Rectangular Spectrum Research Articles

Investigation on Nyquist pulse generation by optical frequency comb

Compared with OFDM, Nyquist signal transmission has several unique advantages, such as lower receiver complexity, lower receiver bandwidths, and lower peak-to-average power ratios, which give better performances under fiber nonlinear impairments. Since the sinc-shaped waveforms in the time domain correspond to a rectangular spectrum in the frequency domain, the Nyquist pulses can also be obtained directly from the generation of a flat frequency comb with electro-optic modulators. In this paper, a complete theoretical analysis of Nyquist pulse generation with 3 comb lines generated with a single intensity modulator is developed. It is proved that both the amplitude and phase of the sidebands in the optical frequency comb are important for generation of Nyquist pulses. Theoretically, it is found that it is impossible to generate Nyquist pulses with more than 3 comb lines using a single intensity modulator even if 5 flat comb lines are realized. A Nyquist pulse can be generated with 9 comb lines by two cascaded intensity modulators, but the sum of the phase shift caused by the two DC voltages of the intensity modulators must be π.

Systems performance comparison of three all-optical generation schemes for quasi-Nyquist WDM.

Orthogonal time division multiplexing (OrthTDM) interleaves sinc-shaped pulses to form a high baud-rate signal, with a rectangular spectrum suitable for multiplexing into a Nyquist WDM (N-WDM)-like signal. The problem with generating sinc-shaped pulses is that they theoretically have infinite durations, and even if time bounded for practical implementation, they still require a filter with a long impulse response, hence a large physical size. Previously a method of creating chirped-orthogonal frequency division multiplexing (OFDM) pulses with a chirped arrayed waveguide (AWG) filter, then converting them into interleaved quasi-sinc pulses using dispersive fiber (DF), has been proposed. This produces a signal with a wider spectrum than the equivalent N-WDM signal. We show that a modification to the scheme enables the spectral extent to be reduced for the same data rate. We then analyse the key factors in designing an OrthTDM transmitter, and relate these to the performance of a N-WDM system. We show that the modified transmitter reduces the required guard band between the N-WDM channels. We also simulate a simpler scheme using an unchirped finite-impulse response filter of similar size, which directly creates truncated-sinc pulses without needing a DF. This gives better system performance than either chirped scheme.

Multiwavelength pulse generation using a SESAM-based mode-locked fiber laser together with Fabry–Perot filter

A simple and compact configuration of multiwavelength pulse generator is proposed and experimentally demonstrated, using a SESAM-based passively mode-locked fiber laser together with fiber Fabry–Perot filter. By optimizing the dispersion of fiber ring cavity, a flat rectangular optical spectrum with 3 dB bandwidth of 8.1 nm is obtained, with power fluctuation of <0.5 dB. Inserting a fiber Fabry–Perot filter at the output of passively mode-locked fiber laser, we can simultaneously obtain 40 channels with 0.2 nm wavelength spacing, under the condition of <3 dB power uniformity. After wavelength-division demultiplexing and optic-to-electronic conversion, the full width at half maximum (FWHM) of single channel pulse is measured to be 30 ps while the repetition rate of pulse train is 20.3 MHz.

Three types of pulses delivered from a nanotube-mode-locked fiber laser

Three types of pulses are experimentally investigated in a switchable normal-dispersion nanotube-mode-locked fiber laser by adjusting polarizer controller and pump power. They are a standard dissipative-soliton (DS), conventional soliton (CS)-like pulse, and noiselike pulse, which correspond to three mode-locking states. The standard DS with a rectangular spectrum possesses a Gaussian-shape pulse. The CS-like operation has a Lorenz shape, and the spectrum involves several sidebands similar to the CS case. For the noiselike pulse with a bell-shaped spectrum, a 317 fs peak rides upon the 132.5 ps pedestal in the autocorrelation trace. The spectra of these three pulse operations are centered at three close wavelengths. The generation of three such different types of pulses in one identical normal- dispersion laser cavity may find an important application for the future of mode-locked laser research.

