Yuriy Zachinyaev, Konstantin Rumyancev, Aleksandr Ermolaev

Yuriy Zachinyaev, Konstantin Rumyancev, Aleksandr Ermolaev

Southern Federal University, Russia

Evaluation Of Dispersion And Non-linear Effects Influence On The Properties Of

The Fiber-optic Based Chirp Signal Shaper

The applications of complex frequency modulated radio signals have been considerably extended for last decades. In the areas connected with a high speed processing of the information and not requiring a long-range coverage of devices the most expedient use is seen by applying short broadband linear-frequency modulated (LFM) or chirp signals [1].

Impossibility of traditional methods for high-speed shaping and processing of broadband radio signals including LFM radio signals leads to the necessity of using the optical processing methods of the information, among them the application of an optical fiber (ОF) for these purposes [2, 3]. Thus, an actual challenge is to develop and analyze the nanosecond frequency-modulated radio signal shaper using fiber optics and the characteristics of such a device is also to be analyzed. Prospects of using fiber optics for shaping the linear frequency modulated signals (LFM) are determined earlier [1] and also the device circuit design has been synthesized. The problems related to the ОF properties influence on the device functions are however not analyzed.

The method of shaping chirp signals based on the binary fiber-optical structures (BFOS), analyzed in [1], involves a source of picosecond duration optical pulses, a fiber-optic splitter with outputs, the fiber-optic delay lines, a fiber-optic connector (FOС) having input, an optical amplifier (OA), a receiver optical module (ROM), a band-pass filter (BPF), an electronic amplifier (EA) and a low-pass filter (L-PF). The block diagram of the shaper of LFM-signals based on the the binary fiber-optical structures is shown on Fig. 1.

Fig. 1

The binary fiber-optical structure (Fig. 2) consists of the Q splitting directional fiber-optics couplers of the Y-type, the Q summing-up directional fiber-optics couplers of the Y-type, the Q additional fiber-optic delay lines with a delay time

τ_{delay ij} = 2 ^{j - 1} τ_{delay i1},

where the j is the number of an additional fiber-optic delay line.

Fig. 2

The design features of the binary fiber-optical structures are determined with the parameters of a shaped LFM-signal such as an initial frequency, a frequency modulation rate and a pulse width and are analyzed in literature [4].

The impulse pack generated by the binary fiber-optical structures and integrated with the fiber-optic connector is then amplified and supplied to the receiver optical module for transducing optical radiation into an electric signal. The generated signal is supplied to the band pass filter to separate a chirp signal spectrum and amplified with the electronic amplifier.

While analyzing the possibility of shaping the fiber-optic based chirp signals the limiting values of the central frequency [4], deviation and duration of a formed chirp were obtained depending on the values of the process tolerance in manufacturing optical delay lines. They are shown in Table 1.

Table 1

Parameter	The parameter values of the process tolerance on accuracy of manufacturing the fiber-optic delay lines
Parameter	1 mm	0.1 mm
The central frequency of chirp, GHz	10	10
Spectrum width of chirp, GHz	5.65	6.6
Chirp pulse width, ns	2.28	181.8

Since the quality of chirp signal shaping directly depends on the optical fiber parameters the research of the influence of phenomena and factors typical for fiber optics on the shaper functioning is actual. The article goal is to evaluate the influence of the physical factors on the properties of the fiber-optic based LFM-shaper and to determine the operating conditions of the device taking into account the optical fiber features.

As known, a major factor restricting a frequency range of the input signal supplied into the binary fiber-optical structure while forming the copies and hence in the fiber-optic based shaper of the chirp signals is the optical fiber dispersion at which various frequency components of a transmitted signal are propagated within the optical fiber at a different speed. The dispersion restricts a communication range and the upper frequency of the transmitted signals due to the "washing-out" the pulses what can lead to the pulse overlapping with time.

Since a single-mode optical fiber is used in the chirp signal shaper based on the binary fiber-optical structures the chromatic dispersion [5] is predominating. It is caused with a difference of the rates of propagating the frequency components within the mode. For the characteristic of a chromatic dispersion the value of the specific chromatic dispersion measured in ps/(nm∙km) is usually used.

To evaluate the influence extent of a chromatic dispersion on the signal form the parameter of the dispersive length determined with the formula brought into use [6]

, (1)

where the is an initial duration of the transmitted pulse by the source of optical pulses, is a parameter of the dispersion of a group velocity.

The physical sense of the dispersive length consists in the following: the optical pulse of the Gaussian form of the initial duration after passing a fiber with a length of and havingthe parameter of the dispersion of a group velocity will have a duration , where .

