Set-up modelingfor recording of fiber optic bragg gratings

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Set-up modelingfor recording of fiber optic bragg gratings

A.V. Kulikov, G.E. Romanova, A.O. Voznesenskaya

ITMO University

A scheme for recording of chirped Bragg diffractive structures in optical fibers based on modified Talbot interferometer with cylindrical lenses is considered and analyzed. diffractive optical fiber lens

Nowadays fiber Bragg gratings (FBG) are used widely for spectral packaging (WDM-technology), optical signal filtration, as resonator mirrors in fiber and semiconductor lasers, smoothing filters in optical amplifiers, for dispersion compensation in communications links. Other application area of FBG is different measurement devices like sensors for environment variation registration such are temperature, pressure, deformations, chemical inclusions etc. [1, 2].

Widely used FBG recording methods make possible manufacturing Bragg gratings with the reflection index of 0.1-99.9% and bandwidth of 0.05-10 nm [1, 2] using UV laser exposure [3, 4]. Existing methods for FBG recording with the reflection bandwidth of more than 0.5 nm require recording with a variable interference pattern period. Bragg gratings with the variable index modulation period are called as chirped FBG.

In this work a modified Talbot interferometer setup with cylindrical lenses for chirped FBG recording is simulated.

Talbot interferometer consists of a UV laser source, a phase mask, two plane mirrors tilted symmetrically to the optical axis, and an optical fiber located perpendicularly to the optical axis (figure 1, (a)). The mirrors reflect diffracted beams which then form an interference pattern.

If the mirrors are parallel to the optical axis according to the general diffraction equation the phase mask period

Л_pm=л_laser ?/sin???и/2?, (1)

where л_laser is the laser wavelength and и/2 is the angle of diffraction order.

The diffraction grating period

Л=л_laser/2sin?ц, (2)

where ц is an angle between the diffracted beams.

The mirror angle variation д causes the light direction change equal to 2д (Figure 2) [5]. The diffraction grating period in respect to и/2+2д

Л=л_laser/2sin??(и/2+2д)?. (3)

The angle и/2+2д defines (together with the recording wavelength) the period of the interference pattern and therefore also the period of the Bragg grating and its re?ection wavelength [6]

sin??(и/2+2д)=(n_eff л_eff)/л_Bragg ?, (4)

where n_eff is the effective refractive index of the guided mode.

Chirped gratings may be produced using different setups - with a cylindrical lens located after the phase mask [7], using a spherical lens and tilting the fiber [8], or using a system of cylindrical lenses to form curved wavefronts [9]. As well as using some environment deformations like temperature influence [10], fiber curve [11], etc. In our apparatus different setups utilizing cylindrical lenses are simulated and compared aiming to define the chirping tendency depending on the system geometry (figure 1, (b)).

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(a)

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(b)

Fig.1. Talbot interferometer scheme: (a) FBG recording without chirping, (b) with cylindrical lens for chirped FBG

Talbot interferometer model is realized in non-sequential mode in ZemaxTM software. Tis software has some limitations for given task: maximum quality of pixels for one detector is equal to 5000. This fact leads to the limited detector size because of the very small interference pattern period ant to the very large number of rays that are needed to be traced for obtaining results with high enough accuracy [12].

Two coherent beams from the source were represented as two rectangular UV sources with sizes 10x2 mm and 1 watt power located in the same point with given cross-section dimensions tilted under angles ±и/2=?13.546?^0, correspondingly. To provide enough signal to noise ratio 108 rays from each source were traced.

Two plane mirrors were located at the distance 128.67 mm along the optical axis (z direction) and shifted from the optical axis on W?2=±31 mm, correspondingly (y direction, figure 1). A detector represented a plane surface located in the diamond-shaped interference area, where the optical fiber is to be located. Talbot interferometer model forms interference fringe with equal periods is shown in figure 2.

To investigate accuracy of modeling an interferometer without cylindrical lens was considered. We placed UV laser with different wavelengths л_laser mirrors tilted by the angle д and for each case we found the interference area and defined the detector position z_D, FBG period Л, number of FBG periods per a mm, and deviation of modeling results from calculation with (3) and (4). Results of the model accuracy studies are shown in the Table 1. The accuracy deviation does not exceed 10%.

Table 1. Model parameters and accuracy

Next stage was analysis of the schemes with different cylindrical lens. One of the considered and analyzed schemes is shown in fig. 2. Due to the optical path length variation for different rays tracing through the lens the resulting interference periods become of variable widths.

