Evolution of polarization properties in circular birefringent fiber Bragg gratings and application for magnetic field sensing

Optical Fiber Technology 18 (2012) 177–182

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Optical Fiber Technology www.elsevier.com/locate/yofte

Evolution of polarization properties in circular birefringent fiber Bragg gratings and application for magnetic field sensing Hui Peng a,b,⇑, Yang Su a, Yuquan Li a a b

Institute of Communications Engineering, PLA University of Science and Technology, Nanjing, China 92913 Army, PLA, Haikou, China

a r t i c l e

i n f o

Article history: Received 16 November 2011 Revised 15 December 2011 Available online 22 March 2012 Keywords: Polarization properties Fiber grating Magnetic field 3rd Normalized Stokes parameter

a b s t r a c t The transmission and polarization properties of Fiber Bragg Grating (FBG) with Faraday Effect are studied in this paper. The evolutions of transmission spectrum for different circular birefringence, grating parameter (physical length, index modulation) and input polarizations are simulated with Jones Matrix method. It is demonstrated that the monitoring of the 3rd normalized Stokes parameter peak values provide a new magnetic field measurement. The magnetic field strength sensitivity value is 1.482  105/Gs by using the optical vector analyzer whose precision is 105 in experiment and a very good agreement between theory and experience is reported. Ó 2012 Elsevier Inc. All rights reserved.

1. Introduction Nowadays, magnetic field measurement has become a fundamental procedure in many industrial and scientific applications. The measurement of magnetic field strength has been achieved through the three principal methods: the use of bulk optics or fiber coils exploiting the magneto-optic effect over extended path lengths, various arrangements exploiting magnetostriction, and optical detection of the Lorentzian force [1–6]. Based on the Faraday Effect, Kersey described a fiber probe for monitoring magnetic fields which was based on detecting the shift in Bragg condition of a FBG due to magnetically induce circular birefringence. This method needs interferometer detection technique due to the weak level of magneto-optical interaction of the induced circular birefringence [7,8]. In practical, the polarization properties of a device become more and more important in optical sensing. Recently, it is reported that the polarization propertied of FBG can be used for sensing other parameters, such as transverse strain and temperature [9–11]. Consequently there is high interest to study the polarization properties of FBG in presence of Faraday Effect. In this paper, we review our research on polarization properties of FBG and demonstrate it can be used for magnetic field sensor. Section 2 gave the theory models about the Stokes parameters of fiber Bragg grating. We use, on the one hand, the Jones formalism to take into account the effect of magnetic field in the FBG and, on ⇑ Corresponding author. Address: P.O. Box 32, No. 2 Biaoying Rd., Yudao St., Nanjing, Jiangsu 210007, China. E-mail address: [email protected] (H. Peng). 1068-5200/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.yofte.2012.01.005

the other hand, the solution of the coupled modes theory to obtain the complex transmission response of the FBG. Based on the combination of these two theories, we drive a simple analytical expression of normalized Stokes parameters for FBG. In Section 3, simulation results of normalized stokes parameters are presented as a function of magnetic field and gratings parameters. Finally experimental results are depicted in Section 4. The relatively good agreement between simulation and experiment results are commented. Conclusions are drawn in Section 5. 2. Theory The Bragg resonance condition is given by kB = 2neffK, where neff is the refractive index of fiber and K is the grating period [12]. In presence of a longitudinal magnetic field applied to the FBG, the index is changed due to Faraday Effect. The magnetically-induced circular birefringence Dnc is the difference in refractive indexes experienced by right and left circular polarizations [13]. The Dnc can be expressed as:

Dnc ¼ VHk=p

ð1Þ

where H is magnetic field strength in Gs, k is the optical wavelength in meters, and V is the Verdet constant, a measure of the strength of the magneto-optical effect in medium with units rad/(Gs m). At 1550 nm, the value of V in silica fiber is approximately 0.57  104 rad/(Gs m) [14] and is weakly proportional to temperature [15]. From Eq. (1), we can know the different between the two Bragg condition is Dk = 2VHKk/p. Consequently, for a field of 104 Gs, the order of magnitude of Dnc is about 106 and Dk is a few pm. Conventional tunable laser sources and optical spectrum

