Magnetic field sensing based on V-shaped groove filled with magnetic fluids

Transcription

1 Magnetic field sensing based on V-shaped groove filled with magnetic fluids Hongzhu Ji, Shengli Pu,* Xiang Wang, and Guojun Yu College of Science, University of Shanghai for Science and Technology, Shanghai 93, China *Corresponding author: Received 5 October 11; accepted November 11; posted 1 December 11 (Doc. ID ); published March 1 A magnetic field sensing system based on V-shaped groove filled with magnetic fluids is developed in this work. The propagation direction of the emergent light after the V-shaped groove (or the position of the emergent light on the detecting plane) is related to the strength of the externally applied magnetic field. The analytical expressions for the sensing system are derived in detail. The sensitivity and other sensing properties of the sensing system are investigated numerically and experimentally. The sensing mechanism is analyzed and ascribed to the magnetically tunable refractive index of magnetic fluids. 1 Optical Society of America OCIS codes: 16.38, Introduction X/1/811-11$15./ 1 Optical Society of America Magnetic fluid (MF) is a kind of homogeneous colloidal dispersion [1] of very fine magnetic nanoparticles (usually 3 15 nm in diameter) dispersed in a suitable liquid carrier with the aid of surfactant coated on the surface of the particles, which will prevent the particles from sticking to each other due to van der Waals attraction. The sizes of the magnetic particles are so small that the thermal energies are comparable to their gravitational ones [] and then the sedimentations are avoided. MFs possess both the fluidity of liquids and the magnetism of magnetic nanoparticles. The conventional optical properties of MFs including linear birefringence, linear dichroism, and Faraday effect have been investigated for several decades [3 5]. The latest study of optical properties of MFs have been extended to magnetically tunable optical scattering [6,7], field dependent refractive index [8 1] and optical transmission [11,1], tunable magnetic photonic crystals [13 16], etc. Several potential MF-based optical devices have been proposed and demonstrated, for instance, MF tunable optical gratings [17,18], MF optical switch [19,], MF optical modulator [1 4], MF optical capacitor [5], MF optical limiters [6,7], and MF sensors [8 3]. On the other hand, conventional electromagnetic current transformers (EMCTs) are unable to meet the requirements of current measurement devices in the new generation of power system due to their numerous defects, e.g., small dynamic range, saturated magnetic circuit, insulation problems, large size, inflammable and explosive, severe electromagnetic interference, and large measurement errors [33]. Then, the optical current transformers (OCTs) based on Faraday effect are proposed [34,35]. Though the performance of OCTs can surpass those of EMCTs, OCTs have low signal to noise ratio (SNR) owing to their high sensitivity to environmental disturbance. Moreover, OCTs usually need complex polarization maintaining devices to attain high performance. If the optical fiber is applied to the OCTs system (which is widely used at present), their sensitivity, linearity, and stability [36 38] may be reduced owing to the degradation of polarization state caused by the inherent birefringence of the sensing medium and the additional birefringence effect caused by various factors, e.g., change of outside temperature and pressure. Besides, multimode fiber as a sensing medium will lead to complex mode coupling and great depolarization phenomenon. As a result, 11 APPLIED OPTICS / Vol. 51, No. 8 / 1 March 1

