Presence Of Self-phase Modulation Research Articles

Effect of inter modal dispersion on modulational instability of optical soliton in Kundu–Eckhaus equation with the presence of SPM and XPM

We investigate analytically the role of inter modal dispersion on modulation instability of optical soliton in Kundu–Eckhaus (KE) equation with the presence of self phase modulation (SPM) and cross phase modulation (XPM). We consider the model of two component Kundu–Eckhaus with the inclusion of inter modal dispersion and in absence of four wave mixing term. The modulational instability (MI) criterion for KE equation is obtained based on the standard linear stability analysis. The effect of inter modal dispersion on MI of optical soliton in birefringent fiber with the presence of SPM and XPM is analyzed by using MI criterion. Through graphical illustration of MI gain, the role of inter modal dispersion on MI in optical fiber for the case of absence and presence of SPM and XPM are discussed.

Effects of Order Super Gaussian Pulses on the Performance of High Data Rate Optical Fiber Channel in the Presence of Self Phase Modulation

Abstract The work has simulated different order Gaussian pulses effects on the high data rate fiber communication channel and optical receiver sensitivity with/without self-phase modulation (SPM). The light signal per noise ratio, and total dispersion coefficient after optical fiber communication channel are measured at different order Gaussian pulses. Receiver sensitivity and maximum Q-factor are also measured for an optical receiver at high transmission data rates at different order Gaussian pulses. As well as Soliton peak power is measured for different transmission data rates with/without SPM effects. It is observed that the system performance is degraded over 100 Gb/s data transmission and 50 km fiber distance especially in the presence of SPM effects. It is evident that the system performance efficiency is degraded with high order Gaussian pulses. It is recommended to use first-order Gaussian pulse for upgrade optical communication system performance efficiency.

MCRB for timing, phase and frequency estimation in presence of self-phase modulation for low-rate optical communication

In this paper we derive the theoretical lower bound, namely Modified Cramer-Rao bound (MCRB) for symbol timing, phase and frequency offset in presence of nonlinear self-phase modulation (SPM) in a dispersion compensated long-haul coherent fiber link. The system model considers multiple span of fiber each associated with optical amplifier. Dual polarization multilevel quadrature amplitude modulation is opted for data transmission to support the data rate lower than 10 Gigabaud. We find that SPM induces underdamped oscillation on the MCRB bounds depending on the pulse shapes (symmetric and asymmetric) utilized. In presence of realistic low-pass filter at the receiver front end, the MCRB degrades significantly due to SPM. We also show the effect of SPM on symbol error rate degradation. Simulation is carried out with symmetric return-to-zero pulse with duty cycles of 33, 67 % and self-generated asymmetric pulse to verify the theoretical results.

Effects of nonlinear absorption and third order dispersion on soliton propagation in optical fiber

In this work, we use the generalized nonlinear Schrödinger equation to study propagation of ultrashort optical pulses in the presence of self-phase modulation, nonlinear absorption and third-order dispersion. The combined effect of the third-order dispersion and nonlinear absorption on amplitude, center location and phase of the soliton has investigated by approximate analytical method. Full Text: PDF References Govind. P. Agrawal, Nonlinear Fiber Optics, Academic Press, San Diego (California), 2001. DirectLink Hasegawa. A, M. Matsumoto, Optical solitons in fibers, Springer-Verlag Berlin Heidelberg 2003. CrossRef G. Tsigaridas, I. Polyzos, V. Giannetas and P. Persephonis, "Compensation of nonlinear absorption in a soliton communication system", Chaos, Solitons & Fractals, Vol. 35, 2008, pp.151-160. CrossRef Haus H., "Optical-fiber solitons, their properties and uses", P. IEEE 81:970-83 (1993). CrossRef Chan VWS, Hall KL, Modiano E, Rauschenbach KA., "Architectures and technologies for high-speed optical data networks", J Lightwave Technol 16:2146-68 (1998). CrossRef Newhouse MA, Weldman DL, Hall DW, "Enhanced-nonlinearity single-mode lead silicate optical fiber", Opt Lett, vol.16, 1185 (1990). CrossRef Okuno T, Onishi M, Kashiwada T, Ishikawa S, Nishimura M., "Silica-based functional fibers with enhanced nonlinearity and their applications", IEEE J Sel Top Quant, Vol. 5, 1385(1999). CrossRef G. I. Stegeman, in Contemporary Nonlinear Optics, edited by G. P. Agrawal and R. W. Boyd (Academic, San Diego), 1992. M. A. Newhouse, D. L. weidman, and D. W. Hall, "Enhanced-nonlinearity single-mode lead silicate optical fiber", Opt. Lett. Vol,15, 1185 (1990). CrossRef M. A. Newhouse, in Proceedings of a Symposium on Optical Waveguide Materials, Boston, 1991. Dinh Xuan Khoa, Bui Dinh Thuan, "Influence of loss and high-order dispersion on soliton?s transmision in optical fibers", Communications in Physics, Vol.17, 17 ? 22 (2007). DirectLink

