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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 6 — Mar. 25, 2013
  • pp: 6997–7007
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Detailed analysis of the longitudinal acousto-optical resonances in a fiber Bragg modulator

Ricardo E. Silva, Marcos A. R. Franco, Paulo T. Neves, Jr., Hartmut Bartelt, and Alexandre A. P. Pohl  »View Author Affiliations


Optics Express, Vol. 21, Issue 6, pp. 6997-7007 (2013)
http://dx.doi.org/10.1364/OE.21.006997


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Abstract

The interaction frequencies between longitudinal acoustic waves and fiber Bragg grating are numerically and experimentally assessed. Since the grating modulation depends on the acoustic drive, the combined analysis provides a more efficient operation. In this paper, 3-D finite element and transfer matrix methods allow investigating the electrical, mechanical and optical resonances of an acousto-optical device. The frequency response allows locating the resonances and characterizing their mechanical displacements. Measurements of the grating response under resonant excitation are compared to simulated results. A smaller than <1.5% average difference between simulated-measured resonances indicates that the method is useful for the design and characterization of optical modulators.

© 2013 OSA

1. Introduction

In this paper, the multiphysics analyses of the modulator response and displacement behavior of longitudinal acoustic waves are performed, and the experimental characterization of the resultant acousto-optical effect in a Bragg grating is assessed. The device is numerically modeled using 3-D finite element method (FEM) [8

8. H. A. Kunkel, S. Locke, and B. Pikeroen, “Finite-element analysis of vibrational modes in piezoelectric ceramic disks,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37(4), 316–328 (1990). [CrossRef] [PubMed]

10

10. C. M. B. Cordeiro, M. A. R. Franco, G. Chesini, E. C. S. Barretto, R. Lwin, C. H. Brito Cruz, and M. C. J. Large, “Microstructured-core optical fibre for evanescent sensing applications,” Opt. Express 14(26), 13056–13066 (2006). [CrossRef] [PubMed]

] and the transfer matrix method (TMM) [6

6. R. A. Oliveira, P. T. Neves Jr, J. T. Pereira, and A. A. P. Pohl, “Numerical approach for designing a Bragg grating acousto-optic modulator using the finite element and the transfer matrix methods,” Opt. Commun. 281(19), 4899–4905 (2008). [CrossRef]

] to obtain the piezo spectral response, fiber displacements and modulated FBG spectrum. PZT anisotropy is included in the simulations and takes into account the displacement change of the PZT when excited at different frequencies. The PZT is electrically excited and its deformations are automatically coupled to the horn-fiber setup. The method is based on the frequency response of the entire modulator which allows estimating the modes that are useful in the real device. Simulation results are compared to experimental measurements of the wavelength shift, as the grating is under the excitation of the resonant acoustic modes. The proposed approach allows investigating the main intrinsic properties of an acousto-optical driver when is excited. The combined characterization is essential to the design, efficiency control and operation of acousto-optical devices.

