Phase Conjugate Wave Research Articles

Mitigation of nonlinear distortion in hybrid Raman/phase-sensitive amplifier links.

Hybrid systems combining distributed Raman amplification and phase-sensitive amplifiers (PSAs) are investigated in numerical simulations. We focus on the mitigation of fiber nonlinearities and the impact of the span power map which is also important in systems employing optical phase conjugation or phase-conjugated twin waves. We simulate multi-span PSA links with and without distributed Raman amplification and show that by including distributed Raman amplification, the transmission distance increases more at optimum launch power than in the linear regime. For a 5-channel WDM QPSK PSA-amplified system, we observe a transmission reach increase by a factor of 8.1 by including ideal distributed Raman amplification.

Scattering of phase-conjugate ultrasonic waves by microinclusions in a liquid flow

The paper presents the results of experimental and theoretical studies of processes of phase-conjugate ultrasonic wave propagation in a liquid flow containing gas microbubbles. It is shown that a signal from a phase-conjugate wave, which is recorded by a transceiving transducer, contains information on the flow velocity of scatterers and their concentration. In this case, the flow velocity is determined both in the presence and absence of moving scattering objects. A theory developed on the basis of the generalized reciprocity principle for a moving inhomogeneous medium represents the main experimentally observed features of the formation of signals from a phase-conjugate wave scattered by a disperse liquid flow.

Qualitative Comparison of Kerr Nonlinearity Mitigation Schemes in a Dispersion-Managed Link for 4 × 28-GBd 16-QAM Signals

We present an experimental investigation of different Kerr nonlinearity mitigation schemes in a 2-span dispersion–compensated link of 160–km length for 4 × 28–GBd single–polarization 16–QAM signal transmission. We consider optical phase conjugation (OPC) based on mid–link spectral inversion, digital backpropagation (DBP), and transmission of phase-conjugated twin-waves with either digital coherent superposition (DCS) or all–optical coherent superposition employing phase–sensitive amplification (PSA). The experiments are performed in a single–channel and a wavelength-division multiplexing (WDM) scenario. For single–channel operation, phase-conjugated twin waves with DCS provided superior performance compared to all the other mitigation schemes with a maximum Q2–factor improvement of 1.7 dB compared to signal transmission without any nonlinearity mitigation. The DBP, however, showed a higher nonlinear threshold than all the other schemes in our experiments. In the WDM scenario, DBP showed worse performance than the other mitigation schemes whereas the DCS again provided a higher Q2–factor improvement than the other techniques with a maximum Q2–factor improvement of 1.9 dB. The PSA and the mid–link OPC showed similar nonlinearity mitigation performance both in single-channel and WDM scenarios.

Modified phase-conjugate twin wave schemes for fiber nonlinearity mitigation.

The conventional phase-conjugate twin wave (PCTW) scheme can effectively mitigate the fiber nonlinear distortions but reduce the spectral efficiency (SE) by half. In this paper, we show that by modulating one of the conjugated signals with additional bits, the information encoded in the conjugated variants can still suppress the nonlinear distortions in a similar manner as in the conventional PCTW method, while that encoded in the additional bits, representing the improved SE, is the dominant source limiting the system performance. We further introduce redundancy to the additional bits via error correction coding to overcome this performance bottleneck. The overall system performance can thus approach that of the conventional PCTW method while the SE is significantly enhanced. Simulations of a 25-Gbaud polarization-division-multiplexed quadrature phase shift keying system over 15,200 km show that the proposed scheme can increase the normalized SE from 50% to 80% for a similar performance as the conventional PCTW method. We also show that the proposed concept can be applied to higher-level formats.

Coherent backscattering of phase conjugate ultrasound waves in dispersive systems

Processes of the propagation of phase conjugate ultrasound waves in stationary and moving random media containing micro-inclusions in the form of gas bubbles and solid spheres are studied experimentally and theoretically. The wave phase conjugation of sound at a frequency of 10 MHz is conducted via supercritical parametric conversion. The qualitative difference between the statistical properties of scattered and phase conjugate acoustic fields is established. Unlike the detected stochastic signals from scattered waves, the signals of the phase conjugate waves are regular and more useful in determining the concentrations and parameters of the scatterers. A theoretical model describing the observed features of the coherent backscattering of phase conjugate waves is developed.

Cascade generation of a phase conjugate wave in a magnetoordered acoustic medium

The cascade generation of second acoustic harmonics accompanied by simultaneous parametric wave phase conjugation in an α-Fe2O3 antiferromagnetic crystal in a transverse electromagnetic field is studied experimentally and theoretically. The necessary conditions for generation upon varying the direction of magnetization relative to the crystallographic axes and the direction of transverse sound wave propagation are determined. The observed effect is caused by magnetoelastic interaction and is described using the theory of giant effective elastic anharmonicity.