Modified Cramér–Rao Bound for Clock Recovery in the Presence of Self-Phase Modulation

We investigate the effect of nonlinear self-phase modulation (SPM) on clock recovery in long-haul coherent optical communication systems with low to moderate baud rates. We consider dual-polarization, multilevel quadrature amplitude modulation, and evaluate conventional timing estimators as well as a modified Cramer-Rao bound. As the latter is hard to compute in the presence of nonlinear channel impairments, we derive an approximate closed-form expression. Contrary to linear channel impairments, the nonlinear impairments can degrade the performance for higher input powers. In addition, the bounds exhibit oscillatory behavior due to the oscillations in the signal spectrum in the presence of SPM.

Soliton shedding from Airy pulses in Kerr media

We simulate and analyze the propagation of truncated temporal Airy pulses in a single mode fiber in the presence of self-phase modulation and anomalous dispersion as a function of the launched Airy power and truncation coefficient. Soliton pulse shedding is observed, where the emergent soliton parameters depend on the launched Airy pulse characteristics. The Soliton temporal position shifts to earlier times with higher launched powers due to an earlier shedding event and with greater energy in the Airy tail due to collisions with the accelerating lobes. In spite of the Airy energy loss to the shed Soliton, the Airy pulse continues to exhibit the unique property of acceleration in time and the main lobe recovers from the energy loss (healing property of Airy waveforms).

Analysis of signed chromatic dispersion monitoring by waveform asymmetry for differentially-coherent phase-modulated systems

We analytically study received waveform asymmetries induced by chromatic dispersion (CD) for signed CD monitoring in differential quadrature phase-shift keying (DQPSK) systems and show that the asymmetries are results of differential detection and the ±π/4 phase shifters used in conventional DQPSK receivers. The theoretical insights developed help explain various published results on signed CD monitoring based on waveform asymmetries and allow us to further propose signed CD monitoring for differential eight phase-shift keying (D8PSK) systems without any modification to the receiver. Simulation results also show that the CD-induced waveform asymmetric features are preserved in presence of self-phase modulation (SPM) and polarization-mode dispersion (PMD).

A long-haul wavelength division multiplexed system using standard single-mode fiber in presence of self-phase modulation

Performance of a long-haul wavelength division multiplexed (WDM) communication system has been evaluated in presence of nonlinear effects using standard single-mode fiber. Different compensation configurations, namely, post-, pre- and bi-end compensation, have been investigated to mitigate the fiber nonlinear effects. Eye-opening degradation due to mutual interplay between self-phase modulation (SPM) and group velocity dispersion for the compensating techniques has been estimated with respect to the transmission length and the residual dispersion in case of WDM system. Maximum threshold power levels at the bit error rate of 10 −9 limited by the SPM effect have been determined. From a comparison among the compensating techniques, bi-end compensation configuration has been found to be the most suitable technique for any fiber length in case of a WDM communication system.

Passive mode locking of inhomogeneously broadened lasers

Passive mode locking of inhomogeneously broadened lasers is studied in three typical regimes: pure self-amplitude modulation (SAM) mode locking, soliton mode locking, and mode locking in the presence of self-phase modulation (SPM) and positive group-delay dispersion (GDD). When the mode-locking strength becomes weak and/or the GDD is large, the lockable spectral width reduces and mode locking becomes unstable, which is a common and unique feature for broadband inhomogeneously broadened lasers. Mode locking by the pure SAM is essentially a phase-locking process. The soliton mode locking best resists the impact of insufficient gain filtering, while mode locking in the presence of strong SPM and positive GDD is the weakest, and a certain amount of gain filtering (narrowing) is necessary for stable mode locking. The scaling relations of mode-locking characteristics with the gain linewidth, GDD, and nonlinearities, and the influence of the degree of inhomogeneity of the gain medium are examined. A linearized saturable absorber may not be able to mode lock a strongly inhomogeneously broadened laser, and a minimum unsaturated absorber loss is required for stable mode locking in most situations.