2. Operation principle of the modulator

3. Numerical modeling

4. Experimental setup

The modulator is assembled considering the same components and boundary conditions illustrated in Fig. 2. The device includes a 5 cm long FBG, in which the reflectivity is 25 dB and the Bragg wavelength, is set at λΒ = 1538.42 nm. The FBG was inscribed by the direct UV exposure of the fiber through a 5 cm long phase mask using a 248nm KrF laser. Figure 3
Fig. 3 Experimental setup used to characterize the FBG acousto-optical interaction.
illustrates the experimental setup used for the characterization of the reflectivity spectrum when the resonant longitudinal acoustic waves are excited in the grating. The FBG is illuminated by a superluminescent Amonics LED (SLED) with central wavelength of λ = 1475.7 nm and full width at half maximum FWHM = 37.6 nm. The reflection spectrum is obtained through a circulator and an optical spectrum analyzer (OSA) Agilent 86142B, with a 60 pm wavelength resolution and −90 dBm optical sensitivity. The fiber was carefully adjusted and aligned with help of XYZ positioning stages and microscopes to avoid the presence of stress when no acoustic wave is applied. Bragg wavelength shifts were also monitored during the alignment. Since a stress applied in the fiber or horn can induce block forces on the PZT, the presence of initial stress can cause a change of resonances of the PZT, since that PZT, horn and fiber work as a resonant cavity. Considering that a longitudinal fiber stress can induce an initial strain in the grating and consequently a Bragg wavelength shift, the “DC” strain can also induce a side lobe shift. The PZT is excited by a 10 V maximum sinusoidal signal from an arbitrary signal generator (SG) Tektronix, in the 600 – 1200 kHz frequency range. By fixing the PZT base and the fiber tip, the modulator works as a resonant acoustic cavity that allows exciting standing acoustic waves at certain resonant frequencies. The grating spectrum is obtained for the resonances in which the acousto-optical effect is observed. In order to verify the natural PZT frequency response, the PZT is set free of load and excited by a 500 mV harmonic voltage in the 1-1200 kHz range using an arbitrary impedance analyzer.

5. Results

The displacement vibration behavior of the resonant modes is shown in Fig. 5
Fig. 5 PZT vibration modes and qualitative displacement behavior in resonances.
and illustrates the lateral yz and frontal xy planes for each resonance. The PZT analysis of these profiles allows verifying the longitudinal and radial deformations, respectively. The displacements of the transducer are magnified to provide better observation of the maximum (red) and minimum (blue) displacements. It is observed that all modes possess points of longitudinal displacements at their polarization surfaces, which is required for the excitation of axial waves in the fiber. However, due to particular and different electromechanical properties that each mode presents in resonance, the deformation shows that the displacements are not perfectly uniform and axial. More uniform z displacement is observed only at 958, 1049, 1058.5 kHz resonances, in which the maximum deflection is located at the disc center. It is observed in Figs. 5(h) and 5(i) that the 1049 and 1058 kHz resonances are strongly coupled and present a similar deformation behavior.

Figure 6(a)
Fig. 6 (a) Modulator frequency response in terms of the fiber transversal and axial displacements and (b) longitudinal acoustic resonances obtained by the ratio between axial (z direction) and transversal displacements (xy directions).
shows the modulator response (PZT is coupled to the horn-fiber) in terms of fiber displacements, which is decomposed into axial (z direction) and transversal displacements (xy directions). Although all analyzed acoustic modes present components of both xyz displacements, the longitudinal acoustic waves are characterized by the larger displacements in z direction. The transversal displacements are composed by lower amplitude flexural oscillations which are polarized in xy plane transversally to the fiber axis. The proximity between the axial-transversal displacements observed in some resonances (for example in the narrow frequency band around 1150 kHz) can produce complex acoustic waves that are not useful for grating modulation. An increase in the number of resonances is also observed if compared to PZT ones in Fig. 4(a). The modulator response shows that the device only works at certain frequencies, which limits the wavelength shift step of the Bragg side lobe in grating spectrum. Figure 6(b) shows the ratio between axial and transversal displacements (z/x and z/y displacement ratios), which allows improved distinction of the longitudinal acoustic resonances. The agreement between fiber-PZT resonances allows verifying the strong dependence of the fiber deformations originated by the PZT excitation. Because of the different deflection that each PZT mode shows at resonance, amplitude variations in fiber displacements are also observed. Since the acousto-optical efficiency is proportional to the strain amplitude, theses discrepancies can induce optical variations in a FBG spectrum. It is important to note in Fig. 6(b), that although the main longitudinal modes present a well-defined frequency, the fiber resonances are composed by narrow frequency bands in which other modes oscillate with lower intensity. Consequently, variations in the geometry or material parameters, or alterations in device boundary conditions can suppress, reinforce or even couple energy from one mode to other. However, the analysis allows locating the fiber resonances and identifying the longitudinal modes that control the optical grating spectrum.

