All fiber electro-optic modulation using a polarimetric cell based on an electro-optic fiber with internal Pb-Sn electrodes was demonstrated. For the polarimetric cell, the electro-optic fiber with two 149 cm long internal electrodes was fabricated by injection of a molten Pb-Sn alloy into the holes of the fiber. The characteristics of the modulation were explained by the electric field induced phase retardation due to the polarization dependent electro-optic Kerr effect. The difference in the effective second order nonlinearity between TM and TE polarization directions was obtained to be 0.0035 pm/V at the applied DC voltage of 6.5 kV.
©2006 Optical Society of America
Optical devices based on all fiber configurations have attractive features in communication, laser, and sensing applications because of the many advantages such as high optical transparency and damage threshold, low production cost, and direct integratability with another fiber based devices. It is well known that the second order optical nonlinearity is originally prohibited in glass because of its isotropic structural characteristics, however, the large second optical nonlinearity of 1–12 pm/V in the glass fibers could be successfully induced by introducing the frozen-in electric field that break the structural symmetry through glass poling process accompanied with heat-treatment or UV irradiation [1, 2].
Recently, an electrode formation technique was developed using injection of conducting alloy at liquid state to form electrodes in the holes of glass fibers . The technique made it possible to form very long internal electrode more than 100 cm inside the fibers with high thermal, electrical, and mechanical stabilities. By use of fibers with an internal single- or twin-electrode, a polarization controller based on the stress-induced birefringence of an internal electrode  and an active mode-locked laser constructed by an all fiber electro-optic modulator  were demonstrated. Electro-optic data conversion for video signal transmission was also demonstrated at the rate of 10 MHz using all fiber modulator based on an electro-optic fiber . More recently, possibility of an electro-optic fiber for polarization control was examined by introducing the relative phase change in an arm with the orthogonal polarization state to the other arm of a Mach-Zehnder interferometer (MZI) . AC voltage sensing application at the modulation frequency range of 50–60 Hz was investigated in a low coherent interferometer using the electric-field induced birefringence of an electro-optic fiber .
However, most applications of the electro-optic fibers with internal electrodes including planar waveguides have been studied with the structure based on a MZI [5–7, 9–11]. We expect that a polarimetric cell is capable of being used as an alternative modulation device with its simplicity in structure, although the polarization dependence of the refractive index change by the electric field was not so significant in the electro-optic fibers [7, 8, 12]. In this paper, therefore, we investigate an all-fiber electro-optic modulation device using a polarimetric cell based on an electro-optic fiber with internal Pb-Sn alloy electrodes. An electro-optic fiber with two internal electrodes was fabricated by injection of molten 37% Pb-63% Sn alloy into the holes of a germanium doped fiber. Effect of the externally applied DC voltage, used as the role of the frozen-in electric field in electric-optic fibers with poling treatment, on the modulation capability of the device was examined using the fiber without poling treatment. As a result, electro-optic modulation could be achieved by applying the DC voltage superimposed on the electric modulation signal. The intensity of the modulation was shown to increase with the increase of the applied DC voltage and the stability of the modulation was testified in the range, 0–50 kHz. The operating mechanism and characteristics of the modulation were examined.
2.1. Fabrication of an electro-optic fiber with internal electrodes
An optical fiber preform with a germanium doped core and a silica cladding was made by the modified chemical vapor deposition (MCVD) process and then two holes with diameter of 4 mm were drilled at both sides of the core. The preform with two holes was drawn into an optical fiber with diameter of 125 µm preserving the holes during the fiber drawing process. The diameters of the fiber core and the holes were 6.1 µm and 20.1 µm, respectively, and the refractive index difference between the core and cladding was 0.0046 for the single mode operation at 1550 nm.
For the formation of conductive electrodes in the fiber, the molten alloy injection technique was used . A molten alloy with the composition of 37% Pb-63% Sn was injected into the holes of the fiber by the aid of nitrogen gas at 10 bar, resulting in an optical fiber with two continuous internal electrodes with the length more than 100 cm. Figure 1 shows the cross-section of the fiber before and after the formation of the electrodes. The distances between the center of the core and the nearest surface of the electrode and the edge to edge distance between the electrodes were 14.6 and 39.7 µm, respectively. For electric contact with the electrodes of the fiber, the side of the fiber was polished using an abrasive pad and the electrode was connected with a metal wire using a conductive silver epoxy. Then, the electric resistance of the electrode was investigated and the resistance of the electrode was measured to be ~4.2 Ω/cm.
