A Review onNon linearity in optical fiber due to Self-phase modulation
ShafaqMehmood, AshiqHussain
University College Of Engineering And Technology
Islamia University Bahawalpur, Pakistan
1
Abstract:
Nonlinear effects are just a consequence of increasing need for high data rates, number of wavelengths, transmission lengths and optical power levels.Nonlinear effects can be minimized using suitable optical fiber although there are many techniques mention in this paper which are using now a days.Highly Accurate Compensation Technique for 10-GHz Pulse Intensity Fluctuation is one of the best techniques.
Keywords: Kerr effect, Nonlinear effects,Nonlinear photonics, Optical telecommunication
Introduction:
Self-phase modulation (SPM) is a nonlinear optical effect of light-matter interaction. Due to the optical Kerr effect an ultra-short pulse of light when travelling in theoptical fiber will induce a changingrefractive index of the medium. Due to this variation in refractive index will yield a phase shift in the pulse, leading to a change of the pulse's frequency spectrum[1]. In long-haul light wave transmission systemswith the increased demand for capacity, the selection of a suitable optical modulation format is a key issue to confirm the optimum system performance. Self-phase modulation (SPM) is one of the main nonlinear degradation effects in optical amplified systems, specifically when the per-channel data rate is higher than 10 Gb/s.[2] SPM-induced phase modulation is proportional to the Kerr-effect nonlinearity in the fiber and through accumulated chromatic dispersion this phase modulation is changed into intensity modulation. Bydecreasing the efficiency of PM/AM conversion dispersion compensation may decrease the impact of SPM, but it cannot be remove completely [3].If the amplitude of a phase-modulated optical signal is constant before transmission,chromatic dispersion is caused by fiberamplitude modulation.Due to which self-phase modulation (SPM) is induced. In optical heterodyne detection, SPM cannot be compensated by the delay equalizer (electrical domain) used to compensate fiber chromatic dispersion. However,in the presence of SPM the transmission distance restriction of multi-repeated coherent transmission systems has not been examined. When a phase/frequency modulated optical signal at the wavelength of 1.55 pm is transferred through a conventional single-mode (SM) fiber, changes in the phase and frequency are converted to adjustment of the signals' amplitude, which then modulates the refractive index of the fiber. This self-phase modulation (SPM) lowers the receiver sensitivity. This mechanism severely degrades system performance irrespective of
the number of optical amplifiers At high bit rates exceeding 10 Gb/s.[4]
1
Nonlinearity & SPM due to high data rate:
For error free detection at high data rate systems howeverrequire larger received power. As peak powers of input approach 10 mw and data rates beat 10 Gb/s, self-phase modulation (SPM), which is caused by the nonlinear dependence ofthe refractive index on intensity. At 50 Gb/s data rates the modulation bandwidth is so large, that even for an ideal source without phase noise, fiber dispersion broadens the optical pulses and limitstransmission. The deadly influence of linear fiber dispersion may be minimized by operating at the minimum group velocity dispersion (GVD) wavelengthdispersion is not eliminated completely. Asthe fiber-input poweramplified beyond approximately 5mWfor very high-bit rate systems, the fiber cannot be assumed to behave as a linear transmission medium. The nonlinear Kerr effect also needs to be included in a more accurate model [5].It can be defined by the nonlinear dependence of the effective fiber refractive index n on intensity Ias
------(1)
Whereno(w)is the linear index of refraction, and n2is the Kerr coefficient which is approximately 3.2 X cm/W in silica fibers.[6]The propagation constant β (, I ) depends on n (, I ) as
------(2)
The propagation constant changes in timewhen the intensity I ( t ) is modulated. The “instantaneous” optical frequency dw/dtis related to thepropagation constant’s time derivative thus new frequency components are caused due to the intensity variation of the pulse.The interaction of nonlinear SPM and linear GVD,depending on the sign of the dispersionproduces different things on the temporal pulse profile. In the positive dispersion region (i.e., X < Xo), a pulse develops a linear frequency chirp, and the pulse broadens temporally. The pulse broadening can be compensated by a negative dispersive delay line, such as a grating pair [7].The positive chirp of the SPM and the negative dispersion cancel in the negative dispersion wavelength region (i.e., A>Xo). They can be made to compensate exactly if the input power is accurately adjusted to the pulse widthand to thefiber dispersion.