Figure 8(a)
Fig. 8 (a) FBG measured-simulated spectra and (b) spectral response in resonances. (c) FBG spectra and (d) side lobe reflectivity response for f = 1072 kHz.
shows the measured FBG spectrum when the grating is excited with the 679 and 1019 kHz resonances. The measured spectra are compared to the modeled TMM spectra obtained from previously assessed FEM simulations shown in Fig. 7. The differences in reflectivity and wavelength bandwidth between measured-simulated results is due to grating variations originating in the grating inscription process and the OSA resolution that cannot distinguish the lowest side lobes. However, an experimental side lobe reflectivity of about 40% higher with the 679 kHz resonance is observed, which corresponds to the strongest longitudinal mode in Fig. 7(a). The comparison is also made considering other resonances and the measured-simulated side lobe wavelength shift Δλ is compared to theoretical curve and plotted in Fig. 8(b). The results show that the acousto-optic effect occurs only at specific frequencies that depend on the PZT-horn-fiber resonances. The response is approximately linear and the frequency tuning resolution is discrete and non-uniform. The modulator is adjusted to the 1072 kHz longitudinal resonance and the measured amplitude of the side lobe reflectivity is also investigated for a 10 V maximum voltage variation. Figures 8(c) and 8(d) show the FBG modulated reflection spectrum and side lobe reflectivity variation, respectively. Although it is not demonstrated, this behavior has also been observed for other acoustic resonances and the linear response allows the modulator to be used as a tuned optical power modulation at specific resonances.

The reflectivity of the side lobe is proportional to the FBG length [6

6. R. A. Oliveira, P. T. Neves Jr, J. T. Pereira, and A. A. P. Pohl, “Numerical approach for designing a Bragg grating acousto-optic modulator using the finite element and the transfer matrix methods,” Opt. Commun. 281(19), 4899–4905 (2008). [CrossRef]

] and the voltage applied to the PZT. As the voltage has been limited by the signal generator, the use of a long FBG was useful to obtain a better distinction of side lobes, which facilitates the location of the side lobe wavelength. The use of different grating lengths would change the reflectivity, but would not change the side lobe shift, since it does not depend on the FBG length, but on the excitation frequency. However, variations in the fiber length change the modulator resonances.

Table 1

Table 1. Measured FBG and simulated PZT-fiber resonances.

table-icon
View This Table
summarizes the FBG resonances measured experimentally in comparison to the resonances obtained in simulations with the PZT and the modulator (shown in Figs. 4(b) and 8(b), respectively). The relative maximum differences, rd, between FBG-PZT and FBG-fiber values are 4.09% and 2.53%, respectively. However, the average differences are 1.45% and 1.07%, respectively. The better agreement between FBG-fiber results shows that the decomposition of the fiber displacements is useful to accurately locate the longitudinal acoustic modes that induce axial strain in the grating. Since the PZT modes can also induce transversal deflections in the horn-fiber setup, the analysis of the entire AOM device is necessary for this purpose. The results indicate that the non-uniform axial PZT deformations coupled to the horn basis induce transversal displacements in the horn-fiber setup, which can cause acoustic loss, reflections and reduction of the strain in grating.

Differences between experimental-simulated values are caused by geometric variations in the modulator components due to fabrication process or experimental setup building, piezoelectric constants tolerances, element size used in the FEM mesh and step resolution in frequency response used in the simulations. A quantitative analysis of the PZT-fiber deflections, amplitude strain and FBG reflectivity can be obtained by considering the imaginary part of the piezoelectric constants, which were not available from the manufacturer.