2 the emergent light will turn out to be elliptically polarized light, which will decrease the performance of the OCTs. Under such circumstances, MFs with magnetically sensitive properties are used as sensing media to develop OCTs. I98, Presley and Rex developed highly-reliable sensors based on the magnetic hydrodynamics (MHD) of MF, which are widely used in the aircraft or the tank gun stabilization system [39]. Recently, many researchers have developed various MF-based sensors and the related patents are published [4 43], which are widely used in the field of aerospace, national defense, and military. These resolve the various testing problems in the peculiar, complex, and harsh conditions. In this work, the magnetic field sensing system based on V-shaped groove filled with MFs is developed, which does not necessarily need linearly polarized light. The V-shaped groove structure is relatively simple when compared with other sensing cells and the sensing sensitivity of the system can be tuned by adjusting the vertex angle of the V-shaped groove. Besides, the system can operate at any incident angle. Simultaneously, there is no inherent linear birefringence accompanying with the system because the sensing medium is in colloidal state. These make the MF-based OCT superior than other EMCTs and OCTs. Detailed theoretical derivation and simulation of the sensing system are conducted and verified by the experimental results.. Operating Principle It is well-known that magnetic particles within the MFs are dispersed randomly in the carrier liquid under zero external magnetic field owing to the Brownian motion [44 46]. When the external magnetic field strength exceeds a critical value (denoted by H c ), the magnetic particles will agglomerate to form magnetic chains which are distributed in the MF along the field direction owing to the magnetic attraction [47]. This variation of structure results in the refractive index (n MF ) change of MF. For the transverse field configuration (the applied magnetic field is perpendicular to the propagation direction of the incident light), n MF will decrease monotonously with the increase of magnetic field [48]. When the strength of magnetic field is very large, n MF will reach a saturated value due to the saturated state of the agglomeration at high field [49,5]. Figure 1 illustrates the cross-section view of the system used to realize the magnetic field sensing. d is the thickness of the glass slide; n, and n MF are the refractive indices of the outside medium, glass slide, and MF, respectively; θ is the angle of incidence on the interface between the outside medium and the glass slide; θ is the included angle of the V- shaped groove; θ (θ ) is the refraction angle on the interface between the glass slide and the MF (between the glass slide and the outside medium); h and h 1 are the heights of the incident point (denoted as A) and the emergent point (denoted as B 1 and B Fig. 1. (Color online) Cross-section view of the magnetic field sensing system based on V-shaped groove filled with magnetic fluids. corresponding to the situations at different magnetic fields) on the glass slide; Y 1 and Y are the heights of the emergent light on the detecting plane corresponding to the situations at different magnetic fields; L is the distance along z direction between the vertex of the V-shaped groove and the detecting plane; L is the distance along z direction between B and the vertex of the V-shaped groove. L 1 is the distance along z direction between B and the detecting plane. The solid and dashed lines correspond to the situations at different external magnetic fields. The propagation of the incident light passing through the index-tunable MF will be influenced when the externally applied magnetic field is changed. In our proposed sensing system (see Fig. 1), the direction of the emergent light is related to the strength of the externally applied magnetic field. Then, measuring the location of the emergent light on the detecting plane can be used to meter the strength of the externally applied magnetic field. 3. Theoretical Analysis A. Analytical Expression From Fig. 1, the following relationships can be obtained according to the Snell s law: n sin θ sin θ 1 n MF sin θ ; (1) n MF sinθ θ sin θ 1 n sin θ ; () where θ 1 (θ 1 ) is the refraction angle on the interface between the outside medium and the glass slide at point A (between the MF and the glass slide at point C as shown in Fig. 1), θ θ is the incident angle on the interface between the MF and the glass slide at point C. Equations (1) and () show that the glass slides are just like a bridge between the outside medium and the MF, so the thickness of the glass slide (d ) is ignored at first for the sake of the simplification (in the later context, the influence of d will be further considered). Accordingly, the modified Snell s laws for this system are 1 March 1 / Vol. 51, No. 8 / APPLIED OPTICS 111

