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Abstract
We propose a novel configuration for an improved and compact all fiber Faraday rotator based on phase matching between the Faraday rotation and bend-induced birefringence. The device utilizes a coiled fiber within two electro-magnetic toroids, such that the fiber length required for getting the beat length is quite long and several rounds of fiber are needed. Analysis of the capabilities of the proposed device and its sensitivity to different parameters is presented. Faraday rotation of 13° was experimentally measured in six meters of single mode silica fiber, with a magnetic field of about 0.06T at a wavelength of 1064nm. We show that phase matching between the two phenomena significantly improves the polarization rotation by a factor of 4-10. In addition, we demonstrate the ability to achieve higher rotation by using Fabry Perot resonator in low terbium doped glass.
© 2017 Optical Society of America
1. Introduction
Faraday rotators are widely used for the realization of several components applicable to optical communication systems and fiber lasers, such as: isolators, optical Faraday mirrors and current or magnetic field sensors. Faraday rotator is an optical polarization rotator based on the Faraday effect, which rotates the plane of linearly polarized light when a magnetic field is applied parallel to the propagation direction. The amount of rotation is dependent on the material Verdet constant (V), the induced magnetic field (B) and the length of the optical path in which the magnetic field is present (l). Its value is given by the following well known formula:
Traditionally, the Faraday rotators are based on bulk optics. As a result, usage of such devices in optical communication networks or in high power laser systems suffers from facet damage, which limits their applicability, especially for high-power lasers [1]. Therefore, all fiber Faraday rotators can be very attractive devices. However, the Verdet constant of standard silica fiber is very low [2], so very long fiber is required in order to achieve large rotation angle, which renders those devices not too practical [3].There are many different configurations that were suggested in order to achieve compact all fiber Faraday devices [4–6]. One technique utilizes Terbium doped optical fiber [7]. By doping silica fiber with magnetic material such as Terbium, an increase in the total effective Verdet constant can be achieved [8–10]. Therefore, it is possible to achieve the desired polarization rotation by using relativity short fiber length. The main drawback of this method is that high concentration of Terbium in silica fibers renders the splice process more difficult, due to the low melting point of those fibers, compared with the standard Germanium doped fiber [11]. In addition, high Terbium concentration leads to power losses, so it limits the ability to use such devices in high power applications.
Recently, many other kinds of doped fibers were suggested and fabricated in order to improve the standard fiber's Verdet constant, like europium-doped silica fiber [12] and lanthanum boroaluminosilicate glass fiber [13]. In those fibers a Verdet constant of about −4.56 rad/(Tm) was measured for wavelength of 660 nm. Another technique to construct all fiber Faraday rotator is to use CdSe quantum dots doped Optical Fiber, which has Verdet constant of 5.3 rad/(Tm) [14]. More significant improvement in the fiber's Verdet constant was achieved by utilizing erbium-doped fiber Bragg grating, which gives Verdet constant −12.42 rad/(Tm) for high wavelength of 1550 nm [15].
Another technique is to use standard silica fiber that is coiled in multiple turns, in order to get a compact Faraday device [16] based on relatively long fiber. This Faraday rotator is based on the combination of two different effects: Faraday rotation and bend-induced birefringence. In this device, the fiber is coiled on a small radius mandrel and a magnet is placed near the fiber coil such that the magnetic field direction, with respect to the light propagation, is changed every half round of the coil. If the fiber is coiled in a way that assures that half the coil circumference is equivalent to half of the birefringence beat length, a phase matching between the Faraday rotation and the bend induced birefringence is achieved, so the Faraday contribution will continue to add accumulatively [17]. This principle allows for a compact Faraday rotator in fibers with low Verdet constant and without the need for doping the silica fiber with high concentration of magnetic materials.
The above illustrated setup suffers from many significant obstacles. Its main obstacle is its wavelength limitation. Since the induced birefringence due to fiber coiling is inversely dependent on wavelength, this setup corresponds only to short wavelengths of about 632nm. For higher wavelengths, a very small coiling diameter is required for getting phase matching between Faraday rotation and the phase retardation. Such small coiling radius is not feasible [4]. Since most of the high power fiber lasers operate at higher wavelength, in the order of 1000nm and up, a new design of compact all fiber isolator is required.
In this paper we introduce new compact and enhanced design of an all fiber Faraday rotator. The suggested device consists of two electro-magnetic toroids which have opposite current directions. The radius of the toroids is chosen such that the fiber length required for getting to a beat length (in which the magnetic field should be reversed) is quite long and requires several rounds. The optical fiber is coiled within these two toroids such that the direction of the magnetic field, related to the light propagation direction, is changed every half-beat-length. In that manner one can achieve the desired phase matching between the Faraday rotation and the bend-induced birefringence for large wavelength values. In the experimental test of the device, presented in this paper, we performed its characterization at wavelengths of 1064nm, customary to fiber lasers and amplifiers.