6. Conclusions

The interaction analysis of the longitudinal acousto-optical resonances of a fiber Bragg modulator is numerically and experimentally investigated. Electromechanical anisotropy, 3-D finite element and transfer matrix methods are used to simulate the modulator response and locate the resonant modes. The simulated impedance-phase response can be used to localize the transducer vibration modes and characterize its mechanical displacements. The decomposition of the fiber displacements allows accurately locating the longitudinal acoustic resonances, and estimating the axial core strain, which is required for FBG TMM spectrum simulations. It allows identifying the electric voltage frequencies in which the driver should be excited to obtain better operation efficiency. Experimental measures of the grating spectrum at resonances are compared to simulations. The agreement between measured-simulated values shows that the acousto-optic effect occurs only at specific frequencies that depend on the entire modulator. The grating spectral response is approximately linear, but the frequency tuning resolution is discrete and non-uniform. A better accuracy between measured-simulated values can be obtained by considering the imaginary part of the piezo constants, by refining the FEM mesh and reducing the frequency response step, which result in more computational cost and time processing. However, the results indicate the proposed approach is useful to investigate the intrinsic properties of the acousto-optical modulator as it is electrically excited. The numerical method is useful to characterize and estimate possible operation instabilities and to improve the device efficiency. In addition, it assists the design of novel acousto-optical drives, in which acoustic waves can be controlled to produce specific reflectivity or spectral modulation of fiber gratings.

Acknowledgments

This work was supported in part by the Cordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Ministério da Defesa - Projeto Pró-Defesa, and CNPq/FAPESP – INCT (FOTONICOM).

References and links

1.

W. F. Liu, P. S. Russell, and L. Dong, “Acousto-optic superlattice modulator using a fiber Bragg grating,” Opt. Lett. 22(19), 1515–1517 (1997). [CrossRef] [PubMed]

2.

R. E. Silva and A. A. P. Pohl, “Characterization of flexural acoustic waves in optical fibers using an extrinsic Fabry–Perot interferometer,” Meas. Sci. Technol. 23(5), 055206 (2012). [CrossRef]

3.

R. A. Oliveira, K. Cook, J. Canning, and A. A. P. Pohl, “Bragg grating writing in acoustically excited optical fiber,” Appl. Phys. Lett. 97(4), 5–6 (2010). [CrossRef]

4.

M. Delgado-Pinar, D. Zalvidea, A. Diez, P. Perez-Millan, and M. Andres, “Q-switching of an all-fiber laser by acousto-optic modulation of a fiber Bragg grating,” Opt. Express 14(3), 1106–1112 (2006). [CrossRef] [PubMed]

5.

P. de Tarso Neves and A. de Almeida Prado Pohl, “Time analysis of the wavelength shift in fiber Bragg gratings,” J. Lightwave Technol. 25(11), 3580–3588 (2007). [CrossRef]

6.

R. A. Oliveira, P. T. Neves Jr, J. T. Pereira, and A. A. P. Pohl, “Numerical approach for designing a Bragg grating acousto-optic modulator using the finite element and the transfer matrix methods,” Opt. Commun. 281(19), 4899–4905 (2008). [CrossRef]

7.

R. A. Oliveira, P. T. Neves Jr, J. T. Pereira, J. Canning, and A. A. P. Pohl, “Vibration mode analysis of a silica horn–fiber Bragg grating device,” Opt. Commun. 283(7), 1296–1302 (2010). [CrossRef]

8.

H. A. Kunkel, S. Locke, and B. Pikeroen, “Finite-element analysis of vibrational modes in piezoelectric ceramic disks,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37(4), 316–328 (1990). [CrossRef] [PubMed]

9.

G. Chesini, V. A. Serrão, M. A. R. Franco, and C. M. B. Cordeiro, “Analysis and optimization of an all-fiber device based on photonic crystal fiber with integrated electrodes,” Opt. Express 18(3), 2842–2848 (2010). [CrossRef] [PubMed]

10.

C. M. B. Cordeiro, M. A. R. Franco, G. Chesini, E. C. S. Barretto, R. Lwin, C. H. Brito Cruz, and M. C. J. Large, “Microstructured-core optical fibre for evanescent sensing applications,” Opt. Express 14(26), 13056–13066 (2006). [CrossRef] [PubMed]

11.

A. Ballato, “Modeling piezoelectric and piezomagnetic devices and structures via equivalent networks,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48(5), 1189–1240 (2001). [CrossRef] [PubMed]

12.