Experimental study of localized heating of a biological tissue phantom by high-power phase conjugate ultrasonic beams

Experimental results on heating a biological tissue phantom using phase conjugate ultrasonic beams are presented. A polymer with acoustic properties close to those of biological tissues is used as the phantom. Heating is measured by thermocouples. The advantages of the proposed method of heating via wave phase conjugation include self-targeting of an ultrasonic beam on the region of heating and the weak effect the sample’s position or movement has on the heating parameters within a certain region.

Phase conjugation of ultrasound waves in comparison with backscattering in disordered medium

Ultrasound wave phase conjugation in randomly scattering media is studied experimentally and treated theoretically in comparison with ordinary backscattering phenomenon. The experiments are carried out on a scattering sample made of a cylindrical agar gel matrix containing a set of glass micro-spheres of 300μm diameter. The sample was immersed in water and turned slowly for simulation of a statistical ensemble of scatterers. Phase conjugation of the scattered acoustic waves at frequency 10 MHz was implemented by the parametric technique. The signals of backscattered (BSW) and phase conjugate (PCW) waves were detected by the same ultrasonic transceiver. In contrast with the stochastic behaviour of the BSW signal, the PCW amplitude is found almost regular and insensitive to the statistical features of the scattering ensemble. The mean values of amplitudes and the signal to noise ratios for PCW are one order of value higher than for BSW. A variation of the number of scatterers in the aperture of the incident acoustic beam revealed the proportionality of the mean values of PCW amplitude and BSW signal intensity. The results are in quantitative agreement with the developed theory. The advantages of the phase conjugation technique in comparison with the backscattering method for testing of randomly scattering media are discussed.

Image restoration based on phase conjugation in second-order nonlinear materials under reflection configuration.

We have demonstrated the recovery of the distorted images by a phase plate to nearly their original qualities under a refection configuration. This is made possible by utilizing difference-frequency generation in a bulk KTiOPO(4) (KTP) crystal and an AFB-KTP crystal composite. In such a geometry, both input and phase-conjugated waves propagate through the distorted phase plate for a round trip. They are reflected by the object, which can be far away from the imaging system, and captured by the cameras. Therefore, such a configuration is much more practical for eventually deploying our imaging system for realizing practical applications. We have demonstrated the advantages of the imaging system such as polarization insensitivity and broadband capability.

Enhanced performance of phase-conjugated OFDM subcarriers using digital coherent superposition

We have recently demonstrated the improved phase noise tolerance in coherent optical OFDM by digital coherent superposition of optical OFDM subcarriers, which are phase-conjugated pairs with Hermitian symmetry. In this approach, we realized DCS of OFDM subcarriers in single polarization (or channel), denoted as SP-DCS-OFDM. In this paper, we show that another approach is in dual polarizations, or DP-DCS-OFDM. According to the concept of phase-conjugated twin wave, both approaches can also mitigate the fiber nonlinearity to the first order. We prove that both approaches can cancel the inter-carrier interference (ICI) due to phase noise to the second order, and we derive the reduced ICI power to the fourth order using the Wiener phase noise model. In simulation, we show the enhanced tolerance to the laser phase noise and fiber nonlinearity.

Coherent scattering of phase conjugate ultrasound waves in bubbly media.

Wave phase conjugation of ultrasound scattered by clouds of micro-bubbles in water has been studied experimentally and expounded theoretically. The clouds of microbubbles with variable concentration and sizes have been generated here using electrolytic method. The wave front of the ultrasound beam of frequency 10 MHz was reversed by a parametric phase conjugator. The signal of phase conjugate wave (PCW) detected by an acoustic transceiver was compared with the signal of the wave scattered toward the phase conjugator. The scattered wave (SW) signal was detected by the transducer substituting the phase conjugator. It is shown that, in contrast with stochastic SW signal, wave phase conjugation forms regular PCW signal on the transceiver in spite of random distribution of the scatterers. The PCW signal is found to be much more sensitive to variations of bubbles concentration comparing with the mean value of the SW amplitude. Moreover, the relative error of measurements of PCW signals is much smaller than that of the SW signal. The revealed properties of phase conjugate waves are applicable for testing of concentration of scatterers in dispersive systems.

The signal synchronization transmission among uncertain discrete networks with different nodes

This paper investigates the signal synchronization transmission among uncertain discrete networks with different nodes based on Lyapunov theorem. A novel synchronization technique and an identification law of adjustment parameter are designed. In order to testify the effectiveness of synchronization technique, laser phase-conjugate wave, Gibbs electro-optical system and Bragg acousto-optical system are taken as the nodes of the complex networks to make a simulation. It shows the synchronization technique can be applied to any network connected arbitrarily, and the network number and the number of network nodes can be selected freely.

Mitigation of nonlinearities using conjugate data repetition.