3 n sin θ n MF sin θ ; (3) Y y Δy: (7) n MF sinθ θ n sin θ : (4) Then, the analytical expression for y (the height of the emergent light on the detecting plane when ignoring d ) can be derived as (see Appendix A for detailed mathematic operations) B. Simulation Results and Discussion Figure simulates the height of the emergent light (Y) as a function of refractive index of MF (n MF ) under various different parameters based on Eqs. (5) 3 P tgθ 6 sin θ h h tgθ Ptgθ sin θ y 4L 7 5 π P tgθ sin θ tg θ Ptgθ sin θ p sin θ P Q tgθ 1 sin θ P Q sin 4θ sin θp p 1 sin θ P Q sin 4θ sin θp sin θ tgθ P Qtgθ h P tgθ sin θ h tgθ Ptgθ sin θ π tg π P tgθ sin θ tg θ Ptgθ sin θ θ : (5) r where P sin θ and Q cos θ sin θ. n MF n Actually, the emergent light will have an offset after passing through a parallel glass plate. For this reason, the height of the emergent light on the detecting plane may also depend on the thickness of the glass slide. So, it is necessary to consider the influence of d on the height of the emergent light on the detecting plane for improving the accuracy and precision of the potential sensor. The analytical expression for the practical offset (Δy) on the detecting plane is obtained as (see Appendix B for detailed mathematic operations) (7). From Fig., we can conclude that the sensitivity of the sensing system (the slope of the Y-n MF curve) changes with the included angle of the V-shaped groove (θ ), the distance along z direction between the vertex of the V-shaped groove and the detecting plane (L) and the type (refractive index) of the outside medium (n ). While it does not change with the incident angle (θ), the height of the incident light on the glass slide (h ), the material type (refractive index) of the glass slide ( ), and the thickness of the glass slide (d ). sin θ Δy P Q n p d sin θ P n Q q d 1 sin θ P Q sin 4θ sin θp n 1 n sin θ P Q sin 4θ sin θp q d P n 1 n sin θ sin θ n sin θ cos θ q cos θ n 1 n sin θcos θ P sin θ sin θ p 1 sin θ P Q sin 4θ sin θp p cos θ 1 sin θ P Q sin 4θ sin θp sin θ sin θ P Q : (6) Therefore, the actual height of the emergent light on the detecting plane can be expressed as In Fig., the refractive index of MF (n MF ) rather than the actual magnetic field (H) is used as the variable. This is assigned to the multiple-parameter 11 APPLIED OPTICS / Vol. 51, No. 8 / 1 March 1

4 dependent property of n MF. For instance, n MF is not only related to H, but also related to ambient temperature T. The detailed expression for n MF H; T has a complex Langevin-function-like form [51]. Moreover, even under constant H and T, n MF also depends on many other factors, such as the type and concentration of the MF, the thickness of the sample. Consequently, n MF is employed as the variable, which is proportional to the magnetic field. For any specific situation, n MF can be replaced with the actual value of H. And then, the purpose of magnetic field sensing is obtained. For convenience and simplification (while without loss of generality), air (n 1) is chosen as the outside medium (n has a very slight influence on the sensitivity of the sensing system). This is the most cases for practical applications. The glass slide s refractive index ( ) and thickness (d ) are set as 1.5 and 1 mm, respectively, which do not influence the sensitivity of the sensing system. Because the sensitivity of the sensing system is independent of the incident angle θ, θ is adjusted to be equal to the included angle of the V-shaped groove (θ ) for simplification. Afterwards, on the basis of Taylor s formula, Eqs. (5) (7) can be simplified as (see Appendix C for detailed mathematic operations) Y θ Ln MF h 3θ L: (8) Equation (8) indicates that the relationship between the height of the emergent light (Y) and the refractive index of the MF (n MF ) is linear, which can also be seen in Fig.. This is favorable for practical application to sensors. To evaluate the accuracy of the simplified expression [Eq. (8)], simulations about the height of the emergent light (Y) as a function of refractive index of MF (n MF ) are implemented with the simplified [Eq. (8)] and