The dielectric property and magneto-optical effects of ferrofluids have been investigated in the terahertz (THz) regime by using THz time-domain spectroscopy. The experiment results show that the refractive index and absorption coefficient of ferrofluid for THz waves rise up with the increase of nanoparticle concentration in the ferrofluid. Moreover, two different THz magneto-optical effects have been found with different external magnetic fields, of which mechanisms have been theoretically explained well by microscopic structure induced refractive index change in the magnetization process and the transverse magneto-optical effect after the saturation magnetization, respectively. This work suggests that ferrofluid is a promising magneto-optical material in the THz regime which has widely potential applications in THz functional devices for THz sensing, modulation, phase retardation, and polarization control.
© 2014 Optical Society of America
In recent years, the development of terahertz (THz) techniques has dramatically accelerated THz applications in imaging, sensing and communication [1–3], which need various THz functional devices, such as THz filter , modulator , polarizer , isolator , and sensor . To realize these devices, THz functional materials are indispensable, such as liquid crystal [4, 9], vanadium dioxide [10, 11], semiconductors [12, 13], and graphene . Magneto-optical devices have an irreplaceable role in the THz systems  for one-way transmission [7, 16], polarization and phase control [17, 18], and magnetically active manipulation . However, the existing magneto-optical materials in the THz regime have some limitations which confine the development of THz magneto-optical functional devices. For example, high electron mobility semiconductors such as InSb , HgTe  and graphene  need low temperature, while ferromagnetic materials  usually have a significant loss and needs an extremely strong operating magnetic field in the THz regime.
Recently, ferrofluid has been drawing much attention due to its flow characteristics and sensitivity under a weak external magnetic field (EMF). Ferrofluid is a colloidal suspension composed of magnetic nanoparticles in a carrier liquid, of which optical and magneto-optical properties have been extensively investigated in the optical frequency range [22, 23], especially in liquid-filled photonic devices [24–26]. However, its optical and magneto-optical properties in the THz regime have been reported rarely, until recently, Shalaby et.al  has demonstrated the Faraday rotation effect in the ferrofluid under the weak EMF and its absorption loss is low in the THz regime. Fan et.al  found the THz magneto-plasmon splitting and induced THz transparency phenomenon in a photonic crystal filled with magnetized ferrofluid. These reports have confirmed the ferrofluid has a magneto-optical response under a weak EMF in the THz regime at room temperature, but its optical and magneto-optical properties have not been studied comprehensively.
In this paper, we investigated the optical and magneto-optical properties of ferrofluid in the THz regime by using THz time-domain spectroscopy (THz-TDS) system. We demonstrated the influence of magnetic nanoparticle concentration on the optical properties of ferrofluid, and furthermore, found the magnetic optical effects of ferrofluid under different EMF in the THz regime, experimentally and theoretically confirmed that its magnetically induced refractive index changes result in two different mechanisms: one is the birefringence induced by the microstructural changes of ferrofluid under a low EMF, and the other one is transverse magneto-optical effect after the saturation magnetization of the ferrofluid under a higher EMF.
2. Dielectric properties of ferrofluid in the terahertz regime
The ferrofluids used in our work are Fe3O4 nanoparticles dispersed in the carrier liquid of iso-paraffinic light hydrocarbon oil (C25H43NO3), and three different concentrations of the nanoparticles are 3.9% (Sample A), 7.9% (Sample B) and 17.7% (Sample C) in volume. Sample A has been taken by the transmission electron microscope (TEM) images shown in Figs. 1(a) and (b) with and without EMF, respectively. The ferrofluid was dried into the nanoparticle powder on a TEM standard grid in the vacuum when we took TEM photos. Thus in fact this is a photo of overlapped multilayers of the nanoparticles projected form space into the grid plane. The regions of a high nanoparticle concentration appear dark, while the regions of few nanoparticles appear bright. Figures 1(a) and 1(b) show that the nanoparticle concentration accompanying with its grouping and alignment changes when the EMF is applied, but they are not the real states for the ferrofluid because they are the dry powder not the flowing liquid. The more realistic observations for the ferrofluid are shown in Figs. 1(c)–(e) by a 50 × optical microscope. When the ferrofluid is not magnetized, there is no cluster in the ferrofluid. After magnetized by a weak EMF, the particles were triggered to form the magnetic cluster chains with the same size along the direction of the EMF. We have also found that these magnetic cluster chains can remain stable after taking out the EMF if there is no external disturbance.
We used a standard four parabolic mirror THz-TDS system in the experiments . THz pulses are generated by GaAs photoconductive antenna which is excited by a femtosecond laser. The excitation source is a Ti:sapphire laser with 75 fs duration of 80MHz repetition rate working at 800nm. ZnTe crystal is used for electro-optic sampling probe. The experment temperature is 25°C. The ferrofluid is filled in a 3mm gap quartz cuvette which is highly transparent for THz waves, and the sample is settled at the focal point of the THz-TDS system as shown in Fig. 2(a). The EMF is tunable and arranged to be orthogonal to the propagation and polarization directions of THz waves as a Voigt configuration .
