Dispersion In Single-mode Fibers Research Articles

Analysis of Nonlinear Fiber Kerr Effects for Arbitrary Modulation Formats

Coherent optical transmission systems can be modeled as a four-dimensional (4D) signal space resulting from the two polarization states, each with two quadratures. Recently, nonlinear analytical models have been proposed capable of capturing the impact of Kerr nonlinearity on 4D constellations. None of these addresses the inter-channel nonlinear interference (NLI) imposed by arbitrary modulation formats in multi-channel wavelength division multiplexed (WDM) systems. In this paper, we introduce a general nonlinear model for multi-channel WDM systems that is valid for arbitrary modulation formats, even asymmetric ones. The proposed model converges to the previous models, including the EGN model, in the special case of polarization multiplexed systems. The model focuses on the cross-phase modulation (XPM) nonlinear term that lies at the heart of the NLI in multi-channel WDM systems operating on standard high dispersion single-mode fiber. We show that strategic mappings of the modulation format's coordinates to the polarization states can reduce the NLI undergone by these formats.

Optical Performance Monitoring for Intra-LP-Mode Dispersion in Weakly-Coupled Mode-Division Multiplexed Systems

Weakly-coupled mode-division multiplexing (MDM) technique based on linearly-polarized (LP) modes in ultralow-modal-crosstalk few-mode fiber (FMF) has been considered as a promising candidate for capacity enhancement of next-generation optical transmission systems. Similar to polarization mode dispersion in single-mode fibers (SMFs), signals in weakly-coupled FMFs suffer from the impacts of intra-LP-mode dispersion (ILMD) for both degenerate and non-degenerate LP modes.In this paper, we propose an effective method for ILMD monitoring in weakly-coupled MDM systems. The ILMD evaluation method for degenerate LP modes is designed by the analysis of channel transfer matrix in a digital coherent receiver. Then the ILMD monitoring scheme is experimentally validated for all the 6 LP mods in a weakly-coupled FMF. The influences of chromatic dispersion, optical signal to noise ratio and inter-LP-mode crosstalk to the method are also investigated.

Dispersion Measurement with Optical Computing Optical Coherence Tomography

We propose a novel technique to measure fiber dispersion without any derivative operation and index measurement. Based on the relationship between the dispersion and the signal in optical computing optical coherence tomography, dispersion can be deduced with high accuracy from optical computing OCT signal position and resolution. The group velocity dispersion and third order dispersion of single mode fiber and dispersion compensating fiber with lengths of 10 m–10 km are measured to be in good consistence with the nominal value.

Performance Analysis Of Optical Modulation Techniques Based On Reduction Of Second Order Harmonics And Chromatic Dispersion on OFDM Signals

ABSTRACT This work explains the theoretical and mathematical investigations of the transmission performance of an optical Single Sideband (SSB) modulation technique generated by a Mach Zehnder Modulator (MZM) with a 90° and 120° phase shift using hybrid coupler (Modified SSB) in addition to the Vestigial Sideband technique (VSB). The problem addressed in this paper is the effect of non-linearity of the transmitter system and the chromatic dispersion in single mode fiber due to the presence of second- and higher order harmonics. The non-linearity of the transmitter generates second and higher order harmonics, which affects the system performance leading to reduction in the data rate and increased distortion. The transmission performance of SSB, M-SSB and VSB is evaluated based on the extinction ratio of the MZM, different transmission lengths of the fiber, optical signal modulation index and the receiver sensitivity. A mathematical model has been developed for all the systems representing the modulation techniques till the second order. The baseband modulation consists of an RF signal of frequency 18 GHz and an Orthogonal Frequency Division Multiplexing (OFDM) signal with 4-QAM modulation technique converted to optical signal, using the MZM and transmitted over a SMF of distance of 75 Km. Our results show that the M-SSB technique proves to be more immune toward transmitter nonlinearity and chromatic dispersion as compared to its counterparts. In addition to this, it improves the receiver sensitivity by 6.56 dBm. The results generated by software simulation are in tandem with the mathematical model.

Symmetric 10 Gbit/s 40-km reach DSP-based TDM-PON with a power budget over 50 dB.