exactly analytical expressions [Eq. (7)], which are shown in Fig. 3(a). From Fig. 3(a), it is obvious that the curves for the simplified expression almost overlap with those for the exactly analytical expression. The quantitative difference (denoted as Δ) between the simplified [Eq. (8)] and exactly (a) L5mm n = h.5 d (b) n = h.5 d L=mm L5mm L=5mm L=mm L L=5mm (c) h L5mm.5 = d n. n.333 n.361 n (e) (f) (g) h 9 =mm h 5mm.49 d h 75.5 d 7 7 =mm h =6mm.61 d =4mm L5mm 6 6 n n 1 = n = = h L5mm d d (d) L5mm n h.5 d 4 =.45 =5 L5mm n = h Fig.. (Color online) Height of the emergent light (Y) as a function of refractive index of MF (n MF ) under several different parameters: (a) different θ, (b) different L, (c) different n, (d) different θ, (e) different h, (f) different, and (g) different d. 1 March 1 / Vol. 51, No. 8 / APPLIED OPTICS 113

5 (a) Eq. 7 (exactly analytical expression) Eq. 7 (exactly analytical expression) Eq. 7 (exactly analytical expression) Eq. 7 (exactly analytical expression) =3. = Eq. 8 (simplified expression) Eq. 8 (simplified expression) Eq. 8 (simplified expression) Eq. 8 (simplified expression) (b).3 Difference (mm) =3. = Fig. 3. (Color online) (a) Comparison of the Y-n MF curves calculated with the simplified [Eq. (8)] and the exactly analytical expressions [Eq. (7)] and (b) Difference (Δ) between the two sets of equations as a function of n MF analytical expressions [(Eq. (7)] is shown in Fig. 3(b). From Fig. 3(b), we can see that the approximation error between the simplified [Eq. (8)] and exactly analytical expressions [Eq. (7)] is so small that we can ignore it, especially when the included angle of the V-shaped groove is very small. Therefore, the simplified expression Y θ Ln MF h 3θ L and the derived linear relationship between H and n MF are reliable. 4. Experimental Verification The MF we utilize for experimental investigation in this work is oil-based MF with saturation magnetization of 1 Oe and viscosity of 9 mpa s, which is provided by the Ferrotec Corporation. The magnetic nanoparticles are ferrite materials with average diameter of about 1 nm. The MF was injected into a V- shaped groove made of cover glasses and glass slides as shown in Fig. 4. The included angle of the V- shaped groove can be adjusted through changing the number of the cover glasses. Figure 5 shows the experimental diagram for investigating the proposed sensing system. A highly stable He-Ne laser generating a visible light of 63.8 nm is employed, whose electric vector is perpendicular to the magnetic field direction. The V-shaped groove sample is placed in the gap between two poles of the electromagnet which generates a uniform magnetic field (with nonuniformity of less than.1%) paralleling the sample surface. The strength of the external magnetic field is adjusted by tuning the magnitude of the supply current. The combination of lenses with long and short focal lengths is utilized to improve the collimation effects of the laser beam. The movable diaphragm at the detecting plane can be moved in two dimensions to let the emergent light pass through it. The transmitted light after the diaphragm is recorded by a digital power meter. Figure 6 displays the experimental sensing property of the system at several included angles of the V-shaped groove: (a) θ 1.4, (b) θ 1.77, (c) θ.49, (d) θ.84, (e) θ 3., and (f) θ From Fig. 6, we can see that the height of the transmitted light decreases with the current (to which the external applied magnetic field is linearly proportional) under certain included angle of the V-shaped groove. The slight fluctuations between the experimental and data are also observed. These may be originated from the instability of the experimental setup, the variation of the ambient temperature, and the light power. The variation range of the height of the transmitted light ΔY (the difference between the maximum and minimum values of the curve) increases with the included angle of V-shaped groove, which is more evident in Fig. 7. The physical mechanism in charge of the magnetic field sensing is the magnetically tunable refractive index of the MF. The electric susceptibility (χ) of MF is dependent on the magnitude of the applied Fig. 4. Schematic drawing of the V-shaped groove. Fig. 5. (Color online) Schematics of experimental setup for studying the sensing system based on the V-shaped groove filled with MF. 114 APPLIED OPTICS / Vol. 51, No. 8 / 1 March 1

