1. INTRODUCTION

Daniel Colladon initiated the field of optical waveguiding by demonstrating the possibility of guiding light through a curved stream of water in 1841. In 1953, image transmission through the first fiberscope was demonstrated ^[1]. Today, optical fiber has become an integral part of many fields, including telecommunications ^[2], medicine ^[3], and metrology ^[4].

Fiber sensors can, in principle, provide the same quality features as their free-space counterparts while being cheaper, more compact, and easier to use. Passive fiber sensors are usually implemented as Sagnac interferometers ^[5,6], Michelson interferometers ^[7], Fabry–Perot interferometers ^[8], or microfibers ^[9] to measure magnetic fields, strain, torsion, and temperature. These sensors monitor the phase shift or spectral changes of transmitted broadband light ^[8,10].

It is shown here that simply monitoring the polarization of initially circularly polarized light transmitted through a polarization-maintaining (PM) fiber leads not only to new sensing methods, but also to power control, saturable absorption, and the possibility of optical path stabilization. Even at peak power levels not exceeding a few mW, nonlinear transmission is detected, with time constants in the microsecond range. All effects related to the Kerr nonlinear index can be neglected in the range of powers considered here.

Single-mode (SM) fibers exhibit some birefringence, typically stress-induced, such that the polarization of a beam sent through the fiber varies with the positioning and bending of the fiber. This effect has been exploited for generating short pulses through polarization mode-locking ^[11]. PM fibers were introduced to maintain linear polarization along a preferred axis. As a very high-order waveplate, it is designed with different indices of refraction along two orthogonal axes (the “slow axis” for the higher index, the “fast axis” along the direction of lower index). One defines the “beat length” (typically a few millimeters) as the distance over which the retardation between slow and fast light equals 2π. Any input polarization other than linear (along a principal axis) will be periodically modified along the fiber. While the beat length is considered to be a constant, small variations can take place because of environmental conditions (temperature, stress, magnetic field) or power variations of the propagating light. By accumulating beat length variations over long distances, we demonstrate extreme sensitivity in the measurement of many parameters affecting the fiber birefringence.

2. POLARIZATION ELLIPSE MEASUREMENTS

To make a comprehensive determination of the polarization modification, the polarization ellipse is measured for each value of a given parameter affecting the beat length. The setup to measure the change in polarization of the transmitted beam is shown in Fig. 1. A CW laser diode at 1550 nm generates linearly polarized light that is made circularly polarized by a quarter-wave plate at 45° to excite both modes of the PM fiber independently of the orientation of the input end of the PM fiber. Fibers of the PANDA type were used, where the principal axis is defined by “stress rods,” as illustrated in Fig. 2(a). The transmitted light is collimated and sent through a polarizer mounted on a LabVIEW-controlled rotational mount. The polarization ellipse is determined by measuring the power (Pt) transmitted through the rotating polarizer, which has a transfer function of the form of a Jones matrix of M=[cos2θsinθcosθsinθcosθsin2θ], where θ is the angle between the transmission axis of the polarizer and the slow axis of the PM fiber in Fig. 2(a). As the polarizer is rotated from 0° to 360°, the power meter measures the projection of the polarization transmitted by the fiber along the transmission axis of the polarizer ^[12]. Polarization measurements are performed at angular increments of 2°. The ellipticity and the angle of the polarization ellipse are extracted by fitting the projection data. The accuracy of the reconstruction of the polarization state is demonstrated by comparing the normalized raw data and the fitted ellipse projection [Fig. 2(b)]. The normalized fitted projection has been used to show the results that follow.

Fig. 1. Experimental setup for polarization measurement of the transmitted circularly polarized light through the PM fiber at different temperatures or powers of light. QWP: quarter-wave plate.

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Fig. 2. (a) Cross section of a PANDA PM fiber. (b) An example of elliptically polarized light with ellipticity of 0.37 and angle of 135° with respect to the slow axis of the PM fiber.

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3. POWER DEPENDENT POLARIZATION CHANGES

3.1 A. Measurements

Intensity dependent polarization changes are well known in fibers. The Kerr effect induced change of index n2I is at the origin of mode-locking by polarization rotation. Since the nonlinear index in silica is of the order of 10−16cm2/W, this mode-locking technique involves peak powers on the order of tens of watts. Instead, our measurements are performed with continuous radiation in a much lower power range. Figure 3 shows the polarization modification for a 17.5 cm PM fiber, as the power is increased from 0.7 to 35 mW. The data presented in Fig. 3(a) show a polarization ellipse rotating as the power of circularly polarized light input to the PM fiber is increased. The changes in ellipticity and angle of the ellipse are plotted as a function of the input power in Fig. 3(b). Even with such a short fiber section, the polarization state is sensitive to a mW change in light power. Figure 4(a) shows the normalized transmission through the PM fiber followed by a polarizer at different angles, as a function of input power. At the polarizer angle of 58°, the change in transmission with increasing power reaches 86% [Fig. 4(b)]. Therefore a short piece of PM fiber can be used as a saturable absorber of very low saturation power. This nonlinearity can be exploited for making pulsed lasers and sensors of very small energy consumption. The grey regions in Figs. 3(a) and 4(a) correspond to the range of polarizer angles (from 15° to 90°) for which the saturable absorption is observed.