This paper introduces the concept of a symmetric 10 Gbit/s high power-budget TDM-PON based on digital coherent technology and confirms its feasibility through a bidirectional transmission experiment with a transmission distance of 40 km and power budget of more than 50 dB. Burst-mode upstream 10 Gbit/s binary-phase-shift-keying (BPSK) signals synchronized by the clock recovered from downstream 10 Gbit/s NRZ signals are detected by using an optical pre-amplifier and coherent detection based on real-time burst-mode digital signal processing (DSP) in the optical line terminal (OLT). The real-time DSP implements coefficient handover in the adaptive equalizer to allow the reception of burst-mode upstream BPSK signals with short preamble length. An experimental bit error performance evaluation of the real-time burst-mode DSP yields the receiver sensitivity of -45.1 dBm for upstream burst-mode BPSK with a preamble length of 1.3 μs. For downstream signals, the receiver sensitivity of -38.9 dBm is achieved by using a chirp-controlled transmitter with optical post-amplifier so as to avoid the signal distortion created by the chromatic dispersion of single mode fiber (SMF) when the launched power is increased.

Polarization-dependent pulse dynamics of mode-locked fiber laser with near-zero net dispersion

We demonstrate novel polarization-dependent pulse dynamics in a fiber laser cavity mode-locked by single-wall carbon nanotubes. By managing the net dispersion and polarization state, we obtain two noise-like pulsing procedures with distinctive polarization characteristics. Ultrafast polarization measurements reveal double pulses are produced by the combined effects of double-scroll chaotic polarization attractors and the polarization mode dispersion of single-mode fiber. The corresponding single-shot spectra provide evidence of coherent energy coupling between pulses during the switching process, due to the polarization hole burning of the active medium. The relative results provide new information for the polarization control of ultrafast lasers.

The Influence of Dispersion on Stimulated-Brillouin-Scattering-Based Microwave Photonic Notch Filters

In this paper, the detrimental effects due to the inevitable dispersion of single-mode fibers for stimulated Brillouin scattering (SBS) based microwave photonic notch filters (MPNF) with sideband amplitude and phase control are investigated. With an inappropriate dispersion compensation, the experimental demonstration shows a notch center frequency shift of 8.3 MHz in maximum and a stopband rejection reduction by 21 dB for the MPNF. The simulation and experiment are in good agreement. Furthermore, the criteria of optimizing the filter performance are also discussed both theoretically and experimentally. These results can help design MPNF based on SBS and benefit other microwave photonic applications, which rely on the phase difference of optical waves.

Clock Recovery Challenges in DSP-Based Coherent Single-Mode and Multi-Mode Optical Systems

We present an analysis of clock recovery algorithms in both polarization division multiplexing systems and mode division multiplexing systems. The impact of inter-polarization time skew and polarization mode dispersion in single-mode fibers, as well as the combined impact of mode mixing and mode group delay spread in multi-mode fibers under different coupling regimes are investigated. Results show that although the clock tone vanishing has a known solution for single-mode systems, in multi-mode systems even for low group delay spread, strong coupling will cause clock tone extinction, making it harder to implement an effective clock recovery scheme.

Harmonic dissipative soliton resonance pulses in a fiber ring laser at different values of anomalous dispersion

The pulse dynamics of harmonic mode-locking in a dissipative soliton resonance (DSR) region in an erbium-doped fiber ring laser is investigated at different values of anomalous dispersion. The fiber laser is mode-locked by a nonlinear polarization rotation technique. By inserting 0–200 m anomalous dispersion single-mode fiber in the laser cavity, the cavity length is changed from 17.3 to 217.3 m, and the corresponding dispersion of the cavity ranges from −0.27 to −4.67 ps2. The observed results show that the tuning range of repetition rate under a harmonic DSR condition is highly influenced by the cavity dispersion. Furthermore, it is found that, by automatically adjusting their harmonic orders, the lasers can work at certain values of repetition rate, which are independent of the cavity length and dispersion. The pulses at the same repetition rate in different laser configurations have similar properties, demonstrating that each achievable repetition rate represents an operation regime of harmonic DSR lasers.