Performance improvement using SPM:
The use of dispersion compensating fibers (DCF’s) has now appeared as the most practical technique to compensate for the chromatic dispersion in the long-haul, optically amplifiedstandard fiber transmission systems. [8]
The fiber nonlinearities and dispersion has become the main problem in extending the high-speed transmission distance, long haul standard fiber transmission systems. Among the many methods reported [9]-[13],to compensate chromatic dispersion the use of DCF’s has been emerging as the most practical technique due to its constancy over temperature and wide-band dispersion compensating characteristics. So far, it has been believed that the SPM in the DCF degrades the system performance although the SPM in the standard fiber enhances the performance by compressing the pulse. For this reason, the importance of launching a short power into the DCF in order to reduce the SPM effect in the DCF and to operate the DCF in the linear regime[14]-[21]. The system configuration that we considered is a 120-km standard fiber transmission system with a DCF at the receiver. The total dispersion of the standard fiber was D ~ M=F +2131 ps/nm at the 1557 nm wavelength. The transmitter was a DFB-laser externally modulated by a zero-chirp LiNb03 modulator with NRZ (non-return to zero), 223- 1 PRBS data. To conquer stimulated Brillouin scattering (SBS) the DFB-laser was dithered [ 22]. The power booster was a two-stage EDFA pumped with two 1480-nm pump lasers. The amplifiers at the receiver were 980-nm double pumped dual stage EDFA’s with a noise figure of 4 dB. The receiver/regenerator consisted of a PIN-HEMT front end and an AGC with a total bandwidth of 8.5 GHz, clock and data recovery circuitry and a decision circuit. We first calculated the signal spectrum at the transmitter,standard fiberat the output of the 120 km and after the DCF to show the spectral broadening by the SPM in the standard fiber and the subsequent spectral compression due to the SPM in the DCF.
SPM based reshaping in receiver:
Dispersion tolerance improvement through self-phase modulation-based all-optical reshaping in receiver was experimentally explored using 10-Gb/s return-to-zero signal. This scheme is quite effective to return the optical signal deformed due to chromatic dispersion.[23]
For high bit rate optical communication systems all optical reshaping is an attractive technology, where the signal waveform is easily damaged by unavoidable dispersion and nonlinearity of the transmission fiber. Among these schemes, a technique based on self-phase modulation (SPM) in a nonlinear medium with optical band pass filtering [24] is one of the simplest ways to provide such functionality. Furthermore, this method has benefits of polarization insensitivity andbit-rate transparency. However, the effectiveness of this method to the signal the waveform, which is damaged due to chromatic dispersion, has not yet been investigated, although the dispersion tolerance is very tight in such high bit rate wavelength-division-multiplexing (WDM) transmission systems [25].
Fig.1 experimental setup.[26]
In the transmitter, the light from a continuous-wave (CW) distributed feedback laser diode (DFB-LD) oscillating at 1554.5 nm was fed into two LiNbO Mach–Zehnder modulators connected in cascade for RZ-formatting and data coding with a 9.953-Gb/s, pseudorandom binary sequence. To simulate the signal degradation due to dispersion compensation error, the chromatic dispersion fluctuating from 50 to 200ps/nm was applied to the signal using several lengths of dispersion compensating fiber (DCF) at the output of the transmitter. In the reshaping part, SAOR in a 5-km-long high-nonlinear dispersion-shifted fiber (HNL-DSF) was used. The zero dispersion wavelength and dispersion slope of the HNL-DSF were 1554.5 nm and 0.04 ps/nm2 /km, respectively. With a high-power erbium-doped fiber amplifier (EDFA), the input power to the HNL-DSF was boosted to 20 24 dBm, which was optimized in order to obtain the best performance for various applied dispersion. An optical bandpass filter (OBPF) with a 3-dB bandwidth of 0.28 nm was placed at the output of the HNL-DSF to slice the signal spectrum broadened due to the SPM effect in the HNL-DSF.