Fig. 3. (a) Projection patterns of the transmitted circularly polarized laser light at different powers through a 17.5 cm PM fiber (at room temperature) followed by a rotating polarizer. (b) Ellipticities and angles of the polarization ellipses associated to (a).

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Fig. 4. (a) Color-coded transmission of circularly polarized light at different powers through a 17.5 cm PM fiber followed by a rotating polarizer. (b) Transmission versus power of circularly polarized light for the optimum polarizer angle of 58° shown in (a).

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3.2 B. Interpretation of the Power Dependence

At such low power levels, power-dependent index changes could be caused by thermal effects. However, there is no theoretical study quantifying thermal effects in low-loss undoped silica PM fiber in the mW powers investigated here. It is experimentally shown that a few mW change in the power of light sent through a PM fiber raises the temperature of the core sufficiently to modify the fiber birefringence. To verify that the same temperature sensitivity is involved in the power measurements of Section 3.A, we used the same fiber at a constant power of 30.4 mW, and varied the temperature. A short piece (6 cm) of Corning fused silica PM fiber in Fig. 1 is exposed to different temperatures by attaching it to a temperature-controlled plate (Peltier cooler). The birefringence of the PM fiber is Δn=0.0005 with beat length of 3.1 mm at 1550 nm. As shown in Fig. 5(a), the polarization state of the transmitted light gradually changes by increasing the temperature from 2°C to 30°C. The calculated ellipticities and angles of the polarization ellipses associated to Fig. 5(a) are depicted in Fig. 5(b) as a function of temperature. As can be seen in Fig. 5(b), the phase shift of π occurs between two modes of polarization by increasing the temperature from 10°C to 29°C. It means that the birefringence of the fiber is changed by 1.3×10−5 using the phase shift equation of Δφ=2πΔnL/λ in which L is the length of the PM fiber exposed to heating/cooling source (6 cm in this experiment) and λ is the wavelength of the light. Therefore, a change of 4.1 μm/°C is expected in the beat length of the PM fiber. The results are comparable to those of Ref. ^[13]. In Fig. 5(b), the discontinuity in the angle of ellipse at about 20°C arises from the transition of polarization from circularly (at 20°C) to rotated elliptically (at 21°C) polarized light. The fitting algorithm only defines angles from 0° to 180° to the slow axis of the PM fiber and does not unwrap the curve so that a discontinuity appears when the ellipse rotates past 180°. Used as a temperature-dependent sensor, placing the system at this transitional location by tuning the fiber length allows the best sensitivity. The sensitivity at the turning point is experimentally measured by increasing the temperature from 20°C to 20.8°C in very small increments, as shown in Fig. 5(c). A significant transition of the polarization state of light can be seen with only a 0.8°C change in the temperature of the fiber. The ellipticities and the angles of the polarization ellipses at different temperatures from 20°C to 20.8°C are depicted in Fig. 5(d). The inset shows that the difference between temperatures of 20.68°C and 20.70°C is clearly resolved.

Fig. 5. Projection patterns of the transmitted circularly polarized laser light (at 30.4 mW) through a 17.5 cm PM fiber with 6 cm exposed to different temperatures from (a) 2°C to 30°C and (c) 20°C to 20.8°C. (b) and (d) Ellipticities and angles of the polarization ellipses associated to (a) and (c), respectively.

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It is not necessary to measure the full polarization ellipse to determine the temperature. One can simply measure the transmission of light through a polarizer (Fig. 1) at a fixed orientation. There is an optimum polarizer angle for a given temperature range. In this experiment, the optimum angles to get the maximum change in transmission at different temperatures are 46° and 136°, as illustrated in Figs. 5(a) and 5(c) by the dashed lines. The direct measurement of the transmitted light through the polarizer at 46° for different temperatures is plotted in Fig. 6. The response r to temperature change of ΔT is a relative transmitted power change of ΔPt/Pt, inversely proportional to the fiber length of L, so r=ΔPtPt1ΔTL.(1)Considering the two data points at 20.68°C and 20.70°C shown in the inset of the Fig. 6 and for L=0.6dm, the calculated response r to the temperature change is 1.2°C−1·dm−1. It means that for a given resolution of ΔPt/Pt of 1%, we can resolve a temperature change of ΔT=0.008°C for 10 cm of fiber.