We investigate a time-domain implementation of generalized phase-conjugated twin waves which we call conjugate data repetition. A theory based on time-domain perturbation analysis explaining the mitigation of nonlinear effects is provided, and the concept is evaluated using numerical simulations. Compared to PM-QPSK at the same channel bit rate, the single-channel transmission reach in a conventional system with standard single-mode fiber of conjugate data repetition-QPSK is increased by approximately a factor of 2.

Synchronous heating of two local regions of a biological tissue phantom using automated targeting of phase conjugate ultrasound beams

Synchronous heating of two local regions of an absorbing medium by phase conjugate ultrasound beams focused on them has been experimentally demonstrated. A polymeric biological tissue phantom with two small air cavities scattering sound has been used as the medium irradiated by a 5-MHz “probe” ultrasound beam. The scattered field is incident on a parametric device for ultrasonic wave phase conjugation. The conjugate and amplified field is self-adaptive focused on scatterers and heats the medium owing to the absorption of the ultrasonic energy. In this case, these regions are heated by about 5°C in 70 s. Only an insignificant increase in the temperature owing to the heat conduction effect is observed in the remaining volume of the phantom. The implemented effect can be used in medical applications of phase conjugate ultrasound beams.

Twin-Wave-Based Optical Transmission With Enhanced Linear and Nonlinear Performances

We review recent progresses on the use of twin-wave-based diversity schemes to enhance optical transmission performances in both nonlinear and linear regimes. Phase-conjugated twin waves with and without spectral redundancy are presented. The implications to perturbation-based fiber nonlinearity compensation are discussed. Performance enhancement techniques for real-valued orthogonal frequency-division multiplexed (OFDM) signals with a built-in Hermitian symmetry, as well as positive-valued OFDM twin signals suitable for cost-effective intensity modulation and direct detection, are also discussed.

Recovery of image distorted by turbulent atmosphere using phase-conjugate image generated by difference frequency generation

We demonstrate dynamic recovery of blurred images caused by atmospheric turbulence. In particular, using a phase-conjugate wave generated by a second-order nonlinear crystal or composite, we restore the original quality of the image after the optical radiation forming the image propagates through the turbulent atmosphere. One of the key elements for our experiment is a rotating phase plate being placed in the beam path for simulating turbulent atmosphere. Using the nonlinear composite, we demonstrate that the image recovery is insensitive to the polarization of the optical radiation forming the image.

Phase conjugation of vector fields by degenerate four-wave mixing in a Fe-doped LiNbO₃.

We propose a method to generate the phase-conjugate wave of the vector field by degenerate four-wave mixing in a c-cut Fe-doped LiNbO3 crystal. We demonstrate experimentally that the phase-conjugate wave of the vector field can be generated. In particular, the phase-conjugate vector field has also the peculiar function of compensating the polarization distortion, as the traditional phase-conjugate scaler field can compensate the phase distortion.

Generation of 1024-Tb/s Nyquist-WDM phase-conjugated twin vector waves by a polarization-insensitive optical parametric amplifier for fiber-nonlinearity-tolerant transmission

We experimentally demonstrate the generation of 1.024-Tb/s Nyquist-WDM phase-conjugated vector twin waves (PCTWs), consisting of eight 128-Gb/s polarization-division-multiplexed QPSK signals and their idlers, by a broadband polarization-insensitive fiber optic parametric amplifier. This novel all-optical signal processing approach to generate WDM-PCTWs enables a 2-fold reduction in the needed optical transmitters as compared to the conventional approach where each idler is generated by a dedicated transmitter. Digital coherent superposition of the twin waves at the receiver enables more than doubled reach in a dispersion-managed transmission link. We further study the impact of polarization-mode dispersion on the performance gain brought by the phase-conjugated twin waves, showing a gain of ~3.8 dB in signal quality factors.

Measuring the acoustic absorption coefficient in biological tissue specimens using ultrasonic phase conjugation

Acoustic absorption has been measured in a series of biological tissue specimens—porcine muscle, renal and fat tissues—by the standard insert-substitution method, as well as by ultrasonic phase conjugation. Comparison of the experimental results and revealed differences confirm the promise of using phase conjugate waves to measure acoustic losses in biological objects. It is demonstrated that in inhomogeneous tissues, the phase conjugation method makes it possible to obtain a more reliable estimate of dissipative losses.

Photorefractive effect in ferroelectric liquid crystals

In this paper, we review recent progress of research on the photorefractive effect of ferroelectric liquid crystals. The photorefractive effect is a phenomenon that forms a dynamic hologram in a material. The interference of two laser beams in a photorefractive material establishes a refractive index grating. This phenomenon is applicable to a wide range of devices related to diffraction optics including 3D displays, optical amplification, optical tomography, novelty filters, and phase conjugate wave generators. Ferroelectric liquid crystals are considered as a candidate for practical photorefractive materials. A refractive index grating formation time of 8–10 ms and a large gain coefficient are easily obtained in photorefractive ferroelectric liquid crystals.