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analyzers possess a wavelength resolution of the order of a few pm. Consequently, it is difficult to measure Dnc by spectral measurements. However, if we measure the polarization properties of an FBG, their wavelength evolution provide sufficient information to estimate the value of Dnc. We focus here on the wavelength evolution of the 3rd normalized Stokes parameter corresponding to the transmitted signal of the FBG. Since the eigenmodes of Faraday Effect are circular polarization, we use the L and R subscripts to indentify the eigenmodes corresponding to the left and circularly polarized light [16]. Due to Dnc, the two eigenmodes undergo different couplings through the grating, and the corresponding transmission coefficients are denoted as tR and tL. The Jones matrix expressed in a circular frame of reference can be described as:

 J¼

tR

0

0

tL

 ð2Þ

From the Refs. [16,17], the right and left circularly polarized light propagating in FBG are independent of each other in the absence of nonlinear effects and the transmitted signal is derived from the product between the matrix J and the input signal, that is,



Et;R



Et;L

 ¼

tR 0

0 tL



Ei;R Ei;L



 ¼

t R Ei;R t L Ei;L

 ð3Þ

The transmission coefficient tR(L) is derived from the coupled mode theory [18]:

aRðLÞ t RðLÞ ¼ rRðLÞ sinhðaRðLÞ LÞ þ iaRðLÞ coshðaRðLÞ LÞ

ð4Þ

ð6Þ

Eq. (3) can be rewrite in Cartesian frame:



Ex Ey

 out

¼ Jc



Ex

"



Ey

¼ in

1 ðt þ tL Þ 2 R 1 jðt R  tL Þ 2

 12 jðtR  t L Þ 1 ðt 2 R

þ tL Þ

#

Ex Ey

 ð7Þ in

where JC is Jones matrix expresses in Cartesian frame of Eq. (2). Eq. (7) indicates that Faraday Effect makes mode-conversion of linearly polarized in a Cartesian coordinates system. When light beam is propagating in a FBG with circular magnetic birefringence, the transmission and polarization properties will be affected by many factors such as the circular birefringence value, the grating length and state of polarization (SOP) of incident light. Next we will analyses the relationship between the polarization properties and the magnetic field strength. In optical sensing, polarization properties of gratings also play an important role since they are used to develop new types of FBG-based sensors through polarization dependent properties measurements [10]. The Stokes parameters represent the state of polarization. They can be deduced from the Jones vector by means of the follows equations [19]:

S0 ¼ hjEx j2 i þ hjEy j2 i S1 ¼ hjEx j2 i þ hjEy j2 i S2 ¼ 2Re½hEx Ey i

ð8Þ

S3 ¼ 2Im½hEx Ey i

With

aRðLÞ ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 k  r2RðLÞ k¼

rRðLÞ ¼

1 1 ~ ex  j~ ex þ j~ ey Þ; ~ eL ¼ pffiffiffi ð~ ey Þ eR ¼ pffiffiffi ð~ 2 2

pdn k

ð5Þ

2pðneff ;RðLÞ þ dnÞ p  K k

The aR(L) and rR(L) correspond to the parameters a and r defined in [17], where neff has been replace by neff,R(L) with neff,R = neff + Dnc/ 2 and neff,L = neff  Dnc/2. Where L is the grating length, k is the wavelength and dn is the core refractive index modulation. By the transform of the unit vectors,

The 3rd normalized Stokes parameter s3 represents the power difference between the right and left circular polarizations and it is simply defined as the ratio between S3 and S0,such as s3 = S3/ S0. This parameter is wavelength dependent. Fig. 1a gives the total transmission spectra and s3 spectra. When the magnetic field is small, the influence on the total power transmission is weak, but the amplitude of s3 is clearly linked to magnetic field. Fig. 1b shows the transmission spectra of different modes, TR and TL denote the transmission spectrum of the right and left circular polarizations, respectively. Tx and Ty represent the transmission spectrum of the x(y) mode. In this paper we describe a method to measure the magnetic field by measuring the s3 spectra of the transmitted signal.

Fig. 1. The wavelength dependency of (a) total transmission spectra and the 3rd normalized Stokes parameters and (b) transmission spectra of the right circularly, left circularly, x and y polarized modes.