Ferroperm piezoceramics, “Full data matrix,” http://app04.swwwing.net/swwwing/app/cm/Browse.jsp?PAGE=1417.

OCIS Codes
(060.2340) Fiber optics and optical communications : Fiber optics components
(060.4080) Fiber optics and optical communications : Modulation
(230.1040) Optical devices : Acousto-optical devices
(060.3735) Fiber optics and optical communications : Fiber Bragg gratings

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: October 8, 2012
Revised Manuscript: December 21, 2012
Manuscript Accepted: December 30, 2012
Published: March 13, 2013

Citation
Ricardo E. Silva, Marcos A. R. Franco, Paulo T. Neves, Hartmut Bartelt, and Alexandre A. P. Pohl, "Detailed analysis of the longitudinal acousto-optical resonances in a fiber Bragg modulator," Opt. Express 21, 6997-7007 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-6-6997


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References

  1. W. F. Liu, P. S. Russell, and L. Dong, “Acousto-optic superlattice modulator using a fiber Bragg grating,” Opt. Lett. 22(19), 1515–1517 (1997). [CrossRef] [PubMed]
  2. R. E. Silva and A. A. P. Pohl, “Characterization of flexural acoustic waves in optical fibers using an extrinsic Fabry–Perot interferometer,” Meas. Sci. Technol. 23(5), 055206 (2012). [CrossRef]
  3. R. A. Oliveira, K. Cook, J. Canning, and A. A. P. Pohl, “Bragg grating writing in acoustically excited optical fiber,” Appl. Phys. Lett. 97(4), 5–6 (2010). [CrossRef]
  4. M. Delgado-Pinar, D. Zalvidea, A. Diez, P. Perez-Millan, and M. Andres, “Q-switching of an all-fiber laser by acousto-optic modulation of a fiber Bragg grating,” Opt. Express 14(3), 1106–1112 (2006). [CrossRef] [PubMed]
  5. P. de Tarso Neves and A. de Almeida Prado Pohl, “Time analysis of the wavelength shift in fiber Bragg gratings,” J. Lightwave Technol. 25(11), 3580–3588 (2007). [CrossRef]
  6. R. A. Oliveira, P. T. Neves, J. T. Pereira, and A. A. P. Pohl, “Numerical approach for designing a Bragg grating acousto-optic modulator using the finite element and the transfer matrix methods,” Opt. Commun. 281(19), 4899–4905 (2008). [CrossRef]
  7. R. A. Oliveira, P. T. Neves, J. T. Pereira, J. Canning, and A. A. P. Pohl, “Vibration mode analysis of a silica horn–fiber Bragg grating device,” Opt. Commun. 283(7), 1296–1302 (2010). [CrossRef]
  8. H. A. Kunkel, S. Locke, and B. Pikeroen, “Finite-element analysis of vibrational modes in piezoelectric ceramic disks,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37(4), 316–328 (1990). [CrossRef] [PubMed]
  9. G. Chesini, V. A. Serrão, M. A. R. Franco, and C. M. B. Cordeiro, “Analysis and optimization of an all-fiber device based on photonic crystal fiber with integrated electrodes,” Opt. Express 18(3), 2842–2848 (2010). [CrossRef] [PubMed]
  10. C. M. B. Cordeiro, M. A. R. Franco, G. Chesini, E. C. S. Barretto, R. Lwin, C. H. Brito Cruz, and M. C. J. Large, “Microstructured-core optical fibre for evanescent sensing applications,” Opt. Express 14(26), 13056–13066 (2006). [CrossRef] [PubMed]
  11. A. Ballato, “Modeling piezoelectric and piezomagnetic devices and structures via equivalent networks,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 48(5), 1189–1240 (2001). [CrossRef] [PubMed]
  12. Ferroperm piezoceramics, “Full data matrix,” http://app04.swwwing.net/swwwing/app/cm/Browse.jsp?PAGE=1417 .

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