This paper introduces a new way of two-dimensional wavefront reconstruction based on the Fourier modal method. Expending the target wavefront by using Fourier series, calculating the expansion coefficient based on the differential phase measured from the experiment, and fitting the coefficients at the missing points by averaging adjacent values, the target wavefront could be reconstructed eventually by using inverse Fourier transform on the expansion coefficients. The paper also introduces our numerical simulation study on the precisions of both the wavefront reconstruction under ideal situation and under the situation with simulated noise respectively. Corresponding verification experiment for the two-dimensional wavefront reconstruction based on the Fourier modal method is also done by using a two-grating lateral shearing interferometry system, with the 3D profile of the sample obtained.
A novel dispersion-compensation superstructure fiber Bragg grating (SFBG) based comb gain equalizer for fiber optical
parametric amplifier (FOPA) is proposed. It is characterized by its eight-channel 100GHz DWDM-channel separations
and 80 km dispersion compensation function. The object reflectivity spectra of gain equalizer are calculated in two parts
independently. Inner channel part for every channel is designed according to the gain spectrum of fiber OPA. Inter-channel
part is calculated with Gaussian hypergeometric function (-0.5dB bandwidth 0.1nm, -45dB bandwidth 0.3nm) to
obtain slower rising and descending edges than the simply zeroed case. Then the SFBG is designed with layer-peeling
inverse scattering technique. Simulation results show that this SFBG satisfies all requirements. Using this SFBG as
comb gain equalizer, the gain of fiber OPA is flattened in every channel to within ±0.4dB among 8 ITU-T regulated
channels, with 80 km dispersion compensated.
Widely tunable All-optical wavelength conversion between picoseconds pulses based on Four-wave mixing is proposed
and experimentally demonstrated in cascaded highly nonlinear fiber. The signal pulse with 40-GHz repetition rate and
1.57-ps pulse width is adopted. The converted idler wavelength can be tuned continuously from 1540.6 to 1594.8 nm as
the CW laser wavelength is changed from 1514.5 to 1565.7 nm. No obvious changes of the pulse shape and width, also
no chirp are observed in the converted idler pulse.
Vector soliton is obtained in erbium-doped fiber laser via nonlinear polarization rotation techniques. In experiment, we
observe the every 4- and 7-pulse sinusoidal peak modulation. Temporal pulse sinusoidal peak modulation owes to
evolution behavior of vector solitons in multiple polarization states. The polarizer in the laser modulates the mode-locked
pulses with different polarization states into periodical pulse train intensities modulation. Moreover, the
increasing pumping power lead to the appearance of the harmonic pulses and change the equivalent beat length to
accelerate the polarization rotation. When the laser cavity length is the n-th multiple ratios to the beat length to maintain
the mode-locking, the mode-locked vector soliton is in n-th multiple polarization states, exhibiting every n-pulse
sinusoidal peak modulation.
This paper presented a bicubic uniform B-spline wavefront fitting technology to figure out the analytical expression for object wavefront used in Computer-Generated Holograms (CGHs). In many cases, to decrease the difficulty of optical processing, off-axis CGHs rather than complex aspherical surface elements are used in modern advanced military optical systems. In order to design and fabricate off-axis CGH, we have to fit out the analytical expression for object wavefront. Zernike Polynomial is competent for fitting wavefront of centrosymmetric optical systems, but not for axisymmetrical optical systems. Although adopting high-degree polynomials fitting method would achieve higher fitting precision in all fitting nodes, the greatest shortcoming of this method is that any departure from the fitting nodes would result in great fitting error, which is so-called pulsation phenomenon. Furthermore, high-degree polynomials fitting method would increase the calculation time in coding computer-generated hologram and solving basic equation. Basing on the basis function of cubic uniform B-spline and the character mesh of bicubic uniform B-spline wavefront, bicubic uniform B-spline wavefront are described as the product of a series of matrices. Employing standard MATLAB routines, four kinds of different analytical expressions for object wavefront are fitted out by bicubic uniform B-spline as well as high-degree polynomials. Calculation results indicate that, compared with high-degree polynomials, bicubic uniform B-spline is a more competitive method to fit out the analytical expression for object wavefront used in off-axis CGH, for its higher fitting precision and C2 continuity.
Taking into account pump depletion, numerical simulations have been undertaken to investigate the amplification of strong optical signal pulses in fiber optical parametric amplifiers (FOPAs). It is shown that a strong signal pulse experiences not only amplitude amplifying and temporal width broadening but also pulse splitting processes, which never be addressed in the FOPA studies. The pulse splitting phenomenon that the underlying mechanism is attributed to four-wave mixing, is explained intuitively by employing concept of signal gain saturation and optimum fiber length. Further calculations indicate that this phenomenon appears repeatedly as fiber length increased. Another interesting result is that a sub-pulse formed in the pulse splitting process is compressed by a factor of 9 and amplified by 19 times after evolution in FOPA for 2000m, compared with the incident Gaussian pulse. It indicates that there are potential applications of pulse splitting phenomenon in pulse compression, signal sampling and time-division multiplex system.
On amplifying of picosecond pulses in fiber optical parametric amplifiers, group-velocity dispersion (GVD) and third-order dispersion (TOD) effects are numerically investigated. It comes to two very interesting results. One is that GVD of the signal (idler) induces obviously the idler (signal) pulse broadening even though GVD of the idler (signal) is zeroed. The other is: on condition that signs of TOD coefficients for signal and idler are quite the contrary, TOD would lead to two oscillatory structures respectively near the trailing edge and the leading edge, rather than conventional one oscillatory structure. In conclusion, any dispersion-induced modifying of the signal (idler) pulse shape will be coupled to the idler (signal) and result in corresponding modifying of the idler (signal) pulse shape. It is extremely helpful for further experimental study.