Optical phase conjugation technique:
In optical fiber communicationsoptical phase conjugation (OPC) is a promising technique to compensate the nonlinear damage [27].Compensation for nonlinearity by OPC is limited by the asymmetry of the strength of the Kerr effect along the fiber with respect to the OPC position [28],[29]. In order to defeat the nonlinearity impairments to a large extent, the system parameters of an OPC link, need be optimized. When proposing a novel design of OPC link it is necessary to predict the nonlinearity-compensation efficiency of the new link. Generally, optimization of an OPC link or evaluation of nonlinear impairment depends on numerical simulation, which is time consuming and shortages physical insight. Thus, fast approaches for first-order system design are required.Minzioniet al. presented two simple techniques to design OPC systems [30]–[32]. The two methods are powerful for designing intrachannel cross-phase modulation/four wave mixing (IXPM/IFWM) compensation systems; however they have certain restriction for the design of self-phase-modulation (SPM)-limited systems. This is due to the superior character of SPM, i.e., the SPM-induced chirp can compress signal pulse combined with chromatic dispersion [33]. Thus, SPMcan assist signal transmission in some cases. It was found that, for SPM-limited systems, net residual dispersion (NRD) can improve the system presentation significantly[34].An equivalent principle is suggested, through which almost all the analytical models of conventional transmission systems proposed in the literature can be extended to OPC systems. This analytical method raises system performance taking advantage of the fiber nonlinearity while the method [29]–[30] is studiedto compensate nonlinearities. This is the main difference between the optimization methods for SPM-limited systems and those for IXPM/IFWM-limited systems.Considering an electric field transmission along a fiber with attenuation or gain α(z), group velocity dispersion (GVD) β2(z), and nonlinear coefficient γ(z) , the propagation of the amplitude envelope A(z, t) follows the nonlinear Schrödinger equation[31].
[]A=0---(3)
Taking the complex conjugate of (3) yields
[+(-γ(z))|A*|2]A*=0---(4)
Comparing (3) and (4) shows that the transmission of along a fiber with α(z),β(z), and γ(z) is equivalent to the propagation of its complex conjugate A*(z,t)along a hypothetic fiber with α(z),-β(z)and -γ(z). Therefore, in OPC links, the phase conjugated signal transmitting along the fiber link after OPC is equivalent to the original signal propagating along a fiber link with the same attenuation/gain, negative GVDand negative nonlinear coefficient, and then taking the conjugate of the output. In the following text, that is called “equivalent principle.”The analytical model to optimize the dispersion of SPM-limited dispersion managed systems.
Fig. 2 (a) system setup for general OPC link and (b) the corresponding dispersion map.[35]
Combining this model with the equivalent principle one can obtain the single-pulse broadening factor for OPC systems, where and are the rms widths of the output and input pulse, respectively.
------(5)
Where ------(6)
R=the amount of NRD-----(7)
c=(8)
d=------(9)
------(10)
N(z)=, G(x)=, Lois the length of whole link Po and To are the peak power and width of input pulse, respectively.bo,b2,
a0,a41 and a42are coefficients onlydepending on the input signal pulse. [27]
Optical Signal Processing by Phase Modulation:
Optical signal processing based on optical phase modulation and subsequent optical filtering, which is appropriate to 160-Gb/s optical time-division multiplexed (OTDM) subsystems. When an optical pulse passes over a nonlinear optical fiber ultrafast phase modulation of an optical signal is done by self-phase modulation (SPM) and cross-phase modulation (XPM). Such phase modulation brings the spectral shift of the signal in optical fiber. Many types of optical signal processing are realized simply by filtering out the spectral-shifted component. Using SPM-based pulse reshaping in a 500-m-long silica-based highly nonlinear fiber (HNLF).[36]
An incoming optical signal is phase modulatedthe spectral component frequency shifted by such phase modulation is filtered out with a band pass filter (BPF). The phase modulation in optical signal can be done through the following procedures: 1) SPM, which is the phase shift dependent on the strength of the incoming optical signal itself; 2) XPM, which is the phase shift caused by the power of another optical signal; and 3) electro optic modulation (EOM), which is the phase shift induced by the electrical RF signal.