Single-polarization, dual-wavelength mode-locked Yb-doped fiber laser by a 45°-tilted fiber grating

We experimentally demonstrate an all-fiber single-polarization dual-wavelength Yb-doped fiber laser passively mode-locked with a 45°-tilted fiber grating for the first time. Stable dual-wavelength operation exhibits double-rectangular spectral profile centered at 1033 and 1053 nm, respectively. The 3 dB bandwidth of each rectangular optical spectrum is estimated as 10 nm. The separation of two fundamental repetition rates is 6 kHz. By employing the 45° TFG with the polarization-dependent loss of 33 dB, output pulses with 27 dB polarization extinction ratio are implemented in the experiment. The single pulse centered at 1053 nm is researched by using a filter at the output port of the laser, and the experimental results denote that the output ps pulses are highly chirped. The formation mechanism of dual-wavelength operation is investigated.

Design and Analysis of an all-fiber MZI Interleaver Based on Fiber Ring Resonator

An all-fiber Mach-Zehnder interferometer (MZI) interleaver using one planar 3×3 fiber coupler, one 2×2 fiber coupler and one 8-shaped fiber ring resonator is developed by the new configuration. Based on its structure, the output spectrum expression is established and described by using the principle of fiber transmission and the matrix transfer function. The results of numerical simulation indicate that when the length difference of interference arms and the coupling coefficients of the couplers are some certain values, it obtains a uniform flat-top passband and similar to rectangular output spectrum. Compared with the traditional MZI interleaver, the isolation in stopband and the rolloff in transition band are strengthen, the 25dB stopband bandwidth and 0.5dB passband bandwidth are simultaneously remarkably improved. Compared with the asymmetrical ring resonator MZI interleaver, the influence of transmission loss on extinction ratio can be effectively reduced. The device has a certain ability to resist the deviation, which reduces the difficulties in fabricating it. The experiment results agree with the theoretical analysis well. The interleaver designed by the proposed approach has favorable performance, which has the potential application value in optical fiber communication system.

A 2-GHz discrete-spectrum waveband-division microscopic imaging system

Limited by dispersion-induced pulse overlap, the frame rate of serial time-encoded amplified microscopy is confined to the megahertz range. Replacing the ultra-short mode-locked pulse laser by a multi-wavelength source, based on waveband-division technique, a serial time stretch microscopic imaging system with a line scan rate of in the gigahertz range is proposed and experimentally demonstrated. In this study, we present a surface scanning imaging system with a record line scan rate of 2GHz and 15 pixels. Using a rectangular spectrum and a sufficiently large wavelength spacing for waveband-division, the resulting 2D image is achieved with good quality. Such a superfast imaging system increases the single-shot temporal resolution towards the sub-nanosecond regime.

Mode-Locked Soliton Fiber Laser Using an Intracavity Polarization Maintaining Photonics Crystal Fiber

A passively mode-locked soliton fiber laser assisted with an interference filter is proposed and experimentally demonstrated. Self-started mode-locked soliton generation is based on the nonlinear polarization evolution (NPE). Of which, a polarization maintaining photonics crystal fiber (PM-PCF) is incorporated as an interference filter with tunable transmission bandwidth by controlling length of PM-PCF. In the experiment, we achieve a clean spectrum of dissipative soliton (DS) without sidebands, and a corresponding repetition rate of 6.554 MHz. Further adjusting the intracavity polarization with two polarization controllers (PCs) can transform the conventional DS to a vector DS with a rectangular spectrum. It is seen that the soliton operation regime can be dynamically managed by controlling the intracavity polarizations and net birefringence.

Experimental Demonstration of 429.96-Gb/s OFDM/OQAM–64QAM Over 400-km SSMF Transmission Within a 50-GHz Grid

We experimentally demonstrate a 429.96-Gb/s signal transmission over a 400-km standard single-mode fiber within the 50-GHz grid and successfully achieve spectral efficiency as high as 8.63 bit/s/Hz. Orthogonal frequency-division multiplexing/offset quadrature amplitude modulation with 64-quadrature amplitude modulation is selected as the modulation format to provide a “perfect” rectangular spectrum that efficiently reduces the channel crosstalk. No timing or frequency alignment is required for the subbands to form the superchannel.