Figure 2 shows the optical transmission spectra of the electro-optic fiber measured by an optical spectrum analyzer (Ando, AQ-6315B) and a white light source (Ando, AQ-4303B). The electrode length of the fiber was 95 cm and the lengths of the unfilled holes were 2.5 cm at both side regions of the electrode in the electro-optic fiber. Normal Ge-doped single mode fibers with the lengths of 100 cm were connected to the fiber at both sides by a fusion splicer for the measurement. As a reference, the transmission of the electro-optic fiber before the formation of the electrode was also measured with the same length.
It was found that the transmission slightly decreased with the increase of the wavelength in the fiber without the electrode. On the other hand, the transmission of the fiber with the electrode more strongly decreased with the increase of the wavelength. The optical loss was considered to be induced by the light absorption at the electrode surface. Larger optical loss was induced at longer wavelength because of smaller optical confinement in the core at longer wavelength. The electrode induced optical loss was estimated to be 10.3 dB at the wavelength of 1550 nm.
2.2. All fiber polarimetric modulation device
Schematic of a polarimetric modulation device using the electro-optic fiber with the internal electrodes is shown in Fig. 3. Polarized light at 1550 nm with the optical power of 5 mW from a tunable laser source (TLS) was injected into the fiber after its polarization state was controlled by a polarization controller (PC). Then it passed through the internal electrode fiber and a linear polarizer, and finally the optical power of the light was detected at the output port by a photo-receiver. To optimize the optical modulation by aligning a polarizer with respect to the principal axes of the fiber at 45° , another PC was used at the front of the polarizer. The principal axes of the fiber corresponds to the polarization directions of light parallel and perpendicular to the direction of the external electric field, as was also described with Eq. (2) in Section 4. The length of the electrode in the electro-optic fiber was 149 cm and the fiber was connected with normal single mode fibers by the fusion splicer. The sinusoidal AC electric signal with the peak-to-peak voltage of 0-1300 Vpp was applied to the electrodes of the fiber and the biased DC voltage with the different magnitude in the range of 0–8 kV was superimposed on the AC signal. The modulation frequency of the applied AC electric signal was also tuned in the range from 1 to 55 kHz for investigation of the frequency dependence.
3. Electro-optic modulation characteristics
At first, the effect of the DC voltage on the modulation characteristics of the optical signal was investigated. Figure 4 represents the optical signal with the different biased DC voltages superimposed on the modulation AC signal with the constant peak-to-peak voltage of 560 Vpp and the modulation frequency of 20 kHz. As shown in the figure, no optical signal was found at the zero DC voltage. This means that there was no initial phase retardation in the fiber and the intensity of AC voltage was too small to induce optical modulation by changing the phase retardation with itself. On the other hand, the clear optical signals well matched with the applied modulation frequency, 20 kHz, were found at the higher DC voltages and the modulation intensity increased with the increase of the DC voltage. The optical modulation obtained by the AC signal with the higher DC voltages resulted from the electro-optical generation of the initial phase retardation by the DC voltage and the additional modulation of the retardation by applying the AC signal as discussed in Section 4.
The frequency dependence of the optical modulation was investigated by changing the frequency of the applied AC signal. For the investigation, the peak-to-peak intensity of AC signal and the DC voltage were maintained at the constant 560 Vpp and 5 kV, respectively. Figure 5(a) represents the modulated optical signal with the different modulation AC frequencies of 10, 30, and 50 kHz, respectively. The periods of the optical modulations, 100, 33.3, and 20 µsec, were well matched to the modulation frequencies of the applied AC signals, 10, 30, and 50 kHz, respectively. The peak-to-peak intensity of the optical signal with the frequency of the applied AC signal in the range 1–55 kHz is shown in Fig. 5(b). The modulation intensity of optical signal was found to be very stable in the frequency range with the fluctuation below ±4.5%.
Figure 6(a) shows the modulated optical signal obtained by applying different peak-to-peak AC voltages of 560, 840, and 1300 Vpp with the constant biased DC voltage of 6.5 kV at the constant modulation frequency of 20 kHz. The optical modulations of 11, 21, and 36 % in the optical intensity were obtained at the AC voltages of 560, 840, and 1300 Vpp, respectively. The peak-to-peak intensity of the optical modulation increased with the increase of the intensity of the applied AC voltage as shown in Fig. 6(b).
4. Electro-optic Kerr effect in the fiber
The modulation characteristic with the different DC voltage could be explained by the phase retardation due to the electro-optic Kerr effect in the polarimetric cell made by the electrooptic fiber with internal electrode.
where n and n 0 are the refractive indices with and without the electric field, respectively, χ (3) is the third order nonlinear optical coefficient, and =3χ(3)E is the effective second order nonlinear optical coefficient.