Stokes Space Representation of Modal Dispersion

Polarization-mode dispersion in single-mode fibers can be viewed as a special case of modal dispersion in multimode and multicore optical fibers. Exploiting the similarity between these two transmission effects, modal dispersion can be modeled in a way analogous to that of polarization-mode dispersion by modifying the conventional Jones–Stokes formalism. In this paper, we review the geometrical representation of modal dispersion in the generalized Stokes space by means of the modal dispersion vector. We summarize and unify the fundamental equations that encapsulate the properties of the modal dispersion vector. We prove that the modal dispersion vector can be expressed as a linear superposition of the Stokes vectors representing the principal modes. The coefficients of this expansion are the corresponding differential mode group delays. This concise and elegant expression can be considered as a simplified definition of the modal dispersion vector and can be used to facilitate analytical calculations.

Generation of an arbitrary chirped microwave waveform with high time-bandwidth product for increasing range resolution of RADAR by using photonic technique

An approach for photonic generation of an arbitrary chirped microwave waveform with an increased time-bandwidth product (TBWP) is proposed and experimentally demonstrated. In the proposed model, light from the mode locked laser is splitted into two parts by using 1 × 2 power splitter: one is sent to linearly chirped fiber Bragg grating (LCFBG) through circulator and the other is time delayed by fiber delay line. The optical pulse in upper arm is time stretched by the LCFBG. Meanwhile, the optical pulse in lower arm experiences a time delay and then stretched by the dispersive single mode fiber. Temporal interference pattern is generated with an increasing or decreasing free spectral range by combination of two time-stretched optical pulses. Finally, the temporal interference pattern which is obtained at the output of optical coupler is transformed into an arbitrary chirped microwave waveform by using a photo-detector. The main advantage of this proposed model is high TBWP in the range of 750–1000 which ultimately results in an increased range resolution of radio detection and ranging.

Assessment of the DC Bias to Mitigate the Clipping Noise in DCO-OFDM, ACO-OFDM; and Non-linear Distortion of DFB Laser Transmitted through Dispersive Single Mode Fibers in IM/DD Systems

An analytical investigation on the impact of the DC bias on the clipping noise and the laser non-linearity in Asymmetrically Clipped Optical Orthogonal Frequency Division Multiplexing (ACO-OFDM) and Direct Current--Biased Optical OFDM (DCO-OFDM) is performed. Clipping noise in the OFDM system is introduced either by transmitter non-linearity or due to the low power sensitivity of the receiver. However the clipping noise in the DCO-OFDM is also dependent upon the DC bias applied to make the bipolar OFDM signal unipolar. The addition of this extra DC bias increases the average signal power of the DCO-OFDM signal. The non-linearity of the DFB laser increases with the optical modulation index, which gives rise to intermodulation and harmonic distortions at the receiver. The OFDM signal when transmitted through the Single Mode Fiber (SMF) suffers from group--velocity dispersion (GVD) which limits its performance in the Passive Optical Networks (PON). In this paper, an assessment of the DC bias to reduce the clipping noise in the two systems under consideration is performed. A practical laser model is considered and analysis is performed to estimate the average laser drive power to maintain its non-linearities within a tolerable region for both the OFDM systems. A simulation is performed to transmit 5 and 8 Gb/s (ACO and DCO) OFDM signal over 120 km SMF where the effect of GVD is taken into consideration. An optimum OFDM drive signal power is calculated to maintain the laser transmitter in its linear region such that the effect of second order harmonic distortions (HD2) and third order intermodulation distortion (IMD3) is low. The SNR requirement of DCO-OFDM being higher than the ACO-OFDM leads to more clipping noise, HD2 and IMD3.

Role of the Input Profile Asymmetry and the Chirp on the Propagation in Highly Dispersive and Nonlinear Fibers

We report the role played by the pulse shape asymmetry and the initial chirp on the propagation in highly dispersive single mode fibers and on the drastic spectral broadening well known as the supercontinuum generation (SCG) in highly nonlinear waveguides. We deal with finite energy Airy pulse (FEAP) for the asymmetric pulse and with the sech-type pulse for a compared study. We find that chirping an Airy pulse allows us to obtain asymmetric spectral outputs and the time domain inversion mechanism in optical systems. For the SCG analysis, the weakly truncated chirped FEAPs are more suitable than the common symmetric profiles to generate coherent and ultrabroadband spectra.

