Phase Conjugate Wave Research Articles

Phase-conjugate mirror for water waves driven by the Faraday instability

The Faraday instability appears on liquid baths submitted to vertical oscillations above a critical value. The pattern of standing ripples at half the vibrating frequency that results from this parametric forcing is usually shaped by the boundary conditions imposed by the enclosing receptacle. Here, we show that the time modulation of the medium involved in the Faraday instability can act as a phase-conjugate mirror--a fact which is hidden in the extensively studied case of the boundary-driven regime. We first demonstrate the complete analogy with the equations governing its optical counterpart. We then use water baths combining shallow and deep areas of arbitrary shapes to spatially localize the Faraday instability. We give experimental evidence of the ability of the Faraday instability to generate counterpropagating phase-conjugated waves for any propagating signal wave. The canonical geometries of a point and plane source are implemented. We also verify that Faraday-based phase-conjugate mirrors hold the genuine property of being shape independent. These results show that a periodic modulation of the effective gravity can perform time-reversal operations on monochromatic propagating water waves, with a remarkable efficiency compared with wave manipulation in other fields of physics.

Optical QPSK Signal Quality Degradation due to Phase Error of Pump Light in Optical Parametric Phase-Sensitive Amplifier Repeaters

The influence of pump phase error on phase-sensitive optical amplifier (PSA) repeaters and the waveform degradation due to chromatic dispersion and fiber nonlinearities in the optical multi-relay transmission of quadrature phase-shift keying phase-conjugated twin waves are considered theoretically. First, the influence of noise from the pump phase error, optical local oscillator, receiver, and the amplified spontaneous-emission (ASE) in PSA repeaters is investigated with the assumption that transmission fibers are linear lossy channels. The bit-error rate (BER) is estimated as a function of the signal-to-noise ratio, and the relationship between the number of transmission relays and the fiber launch power is clarified. Waveform degradation due to chromatic dispersion and the optical fiber nonlinearities in transmission fibers are investigated with the noiseless condition, and the maximum repeatable number as a function of the fiber launch power is calculated. Finally, we show the relationship among the maximum repeatable number, standard deviation of pump phase error in PSA repeaters, and the fiber launch power to clarify the optimum transmission condition with consideration of the noise and the waveform degradation.

Detection of bubble movements via wave phase conjugation

Wave Phase Conjugation (WPC) means reversing the propagation of waves so that initial spatial distributions of amplitudes and phases are conserved. One of the methods to conjugate ultrasonic waves is to modulate the speed of sound in a solid conjugator by an alternating electromagnetic field. The detection of bubble motions in a fluid to be considered in this work is among potentially interesting and omnipresent WPC applications in industry. As the ultrasonic waves have short wavelengths, high-order in space and time numerical methods are required for modeling. In this work, a modified version of the Nodal Discontinuous Galerkin method, which is based on the non-collocated solution and flux bases, is implemented for wave propagation in solids and liquids (for both linear and non-linear flow regimes) in an axisymmetric geometry. Being assured of the accuracy and performance of the numerical technique by evaluating some representative test cases, the detection of bubble motion and growth in a flow field using WPC is simulated with the inclusion of all elements of the WPC process: the transducer, the conjugator, and the bubbly liquid itself. The developed methodology and results can be used to design and improve measurement devices based on the WPC phenomenon.

Twin-Image-Free Holography: A Compressive Sensing Approach.

Holographic reconstruction is troubled by the phase-conjugate wave front arising from Hermitian symmetry of the complex field. The so-called twin image obfuscates the reconstruction in solving the inverse problem. Here we quantitatively reveal how and how much the twin image affects the reconstruction and propose a compressive sensing (CS) approach to reconstruct a hologram completely free from the twin image. Using the canonical basis, the incoherence condition of CS is naturally satisfied by the Fourier transformation associated with wave propagation. With the propagation kernel function related to the distance, the object wave diffracts into a sharp pattern while the phase-conjugate wave diffracts into a diffuse pattern. An iterative algorithm using a total variation sparsity constraint could filter out the diffuse conjugated signal and overcome the inherent physical symmetry of holographic reconstruction. The feasibility is verified by simulation and experimental results, as well as a comparative study to an existing phase retrieval method.