From the formula (1) it follows that the shorter pulses used - the less dispersive length and the distincter dispersion influence on the signal form will be expressed. The conclusion was drawn that the dispersion can be neglected, if the , because in this case .

The formula (1) however is valid for a monochrome optical source. For a optical source having a frequency spectrum width , the initial pulse duration and a parameter of the dispersion of a group velocity the dispersive length can be determined with the formula

. (2)

If a maximum distance with that it is possible to neglect the dispersion influence, and one can accept it is equal to 0.1, the pulse duration after passing a fiber of the extent expressed through the initial pulse duration amounts to and a relative "broadening" of a pulse does not exceed 0.5 % [7].

Let's calculate the values of the dispersive length for various types of the single-mode optical fiber and the values of the duration . We consider therewith that

, (3)

where the is the maximum frequency of a chirp signal being shaped [6].

For determining the limiting values of the optical pulse source pulse width and the length of the optical fiber in the device that are necessary to analyze the phenomena of the dispersion in the chirp signal shaper based on the binary fiber-optical structures, we will use the data from Table 1.

The minimum possible value of the optical source pulse width can be formulated taking into account the expression (3)

In this case, the greatest possible value of the optical fiber length is determined with a maximum number of the optical pulse copies formed by the binary fiber-optical structure:

Considering the above-stated data the minimum possible values of the input pulse duration of = 38 ps and the length of the OF = 37 m are provided.

The value calculation results of the dispersive length according to the formula (2) for various types of the optical fiber and the pulse width are shown in Table 2.

Table 2

The value of the dispersive length in km and for the pulse width
Type of an optical fiber	=38 ps	=50 ps	=100 ps
63	109	437
1130	1960	7870
283	490	1960

A dependence of the dispersive length on the pulse width and the type of the optical fiber in a graphical form is presented in Fig. 3.

Fig. 4

It can be seen in Table 2 and Fig. 4 that the values of the dispersive length for various types of the OF slightly differs and exceeds 63 km if the pulse width is above 38 ps.

Taking into account the value of the maximum length of the OF in the chirp signal shaper based on the binary fiber-optical structures (the length of the fiber-optic delay line, connecting the output of the binary fiber-optical structures and the optical coupler), it is possible to conclude that the magnitude of is valid for any type of the OF what allows one not to take into account the chromatic dispersion effect while considering the properties of the chirp signal shaper based on the binary fiber-optical structures. Besides, with a view of device reduction in price it is expedient to use the SF type optical fiber.

While making use of the single-mode fibers having a small value of a chromatic dispersion and lasers having a narrow spectral emission band it is necessary to consider a polarization modal dispersion (PMD).

The specific dispersion factor is rated to 1 km and has dimensions of ps/, and the time-average differential group delay between two orthogonal polarization states of Δτ_PMDgrows together with a distance growth under the law as follows:

Δτ_PMD= T_D.

The typical value of the specific PMD for individual single-mode fibers having a step profile of the refractive index change amounts to not more than 0.02 ps/ on the 1550 nm wavelength [5]. Hence, for the chirp signal shaper based on the BFOS in that the great number of connections of the individual fibers is carried out, it is necessary to take into account consider the PDM of an extended line (a root-mean-square PDM for the connected fibers). This parameter is used for calculating a statistical upper limit of the PDM in all communication lines. The typical value of the specific PDM of the extended line for a single-mode fiber amounts to 0.2 … 1.0 ps/.

Because of a small value of the PDM magnitude it can manifested itself exclusively in a single-mode fiber and when it is essential to transmit a signal having a very narrow spectral emission band (0,01 nm and less). In this case, the polarization modal dispersion becomes comparable with a chromatic dispersion.

The earlier designed maximum extent of the single-mode fiber having a dispersion SF, that is not displaced, and a minimum duration of an input signal at which a chromatic dispersion influence can be neglected, amounts to the order of 6,3 km (0.1 ·). As this takes place a time-average differential group delay between two orthogonal polarization states Δτ_PMDand with a typical value of the specific PDM of the extended line for the single-mode fiber of the given type = 0.4 ps/[7] amounts to

. (4)

The delay between two orthogonal polarization states calculated with the formula (4), amounts to the order of 3.6 % of the signal duration with input optical pulse width =38 ps. Taking into account the fact that the real maximum length of the optical fiber in the shaper does not exceed Z _max.OF= 37 m it is possible to draw a conclusion that with making use of the single-mode fiber having no displaced dispersion SF in a the binary fiber-optical structures, the polarized modal dispersion can be neglected.

By consideration a provision problem of a required pass-band of the chirp signal shaper based on the binary fiber-optical structures it is necessary to keep in mind the restrictions applied with the nonlinear phenomena in an optical fiber as well. Before to specify the conditions at the fulfillment of which the nonlinear phenomena in the optical fibers of the binary fiber-optical structures may be neglected, and it is necessary to classify the kinds of the nonlinear phenomena in the OF.