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3. Simulation results In this section, we will analyses the impact of grating parameters on the wavelength evolution of the s3 systematically. We use the magnetically-induced circular birefringence Dnc instead of the magnetic field strength H because of the linear relationship between the H and Dnc. Figs. 2–4 represent the wavelength dependency of s3 as a function of the Dnc, the grating length L and the grating modulation index dn, respectively. For all simulation results, we have chosen neff = 1.458 and K = 535 nm. The incident angle is 0°. All other grating parameters used for simulations are detailed into the figures. The relationship between s3 and Dnc is depicted in Fig. 2a. The wavelength evolution of the transmission spectrum and the s3 are affected by Dnc. The s3 remains constant at zero outside the rejection band of the grating. Within rejection band, it evolves and the peak value is clearly linked to the Dnc. As expected, the increase of Dnc leads to a general increase of s3 amplitudes. Fig. 2b gives the SOP on Poincare sphere of transmitted signal for different Dnc. The modification of L and dn has the same effects on the s3 spectra. Indeed, strong gratings are obtained by increasing either L or dn. In this case, the transmission spectrum presents a rapid variation at the edges of the main rejection band. The same effect can be observed in the s3 spectrum (see Figs. 3 and 4): for high values of L

and dn, s3 present a greater variation at the main rejection band. Moreover, one can observe that the increase of L and dn leads to very high values of s3, the value of Dnc remaining constant. Another simulation allowed us to see the influence of the input SOP on the evolution of the s3. Fig. 5 shows that the input SOPS have not an effect on the evolution of the s3. Next, we will analyse the effect of the fiber’s birefringence. Typically, the order of magnitude of birefringence is about 106, we suppose the value is 5  106. Fig. 6 shows the error caused by the fiber’s birefringence. From Fig. 6, we can see the influence is very small and can be ignore. Fiber Bragg gratings experience a shift of their Bragg wavelength with temperature, given by [20,21]:

DkB ¼ kB

  DK Dneff ¼ kB ða þ nÞDT þ neff K

ð9Þ

where DT is the temperature change, the n = 6.67  106 C1 is the thermo-optic coefficient and a  5.5  107 C1 is thermal expansion coefficient of common silica fiber. The total is dominated by the thermo-optic coefficient. Fig. 7 shows the relationship between s3 change and temperature change. From Fig. 7, we can find that the spectra of s3 are move on the wavelength axis and the value of s3 are not change. The method is temperature insensitive to measure magnetic field from above analysis.

1

s3

0.5 0 -0.5 -1 1 Δnc=6e-5

s2 0 -1

Δnc=2e-5

Δnc=4e-5

(a)

0.5

0

-0.5

-1

1

s1

(b)

Fig. 2. (a) Wavelength dependency of T and s3 for different Dnc (b) the SOP on Poincare sphere of transmitted spectrum for different Dnc.

1 L=0.015

0.5

s3

0

-0.5 L=0.02 L=0.01

-1 -1

(a)

1 -0.5

0

s1

0 0.5

1

-1

s2

(b)

Fig. 3. (a) Wavelength dependency of T and s3 for different grating length. (b) The SOP on Poincare sphere of transmitted spectrum for different grating length.

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1

0.5 δn=4e-5

s3

0

-0.5

-1 -1

δn=6e-5

δn=8e-5

s10 1

(a)

-1

0

-0.5

s2

0.5

1

(b)

s3

s3

Transmission

Fig. 4. (a) Wavelength dependency of T and s3 for different modulation index. (b) The SOP on Poincare sphere of transmitted spectrum for different modulation index.

1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -1

30 60

45

0

s2

1 1

(a)

0.5

0

-0.5

-1

s1

(b)

Fig. 5. (a) Wavelength dependency of T and s3 for three different phase angles of the input state of polarization. (b) The SOP on Poincare sphere of transmitted spectrum for three different phase angles of the input state of polarization.

0.016

Δmax(s3)/max(s3)

0.014 0.012 0.01 0.008 0.006 0.004 0

1

nc

2 x 10

-4

Fig. 6. The error caused by the fiber’s birefringence. Fig. 7. Wavelength dependency of T and s3 for three different temperature.

These analysis shows that the s3 spectra is affected by both the Dnc and the grating physical parameters. When the grating physical parameter is decided, the s3 is only decided by Dnc, namely the magnetic field strength. Fig. 8 shows the linear relationship between the peak values of s3 and Dnc in certain range. Based on this characteristic curve we can monitor the applied magnetic field.

4. Experimental results The FBG that used in experiment is designed and fabricated by our project group. The parameters as fellows: neff = 1.455, K = 535 nm, dn = 5e5 and the length of FBG is 10 mm.