Influence of physical dimensions on efficiency of phase-conjugated twin waves technique in coherent optical communication systems

Abstract The potential of phase-conjugated twin waves (PCTWs) technique has increased interests in optical communication systems due to its ability to mitigate the fiber nonlinearity. In this paper, the influence of the multiplexing dimensions of twin waves on the effectiveness of PCTWs technique is analytically modeled and numerically investigated. Moreover, the analytical models that characterize the phase noise suppression in both spatial and frequency domains are developed. In the spatial dimensions (SD), the 20 Gsymbol/s quadrature phase shift keying (QPSK) signal and its phase-conjugated copy are spatially multiplexed though two identical optical fiber channels, while in frequency dimensions (FD); these waves are multiplexed and sent through the same fiber channel. At receiver, the signals are coherently superimposed to cancel the nonlinear phase noise and enhance the signal to noise ratio (SNR). The results show that the mitigation efficiency of the PCTWs technique is governed by the physical dimensions of propagation. The PCTWs technique in SD system can achieve better performance than that in FD system. The achievable transmission distance is extended by 77.8% for SD system and 44.5% for FD system at bit error rate (BER) of 10−5.

Semi-analytic modeling of FWM noise in QAM Nyquist-WDM system with phase-conjugated twin waves

Abstract Nonlinear models previously reported for coherent optical fiber transmission have been used to explain the mechanism of nonlinear noise squeezing by phase-conjugated twin waves (PCTW) scheme, but the reduction of four-wave-mixing (FWM) noise by the nonlinearity mitigation method cannot be directly derived from these models for a quasi-symmetric dispersion map, especially when the effect of walk-off between channels is included. Semi-analytic models based on a statistical method are derived herein order to quantify the reduction of FWM noise for quadrature amplitude modulation (QAM) PCTW Nyquist-WDM systems. Our models derived here show that the variance of non-degenerate FWM noise is irrelevant to the number of signal points within a QAM constellation diagram, as is different from the degenerate FWM case. Numerical results by using our models show that even though the effect of walk-off is included, the PCTW scheme is still greatly effective to reduce the impact of FWM noise for a quasi-symmetric map. The performances of central channel for two cases of 16QAM PCTW Nyquist-WDM systems with same total spectral bandwidth and spectral efficiency, 16-channel 32-Gbaud/ch and 32-channel 16-Gbaud/ch, are numerically compared by using our models

Normal Mode Splitting in a Moving-Particles-Pumped Mechanical Oscillator: Clamped-Hinged Homogeneous Beam

The interaction of a mechanical oscillator with the operation actions and environment fields will give rise to the splitting of normal modes. In this study, we investigate the normal mode splitting behaviour of a moving-particles-pumped single-span clamped-hinged elastic homogeneous beam based on the proposed multi-octave modal parametric oscillation model. Numerical experiments show the entangled and squeezed oscillations of the phase-conjugated waves near the resonance tongues. Theoretical analysis predicts the occurrence of multiple simple resonances and the squeezing of the twin waves modal oscillation in the region with a low speed of movement for the studied system.

A novel scheme of cascaded four-wave mixing for phase-sensitive amplification in nonlinear optical fibre