Two categories of the nonlinear phenomena [5] may be distinguished:

1. The phenomena associated with dependence of the refractive index of a fiber from the optical power. This category includes a mixture of four waves (FWM), phase self-modulation (SPM) and cross phase modulation (СРМ).

2. The phenomena associated with the effect of light wave dispersion in a fiber and caused with interacting of light waves with phonons (molecular vibration) in quartz medium. These phenomena are caused with the stimulated Brillouin scattering (SBS) and stimulated Raman (combinational) scattering (SRS).

The self-modulation (SPM) results from the fact that the refractive index of a fiber has a nonlinear power dependent component that causes a phase shift proportional to power of a pulse. For this reason, various components of a pulse undergo different phase displacements that can lead to changing a pulse form because of dispersion.

To evaluate this type of the phenomena the concept of nonlinear length [5] is introduced

where is an optical source operating wavelength, is an effective area of a fiber cross-section (as a rule for one-mоde OF =50 μm²), is a nonlinearity factor of the refractive index (for a quartz fiber =3.2∙10-8 μm²/W), - a peak power of an optical pulse, W.

The SPM influence on pulses can be neglected in that case when pulses are propagated to the distance.

The results of a nonlinear length calculating for various values of a optical pulse peak power of the quantum oscillator are shown in Table 3.

Table 3

, W	0.1	0.3	0.5	1	2	10
, m	3850	1285	770	385	193	39

Taking into consideration that the maximum length of the optical fiber is equal to=37 m in the shaper it is possible to ascertain that the self-modulation phenomenon in the chirp signal shaper based on the binary fiber-optical structures may be neglected if the peak power of an optical pulse does not exceed 1 W what is enough for the majority of applications.

The other nonlinear phenomena associated with the dependence of the refractive index of a fiber on the optical power (a mixture of four waves, FWM, and a cross phase modulation, СРМ), are characteristic only for the multi-signal systems and are do not manifested themselves in the chirp signal shaper based on the binary fiber-optical structures.

The stimulated Raman scattering (SRS is also characteristic only for multichannel systems and leads to an amplification of channels having a longer wave-length at the expense of decrease of the power of channels having a shorter wave-length and takes place with a wave-length separation of channels by the order of 100 nm [5].

With the stimulated Brillouin scattering (SBS) there is also an energy redistribution between the next signals. The acoustic phonons are however involved in this process, and the interacting occurs in very narrow frequency band of the order of 20 MHz. The given phenomena can be accompanied by high distortions within one channel as it creates an amplification in a direction to the radiation source oppositely directed to the signal propagation. As a result, the transmitted signal is decreased, and a potentially powerful signal directed back to the transmitter is generated. It is necessary to protect it making use of an optical insulator [8].

To calculate the threshold power P_thr the following approximate expression [5] is usually used

where is a coefficient of the SBS amplification, approximately equal to 4x10-11m/W, and does not depend on wave length, is an effective length of a fiber,is a frequency spectrum width of an optical signal source, is a frequency band of interacting with acoustic phonons (20 MHz).

Let us calculate the threshold power values with various values of the spectrum line width of the optical source defining a frequency spectrum width of an optical signal source at which the stimulated Brillouin scattering in the optical fiber can be neglected. The results of calculating are shown in Table 4.

Table 4

, nm	0.01	0.1	1	2	3	5
P_thr, W	0.082	0.821	8.2	16.4	24.6	41

It can be seen from Table 4 that the threshold power has the tolerable values to the practical applications with an operating wavelength = 1550 nm and a spectrum line width of radiation in the order of > 0.1 nm.

Generalizing the previously mentioned it is possible to conclude:

- the phenomena of the chromatic and polarized modal dispersions in the chirp shaper can be neglected since the value of the dispersive length with a operating wave-length of 1550 nm is much less than the maximum value of the length of the optical fiber in the shaper, and the differential group delay caused with the polarized modal dispersion is much less than the minimum pulse duration in the binary fiber-optical structure based chirp shaper;

- the nonlinear phenomena in the shaper of the binary fiber-optical structure based chirp shaper can be neglected since the value of dispersive length with a operating wave-length of 1550 nm is much less than the maximum value of the length of the optical fiber in the shaper, and a power of the optical oscillator (laser) does not exceed the threshold power when the nonlinear phenomena of the OF due to using the laser with a spectrum line width exceeding 0.1 nanometers.

Work performed under the state order of the Ministry of Education and Science of higher education in terms of scientific research. Theme № 213.01-11 / 2014-9.

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