In the SPM-based scheme, an RZ data signal is phase modulated by its own strength waveform, while the signal transmits through a nonlinear fiber. The temporal phase variation induces the instantaneous frequency shift; the intensity slope point of the incoming signal is spectrally shifted and broadening the signal spectrum. If we remove the spectral-shifted components by BPF, the intensity slope point of the original signal is selected. Such SPM-based signal processing provides us with the pulse reshaping function [37]–[39]. When the input signal with a base is incident on the nonlinear fiber, the pedestal component does not induce the spectral shift the main pulse component is frequency shifted. Therefore, as far as we filter out the broadened spectrum at off-center wavelengths, we can remove the pedestal component.
There are some requirements for the frequency shift
------(11)
Where in the 160-Gb/s system, we require when N=1.In the case of SPM, we can express the frequency shiftinduced by the maximum slope of the temporal phase variation as
------(12)
Where Po is peak power L and are the length and the nonlinear coefficient of the optical fiber, respectively. Using eq. 11 & 12we obtain the requirement for Po , and L as
------(13)
Where we assume N = 1 since the bit rate of the processed signal is usually the same as that of the incoming signal in the SPM-based signal processing.
Dispersion compensation of SPM impairment in optical channel:
In high power optical channels self-phase modulation (SPM) forces spectral broadening distortions. Consequently over sampling beyond the bitrate is proposed according to Nyquist theorem. Here received signal over sampling collected with maximum likelihood sequence equalizer is demonstrated, indicating of significant enhancement of inter-symbol-interference mitigation due to SPM.[40]
The maximum likelihood sequence estimation (MLSE) has provide increased acceptance to chromatic dispersion (CD) in optical links up to 250 km [41] of Standard Single Mode Fiber (SSMF). MLSE performance was studied in the occurrence of nonlinear effects. [42]-[44]. This standard MLSE method, does not take into account the spectral broadening of the SPM-induced signal, therefore is created on one sample per bit. An extended MLSE approach based on increasing the number of Samples Per Bit (SPB) according to the SPMinduced spectral broadening. Consequently, a vectorial MLSE (VMLSE) is introduced. Considering Nyquist sampling theorem the increase of the MLSE performance along with the increase of the SPB is enabled by passing a wider portion of the electronic bandwidth of the received analog signal prior to the sampler. This is attained by increasing the photodiode's Bandwidth. A very popular and useful way of the MLSE implementation is the Viterbi algorithm [45] that maximizes the conditionalpdf. In the VMLSE, the metric is simply calculated by the sum of the log functions of the conditional pdf of all of the samples of each bit, thus assuming that the samples (in the bit) conditional pdfs are independent. The metric is calculated as follows
------(14)
Wherep(r/s) is the conditional pdf, I is the number of SPB, Rsis the sample rate, Rbis the bit rate, K is the bitsequence length. S(m) is the possible transmitted sequence of bits out of the 2k possible sequences. The rk= [rk,1 …..rk,I] is the sample vector of the k's bit. As noted above it is assumed that the samples in the bit are independent.
Highly Accurate Compensation Technique for 10-GHz Pulse Intensity Fluctuation:
Optical non-linear effects are highly affected by input peak power intensity fluctuation is a serious matter for the all-optical signal processing in communication networks. To compensate for the fluctuation, optical limiter is used because it can output the same intensities for input intensities over a threshold value. Thus far, a lot of optical limiters that utilize saturation properties of some transfer functions of nonlinear phenomena have been proposed. An optical limiter based on such saturation properties can reduce the intensity fluctuation, but not sufficiently. To decrease the residual output intensity fluctuation, the optical limiter must be used continually.The optical intensity is decreased due to the repeated system,several optical amplifiers arerequired. In a large network, the physical broadcast topology must have a minimum number of optical amplifiers to reduce cost and power consumption [47].