A secure communication system based on the error-feedback synchronization of the electronic model of the particle-in-a-box system is proposed. This circuit allows a robust and simple electronic emulation of the mechanical behavior of the collisions of a particle inside a box, exhibiting rich chaotic behavior. The required nonlinearity to emulate the box walls is implemented in a simple way when compared with other analog electronic chaotic circuits. A master/slave synchronization of two circuits exhibiting a rich chaotic behavior demonstrates the potentiality of this system to secure communication. In this system, binary data stream information modulates the bifurcation parameter of the particle-in-a-box electronic circuit in the transmitter. In the receiver circuit, this parameter is estimated using Pecora-Carroll synchronization and error-feedback synchronization. The performance of the demodulation process is verified through the eye pattern technique applied on the recovered bit stream. During the demodulation process, the error-feedback synchronization presented better performance compared with the Pecora-Carroll synchronization. The application of the particle-in-a-box electronic circuit in a secure communication system is demonstrated.

What we believe to be a new phase-contrast technique is proposed to recover intensity distributions from phase distributions modulated by spatial light modulators (SLMs) and binary diffractive optical elements (DOEs). The phase distribution is directly transformed into intensity distributions using a 4f optical correlator and an iris centered in the frequency plane as a spatial filter. No phase-changing plates or phase dielectric dots are used as a filter. This method allows the use of twisted nematic liquid-crystal televisions (LCTVs) operating in the real-time phase-mostly regime mode between 0 and p to generate high-intensity multiple beams for optical trap applications. It is also possible to use these LCTVs as input SLMs for optical correlators to obtain high-intensity Fourier transform distributions of input amplitude objects.

A spread spectrum communication system based on the electronic model of the particle in a box system is proposed. This circuit allows a robust and simple electronic emulation of the mechanical behavior of the collisions of a particle inside a box, exhibiting rich chaotic behavior. The required nonlinearity to emulate the box walls is implemented in a simple way when compared with other analog electronic chaotic circuits. In this system, binary data stream information is transformed in the frequency modulated signal by the binary frequency shift keying (BFSK) modulator. The chaotic signal of the particle in a box electronic circuit is used to generate a broadband signal in the voltage controlled oscillator (VCO) of the transmitter. The frequency hopping signal send to receiver is generated by mixing the binary frequency shift keying and the broadband signal. The demodulation process is done when the VCOs of transmitter and receiver are synchronized by a phase lock loop (PLL) circuit. The performance of the demodulation process is verified through the eye pattern technique applied on the recovered bit stream. A binary data stream information was sent through a transmission channel with the following lengths: 1000 meters and 5000 meters. The experimental results demonstrated that the particle in a box electronic circuit can be used in a spread spectrum communication system.

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