6 (a) 11. Expermental data (b) Expermental data (c) (e) 8.8 Expermental data (d) Expermental data (f) Expermental data Expermental data Fig. 6. (Color online) Sensing property of the system at several included angles of the V-shaped groove: (a) θ 1.4, (b) θ 1.77, (c) θ.49, (d) θ.84, (e) θ 3., and (f) θ 3.55 and the strength of magnetic field H as a function of current I. magnetic field and the relative direction between the electric vector of the incident light and the magnetic field. In our experiments, the electric vector is perpendicular to the magnetic field and χ will decrease with the increase of magnetic field [48,5 54]. So n MF will decrease p with the external magnetic field according to n p ε r 1 χ. Hence, the larger the magnetic field strength is, the smaller the electric susceptibility (χ) of MF is and the smaller the refractive index of MF is. When the magnetic field strength is very low, the agglomeration would not happen and then the height of the transmitted light will almost not change with the applied magnetic field (current) as shown in Fig. 6. While the strength of the external magnetic field is large enough, the refractive index of MF will decrease into the saturated value, so the height of the transmitted light will not (or very slightly) change with the applied magnetic field (current) further as shown in Fig. 6. From the above theoretical analysis and experimental results, it can be concluded that it may be convenient to get the strength of the externally applied magnetic field to a certain extent by measuring the height of the transmitted light. In our experiments, the variation range of the transmitted-light s height, dominated by the tunable range of the refractive index of MF, is not very large due to the low viscosity Y (mm) Y is the difference between the maximum and minimum values of the Included angle of the V-shaped groove ( o ) Fig. 7. Variation range of the height of the transmitted light ΔY as a function of the included angle of the V-shaped groove θ. 1 March 1 / Vol. 51, No. 8 / APPLIED OPTICS 115

7 and small saturation magnetization of the MF. However, it may be possible to improve the variation range of the sensing system through optimizing the correlative parameters (e.g., concentration, viscosity and types of the MF; wavelength of the incident light). 5. Conclusions In summary, the V-shaped groove sensor based on the tunable refractive index of MF has been studied analytically and numerically. The operating principle of the sensor is analyzed in detail. The linear sensing property of the sensing system is obtained. The variation range of the height of the emergent light depends on the included angle of the V-shaped groove and the maximum variation range is around 3 mm in our experiments. Some parameters of the sensor can be optimized to get better results. The sensor based on this principle may lay a solid foundation for designing photonic sensing devices exploiting the tunable refractive index of MF. Appendix A The simplified diagram for the V-shaped groove is showed in the Fig. 8 where the thickness of the glass slide has been ignored. In this diagram, y is the height of the transmitted light in the detecting plane. θ θ is the horizontal angle of the refraction light within the MF. From Fig. 8, the following expressions are obvious: h 1 h L h tgθ tgθ θ ; (A1) π h 1 L tg θ ; (A) L 1 L L ; (A3) Fig. 8. (Color online) Diagram of geometric optical path ignoring the thickness of the glass slide. π y L 1 tgθ θ L tg θ : (A4) According to the triangular transformations and combining Eqs. (3) and (4), the following equations are obtained: tgθ θ tgθ tgθ 1 tgθ tgθ ; (A5) tgθ sin θ cos θ n sin θ q ; (A6) n MF n sin θ tgθ θ tgθ tgθ 1 tgθ tgθ ; (A7) s sin θ sin θ n MF n sin θ cos θ sin θ; (A8) v n s u cos θ 1 sin θ MF n sin θ cos θ sin n t MF θ sin 4θ sin θ n sin θ : (A9) y Combining Eqs. (A1) (A9), the height of the transmitted light on the detecting plane when ignoring the thickness of the glass slide can be expressed as 3 P tgθ sin θh h tgθ Ptgθ sin θ 4L 5 π P tgθ sin θtg θ Ptgθ sin θ p sin θ P Q tgθ 1 sin θ P Q sin 4θ sin θp p 1 sin θ P Q sin 4θ sin θp sin θ tgθ P Qtgθ h P tgθ sin θ h tgθ Ptgθ sin θ π tg π P tgθ sin θ tg θ Ptgθ sin θ θ : (A1) 116 APPLIED OPTICS / Vol. 51, No. 8 / 1 March 1