Nonlinear optical phenomena in silicon waveguides: modeling and applications

<p> <a href="http://oe.osa.org/virtual_issue.cfm?vid=36">Focus Serial: Frontiers of Nonlinear Optics</a> </p>Several kinds of nonlinear optical effects have been observed in recent years using silicon waveguides, and their device applications are attracting considerable attention. In this review, we provide a unified theoretical platform that not only can be used for understanding the underlying physics but should also provide guidance toward new and useful applications. We begin with a description of the third-order nonlinearity of silicon and consider the tensorial nature of both the electronic and Raman contributions. The generation of free carriers through two-photon absorption and their impact on various nonlinear phenomena is included fully within the theory presented here. We derive a general propagation equation in the frequency domain and show how it leads to a generalized nonlinear Schrodinger equation when it is converted to the time domain. We use this equation to study propagation of ultrashort optical pulses in the presence of self-phase modulation and show the possibility of soliton formation and supercontinuum generation. The nonlinear phenomena of cross-phase modulation and stimulated Raman scattering are discussed next with emphasis on the impact of free carriers on Raman amplification and lasing. We also consider the four-wave mixing process for both continuous-wave and pulsed pumping and discuss the conditions under which parametric amplification and wavelength conversion can be realized with net gain in the telecommunication band.

Analytical characterization of SPM impact on XPM-induced degradation in dispersion-compensated WDM systems

This paper proposes the definition of a cross-phase modulation (XPM)-induced power penalty for intensity modulation/direct detection (IM-DD) systems as a function of the normalized variance of the XPM-induced IM. This allows the definition of 1-dB power penalty reference values. New expressions of the equivalent linear model transfer functions for the XPM-induced IM and phase modulation (PM) that include the influence of self-phase modulation (SPM) as well as group-velocity dispersion are derived. The new expressions allow a significant extension for higher powers and dispersion parameters of expressions derived in previous papers for single-segment and multisegment fiber systems with dispersion compensation. Good agreement between analytical results and numerical simulations is obtained. Consistency with work performed numerically and experimentally by other authors is shown, validating the proposed model. Using the proposed model, the influence of residual dispersion and SPM on the limitations imposed by XPM on the performance of dispersion-compensated systems is assessed. It is shown that inline residual dispersion may lead to performance improvement for a properly tuned total residual dispersion. The influence of SPM is shown to degrade the system performance when nonzero-dispersion-shifted fiber is used. However, systems using standard single-mode fiber may benefit from the presence of SPM.

Compensation for depolarisation by a fibre coil in the presence of self-phase modulation

We report on the dependence of the degree of polarisation of an 80 fs pulsed laser beam propagating through a length of a single-mode birefringent fibre on the illumination power. Due to the birefringence and the nonlinear effect of self-phase modulation, the measured depolarisation dependence is oscillatory. It is, however, demonstrated that the oscillatory depolarisation can be compensated for by introducing a loop into the fibre geometry, which maintains the degree of polarisation of the pulsed beam as high as 90%.

Dispersion slope effects of the compensation dispersion fiber for broadband dispersion compensation in the presence of self-phase modulation

We use numerical simulations based on the split-step method to study the compensation of the chromatic dispersion in a point-to point link consisting of a Standard fiber followed by a dispersion compensation fiber in a post-compensation scheme. Two types of compensation fibers, with positive and negative dispersion slope, are considered, and we analyze the propagation of a pulse using three channels located at 1535, 1550 and 1560 nm. Our analysis is done for a wide range of the input peak power (0.6 mW≤ P 0≤80 mW), and includes effects due to loss, first and second chromatic dispersion, and self-phase modulation (SPM). Effects due to the interaction among the channels are not included in this work. The performance using each of the two compensation fibers studied here are compared. Our results show that the choice of the compensation fiber (i.e., its dispersion slope) to be used in a certain DWDM system has to take into account the total width of the wavelength band of operation and the input peak power. Our results suggest that compensation fibers with negative dispersion slope lead to good performance in a wide wavelength band.

