2015) DOI:

[4]. L. Sang, J.Zhang, T. Zhao, M. Virte, L. Gong and Y. Wang, “Optical Boolean chaos”, Opt. Express 28, 29296-29305 (2020). DOI:

[5]. L. Sang, Y. Guo, H. Liu, J. Zhang, and Y. Wang, “Real-time all-optical random numbers based on optical Booleen chaos”, Opt. Express 29, 7100-7109 (2021). DOI:

[6]. J. Wang, G. Meloni, G. Berrettini, L. poti, and A. Bogoni, “All-optical binary counter based on semiconductor optical amplifiers”, Opt. Lett. 34, 3517-3519 (2009). DOI:

[7]. P. Ashok, M. G. Madhan, and N. A. Natraj, “Performace evaluation of free space optical link by incorporating the device parameters of quantum cascade laser-based transmitter”, Laser Phys. Lett. 18, 035301 (2021). DOI:

[8]. N. Li, A. Locquet, M. Bloch, D.S. Citrin, and W. Pan, “Two approaches for ultrafast random bit generation based on the dynamics of a semiconductor laser”, Opt. Express 26, 6634-6646 (2014). DOI:

[9]. R. Sakuraba, K. Iwakawa, K. Kanno, and A. Uchida, “Tb/s physical random bit generation with bandwidth enhanced chaos in three-cascaded semiconductor lasers”, Opt. Express 23, 1470-1490 (2015). DOI:

[10]. X. Tang, Z.M. Wu, G. Wu, T. Deng, J.J. Chen, L. Fan, Z.Q. Zhong, and G.Q. Xia, “Tbits/s physical random bit generation based on mutually coupled semiconductor laser chaotic entropy source”, Opt. Express 23, 33130-331341 (2015). DOI:

[11]. M. Virt, E. Mercier, H. Thienpont, K. Panajotov, and M. Sciamanna, “Physical random bit generation from chaotic solitary laser diode”, Opt. Express 22, 17271-17270 (2014). DOI:

[12]. X. Z. Li, S. C. Chan, “Random bit generation using an optically injected semiconductor laser in chaos with oversampling”, Opt. Lett. 37, 2163-2165 (2012). DOI:

[13]. P. Ashok, S. Piramasubramanian, “An efficient chaotic optical signal generation scheme using gain level effect in bi-section laser diodes”, Opt. Commun. 475, 126202 (2020). DOI:

[14]. P. Li, J. Z. Zhang, Y. Wang, “All-optical fast random number generator”, Opt. Express 18, 20360-9 (2010). DOI:

[15]. T. Steinle, J. N. Greiner, J. Wachtrup, H. Grarsson, and I. Gerhardt, “Unbiased all-optical random-number generator”, Phys. Rev. X7, 041050 (2017). DOI:

[16]. M. Stipčević and J. E. Bowers, “Spatio-temporal optical random number generator,” Opt. Express 23, 11619 (2015). DOI:

[17]. V. Degiorgio, “Phase shift between transmitted and reflected optical fields of a semi-reflecting lossless mirror is π/2”, Am. J. Phys. 48, 81–82 (1980). DOI:

[18]. N. Calabretta, et al, “Multiple-output all-optical header processing technique based on two-pulse correlation principle”, Electron. Lett. 37, 1238-1240 (2001). DOI:

[19]. S. Shinohara, K. Arai, P. Davis, S. Sunada, and T. Harayama, “Chaotic laser based physical random bit streaming system with a computer application interface”, Opt. Express 25 (6), 6461-6474 (2017). DOI:

[20]. F. Raffaelli, P. Sibson, J.E. Kennard, D. H. Mahler, M. G. Thompson, J. C. F. Matthews, “Generation of random numbers by measuring phase fluctuations from a laser diode with a silicon-on-insulator chip”, Opt. Express 6, 19730-19741 (2018). DOI:

[21]. Z. Zheng, Y. Zhang, W. Huang, S. Yu, and H. Guo, “6Gbps real-time optical quantum random number generator based on vacuum fluctuation”, Rev. Scien. Instrum. 90, 043105 (2019). DOI:

[22]. Shen H., Cai L., and Shen X., “Performance analysis of TFRE over wireless link with truncated link-level ARQ”. IEEE Trans. Wirel. Commun. 5, 1479-1487(2006). DOI:

[23]. Zhao J., Liao Q., Huang D. et al, “Performance analysis of the satellite -to-ground continuous-variable quantum key distribution with orthogonal frequency division multiplexed modulation”, Quatum Inf. Process 18, no 36 (2019) DOI:

[24]. M. Rezaei, Md. H. M. Shamim, M. El. Amraoui, Y. Messaddeq, and M. Rochette, “Nonlinear chalcogenide optical couplers”, Opt. Express 30, 20288-20297 (2022). DOI:

[25]. V. Fortin, Y. O. Aydin, M. Bernier, R. Vallee, M. Rochette, F. Chenard, O. Alvarez, L. E. Busse, L. B. Shaw, R. R. Gattas, and J. S. Sangherad, “Post- processing soft glass optical fibers”, Mid-Infrared Fiber Photonics, Elsevier, 233-302, (2022). DOI:

[26]. M. Rezaei and M. Rochette, “All-chalcogenide ring fiber laser”, Opt. Fiber Technol. 71, 102900 (2022). DOI:

[27]. Q. Q. Ho, N. S. Vu, V. H. Nguyen ad T.T.T. Nguyen, “Optical bistability effect of two-port nonlinear fiber Mach-Zehnder interferometers”, Comm. Phys. 21, 161-168 (2011). DOI:

[28]. . Solntsev, A. S. et al. “Generation of nonclassical biphoton states through cascaded quantum walks on a nonlinear chip”. Phys. Rev. X 4(3), 031007. (2014). DOI:

[29]. Barral, D. et al. “Continuous-variable entanglement of two bright coherent states that never interacted”. Phys. Rev. A 96(5), 053822 (2017). DOI:

[30]. Barral, D., Bencheikh, K., Levenson, J. A. & Belabas, N. “Scalable multimode entanglement based on efcient squeezing of propagation eigenmodes”. Phys. Rev. Res. 3(1), 013068 (2021). DOI:

[31]. Barral, D. et al. “Versatile photonic entanglement synthesizer in the spatial domain”. Phys. Rev. Appl. 14(4), 044025 (2020). DOI:

[32]. Barral, D. et al. “Quantum state engineering in arrays of nonlinear waveguides”. Phys. Rev. A 102(4), 043706 (2020). DOI:

[33]. H. Q. Quy, T. D. Thanh, D. Q. Tuan, D. T. Viet, B. X. Kien, N. L. Le, N. M. Thang, “Nonlinear microscope objective using thin layer of organic dye for optical tweezers”, Eur. Phys. J. D 74,1-6 (2020). DOI:

[34]. K.R. Rekha, and A. Ramalingam, “Nonlinear characteristics and optical limiting effect of oil Red O azo dye in liquid and solid media”, J. Mod. Opt. 56, 1096-1102 (2009). DOI:

[35]. G. P. Agrawal, “Applications of Nonlinear Fiber Optics”, The Institute of Optics University of Rochester, New York, (2001).

[36]. A. Yariv, “Optical Electronics in Modern Communications”, 5th ed., Oxford University Press, New York, (1997).

[37]. Katsuniri Okamoto, “Coupled mode theory, Fundamental of Optical Waveguide”, Third edition, (2022). DOI:

[38]. S. Savović, A. Djordjevich, B. Drljača, A, Simović and R. Min, “Calculation of the Coupling Coefficient in Step-Index Multimode Polymer Optical Fibers Based on the Far-Field Measurements”, Fronties, Fronties in Phys. 10, Article 927907 (2022). DOI:

[39]. L.B. Samuel, V.L.Peter, “Quantum information with continuous variables”, Rev. Mod. Phys. 77,513(2005). DOI:

[40]. Fang J. Huang P., and Zeng G., “Multichannel parallel continuous-variable quantum key distribution with Gaussian modulation”, Phys. Rev. Q, 89, 022315(2014). DOI:

[41]. N. Gisin, G. Ribordy, W. Titel, H. Zbiden, “Quantum Cryptography”, Rev. Mod. Phys. 74, 145 (2002). DOI:

[42]. Ikuta T. and Inoue, “Intensity modulation and direct detection quantum key distribution based on quantum noise”, New J. Phys. 18 013018 (2016). DOI:

[43]. H.L. Yin, T.Y. Chen, Z.W. Yu, H. Liu, L. You, Y.H. Zhou, S.J. Chen, Y. Mao, M.Q. Huang, W.J. Zhang, H. Chen, M. Li, D. Nolan, F. Zhou, X. Jiang, Z. Wang, Q. Zhang, X.B. Wang, J.W. Pan, “Measurement device independent quantum key distribution over a 404 km optical fiber”, Phys. Rev. Lett. 117(19), 190501 (2016). DOI:

[44]. Wang T. et al, “High key rate continuous-variable quantum key distribution with a real local oscillator”, Optic. Express 26 (3), 2794-2806 (2018). DOI:

[45]. Singh H,. et al, “Design and analysis of hight-speed free space optical communication system for supporting fifth generation”, IEEE Photonics J. 13, 1-12 (2021). DOI:

[46]. K. Giuliani, V. Kumar Murty, G. Xu, “Passwords Management via Split-Key”, Journal of Information Security 7, 206-214 (2016). DOI:

[47]. R. Sehgal and P. Rathor, “Split Based Encryption in Secure File Transfer, Intern”. J. of Innovative Research in Computer and Communication Engineering 03, 6907-6912 (2015). DOI:

[48]. Ö. E. Müstecaplıoglu, “Quantum entanglement in optical fiber”, Optica, OPN (2008). DOI:

[49]. Robert A. Meyers, “Encyclopedia of Physical Science and Technology”, ScienceDirect, Elsevier, Third Edition, (2001).




How to Cite

Bui, K., C. Dinh, Nguyen Manh Thang, and Pham Thanh Quang. “Capacity to Generate Random Signals by Semi-Nonlinear Coupler”. Journal of Military Science and Technology, vol. 89, no. 89, Aug. 2023, pp. 94-102, doi:10.54939/1859-1043.j.mst.89.2023.94-102.



Research Articles