Fig.2. Talbot interferometer modeling with a cylindrical lens located in one of the ray paths

Like shown in [1] for dispersion compensation the FBG chirping should be of tens of nanometers. Cylindrical lenses with different focal lengths (f^'=50, 70, 500 mm) were simulated aiming to find the chirping tendency and optimum setup configuration.

For given short-focus lenses periods of chirped gratings can be varied from zero chirp to over 170 nm. The less focal length the more chirping, while a long-focus lens (f^'=500 mm) has shown rather weak chirping - less than 5 nm/mm. Cylindrical lens in the Talbot interferometer causes not only variations of grating periods, but shifts the FBG wavelengths according to (3), (4).

(a)

(b)

Fig.3. Talbot interferometer with two cylindrical lenses: (a) negative cylindrical lens is located close to the optical fiber, (b) negative cylindrical lens is located close to the phase mask

Aiming to extend the interference area and increase a zone of FBG recording in the setup with a cylindrical lens (f^'=50 mm) displaced from the symmetry axes on Дy=3 mm was added a second negative cylindrical lens (f^'=-50 mm) located in both ray paths (figure 3). Application of a second negative cylindrical lens allows to increase the recording zone while decrease the chirping (Table 2).

Table 2. Sizes of interference zone for different recording schemes

In this work we have investigated optical setups for chirped FBG recording based on Talbot interferometer with cylindrical lenses. Geometrical parameters of schemes for FBG recording operating at wavelengths of 1300 and 1550 nm are determined. Modeling demonstrated that short-focus cylindrical lenses (f^'<100 mm) provide chirping from zero till hundreds of nanometers, while long-focus lenses shows a weak chirping. It was shown that if a cylindrical lens is located in both path rays gives a poor chirping in a rather small transverse area. Considerable chirping may be achieved if a short-focus cylindrical lens is introduced in one of the interferometer ray paths on a distance from the optical fiber close to its focal length. Long-enough FBG recording area may be distinguished if a second negative cylindrical lens is applied.

References

1. Raman Kashyap, “Fiber Bragg Gratings”, San Diego, CA: Academic Press, 632 (2009).

2. S.A. Vasil'ev, O.I. Medvedkov, I.G. Korolev, A.S. Bozhkov, A.S. Kurkov, E.M. Dianov, “Fibre gratings and their applications”, Quantum Electronics, 35 (12), 1085-1103 (2005).

3. K.O. Hill, B. Malo, F. Bilodeau, D.C. Johnson and J. Albert, "Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask" Appl. Phys. Lett. 62, 1035-1038 (1993).

4. P.E. Dyer, R.J. Farley and R. Giedl, "Analysis of grating formation with excimer laser irradiated phase masks" Opt. Commun. 115, 327-334 (1995).

5. Chuan Li, Yi-Mo Zhang, Xue-Fei Tian, Bing-Heng Xiong, “Study of wedge-adjusted Talbot interferometer for writing fiber gratings with variable inscribed Bragg wavelengths”, Opt.Eng. 42 (12), 3452-3455 (2003).

6. Martin Becker, Joachim Bergmann, Sven BruЁckner, Marco Franke, Eric Lindner, Manfred W. Rothhardt and Hartmut Bartelt, “Fiber Bragg grating inscription combining DUV sub-picosecond laser pulses and two-beam interferometry”, Optics Express 16 (23), 19169-19178 (2008).

7. Y. Wang, J. Grant, A. Sharma, and G. Myers, “Modified Talbot interferometer for fabrication of fiber-optic grating filter over a wide range of Bragg wavelength and bandwidth using a single phase mask”, Journ. of lightwave technology, 19 (10), 1569-1573 (2001).

8. Y. Painchaud, A. Chandonnet, and J. Lauzon, “Chirped fiber gratings produced by tilting the fiber”, Electron. Lett., 31, 171-172 (1995).

9. M.C. Farries, K. Sugden, D.C.J. Reid, I. Bennion, A. Molony, and M.J. Goodwin, “Very Broad Reflection Bandwidth (44 nm) chirped fibre gratings and narrow bandpass filters produced by the use of an amplitude mask”, Electron. Lett., 30 (11), 891-892 (1994).

10. Jocelyn Lauzon, Simon Thibault, Jean Martin, Franзois Ouellette, “Implementation and characterization of fiber Bragg gratings linearly chirped by a temperature gradient”, Optics Letters, 19 (23), 2027-2029 (1994).

11. Q. Zhang, D.A. Brown, L.J. Reinhart, T.F. Morse, “Linearly and nonlinearly chirped Bragg gratings fabricated on curved fibers”, Optics Letters, 20 (10), 1122-1124 (1995).

12. http://www.zemax.com/support/knowledgebase/how-to-produce-photo-realistic-output-images

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