Performance of a Dispersion Compensated Optical Direct Detection Linecoded CPFSK System Impaired by SPM

An analytical approach is presented to evaluate the performance of a point to point optical direct detection linecoded CPFSK transmission system with cacaded in-line amplifiers impaired by group velocity dispersion (GVD) and self phase modulation (SPM). The analysis is carried out for non-return-to-zero (NRZ) as well as alternate-mark inversion (AMI) linecodes with two different schemes for dispersion compensation. Performance results evaluated at a bit rate of 10 Gbit/s show that both NRZ and AMI coded CPFSK systems suffer power penalty due to residual dispersion and SPM even dispersion compensation schemes are used. The minimum penalty for NRZ-CPFSK due to residual dispersion is found to be 0.4 dB in case of lump compensation and 0.25 dB for even compensation. For AMI CPFSK, the minimum penalty is found to be approximately 2.3 dB. There is a further degradation in the system performance in presence of SPM when input power is more than 0 dBm.

Theory of solid-state laser mode locking by coherent semiconductor quantum-well absorbers

Solid-state laser mode locking by semiconductor quantum-well absorbers (QWA’s) is investigated, with the coherent polarization response of the absorbers taken into account. It is shown that femtosecond pulses with durations below the response time and the dephasing time can be generated that are stabilized by Rabi flopping of the absorber population. The shortest pulses are found when the effects of self-phase modulation (SPM) and group-velocity dispersion (GVD) are not present, whereby highly stable 2π pulses are formed inside the absorber. In the presence of SPM and GVD the pulse area deviates from 2π; nevertheless, the absorber’s coherent response results in incomplete Rabi flopping of the population. In agreement with experimental observations, we found limited femtosecond pulse operation regions for the pump rate and the GVD. These parameter regions are bounded by Q-switching instabilities and multiple-pulse operation. Further, the influence of inhomogeneous broadening of the carriers, dynamic bandgap renormalization owing to Coulomb exchange, and excitation-dependent dephasing of highly excited semiconductors is studied. The key absorber parameters are predicted that should permit a reduction of the shortest possible pulse durations.

Ultrashort pulse generation in cw solid-state lasers with semiconductor saturable absorber in the presence of the absorption linewidth enhancement

A theory for ultrashort pulse generation in cw solid-state lasers with a `slow' semiconductor saturable absorber in the presence of self-phase modulation in the active medium and absorption linewidth enhancement in the semiconductor has been developed. It was shown that with increase of pump energy the laser switches from stable ultrashort pulse generation to bistable operation regime. The parameters for stable ultrashort pulse generation were found.

10-Gb/s transmission performance for positive- and negative-chirped transmitters with the self-phase modulation effect

We have estimated the effective /spl alpha/-parameter of the extended transmitters in the presence of self-phase modulation (SPM) induced chirp. The /spl alpha/-parameter of transmitters is effectively lowered to about 1, when the SPM effect is included, compared to the /spl alpha/-parameter of the transmitter alone. This lowered effective /spl alpha/-parameter has improved the transmission performance significantly regardless of the transmitter operating with positive or negative chirp. The SPM-induced effective /spl alpha/-parameter can be used as a design parameter for high-speed (10 Gb/s) transmission systems.

Transmission limitations due to self-phase modulation in optical PSK heterodyne detection systems employing chromatic dispersion equalization

Even if the amplitude of a phase-modulated optical signal is constant before transmission, amplitude modulation is caused by fiber chromatic dispersion. As a result, self-phase modulation (SPM) is induced. In optical heterodyne detection, SPM cannot be compensated for by the delay equalizer (electrical domain) used to compensate fiber chromatic dispersion. However, the transmission distance limitation of multi-repeatered coherent transmission systems has not been investigated in the presence of SPM. This paper theoretically and experimentally investigates the transmission distance achievable with a phase-shift-keying (PSK) heterodyne detection system employing in-line optical amplifiers and delay equalization. The calculated results show that equalization is effective when /spl gamma/P/sub 0//2B/sup 2//spl verbar//spl beta//sub 2//spl verbar/ >