Nonlinear optical pulses with sub-picosecond width will exhibit the phenomena of timing jitter and pulse decay induced by the third-order dispersion and Raman self-frequency shift. The optical phase conjugation is proposed to compensate for the high-order dispersion and high-order nonlinear effect. However, the spectral phase conjugation can’t eliminate the time delay induced by Raman self-frequency shift and the temporal phase conjugation can’t avoid the pulse splitting into two pieces induced by the third order dispersion. Thus, the schemes of the combination of the spectral and temporal phase conjugation are supposed to use for recovering the distorted pulse and reducing the time delay induced by the third-order dispersion and Raman self-frequency shift. There exist the optimized schemes to deploy the relative position between the spectral phase conjugator and the temporal phase conjugator to obtain the optimization transmission qualities with the minimum penalty for timing jitter and pulse distortion. In addition, the spectral phase conjugator and temporal phase conjugator should be settled down after the midway and before the midway, respectively, in order to obtain the residual third-order dispersion to enhance the frequency red-shift trend of two polarization components after the temporal phase conjugator for reducing the time delay.
A novel superstructure fiber Bragg grating (SFBG) based comb gain equalizer for fiber optical parametric amplifier (OPA) is proposed. This gain equalizer is characterized by its comb reflectivity spectrum. It can have two functions at least, one is flattening the gain in multi ITU-T regulated channels, the other is it can be used as multi-channel isolation filters taking full advantage of its comb reflectivity spectrum. In addition it can be dispersionless or have dispersion compensation function. A one-bump fiber OPA, 30dB bandwidth >15nm, is designed with one of its peak gains (41dB) located at the center of work wavelengths in a 16-channel 100GHz spaced WDM optical transmission system according to corresponding Chinese criterion (1548.51nm~ 1560.61nm). The object reflectivity spectra of gain equalizer are calculated in two parts independently. Inner channel part for every channel is designed according to the gain spectrum of fiber OPA. As a comb filter, its inter-channel part reflectivities are the smaller the better. But inter-channel part reflectivities can not be simply zeroed, for which would result in the rising and descending edges of reflectivity spectrum being too sharp to be performed by any filter. To split the difference, inter-channel part reflectivities are calculated with Gaussian hypergeometric function (-0.5dB bandwidth 0.1nm, -45dB bandwidth 0.3nm) to obtain slower rising and descending edges than the simply zeroed case, which is very necessary and important to be sure the object reflectivity spectrum not only has sharp enough edges to take the shape of comb but also is physically realizable. Adopting channel-by-channel windowing method to apodize the object reflectivity spectrum, a superstructure fiber Bragg grating is designed with lay-peeling inverse scattering technique. At last, according to the coupling coefficient calculated, reflection spectrum and group time delay are analyzed based on the method of transformation matrix. Calculation results show that this SFBG satisfies all requirements. Further calculation results show that, using this SFBG as comb gain equalizer, the gain of fiber OPA is flattened in every channel to within ±0.4dB among 16 channels, with channel isolation high up to -35dB. It needs to point out that this method can also be used to design gain equalizer for other optical amplifiers.
A novel 16-channel comb filter based on superstructure fiber Bragg grating (SFBG) is proposed for the first time. It is characterized by single-grating structure, equal reflectivity peaks, narrow channel bandwidth, flat-top, high bandwidth utilization ratio, standard 50 GHz channel-spacing, and realizing dispersion compensation and wavelength filtration simultaneously. Based on ameliorated layer-peeling algorithm, that is adopting channel-by-channel windowing method rather than all-channel integral windowing method, this novel SFBG is synthesized successfully. According to the grating structure of the synthesized SFBG, reflectivity spectrum, group delay and group delay ripper are analyzed based on the method of transfer matrix. The results show this SFBG does an almost perfect job of reproducing the desired spectrum.
With the increasing availability of high output power EDFA as well as the development of highly nonlinear fibers, more and more fiber optical parametric amplifiers are operated near or in the saturated-gain region rather than small-signal gain region, where the signal gain characteristics are expected to be different from those in the linear-gain region. For the first time, two very pithy and powerful analytical expressions for saturated signal gain and signal output power of fiber optical parametric amplifiers are educed with numerical analysis. Those are realized in three steps, first, a series of numerical values are worked out by numerically solving the couple NLS equations that governed the fiber parameter process. Then the function form for saturated signal gain is figured out by control variates method. At last, adopting least square method, three coefficients are finely obtained with the maximum relative error (in terms of calculated saturated signal gain with numerical integration) no more than 0.46%. At the same time, we worked out the analytical expression for saturated signal output power. From those expressions, we can safely come to a conclusion that saturated signal gain of fiber optical parametric amplifiers is related to pump and signal power while saturated signal output power only rely on pump power, but both have nothing to do with nonlinear coefficient and fiber length, which is quite different from small-signal gain but accord well with law of conservation of energy. Two expressions presented in this paper are very useful in designing and analyzing fiber optical parametric amplifiers. Results of this work agree well with existing experiment results.
An optical phase conjugator is used to enhance the robustness of optical pulses to polarization dispersion. The
polarization components of optical pulses form a breather in birefringent fibers firstly and make a polarization
component along fast axis compressed through spectra inversion function of the optical phase conjugator. The two
polarization modes are compressed further due to the cross-phase modulation effect and trap each other fully in time
domain. The optical phase conjugator is required to settle down before higher birefringent fibers in order to suppress the
influence of birefringence effectively. The limit value of δ reaches 7.5 that can be suppressed by enhanced robustness of
the optical pulses by using the optical phase conjugator in the case that each polarization component is a fundamental
soliton. Moreover, the function of the optical phase conjugator will reduce the delay of optical pulses for a different
polarization angle.
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