We propose and numerically verify a scheme of phase-sensitive amplifier (PSA) using four-wave mixing (FWM) in cascaded highly nonlinear fibres (HNLFs), without requiring initial phase-locking between signal and pump. The first HNLF is used to generate two phase-conjugate waves, which act as two pumps for FWM process in second HNLF. We feed the two pumps from opposite ends of second HNLF and a signal co-propagating with one of the pumps. We keep the signal frequency in the middle of two pump frequencies to obtain phase-conjugate wave at the same frequency as the signal by FWM process in second HNLF. Signal and phase-conjugate wave appear at opposite ends of the second HNLF and combined to obtain PSA. The frequency-shift-free operation of phase conjugation helps in preserving the frequency of input signal during phase-sensitive amplification. We derive the expression for PSA signal output and PSA gain and show analytically that PSA gain depends upon signal phase only, as the two pumps are phase conjugate to each other. Thus, eliminating the need of phase locking between signal and pump waves. We show that PSA provides high gain for in-phase component and almost cancellation for quadrature-phase component of signal. We show the broadband nature of PSA due to minimum effect of group velocity and group velocity dispersion owing to counter-propagating nature of signal and conjugate waves. We study the performance of PSA under the effects of pump-signal detuning, amplifier length and input signal phase. Simulation results show that PSA output is forced to attain 0 or phase regardless of large variation of phase in the input signal. Nonlinear phase noise reduction of 100 Gbps DPSK signal transmitted over 1000-km standard single-mode fibre confirms phase regeneration by PSA.

Polarization Dependence of Carrier Extraction from Dual-Polarization Phase-Coujugated Twin Waves with Sum-Frequency Generation

This study aimed to build a numerical model of carrier extraction from dual-polarization phaseconjugated twin waves (DP-PCTWs) to investigate polarization dependence on the carrier extraction in a pump phase-locked loop for phase-sensitive optical amplifier repeaters. First, the numerical model was developed, and extracted carrier power of 40- Gbit/s DP-PCTWs with quadrature phase-shift keying format was calculated. Numerical results show the extracted carrier disappears when the PCTWs are circular polarization, and polarization dependence exists on the carrier extraction. Then, carrier extraction of a 10- Gbit/s DP-PCTW with binary phase-shift keying format was experimentally demonstrated. The extracted carrier power was found to be relatively low when the DP-PCTWs are circular polarization, and this trend agrees closely with the numerical results. These results show the reasonability of the numerical model and existence of polarization dependence on the carrier extraction from DP-PCTWs.

Polymeric particle phase conjugator using degenerate four-wave mixing confocal microscopy

ABSTRACTWe have exploited a new microscope system for absorptive organic materials observation. The microscope includes a confocal optical system with a degenerate four-wave mixing (DFWM) system. The DFWM system increases backward scattering signal intensity. The DFWM causes wave mixing in a nonlinear optical (NLO) microsphere and generates phase conjugate wave by energy coupling based on polarization conversion. As a result, the experimental system, which causes energy coupling, can greatly improve in-plane contrast resolution of the existing microscope by applying it to observation of organic materials.

Three-dimensional measurement of chloroplast with degenerate four-wave mixing nonlinear confocal microscope

ABSTRACTWe report new confocal microscopy using degenerate four-wave mixing (DFWM) geometry for three-dimensional measurement of biological samples. DFWM nonlinear confocal microscope that applies phase conjugate (PC) wave to the conventional confocal microscope obtains optical resonant properties of the focal region. As a result, the microscope provides three-dimensional image of biological samples with high spatial resolution.

Enhancement of Photosensitivity of Photorefractive Ferroelectric Liquid Crystal Blends to Green and Red Wavelength Regions Using Oligothiophene Photoconductive Dopants

The photorefractive effect can be used to generate rewritable holograms in a material, and it is utilized in various devices, including three-dimensional displays, optical tomography units, novelty filters, phase conjugate wave generators, and optical amplifiers. Ferroelectric liquid crystal (FLC) blends composed of a smectic liquid crystalline mixture, a chiral photoconductive dopant, and an electron trap reagent exhibit significant photorefractivity together with rapid responses. In previous studies, terthiophene derivatives were used as chiral photoconductive dopants and the resulting photorefractive effects were examined at 488 nm. In order to utilize the photorefractive ferroelectric liquid crystals in practical devices such as photoacoustic interferometers and ultrasound imaging units, the wavelength sensitivity of the material should be extended to longer regions. In the present work, chiral dopants possessing quarter-thiophene chromophores, sexithiophenes, and other photoconductive compounds with ...