Performance analysis of single sideband modulation technique using Mach Zehnder Modulator based on different phase angles of electrical hybrid coupler

This paper provides an insight on the generation and the performance analysis of two different optical single sideband (OSSB) modulation techniques depending on the phase angle of the electrical hybrid coupler. It takes into account the problem of the chromatic dispersion in the single mode fibers in Passive Optical Networks (PON), which severely degrades the performance of the system. The RF signal at the input of a dual drive Mach Zehnder Modulator (MZM) is divided in two parts equally with an electrical hybrid coupler providing a phase difference of 90° and 120° respectively to generate two different SSB techniques. The conventional OSSB generation technique with 90° phase difference suppresses either lower or upper first order sideband but 2nd order harmonics still exists in the spectrum. The 2nd and higher order harmonics generated due to non-linearity of the MZM depends upon the modulation index. The increase in modulation index leads to increased harmonic distortion at the receiver. The SSB with 120° hybrid coupler suppresses lower first order and upper second order sideband (or upper first order and lower second order sideband). It is shown that, the amount of suppression of the second order sideband (lower or upper) increases with the increase in the Extinction Ratio (ER) of the MZM. Comparing with the conventional OSSB technique, the suppression of second order sideband in the SSB with 120° hybrid coupler reduces the effect of chromatic dispersion in single mode fibers thereby increasing the transmission distance.

High-quality pulse compression in a novel architecture based on a single-mode fiber cascading a nonlinear optical loop mirror

A novel all-fiber low-pedestal pulse compression scheme is proposed and investigated. The scheme is based on an anomalously dispersive single-mode fiber (SMF) cascading a nonlinear optical loop mirror (NOLM) with another anomalously dispersive SMF in the loop. Numerical results show that excellent pulse compression and pedestal reduction can be achieved by using the proposed scheme.

Assessment of Fiber Chromatic Dispersion Based on Elimination of Second-Order Harmonics in Optical OFDM Single Sideband Modulation Using Mach Zehnder Modulator

ABSTRACTThis work addresses the analytical and numerical investigations of the transmission performance of an optical Single Sideband (SSB) modulation technique generated by a Mach Zehnder Modulator (MZM) with a 90° and 120° hybrid coupler. It takes into account the problem of chromatic dispersion in single mode fibers in Passive Optical Networks (PON), which severely degrades the performance of the system. Considering the transmission length of the fiber, the SSB modulation generated by maintaining a phase shift of π/2 between the two electrodes of the MZM provides better receiver sensitivity. However, the power of higher-order harmonics generated due to the nonlinearity of the MZM is directly proportional to the modulation index, making the SSB look like a quasi-double sideband (DSB) and causing power fading due to chromatic dispersion. To eliminate one of the second-order harmonics, the SSB signal based on an MZM with a 120° hybrid coupler is simulated. An analytical model of conventional SSB using 90° and 120° hybrid couplers is established. The latter suppresses unwanted (upper/lower) first-order and second-order (lower/upper) sidebands. For the analysis, a varying quadrature amplitude modulation (QAM) Orthogonal Frequency Division Multiplexing (OFDM) signal with a data rate of 5 Gb/s is upconverted using both of the SSB techniques and is transmitted over a distance of 75 km in Single Mode Fiber (SMF). The simulation results show that the SSB with 120° hybrid coupler proves to be more immune to chromatic dispersion as compared to the conventional SSB technique. This is in tandem with the theoretical analysis presented in the article.

Dissipative soliton resonance in a full polarization-maintaining fiber ring laser at different values of dispersion.

We investigated the dissipative solitons resonance in an ytterbium-doped fiber ring laser in which all the elements are polarization maintaining (PM). A semiconductor saturable absorber mirror was used as a mode-locker. The cavity included a normal dispersion single-mode fiber (SMF) and an anomalous dispersion photonic crystal fiber. The change of the length of the PM SMF allows the variation of the net-normal dispersion of the cavity in the range from 0.022 ps2 to 0.262 ps2. As the absolute value of the net-normal dispersion increases from 0.022 ps2 to 0.21 ps2, a square-shaped single pulse transformed to a single right-angle trapezoid-shaped pulse, and, at the dispersion of 0.262 ps2, to multiple right-angle trapezoid-shaped pulses, per round-trip.