To characterize the electro-optic Kerr effect of the fiber with the internal Pb-Sn electrode, the electric field induced phase change in MZI made by the internal electrode fiber was investigated during applying the DC voltage. The MZI consisted of two 3 dB fiber couplers and the internal electrode fiber with the electrode length of 149 cm as an active arm. The same fiber without the electrode was used as a reference arm. The DC voltage applied to the electrode was in the range 0–6.8 kV and the shift in interference fringe of the MZI was measured by the OSA. Figure 7 shows the phase shift of the interference fringe with the different DC voltage applied and its fitted curve with a parabolic function. The phase shift due to the refractive index change, induced by the electro-optic Kerr effect in the internal electrode fiber, showed the parabolic characteristic as expected in Eq. (1).
The third order nonlinear coefficient was calculated to be 1.79×10-22 m2/V2 from the fitted parameter using Eq. (1).
Dependence of the modulation intensity of the optical signal on the DC voltage was investigated and the result is shown in Fig. 8 with a fitted curve. The different DC voltage in the range 0–7 kV was applied to the fiber with the constant peak-to-peak AC voltage of 560 Vpp and the fixed modulation frequency of 20 kHz. The peak-to-peak intensity of the optical signal gradually increased with the increase of the DC voltage and reached the maximum at 6.5 kV, then decreased with the further increase of the voltage. The shift was well fitted by the curve, y=ax·sin(b+c·x 2), where a, b, and c are the constants and were obtained to be 7.45, -24.4, and 0.0274, respectively.
It is known that the effective second order nonlinear coefficient, induced by the electro-optic Kerr effect in an isotropic material under an DC electric field, has polarization dependence as [15, 16],
where the subscripts of TM and TE indicate the polarization directions of light parallel and perpendicular to the direction of the external electric field, respectively. The γ represents the magnitude ratio of the effective second order nonlinear coefficients between the two polarization directions in the material.
If we take the TM polarization term as ΔnTM = E/(2n 0)=3χ (3) E 2/(2n 0), the TE polarization term yields ΔnTE = E/(2n 0 γ) from Eqs. (1) and (2). Therefore, in the polarimetric modulator made by the internal-electrode fiber with the applied the external electric potential, V(=E·d), the transmitted optical power, T, affected by the retardation due to the electro-optic Kerr effect is expressed as 
where Γ is the total retardation, Γ0 is the retardation from the birefringence of structural asymmetry of the fiber and the polarization controllers, L is the electrode length, λ0 is the optical wavelength, and d is the distance between the electrodes.
When the small AC electric signal, dV, compared with larger DC voltage is applied, the differentiated form, dT, of the power is given by
The peak-to-peak intensity of optical signal with the DC voltages was well fitted by the theoretical Eq. (4) as shown in Fig. 8. From the fitting value of the curve (c=0.0274), γ was obtained to be 1.04 and the difference in between the TM and TE directions was 0.0035 pm/V at the DC voltage of 6.5 kV using χ (3)=1.79×10-22 m2/V2 obtained from Fig. 7. The ratio of the effective second order nonlinear coefficients between the two polarization directions was close to 1 and it differed from the theoretically expected value, γ=3 . In a practical aspect of the modulation device, having a large γ is important since the voltage, Vπ , for the π-phase retardation decreases with the proportional to as expected from Eq. (3). In Fig. 8, the voltage (6.5 kV) for the maximum modulation intensity (In Fig. 6, the modulation of 11% of the maximum of the optical signal was obtained with the same modulation condition.) corresponds to Vπ /2 and is very larger than that of the MZI, ~ 2.2 kV from Fig.7. This point can be considered to be a problem of the device for a practical application typically requiring a low driving voltage.
The similar characteristics of the deficiency of polarization dependence in the nonlinearity were also found in the poled fibers [7, 8] and the planar waveguides before and after glass poling . There are possible explanations for the deficiency such as the electrostrictive contribution to the electro-optic Kerr effect  and the anisotropy of the third-order nonlinearity , however, it is difficult to clearly explain with a conclusion. Thus, further investigations should be followed to fully understand the origin and characteristics of the polarimetric modulation in the internal electrode fiber and the characteristics of the modulation in the fiber after glass poling is presently under examination.
Electro-optic modulation using the all fiber polarimetric cell based on the electro-optic fiber with the internal electrodes was demonstrated for the first time. It was found that electro-optic modulation could be obtained by applying DC electric field superimposed on the modulation electric signal. The operation mechanism was explained by the phase retardation induced by the electro-optic Kerr effect. The difference in the effective second order nonlinearity between TM and TE polarization directions was obtained to be 0.0035 pm/V at the applied DC voltage of 6.5 kV.
This research was partially supported by Korea Science and Engineering Foundation through Ultrafast Fiber-Optic Networks, an Engineering Research Center program of GIST and by the Brain Korea-21 Project, Ministry of Education and Human Resources Development, Korea.
References and links
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