Yuriy Zachinyaev, Konstantin Rumyancev, Aleksandr Ermolaev

Southern Federal University, Russia

Evaluation of Temperature Fluctuation 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) 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 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 are determined earlier [1] and also the device circuit design has been synthesized. The problems related to the optical fiber 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 (B-PF), an electronic amplifier (EA) and a low-pass filter (L-BF). The block diagram of the fiber-optic based chirp signal shaper 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 structure are determined with the parameters of a shaped chirp signal such as an initial frequency , a frequency modulation rate and a pulse width and are analyzed in [4].

The impulse pack generated by binary fiber-optical structure and integrated with the FОС 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 line
	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 chirp signal shaper and to determine the operating conditions of the device taking into account the optical fiber features.

Besides a dispersion and a scattering, one of the key factors having influence on functioning of the optical fiber as a part of the fiber-optic based chirp signal shaper is a temperature factor. In particular, environmental temperature has influence on a refractive index of the optical fiber core and also on the effective length of the optical fiber itself what affects the parameters and the functioning modes of the devices based on the optical fiber.

The materials used for manufacturing of optical fibers display a high thermal stability what provides the better reliability of the delay time. The refractive index of the optical fiber core where there are no fiber deformations (extensions, compression, etc.) depends on temperature [5]:

, (5)

where is a change of the refractive index of the optical fiber core; is a partial derivative of the temperature characterizing the change of the refractive index because of temperature fluctuations, is a partial derivative of the temperature considering the deformations of the optical fiber, is a temperature change,

The augend (5) is analyzed in the expression [9] where its value for quartz glass (0.68∙10^-5 °С ^-1) is derived.

To calculate the addend characterizing the change of the refractive index of the optical fiber core because of the deformations in the expression [9] the following formula is given:

, (6)

where is a refractive index of the optical fiber core, is a radius of the fiber core, accepted for a radius of a mode field is a fiber bend radius in the coil; is a conditional temperature at which the length of the optical fiber would be equal to the nominal length.

It is stated on the basis of the calculation with the formula (6) that the relative change of the refractive index of the optical fiber core caused with a flexural strain or twisting at the expense of a thermal expansion, may amount to the order of 10^-5. Considering the spread in values of the refractive index of the optical fiber core of the various brands the given magnitude takes on different values in the limit (0.8 … 1) ·10^-5. So according to the expressions (5) and (6), we will have obtained the resulting change of the refractive index of the core for the various optical fiber the value of which are in the limits (1.79 … 1.99)·10^-5 .

On the other hand, as the environmental temperature increases the length of a piece of an optical fiber elongates due to the thermal expansion

,

where is a length of an optical fiber, m; is a temperature coefficient of the linear expansion characterizing the optical fiber length change (for quartz glass =0.54∙10⁻⁶ °С^-1).

The resulting change of the time delay at the expense of temperature fluctuations of refractive index and the optical fiber length will amount to

, (7)

where is a velocity of light in vacuum (3·10⁸ m/s).

The value of the addend of the expression (7) is not enough (much less than the value of the augend) what allows us to exclude it from the further consideration. Fig. 5 illustrates a process of changing the time delay of the various fiber-optic delay lines in the shaper

Fig. 5

The time shift of each copy at the output of the fiber-optic connector as a result of the environmental temperature change has two components:

- deviation of the time delay of the additional fiber-optic delay lines in the set of the binary fiber-optical structure ;

- deviation of the time delay of the fiber-optic delay lines connecting various binary fiber-optical structures .

With this time shift of a copy caused by changing the delay time of the additional fiber-optic delay lines in the set of the binary fiber-optical structures is determined with the copy number in a sequence of the k-th binary fiber-optical structure, the temperature change vale and the frequency of the repetition copies of the binary fiber-optical structure f_rep.i

The time shift of a copy caused by changing the delay time of the fiber-optic delay line connecting the binary fiber-optical structures is determined with the number of copies, K, of the binary fiber-optical structures being formed, the temperature change value , the number of the binary fiber-optical structures i and the frequencies of the repetition copies of the various binary fiber-optical structures f_rep.r

.

It is seen in Fig. 5 that a sufficient condition for excluding the superposition of pulses while increasing the environmental temperature is the satisfaction of selecting the values and according to the two conditions:

(8)

The first inequality (8) is valid for any values i and k.

The analysis of the second inequality (8) allows transforming it to an aspect as follows:

. (9)

The expression (9) in the square brackets is less than 0, since > . Hence the inequality (8) is valid for any value .

A sufficient condition for excluding the superposition of the pulses is the specified conditions fulfillment in case of decreasing the environmental temperature.

(10)

The inequalities (10) are also valid for any value .

Generalizing the previously mentioned, it is possible to conclude that the superposition of pulses in the fiber-optic based chirp signal shaper is excluded at any values of temperature fluctuations.

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.

References:

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2. Rumyancev K. E., Gorbunov A. V. Dinamicheskie zapominajushhie ustrojstva na osnove binarnyh volokonno-opticheskih struktur // Radiotehnika. 2002. №12. S.73-80.

3. Kukuyashnyj A. V., Rumyancev K. E. Obobshhennaja model' dinamicheskogo zapominajushhego ustrojstva na volokonno-opticheskih strukturah s opticheskim usileniem. // Severo-Kavkazskij region. Tehnicheskie nauki. 1999. №3. S.61 -67.

4. Kukuyashnyj A. V. Osobennosti formirovanija LChM signalov s ispol'zovaniem volokonno-opticheskih struktur // Informacionnoe protivodejstvie ugrozam terrorizma. 2007. №9. S. 75-88.

5. Rezak E. V., Prokopovich M. R. Uchet pogreshnosti izmerenija dliny opticheskogo volokna // Vestnik TOGU. 2008. №4. S. 167-171.