Flexible Nyquist Pulse Sequence Generation With Variable Bandwidth and Repetition Rate

The rectangular spectrum of sinc-shaped Nyquist pulses enables the encoding of data in a minimum spectral width. Sinc pulses can improve optical sampling devices, could enable the implementation of ideal rectangular microwave photonics filters, and can be used for all-optical signal processing, spectroscopy, and light storage. Recently, the generation of sinc-pulse sequences with extraordinary quality was shown by the utilization of cascaded modulators. However, the line width and repetition rate of the pulses is limited by the modulator bandwidth. Here, we present the nonrestricted generation of flexible Nyquist pulse sequences. Therefore, multiple single lines of a comb generator are extracted with optical filters and subsequently processed by cascaded modulators. In a first proof-of-concept experiment, we achieved almost ideally sinc-shaped Nyquist pulses with a bandwidth of 286 GHz, a pulse width of 3.5 ps, and a duty cycle of 2.2%. However, sinc-shaped Nyquist pulse sequences in the femtosecond range with terahertz bandwidths would be possible with the method.

Multi-Band-Stop Filter for Single-Photon Transport Based on a One-Dimensional Waveguide Side Coupled with Optical Cavities

A model of a multi-band-stop filter is proposed for single-photon transport, using a one-dimensional waveguide side coupled with a series of optical cavities. Its transmission behavior is theoretically studied by a real-space model Hamiltonian and is found to depend on cavity mode frequencies, cavity relative phases, as well as cavity number and the coupling strength between the waveguide and the optical cavities. With proper cavity-mode frequencies and relative phases, the proposed model shows multi-band-stop regions and a rectangular transmission spectrum. Based on these phenomena, optical filters with more than one band-stop regions are simulated with gold material in the THz and communication band.

Wideband LFM Signal Parameter Estimation Based on Compressed Sensing Theory

Compressed sensing (CS) theory breaks through the limitations of the traditional Nyquist sampling theorem, and accomplishes the compressed sampling and reconstruction of signals based on sparsity or compressibility. In this paper, CS theory is used to do the parameter estimation of wideband Linear Frequency Modulated (LFM) signal in order to decrease the sampling pressure. A novel method that reconstructs the edge information of the LFM spectrum based on wavelet transform and CS theory is proposed. On the basis that the wideband LFM signal has approximate rectangular spectrum, the wavelet-based edge detection is introduced to provide sparse representation for the signal spectrum. The edges of the spectrum can be reconstructed by the CS reconstruction algorithms. Consequently, the initial frequency and final frequency of wideband LFM signal can be estimated with high estimation precision. The effectiveness of the proposed method is confirmed with numerical simulation.

Observation of vector- and scalar-pulse in a nanotube-mode-locked fiber laser

We report the experimental observations of vector pulse trapping and scalar dissipative soliton in a compact nanotube-mode-locked all-fiber laser for the first time to our best knowledge. The vector pulse exhibits a smooth Gaussian spectral profile without any sidebands. Although two orthogonally polarized components of the vector pulse have different central wavelengths, they copropagate as a unit in the laser cavity with the same speed. The scalar dissipative soliton shows a rectangular spectrum with pulse duration of ~13 ps, and can be compressed to ~320 fs external to the cavity. This flexible laser provides stable, ultrashort vector- and scalar-pulsed sources, which is convenient and attractive for practical applications.

Single- and cross-channel nonlinear interference in the Gaussian Noise model with rectangular spectra

New semi-analytic formulas of the power spectral density (PSD) of single- and cross-channel nonlinear interference (NLI) in coherent optical links for which the Gaussian Noise (GN) model applies are presented. From the PSD, a new bound on cross-channel NLI power is obtained. The new formulas are useful to both quickly compute single- and cross-channel NLI power, and to test the accuracy of numerical routines that directly solve the double frequency integral in the GN reference formula.

Optical sinc-shaped Nyquist pulses of exceptional quality.

Sinc-shaped Nyquist pulses possess a rectangular spectrum, enabling data to be encoded in a minimum spectral bandwidth and satisfying by essence the Nyquist criterion of zero inter-symbol interference (ISI). This property makes them very attractive for communication systems since data transmission rates can be maximized while the bandwidth usage is minimized. However, most of the pulse-shaping methods reported so far have remained rather complex and none has led to ideal sinc pulses. Here a method to produce sinc-shaped Nyquist pulses of very high quality is proposed based on the direct synthesis of a rectangular-shaped and phase-locked frequency comb. The method is highly flexible and can be easily integrated in communication systems, potentially offering a substantial increase in data transmission rates. Further, the high quality and wide tunability of the reported sinc-shaped pulses can also bring benefits to many other fields, such as microwave photonics, light storage and all-optical sampling.