Linearization of an analog photonic link based on chirp modulation and fiber dispersion

A simple and new method to linearize an analog photonic link is proposed and demonstrated. A dual-electrode Mach–Zehnder modulator is single-electrode driven by a radio frequency (RF) signal, with the other electrode left empty, to achieve a chirp modulation. Then a dispersive single mode fiber (SMF) is followed to introduce different phase shifts on different optical sidebands. By properly selecting the working point of the modulator and the fiber length, the third-order intermodulation distortion can be suppressed. Experimental results show that an improvement of 15.7 dB in the spurious-free dynamic range and 4.5 dB in the link gain is achieved after linearization. The scheme is simple, low cost, and the low-loss SMF can also act as a transmission medium to deliver the RF signal efficiently to a remote location.

High-resolution laser frequency scanning interferometer based on fiber dispersion phase compensation

The laser frequency scanning interferometer has several advantages, such as non-contact, high accuracy and low signal to noise ratio in detection. In order to achieve higher resolution of the laser frequency scanning interferometer, increasing the tuning range of the light source and reducing the tuning non-linearity have become the key factors. The commonly used method is to correct the non-linearity of the wide bandwidth external cavity tuning laser by a fiber optical auxiliary interferometer constructed external frequency sampling clock. When using the broadband external cavity tuning laser and the auxiliary interferometer with an optical path difference of 220 m, it is found experimentally that the single-mode fiber dispersion makes the frequency of sampled signals change over time, causing the spectrum to broaden and resolution to decline. This paper has established the dispersion mismatch model which shows that the fiber dispersion of the auxiliary interferometer causes linear chirp frequency changes during the measurement of signals. The linear chirp frequency is proportional to the tuning bandwidth and measured distance. The phenomenon and theoretical model of dispersion mismatch is verified by experiments. The results for targets in the air are shown to linearly decrease as the tuning range increases with the maximum offset of 156.3 µm for the 20 nm tuning bandwidth. The experiment also proves the peak broadening intensifies with increasing distance measured, and thus verifies as the time delay of free space increase, and the peak broadening and distortion also increases. This result means that it will limit the ranging distance and make large errors in measurement result for long distance targets. The dispersion of the auxiliary interferometer should be compensated in the laser frequency scanning interferometer for large-sized high resolution measurements. In this paper, phase dispersion compensation method based on the evolution of peak variation distortion elimination is proposed, by taking the peak amplitude variation as the criterion; the phase compensation can offset the dispersion and improve the resolution. The original signal is multiplied by the complex phase compensation term, then regulating the phase compensation factor, the chirp becomes smaller as the phase compensation factor is approaching the distortion factor. Under the condition that the phase compensation factor is equal to the distortion factor, the chirp is offset. Then, the relationship between the amplitude and the peak FWHM is studied. It is found that the peak FWHM decreases while the amplitude shows a gradually increasing trend. Therefore, the amplitude can be referred to in order to determine whether the peak FWHM reaches the minimum. The resolution for target's peak can be improved by searching for the maximum amplitude of the spectrum and adjusting the phase distortion coefficient. The experiment shows that the peak FWHM of the target is obviously narrowed after dispersion compensation. The peak value becomes close to the theoretical resolution, and the static target at a distance of 975.216254 mm from the laser frequency scanning interferometer is measured. Results show the measurement accuracy of the interferometer is 584 nm. To further verify the accuracy of the laser frequency scanning interferometer, the laser frequency scanning interferometer is compared with the Renishaw laser interferometer in the measurement range of 0692 mm. The standard deviation between them is 4.5 µm. The proposed method is put forward to provide basis for future studies on the large size high resolution laser frequency scanning interferometer.

All-Fiber Low-Pedestal Spectral Compression in a Novel Architecture Based on an SMF Cascading an HNLF-NOLM

A novel all-fiber low-pedestal spectral compression scheme is proposed and demonstrated. The scheme is based on an anomalously dispersive single-mode fiber (SMF) cascading a nonlinear optical loop mirror with a highly nonlinear fiber (HNLF) in the loop. Both numerical and experimental results show that the spectral pedestal after spectral compression in the HNLF can be efficiently suppressed by the nonlinear optical loop mirror through the chirp-related intensity filtering effect. The measured spectral pedestal energy ratio is 9.59% using the proposed scheme, which is nearly a quarter of that using the conventional alternative based on an anomalously dispersive SMF followed by a feedthrough HNLF.