Nonlinear Compensation Assessment in Few-Mode Fibers via Phase-Conjugated Twin Waves

In this paper, we further explore the concept of phase-conjugated twin waves (PCTW) for nonlinear cancellation in space-division multiplexed (SDM) systems. Previously, we demonstrated that the PCTW technique can successfully provide nonlinear cancellation in SDM systems. In this paper, we investigate the cases where two and four spatial modes are copropagating in a multimode fiber, considering three link lengths (1000, 3200, and 8000 km). Weak- and strong-coupling regimes are also evaluated. Our numerical simulation results show an average performance improvement $>$ 10 dB after a 1000 km transmission link.

Nonlinearities tolerant modulation format enabled Tb/s superchannel transmission over 420 km of unrepeated Raman amplified link

Abstract In this work we investigate different nonlinearities compensation and mitigation techniques for an unrepeated Raman-amplified link over 420 km of ultra-low loss (ULL) optical fiber. For such long links (over 400 km) fiber nonlinearities become very significant as high forward pump power is needed to ensure sufficient optical-signal-to-noise-ratio (OSNR) to acquire a bit-error-rate (BER) not exceeding the forward-error-correction (FEC) threshold. Such nonlinearities will significantly limit the performance. Through numerical simulations, we show successful net 200 Gb/s single carrier and 1 Tb/s superchannel transmission using PM-QPSK and symbol-rate-optimization (SRO). First we implement single carrier 200 G transmission either using 28 Gbaud PM-16QAM or 56 Gbaud PM-QPSK. Nonlinearities are compensated by either using digital-back-propagation (DBP) or phase-conjugated twin waves (PCTWs). We compare the performance of DBP and PCTWs based single carrier 28 Gbaud PM-16QAM, at the same transmission distance and capacity, with single carrier PM-QPSK and find that PM-QPSK does not require any nonlinearity compensation to give better performance than 28 Gbaud PM-16QAM. Following this result, we show a successful unrepeated transmission of net 1 Tb/s PM-QPSK Nyquist-spaced superchannel with an intra-superchannel net spectral efficiency (SE) of ∼3.6 b/s/Hz, over 420 km of Raman amplified ULL fiber without using any nonlinearity compensation. To improve the performance of this superchannel we implement nonlinearity mitigation scheme based on SRO. We investigate 5 × 56 Gbaud, 10 × 28 Gbaud, 20 × 14 Gbaud and 40 × 7 Gbaud PM-QPSK channels and found that the best performance is shown by 20 × 14 Gbaud superchannel. For PM-16QAM, successful transmission is only possible either using DBP or PCTWs based transmission link. DBP has a very high computational complexity whereas PCTWs halves the overall link spectral efficiency. Even then both schemes do not outperform PM-QPSK for the same transmission distance and capacity. So for practical realization the nonlinearity robust modulation format PM-QPSK using SRO has been identified as the most promising approach for superchannel implementation of unrepeated Raman amplified links.

Pump phase-locking to fiber-transmitted QPSK phase-conjugated twin waves for non-degenerate phase-sensitive amplifier repeaters

Pump phase-locking to fiber-transmitted QPSK phase-conjugated twin waves for non-degenerate phase-sensitive amplifier repeaters

Mitigation of Nonlinear Impairment by Coherently Superimposing CAP Sideband Signals

We propose to utilize the Hermitian symmetry of carrier-less amplitude phase (CAP) signals to mitigate distortion caused by fiber nonlinearity. The upper and lower frequency sidebands of CAP signals constitute phase-conjugated twin waves. Hence, coherent superposition of the two sidebands at the receiver can improve signal-to-noise ratio and compensate nonlinear impairment. We experimentally demonstrate that this scheme can improve the $Q$ factor by ~1.6 dB after 80-km transmission. When the fiber length is extended to 240 km, the $Q$ factor still exceeds the 7% hard decision forward error correction threshold by ~0.4 dB, showing potential application of the scheme for access and metro networks.

Optical pump phase locking to a carrier wave extracted from phase-conjugated twin waves for phase-sensitive optical amplifier repeaters.