181

H. Peng et al. / Optical Fiber Technology 18 (2012) 177–182 0.18T 0.2T

0.6

0.04

0.5

0.02

0.4

0.00

s3

The max of s3

0.7

0.3

-0.02

0.2

-0.04

0.1

-0.06

0

0

1

1547.4

2

nc

x 10

1548.0

Fig. 12. s3 Evolution for experimental FBG with magnetic field.

Table 1 The experimental and simulation peak value of s3 under different magnetic field.

Optical Vector Analyzer input

Magnetic field generator

PC

1547.8

Wavelength (nm)

Fig. 8. Maximum s3 value evolution as a function of H.

output

1547.6

-4

Fiber grating Fig. 9. Schematic of measurement system.

Magnetic field (Gs)

Experimental results

Simulation results

400 600 800 1000 1200 1400 1600 1800 2000 2200

– 0.02464 0.02882 0.03265 0.03618 0.03984 0.04238 0.04383 0.04758 0.04789

0.00527 0.0079 0.01053 0.01317 0.0158 0.01843 0.02107 0.0237 0.02633 0.2897

0 0.05

2000 Gs 1800 Gs 0 Gs

-10

experiment data emulation data experiment fit curve emulation fit curve

0.04

-15

Max of s3

Transmission

-5

-20 -25 -30

0.03 0.02 0.01

1547.4

1547.6

1547.8

1548.0 0.00

Wavelength (nm)

0 Fig. 10. Transmission spectrum for experimental FBG.

400

800

1200

1600

2000

2400

Magnetic field (Gs) Fig. 13. The result of the experiment and simulation.

0.08

s3

0.04 0.00 -0.04 -0.08

1547.0

1547.2

1547.4

1547.6

1547.8

1548.0

Wavelength (nm) Fig. 11. s3 evolution for experimental FBG without magnetic field.

Fig. 9 shows the experiment scheme of measurement system. The optical vector analyzer (OVA) is regarded as a light source,

detector and processor. A polarization controller (PC) is used to modify the polarization state of the light emitted by a light source such that the SOP at the input of FBG is linear. A longitudinal magnetic field is applied to the fiber grating. The transmission light was measured and analyzed by OVA. The precision of OVA is 105 [22]. Fig. 10 shows the transmitted spectrum in different magnetic field. From Fig. 10, one can see the influence of the magnetic field is not perceived in the transmitted spectrum. The movement of center wavelength is because of the impact of temperature. Fig. 11 shows the s3 of FBG without magnetic field. In this figure, there are some peak values and the whole spectrum is disorderly and unsystematic because of the twist of the fiber or other factors [19,23]. Those factors is random distribute in the fiber so the s3 is disorderly. Fig. 12 gives us the s3 spectrum with magnetic field. The spectrum becomes orderliness. There are a peak and a valley. As expected, the increase of magnetic field value leads to a general increase of the peak value of s3.

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Table 1 shows the experimental and simulation peak value of s3 with the magnetic field strength in the range of 400–2200 Gs by steps of 200 Gs. Fig. 13 shows the difference between the experimental and simulation results according to Table 1. The difference is caused by the twist of fiber [23] and other factors in the environment. The magnetic field strength sensitivity is 1.482  105/Gs by using the optical vector analyzer whose precision is 105 in our experiment [22]. The experiment agrees well with the theory.

5. Conclusion In this paper, the transmission and polarization properties of FBG in presence of magnetically induced circular birefringence are studied. The influence of magnetic field values, grating parameters, input SOPs and temperature on transmission and polarization properties are discussed in detail. The results show that the maximum amplitude of 3rd normalized stokes parameter (s3) contain the information about the magnetic field values and could be used to gain magnetic field value sensing. Moreover, this method is temperature insensitive. Experimental results have completed the study. Relatively good agreement with simulation result has been presented and commented. We confirm that the method can use to measure magnetic field. Acknowledgments This work was supported by the National Natural Science Foundation of China under Grant No. 60871075. We would like to thank Prof. Xiangfei Chen of Nanjing University for providing OVA in experiment. References [1] A. Othonos, Fiber Bragg gratings, Rev. Sci. Instrum. 68 (1997) 4309–4341. [2] C. Ambrosino, P. Capoluongo, et al., IEEE Sensors J. 7 (2) (2007) 228–229. [3] A.M. Smith, Polarization and magnetooptic properties of single-mode optical fiber, Appl. Opt. 17 (1978) 52–56. 269. [4] H. Okamura, Fiber-optic magnetic sensor utilizing the Lorentzian force, IEEE J. Lightw. Technol. 8 (1990) 1558–1560.

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