Fig. 6. Transmission of circularly polarized light at 30.4 mW sent to the PM fiber at different temperatures followed by a polarizer oriented at 46°, which is shown by the dashed lines located at 46° in Figs. 3(a) and 3(c). Temperature determination is ambiguous in the highlighted regions. Inset: enlarged scale to show the sensitivity of the temperature sensor.

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There is a compromise to make between sensitivity and dynamic range. The longer the fiber, the higher the sensitivity and the shorter the dynamic range. For the 17.5 cm PM fiber length, by increasing the temperature from 2°C to 30°C, the transmission changes periodically (Fig. 6) ^[14]. This makes the sensor impractical for temperatures below 10°C in this case. In Fig. 6, the transmission of light through the PM fiber at temperatures below 10°C (highlighted pink region) is very similar to that of temperatures above 10°C (highlighted green region). This ambiguity could be avoided by shortening the exposed length of the PM fiber.

3.3 C. Power–Temperature Calibration

The strong correlation between the polarization of light at different powers of light (Section 3.A) and different temperatures of the PM fiber (Section 3.B) is illustrated in Fig. 7(a). This correlation is plotted as a calibration curve in Fig. 7(b). As the exposed length of the fiber is different in Sections 3.A and 3.B (the whole 17.5 cm PM fiber is heated by the power of light passing through it while 6 cm of fiber is attached to the temperature-controlled plate), we have to normalize the results to the exposed lengths. Considering the exposed length of the PM fiber in Section 3.B is almost one-third of that in Section 3.A, the temperature change in Fig. 7(b) is divided by 3 to keep the response r and relative transmission of ΔPt/Pt in Eq. (1) unchanged.

Fig. 7. (a) Transmission of circularly polarized light at the power of 30.4 mW through the PM fiber at specific temperatures (solid lines), and the transmission of circularly polarized light at specific powers through the PM fiber at temperature of 19°C (circles). (b) Changes in temperature of the PM fiber versus changes in the power of light passing through the fiber calculated from the legend of (a).

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As shown by black dots in Fig. 7(b), 13 mW change in the power of light passing through the PM fiber corresponds to about a 2.3°C of change in the temperature of the fiber. In other words, a slope of 0.18°C/mW given by the linear fit in Fig. 7(b) shows that a 1 mW change in the power of a CW laser light passing through a 17.5 cm of PM fiber heats the fiber core by 0.18°C. Considering a 4.1 μm/°C change in beat length and the measured correlation between the power and the temperature (0.18°C/mW), a value of 0.7 μm/mW is calculated for the change of beat length by changing the power of light at 1550 nm. It should be noted that the results are reproduced for different lengths of fiber (25 cm PM fiber was also tested) and different ranges of power within a 10% error. Any change in the wavelength of light or type of PM fiber must be taken into account. We believe this method is accurate enough to measure the changes of temperature/power; however, the length of the fiber being tested should be measured within a few μm accuracy to give the absolute value of temperature/power. The accuracy of measuring length was a millimeter in this work. It is therefore recommended to calibrate the system to find the reference polarization.

3.4 D. Response Time of Power/Temperature Changes

The response time of the fiber core temperature to changes in optical power passing through the fiber is measured by analyzing the step function response of the polarization change. The power meter in Fig. 1 is replaced by a fast detector connected to an oscilloscope. The lights from two laser diodes at 980 nm (power/heating source) and 1550 nm (probe) are combined through a wavelength division multiplexer (WDM) and sent to the QWP in Fig. 1. The probe power is fixed while the current of the power/heating source is modulated to create square pulses, as shown in Fig. 8 by black square symbols as a step function from 0 to 40 mW, which is normalized to 1. The response curve of the sensor to this step function is measured by recording the transmission of the 1550 nm laser light through a polarizer at an optimized angle, and plotted as blue circle symbols. The red curve in Fig. 8 is the plot of the difference between the power/heating source and the probe, used to calculate the actual response time. Best fit to this curve is with two exponentials of 1/e values of 0.028 and 0.187 ms corresponding to cutoff frequencies of 35.7 and 5.3 kHz, respectively. The lower time constant corresponds to the conduction from core to cladding. The higher time constant corresponds to the conduction from the fiber to the surroundings. The fast response, extreme sensitivity, and the simplicity of this potentially in-line sensor make it competitive with other techniques ^[15] for specific applications, such as radiation-balanced lasers.

Fig. 8. Response curve of the sensor as measured by 1550 nm laser (probe) to a step function change of the 980 nm laser (power/heating source).

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A very simple and sensitive fiber optical length stabilization can be also devised based on the birefringence properties of PM fibers and the fast thermal response of the fiber core. An application example is where the two arms of a Michelson-type interferometer are made of PM fiber and must be stabilized. It can be done by monitoring the fiber temperature through polarization modification of an initially circularly polarized beam launched through the fiber, and correcting a change in temperature by adjusting the power of a linearly polarized beam of another wavelength sent through the fiber.