Firstly, we measured the THz spectra of these ferrofluids without EMF, and the blank quartz cuvette was set as the reference. The time-domain signals of the reference, carrier liquid without nanoparticles and three ferrofluid samples are shown in Fig. 2(b). In this figure, on the one hand, the delay time of the sample signals compared to the reference is proportional to the average refractive index of the ferrofluid; on the other hand, the attenuation in the amplitude of the sample signals compared to the reference is proportional to the average absorption of the ferrofluid in the THz regime. Therefore, with the increase of nanoparticle concentration, the average refractive index and absorption of the ferrofluid rise up in the THz regime.
The refractive index and absorption coefficient spectra were obtained in Figs. 2(c) and 2(d) by using Fourier transform of the tine-domain data shown in Fig. 2(b) and some simple post calculations. The absorption coefficient α is defined as α = [ln(I1/I0)]/L, where I0 is the initial intensity, I1 is the transmitted intensity, L is the transmission distance, and the unit of absorption coefficient α is cm−1. The refractive indexes of the carrier liquid, Sample A, B and C are 1.46, 1.52, 1.65 and 1.92 at 1THz, respectively. The dispersion in 0.2–1.6THz is very small and the refractive index slightly decreases with the increase of frequency. The absorption coefficients of the carrier liquid, Sample A, B and C are 1.78cm−1, 2.11cm−1, 2.33cm−1, and 3.98cm−1 at 0.2THz, respectively, and increase with the frequency, which means that the ferrofluid compounded in this mineral oil carrier has a low absorption for THz waves. The results indicate that the refractive index and absorption coefficient of the ferrofluid rise up with the increase of nanoparticle concentration in the THz regime. Therefore, this optical property of the ferrofluid shows it can be used as a good refractive index matching (RIM) liquid with a low loss and dispersion in the THz functional devices since its refractive index can be broadly controlled in the range of about 1.5–1.95 by changing its concentration. The THz absorption shown in Figs. 2(b) and 2(d) can be usually ignored, because the applications in THz functional devices usually fill 10–100um thickness of RIM liquid in these devices and thus 3mm thickness ferrofluid would not be required.
3. Terahertz magneto-optical properties of ferrofluid
In this section, the THz spectra of the ferrofluid under the different EMFs were investigated in Voigt configuration. Figure 3(a) shows the THz time-domain signals of Sample B, and Fig. 3(b) shows that the refractive index at 1THz varies with the EMF. We find an interesting phenomenon that the refractive index changes with the EMF increasing and this changes can be clearly divided into two process as shown in Figs. 3(a) and 3(b): the first one is that the THz pulse delay initially increases and thus the refractive index increases from 1.652 to 1.668 at 1THz when B = 0–10mT; the second one is that when the EMF increases beyond 15mT, the THz pulse delay turns back and thus the refractive index decreases from 1.668 at 10mT to 1.656 at 150mT.
Moreover, when we removed the EMF (B = 0T), the THz pulse did not return to the origin location (n = 1.652), only turned back to the rightmost location (n = 1.668) instantaneously. Without any demagnetization to the ferrofluid, we repeated this experiment increasing the EMF form 0 to 150mT again, and found that this change of the refractive index became a monotonic process of descending from 1.668 to 1.656 without the first increasing process from 1.652 to 1.668 shown in Fig. 3(b). And we noticed that the second process was an instantaneous change when the EMF was applied or removed. Apparently, the first process which we define as “Structurally induced refractive index change process” is closely related to the magnetization process of the ferrofluid under a weak EMF, while the second process which we define as “Voigt magneto-optical effect induced birefringence” is only influenced by the EMF after the saturated magnetization and requires the EMF to be continuously applied. In the following discussions, we’ll respectively investigate the physical mechanisms in these two magnetically induced refractive index changes of the ferrofluid in the THz regime based on the experiment data.
3.1 Structurally induced refractive index change
Here, we firstly focus on the first process. Figure 4 shows the refractive index spectra of Sample A, B and C with the different weak EMFs in the THz regime. The maximum changes of the refractive index in these three ferrofluid are 0.012, 0.016, and 0.002, respectively. We can see that although the three samples have the different refractive indexes and dispersions, their changing tendencies with the EMF changes are consistent. Under an EMF, the magnetic dipole moments start to align with the EMF. This is counteracted by the thermal energy that tends to randomize the orientation of the dipole moments. The average number of magnetic moments aligned to the external field can be statistically estimated. For this process (mostly lower than 15mT), the magnetic nanoparticles form the ordered chains along the magnetic field direction as mentioned above shown in Figs. 1(c)–1(e), and this microscope structural change in the magnetization process leads to the refractive index changes of the ferrofluid. Once the magnetic chains trend to be steady after the saturation magnetization, the structural change has no contribution to the refractive index changes. In this case, the refractive index will remain unchanged without any shaking or demagnetization to the ferrofluid.