8 Appendix B The offset within the MF (denoted as D) between the transmitted lights when ignoring and considering the influence of thickness of the glass slide is shown in Fig. 9. In Fig. 9, d is the offset within the MF when n MF is equal to the refractive index of outside medium (n ). D is the practical offset within the MF when considering and ignoring the influence of thickness of the glass slide. The solid and dash lines represent the optical path when ignoring and considering the influence of thickness of the glass slide, respectively. From Fig. 9, the practical offset D within the MF is given by D where d is expressed as d cos θ cos θ ; (B1) d d cos θ 1 sinθ θ 1 : (B) Combining Eqs. (B1) and(b) and using the Snell s law [Eq. (1)] and some triangular transformations, D can be expressed as D d q n MF n sin θ q n MF cos θ n 1 n sin θ q n 1 n sin θ sin θ n sin θ cos θ : (B3) The actual offset on the detecting plane is shown in Fig. 1. In Fig. 1, d is the practical offset in the outside medium when considering and ignoring the influence of thickness of the glass slide and Δy is the offset on the detecting plane. The solid and dash lines represent the optical path when ignoring and considering the influence of thickness of the glass slide, respectively. Fig. 9. (Color online) Offset within the MF between the transmitted lights when ignoring and considering the influence of thickness of the glass slide. From Fig. 1, the expression of the actual offset on the detecting plane is expressed as d Δy cosθ θ : (B4) Meanwhile, the following equalities can be obtained: d BE cos θ ; (B5) D O 1 O cosθ θ CD: (B6) In the RtΔEO 1 D: tan EO 1 D EB BC CD O 1 D tan θ : (B7) In the RtΔBO C: tan BO C BC O C tan θ 1 : (B8) Combining the above equations and the Snell s laws [Eqs. (1) and ()], the actual offset on the detecting plane between consideration and ignorance of the influence of thickness of the glass slide can be expressed as sin θ Δy P Q n p d sin θ P n Q q d 1 sin θ P Q sin 4θ sin θp n 1 n sin θ P Q sin 4θ sin θp q d P n 1 n sin θ sin θ n sin θ cos θ q cos θ n 1 n sin θ cos θ P sin θ sin θ p 1 sin θ P Q sin 4θ sin θp p cos θ 1 sin θ P Q sin 4θ sin θp sin θ sin θ P Q : (B9) 1 March 1 / Vol. 51, No. 8 / APPLIED OPTICS 117

9 Because the value of θ n MF θ is less than n (which is close to 1) and (which is close to 1.5), the Maclaurin formula and θ θ (which is mentioned above) can be utilized to eliminate the radical expression. And then Eq. (C) can be greatly simplified as Y θ L h θ θ n 3 MF h 3θ L Fig. 1. (Color online) Offset on the detecting plane when considering and ignoring the influence of thickness of the glass slide. Appendix C Because the maximum included angle of the V-shaped groove is less than four degrees, which in radian is far less than one. According to the Taylor s formulas of sine and cosine functions, the expression of the height on the detecting plane can be simplified as 3h θ 4θ 3 : (C3) Equation (C3) shows that the height of the transmitted light obeys Y an MF b, where a is equal to θ L h θ 3 θ θ L 3 θ θ L and b is equal to h 3θ L3h θ 4θ 3 h 3θ L 4θ 3 h 3θ L. Therefore, the final simplified form can be described as Y θ Ln MF h 3θ L: (C4) Pθ Y L h Pθ 3 P1 θ θ θ p P θ θ 1 θ P θ P1 θ p θ 1 θ P θ θ P θθ h P1 θ θ θ p P 1.5 θ P θ θ p P θ θ θ θ p 1 θ p 1 θ P θ 1.5 θ P θ p P θ 1.5 θ Pθθ p 1 θ P θ θ θ P θ : (C1) q where P n MF θ. In our experiments, θ is always less than four degrees, so θ (in radian) 1 is satisfied. Therefore the relationships θ n MF or, θ 1, and θθ n MF are satisfied. Then Eq. (C1) can be further simplified as This research is supported by the National Natural Science Foundation of China (No ) and Innovation Program of Shanghai Municipal Education Commission (No. 11YZ1). Y L h θ θ p n MF θ θ 1 θ n MF θ θ p 1 θ n MF θ θ n h n MF θ θ p n MF θ p θ MF θθ 1 θ n MF θ 1.5 θ n MF θ 3 p 1 θ n MF θ p 1 θ n MF θ θ θ n MF θ : (C) 118 APPLIED OPTICS / Vol. 51, No. 8 / 1 March 1