Bound state of dissipative solitons in a nanotube-mode-locked fiber laser

The bound state of dissipative solitons (DSs) in a nanotube-based erbium-doped fiber laser is observed experimentally for the first time to our best knowledge. The bound-state DSs exhibit a rectangular spectrum profile accompanied by high-contrast modulated fringes on the top. The pulse duration of DSs is estimated as ~3.6ps and the pulse–pulse separation is ~30ps. The propagation dynamics of the bound-state DSs are further investigated by utilizing single-mode fiber with different lengths. It is found that the pulses can be compressed to ~208fs and subsequently broadened linearly along the extracavity fiber, while the pu separation between the two bound-state DSs remains constant.

Multiwavelength generation based on a mode-locked fiber laser using carbon nanotube and fiber Fabry–Perot filter

In this paper, a novel and compact configuration of stable multiwavelength generation with a uniform wavelength interval is proposed for the first time to our knowledge. It employs a mode-locked fiber laser using a carbon nanotube and spectrum-slicing technique. A flat rectangular optical output spectrum is demonstrated by adjusting the dispersion value of the fiber-loop cavity and the pump power. With a fiber Fabry-Perot filter, 33 wavelengths with 0.2 nm spacing are obtained among the power uniformity of 2.3 dB. Moreover, the variations of output power at each wavelength are all less than 0.1 dB, which implies excellent stability of the whole structure.

Approximations for the Nonlinear Self-Channel Interference of Channels With Rectangular Spectra

The Gaussian noise (GN) model, in which the fiber nonlinearity is modeled as an additive GN process, has been recently shown in the literature to be accurate for uncompensated coherent systems. Nevertheless, it does not have an exact analytical solution requiring analytical approximations to be made. Herein, we propose a new means of approximating the nonlinear self-channel interference (SCI) in the GN model, for the case of ideal Nyquist WDM channels that have rectangular spectra, bandlimited to the Nyquist bandwidth. We begin by introducing the method to estimate the peak power spectral density of the nonlinear interference before applying it to calculating the total SCI noise of a channel. The analytical solution is compared with the previously reported approximation and the exact numerical solution, to quantify the approximation error. The proposed approximation is accurate to within 0.3 dB of the GN model as the symbol rate is varied from 10 to 100 GBd. Finally, we demonstrate that for a superchannel, the total nonlinear interference for the central channel can be approximated to within 0.3 dB for three or more channels.

Joint digital signal processing for superchannel coherent optical communication systems

Ultra-high-speed optical communication systems which can support ≥ 1Tb/s per channel transmission will soon be required to meet the increasing capacity demand. However, 1Tb/s over a single carrier requires either or both a high-level modulation format (i.e. 1024QAM) and a high baud rate. Alternatively, grouping a number of tightly spaced "sub-carriers" to form a terabit superchannel increases channel capacity while minimizing the need for high-level modulation formats and high baud rate, which may allow existing formats, baud rate and components to be exploited. In ideal Nyquist-WDM superchannel systems, optical subcarriers with rectangular spectra are tightly packed at a channel spacing equal to the baud rate, thus achieving the Nyquist bandwidth limit. However, in practical Nyquist-WDM systems, precise electrical or optical control of channel spectra is required to avoid strong inter-channel interference (ICI). Here, we propose and demonstrate a new "super receiver" architecture for practical Nyquist-WDM systems, which jointly detects and demodulates multiple channels simultaneously and mitigates the penalties associated with the limitations of generating ideal Nyquist-WDM spectra. Our receiver-side solution relaxes the filter requirements imposed on the transmitter. Two joint DSP algorithms are developed for linear ICI cancellation and joint carrier-phase recovery. Improved system performance is observed with both experimental and simulation data. Performance analysis under different system configurations is conducted to demonstrate the feasibility and robustness of the proposed joint DSP algorithms.

Positive and negative focal shifts of an apertured supercontinuum laser with rectangular spectrum

In this paper, diffraction of the supercontinuum beam from aperture and lens are described for the first time. We study the positive and negative focal shift effects of the supercontinuum laser on focusing system in detail. It is found that, apart from the conventional negative focal shift, the positive focal shift is also generated in the supercontinuum laser. The maximum intensity of the focused supercontinuum laser is shifted toward the lens with small truncated parameter. When the truncated parameter is large, however, the maximum intensity exceeded the focus of the central wavelength and the positive focal shift appears. The results also show that the maximum intensities are shifted away from the focus when the bandwidth of the supercontinuum laser increases in the two cases, but the shift direction is opposite.