Based on these, the Bruggman effective medium theory (EMT) can be used to describe this structurally induced refractive index change, because this model treats the two media on equal footing and is able to describe the system across a percolation transition . The refractive index of the ferrofluid is a combined effect of mineral oil and nanoparticles, so the two media we used in our EMT are the mineral oil with unaligned nanoparticles at the dispersed state and the mineral oil with aligned nanoparticles at magnetic chain state. The intermediate state is taken as a mixture state of these two media, and the volume fraction f of the magnetic chain state in the ferrofluid under the different EMF determines the changes of the refractive index of ferrofluid. The refractive index of the ferrofluid in the process of the magnetic chains formation can be expressed as :17]:Fig. 4 can be taken as ε1 and ε2, respectively. According to Eqs. (1) and (2), we calculated the refractive index changes of the three samples at 1THz as shown in Fig. 5. The coefficient k were fitted as 0.94, 0.76, and 0.55 for Sample A, B and C, respectively. Obviously, k decreases with nanoparticle concentration increasing in this model. As shown in Fig. 5, three theoretical curves all agree well with each corresponding experiment data, so the structurally induced THz refractive index change in the ferrofluid can be well described by the EMT and Langevian magnetization models.
3.2 Voigt magneto-optical effect induced birefringence
Next, we turn to focus on the second process. As the microscope structures of the magnetic chain clusters in the ferrofluid are stabilized when the EMF continued to increase, the refractive index of ferrofluid in the THz regime is only influenced by the EMF not the microscope structure. Once the ordered magnetic chain clusters are completely formed in the ferrofluid, the ferrofluid can serve as a kind of ferromagnetic material and show the magneto-optical properties. These magneto-optical properties derive from the spin magnetic moment of the magnetic nanoparticles, and the magnetic clusters of these nanoparticles with an ordered arrangement exhibit macroscopic magneto-optical properties under an EMF, such as Faraday effect and Voigt transverse magneto-optic effect.
Our experiments were set as Voigt configuration as shown in Fig. 2(a). In this configuration, only the p-polarized light can be affected by the EMF and the s-polarized light has no relation with the EMF . As shown in Fig. 6(a), when the EMF was tuned from 10mT to 150mT, the refractive index of p-polarized wave np for Sample A, B and C decreased by 0.009, 0.013 and 0.008 at 1THz, respectively. When we turned the polarization direction of THz source 90° to measure the refractive index of s-polarized wave ns, the ns was changed similarly as the p-polarized wave when the EMF was applied from 0 to 10mT, but it remained unchanged with the EMF continuously increasing. Therefore, the birefringence is totally dependent on the EMF after the formation of magnetic chain clusters, and this property is the same as the Voigt magneto-optic effect of other magneto-optical materials.
According to Eqs. (4)–(6), the dispersion maps of the refractive index np were calculated. The fitting parameters used in the calculations are shown in Table 1. From Table 1, we can find that ωp and γ increase with the nanoparticle concentration increasing from 3.9% for Sample A to 17.7% for Sample C. The gyromagnetic ratio is the same due to the same Fe3O4 nanoparticles in the three samples. The results are shown in Fig. 7 and can be primarily fitted with the experiment data shown in Fig. 6. Therefore, the second process of refractive index changes is well explained by the Voigt magneto-optic effect induced THz birefringence in the saturation magnetized ferrofluid under the EMF by both experiment and theory. At other wavelengths, the structurally induced refractive index change is similar to our results [23–26]. For example, in Yang’s research , the refractive index of the ferrofluid increases from 1.462 to 1.467 as the EMF changes from 0 to 25mT. However, Voigt magneto-optical effect induced birefringence has not been reported at other wavelengths, which is a unique effect for THz waves because the plasma frequency and cyclotron frequency are just located in the THz regime. This effect exists not only after the nanoparticles are aligned but also during the progress of alignment. The first effect leads to the refractive index increase, but the second effect leads to the decrease. In fact, the experiment phenomena shown in Fig. 3 are the results of the competition between the two effects. However, the second effect is unapparent under a weak EMF, so it has been ignored during the first process in our above discussions.
In conclusion, we have investigated the dielectric property and magneto-optical effect of ferrofluid in the THz regime. We have found that the refractive index and absorption coefficient of ferrofluid for THz waves are corresponding to the concentration of Fe3O4 nanoparticles in the ferrofluid. More significantly, two different THz magneto-optical effects under the different EMF have been found. We have theoretically explained their mechanisms as microscopic structural change induced birefringence in the magnetization process and transverse magneto-optical effect after saturation magnetization, respectively. It illustrates that the ferrofluid is a hopeful magneto-optical material in the THz regime which has broadly potential applications in THz functional devices for THz sensing, modulation, phase retardation and polarization controlling.
This work was supported by the National Basic Research Program of China (Grant No.2014CB339800), the National High Technology Research and Development Program of China (Grant No. 2011AA010205), the National Natural Science Foundation of China (Grant No. 61171027), and the Science and Technology Program of Tianjin (Grant No. 13RCGFGX01127). Thanks Dr. Yasu and Dr. Raj from Ferrotec Corporation providing ferrofluid samples for our researches.
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