In this paper, an optical phase-locked loop assisted by sum-frequency and second-harmonic generation (SS-OPLL) for frequency nondegenerate optical parametric phase-sensitive amplifier repeaters is experimentally demonstrated. First, theoretical derivations show that carrier extraction from phase-conjugated twin waves (PCTWs) and reference light generation are achieved by sum-frequency generation; therefore, the SS-OPLL circuit enables optical phase locking between PCTWs and a pump wave by a simple architecture based on a balanced OPLL. Then, optical phase locking between 20-Gbit/s quadrature phase-shift keying PCTWs and an individual pump source is experimentally demonstrated. Experimental results indicate that phase errors were reduced during the SS-OPLL operation.

Inverse focusing inside turbid media by creating an opposite virtual objective.

Limited by the penetration depth, imaging of thick bio-tissues can be achieved only by epi-detection geometry. Applications based on forward-emitted signals or bidirectional illumination are restricted by lack of an opposite objective. A method for creating an opposite virtual objective inside thick media through phase conjugation was first proposed. Under forward illumination, the backward scattering light from the media was collected to generate a phase conjugate wave, which was sent back to the media and formed an inverse focusing light. Samples combined with a diffuser or a mouse skin were used as specimens. Inverse focusing was successfully demonstrated by applying holography-based optical phase conjugation with a BaTiO3. This result indicates the capability to create an opposite virtual objective inside live tissues. The proposed method is compatible with current coherent imaging and super-resolution imaging technologies. It creates a possible way for forward-emitted signals collection and bidirectional illumination in thick specimens.

Effectiveness of phase-conjugated twin waves on fiber nonlinearity in spatially multiplexed all-optical OFDM system

Abstract In this paper, we investigate the effectiveness of using phase-conjugated twin waves (PCTWs) technique to mitigate fiber nonlinear impairments in spatially multiplexed all-optical orthogonal frequency division multiplexing (AO-OFDM) systems. In this technique, AO-OFDM signal and its phase-conjugated copy are directly transmitted through two identical fiber links. At the receiver, the two signals are coherently superimposed to cancel the phase noise and to enhance signal-to-noise ratio (SNR). To show the effectiveness of proposed technique, a spatially multiplexed AO-OFDM system is demonstrated by numerical simulation. AO-OFDM signal and its phase conjugated copy are optically generated by using optical coupler-based inverse fast Fourier transform (OIFFT)/fast Fourier transform (OFFT). The generated signal includes 29 subcarriers where each subcarrier is modulated by 4-quadrature amplitude modulation (4QAM) format at a symbol rate of 25 Gsymbol/s. The results reveal that transmission performance is considerably improved where the transmission distance of the proposed system is increased by ∼45% as compared to that of original system without PCTWs technique.

Fiber Nonlinearity Mitigation in 32-Gbaud 16QAM Nyquist-WDM Systems

Fiber nonlinearity distortion limits the achievable transmission distance and channel capacity of optical transmission systems. In this paper, we demonstrate an experiment of 1400-km standard single mode fiber transmission of 11 × 32 Gbaud 16-ary quadrature amplitude modulation signals with an emphasis on nonlinearity mitigation. Based on the first-order perturbation theory, we present the nonlinearity mitigation principle of the conjugate data repetition (CDR) scheme in a polarization division multiplexed wavelength division multiplexed scenario. Then, we apply several nonlinearity mitigation methods such as CDR, phase-conjugated twin waves (PCTW), digital back propagation (DBP), and the recursive least-squares (RLS) algorithm based filtering to the experiment, respectively. Optical Kerr effects of self-phase modulation, intra- and interchannel cross-phase modulation are considered. The experimental results show that CDR demonstrates similar performance to PCTW. By introducing the CDR scheme, the average bit error rate is reduced from 1.92 × 10−2 to 1.76 × 10−3 at the cost of halving the data rate. This corresponds to 3.2-dB Q2 factor promotion, including 1.5 dB improvement in nonlinearity mitigation. In contrast, 1.0-dB Q2 factor promotion is achieved by employing RLS-based filtering and DBP together without sacrificing the data rate.