10 References 1. R. E. Rosensweig, Ferrohydrodynamics (Cambridge University, 1985).. S. Pu and X. Chen, Dispersion stability requirements of the nanostructured magnetic liquid, J. Univ. Shanghai Sci. Technol. 3, (8), in Chinese. 3. D. Pagliero, Y. Li, S. Fisher, and C. A. Meriles, Approach to high-frequency, cavity-enhanced Faraday rotation in fluids, Appl. Opt. 5, (11). 4. S. Pu, M. Dai, G. Sun, and M. Liu, Linear birefringence and linear dichroism coupled optical anisotropy of magnetic fluids by external magnetic fields, in Proceedings of IEEE Conference on Photonics and Optoelectronics (IEEE, 9), pp R. Patel, V. K. Aswal, and R. V. Upadhyay, Magneto-optically induced retardation and relaxation study in a mixed system of magnetic fluid and cationic micelles, J. Magn. Magn. Mater. 3, (8). 6. H. Bhatt, R. Patel, and R. V. Mehta, Magnetically induced Mie resonance in a magnetic sphere suspended in a ferrofluid, J. Opt. Soc. Am. A 7, (1). 7. R. V. Mehta, R. Patel, B. Chudasama, and R. V. Upadhyay, Experimental investigation of magnetically induced unusual emission of light from a ferrodispersion, Opt. Lett. 33, (8). 8. Y. Zhao, Y. Zhang, R. Lv, and Q. Wang, Novel optical devices based on the tunable refractive index of magnetic fluid and their characteristics, J. Magn. Magn. Mater. 33, (11). 9. C.-Y. Hong, J.-J. Chieh, S.-Y. Yang, H.-C. Yang, and H.-E. Horng, Simultaneous identification of the low-field-induced tiny variation of complex refractive index for anisotropic and opaque magnetic-fluid thin film by a stable heterodyne Mach-Zehnder interferometer, Appl. Opt. 48, (9). 1. S. Pu, X. Chen, Y. Chen, W. Liao, L. Chen, and Y. Xia, Measurement of the refractive index of a magnetic fluid by the retroreflection on the fiber-optic end face, Appl. Phys. Lett. 86, (5). 11. J. Li, X. Qiu, Y. Lin, X. Liu, J. Fu, H. Miao, Q. Zhang, and T. Zhang, Oscillatory-like relaxation behavior of light transmitted through ferrofluids, Appl. Opt. 5, (11). 1. J. Li, Y. Huang, X. Liu, Y. Lin, Q. Li, and R. Gao, Coordinated chain motion resulting in intensity variation of light transmitted through ferrofluid film, Phys. Lett. A 37, (8). 13. C. Z. Fan, E. J. Liang, and J. P. Huang, Optical properties in the soft photonic crystals based on ferrofluids, J. Phys. D 44, 353 (11). 14. S. Pu, X. Bai, and L. Wang, Temperature dependence of photonic crystals based on thermoresponsive magnetic fluids, J. Magn. Magn. Mater. 33, (11). 15. L. Zhang and J. Huang, Photonic band structure of threedimensional colloidal crystals with field-induced lattice structure transformation, Chin. Phys. B 19, 413 (1). 16. S. Pu and M. Liu, Tunable photonic crystals based on MnFe O 4 magnetic fluids by magnetic fields, J. Alloys Compd. 481, (9). 17. A. Candiani, W. Margulis, C. Sterner, M. Konstantaki, and S. Pissadakis, Phase-shifted Bragg microstructured optical fiber gratings utilizing infiltrated ferrofluids, Opt. Lett. 36, (11). 18. S. Pu, X. Chen, L. Chen, W. Liao, Y. Chen, and Y. Xia, Tunable magnetic fluid grating by applying a magnetic field, Appl. Phys. Lett. 87, 191 (5). 19. W. Yuan, C. Yin, P. Xiao, X. Wang, J. Sun, S. Huang, X. Chen, and Z. Cao, Microsecond-scale switching time of magnetic fluids due to the optical trapping effect in waveguide structure, Microfluid Nanofluid, 1 5 (11).. Q.-F. Dai, H.-D. Deng, W.-R. Zhao, J. Liu, L.-J. Wu, S. Lan, and A. V. Gopal, All-optical switching mediated by magnetic nanoparticles, Opt. Lett. 35, (1). 1. P. Zu, C. C. Chan, L. W. Siang, Y. Jin, Y. Zhang, L. H. Fen, L. Chen, and X. Dong, Magneto-optic fiber Sagnac modulator based on magnetic fluids, Opt. Lett. 36, (11).. X. Bai, S. Pu, and L. Wang, Optical relaxation properties of magnetic fluids under externally magnetic fields, Opt. Commun. 84, (11). 3. X. Bai, S. Pu, L. Wang, X. Wang, G. Yu, and H. Ji, Tunable magneto-optic modulation based on magnetically responsive nanostructured magnetic fluid, Chin. Phys. B, 1751 (11). 4. T.-Z. Zhang, J. Li, H. Miao, Q.-M. Zhang, J. Fu, and B.-C. Wen, Enhancement of the field modulation of light transmission through films of binary ferrofluids, Phys. Rev. E 8, 143 (1). 5. R. Patel and R. V. Mehta, Ferrodispersion: a promising candidate for an optical capacitor, Appl. Opt. 5, G17 G (11). 6. S. Pu, L. Yao, F. Guan, and M. Liu, Threshold-tunable optical limiters based on nonlinear refraction in ferrosols, Opt. Commun. 8, (9). 7. H. Wu, X. Li, M. Zhang, D. Stade, and H. Schau, Analysis of a liquid metal current limiter, in Proceedings of IEEE Conference on Transactions on Components and Packaging Technology (IEEE, 9), pp L.-X. Chen, X.-G. Huang, J.-H. Zhu, G.-C. Li, and S. Lan, Fiber magnetic-field sensor based on nanoparticle magnetic fluid and Fresnel reflection, Opt. Lett. 36, (11). 9. Y. Miao, Y. Liu, B. Liu, K. Zhang, H. Zhang, and Q. Zhao, Intensity-modulated temperature sensor based on the photonic crystal fibers filled with magnetic fluid, Proc. SPIE 7753, (11). 3. J. Dai, M. Yang, X. Li, H. Liu, and X. Tong, Magnetic field sensor based on magnetic fluid clad etched fiber Bragg grating, Opt. Fiber Technol. 17, 1 13 (11). 31. P. Childs, A. Candiani, and S. Pissadakis, Optical fiber cladding ring magnetic field sensor, in Proceedings of IEEE Conference on Photonics Technology Letters (IEEE, 11), pp T. Hu, Y. Zhao, X. Li, J. Chen, and Z. Lv, Novel optical fiber current sensor based on magnetic fluid, Chin. Opt. Lett. 8, (1). 33. T. W. Cease and P. Johnston, A magneto-optic current transducer, in Proceedings of IEEE Conference on Transactions on Power Delivery (IEEE, 199), pp T. Verbiest and J. Wouters, Magnetic field sensing based on Faraday rotation in inorganic/polymer hybrid materials, Proc. SPIE 7467, 7467B (9). 35. C. D. Perciante and J. A. Ferrari, Faraday current sensor with temperature monitoring, Appl. Opt. 44, (5). 36. M. Li and Y. Li, Fiber-optic temperature sensor based on interaction of temperature-dependent refractive index and absorption of germanium film, Appl. Opt. 5, (11). 37. H. Zhang, Y. Dong, J. Leeson, L. Chen, and X. Bao, High sensitivity optical fiber current sensor based on polarization diversity and a Faraday rotation mirror cavity, Appl. Opt. 5, (11). 38. P. R. Forman and F. C. Jahoda, Linear birefringence effects on fiber-optic current sensors, Appl. Opt. 7, (1988). 39. Presley and W. Rex, Rate sensor, U.S. patent 4,19,189 (11 March, 198). 4. Suprun, E. Anton, Simonenko, and V. Dmitri, Location tracking device, U.S. patent 7,9,3 (6 November, 7). 41. TDK Corp, Angle sensor, JP Publication No , A (5). 4. O. Baltag, D. Costandache, and A. Salceanu, Tilt measurement sensor, Sens. Actuators 81(1 3), ,. 43. R. P. Bhatt, Magnetic-fluid-based smart centrifugal switch, J. Magn. Magn. Mater. 5, (). 44. R. Patel, Mechanism of chain formation in nanofluid based MR fluids, J. Magn. Magn. Mater. 33, (11). 45. J. Li, Y. Huang, X. Liu, Y. Lin, L. Bai, and Q. Li, Effect of aggregates on the magnetization property of ferrofluids: A model of gaslike compression, Sci. Tech. Adv. Mater. 8, (7). 46. P. Trivedi, R. Patel, K. Parekh, R. V. Upadhyay, and R. V. Mehta, Magneto-optical effects in temperature-sensitive ferrofluids, Appl. Opt. 43, (4). 1 March 1 / Vol. 51, No. 8 / APPLIED OPTICS 119

11 47. Y. F. Chen, S. Y. Yang, W. S. Tse, H. E. Horng, C.-Y. Hong, and H. C. Yang, Thermal effect on the field-dependent refractive index of the magnetic fluid film, Appl. Phys. Lett. 8, (3). 48. T. Liu, X. Chen, Z. Di, J. Zhang, X. Li, and J. Chen, Measurement of the magnetic field-dependent refractive index of magnetic fluids in bulk, Chin. Opt. Lett. 6, (8). 49. S. Pu, M. Dai, and G. Sun, Longitudinal field-induced polarized light transmittance of magnetic fluids, Opt. Commun. 83, (1). 5. Z. Di, X. Chen, S. Pu, X. Hu, and Y. Xia, Magnetic-fieldinduced birefringence and particle agglomeration in magnetic fluids, Appl. Phys. Lett. 89, 1116 (6). 51. C.-Y. Hong, H. E. Horng, and S. Y. Yang, Tunable refractive index of magnetic fluids and its applications, Phys. Status Solidi C 1, (4). 5. R. V. Mehta, R. J. Patel, B. N. Chudasama, H. B. Desai, and R. V. Upadhyay, Effect of dielectric and magnetic contrast on the photonic band gap in ferrodispersion, Magnetohydrodynamics 44, (8). 53. S. Y. Yang, J. J. Chieh, H. E. Horng, C.-Y. Hong, and H. C. Yang, Origin and applications of magnetically tunable refractive index of magnetic fluid films, Appl. Phys. Lett. 84, (4). 54. C.-Y. Hong, S. Y. Yang, H. E. Horng, and H. C. Yang, Control parameters for the tunable refractive index of magnetic fluid films, J. Appl. Phys. 94, (3). 1 APPLIED OPTICS / Vol. 51, No. 8 / 1 March 1