The device proposed in this paper could be used not only for realization of compact all fiber optical isolators, but also for optical switching or optical polarization modulators, since it uses an electromagnetic component as a magnetic field source.
2. Theoretical background
As mentioned above, standard single mode silica fiber has low Verdet constant. At 1064nm, the Verdet constant of standard silica fiber is only about 1.1 rad/(Tm), compared to −40 rad/(Tm) in TGG crystals, often used in bulk optics [18,19]. Therefore, in order to achieve high rotation angle in optical fiber, a very long fiber of few meters is required, which is impractical in most systems. Using coiled fiber is also impossible because of the bend induced birefringence, which acts to quench the polarization rotation. However, it was demonstrated that by alternating the sense of the magnetic field in successive half-beat-length increments, it is possible to obtain large interaction lengths in spite of the birefringence.
The polarization beat length is given by:
where is the bend-induced birefringence of a single-mode silica fiber, given by [20]:where are the x and y axis phase retardations with respect to the refractive index of a straight fiber, λ is the vacuum wavelength, k = 2π/λ is the free space propagation constant, r is the fiber radius and R is the coil radius. When light is coupled along the two principal axes of a birefringent fiber, such that the x-polarized intensity is greater than the y-polarized intensity (i.e. Px>Py) and a magnetic field is applied, the Faraday interaction will transfer power from Px to Py. At phases 0 and 2π this results form an addition to Py, while at π the Faraday contribution is subtracted from Py. In addition, the sense of the Faraday rotation contribution is reversed if the direction of the magnetic field is reversed. So, if the magnetic field changes sign after a length of Lp/2, it is clear that the Faraday contribution continues to accumulate [17]. Therefore, by building the setup such that the magnetic field will change its direction after a length that corresponds to π phase retardation, it is possible to get phase matching between the Faraday rotation contribution to Py and the phase retardation, in a way that contributes to Py along the whole fiber length, at the expense of Px. Based on this principle, compact all fiber Faraday rotators were built and were used for the realization of optical isolators for relatively short wavelength of about 630nm. It is possible to show that the combination between those two effects has nonreciprocal behavior [21].3. The proposed device
In order to adjust the above illustrated principle to higher wavelengths, the next configuration is proposed as shown in Fig. 1.
The device presented in Fig. 1 consists of two electro-magnetic toroids which have opposite current directions. An optical fiber is coiled N rounds inside the first toroid and then coiled for another N rounds in the second one and so on. In that way, light traveling along the fiber experiences constant magnetic field in the same direction for N coils, and then it experiences constant magnetic field in the opposite direction for another N coils. This configuration is different from the previously described work, in which the light experiences different magnetic field orientation at each half round. The number of rounds N is determined by the phase matching condition. Since we use high wavelengths, the birefringence is low, and the fiber’s length required for getting a beat length is quite long and requires several rounds. The phase matching will be achieved if the following condition is fulfilled:
where R is the coiling radius and is the bend-induced birefringence. Since we change the magnetic field after every N coils, we get the required phase matching between the two phenomena. In this way we can get the desired 45° rotation in a compact device, for higher wavelengths range.4. Simulations results
4.1 Principle of operation
We simulated a linearly polarized light at a wavelength of 1064nm, which is propagated along a coiled single mode optical fiber. The fiber's coil radius is R = 4cm. According to Eq. (3), for fiber diameter of d = 125um, the birefringence beat length equals to:
Therefore, the number of coils required for getting the beat length Lp is N = 6. If we consider an electric field with and components at the fiber’s input, the tandem birefringence and Faraday rotation effects result in polarization modification for each fiber section in accordance with the following expression [22]:where the matrix components are: and In order to calculate the state of polarization at each point along the fiber, we use the following matrix multiplication:The fiber's Verdet constant is V = −1.1 rad/(Tm). A magnetic field with strength of B = 0.058T was applied, while the sign of the magnetic field was changed in accordance with the phase matching condition.4.2 Simulation results
In our simulation, a Y polarized light was introduced into the fiber (i.e. = 1 and = 0). For each point along the fiber, the amplitude and phase of the X and Y polarized light were calculated, and the Poincare representation of the light polarization was drawn. The simulation results can be seen in Fig. 2.
Fig. 2 Simulation results. (a) Power transfer between the slow and fast axes along the fiber. (b) Phase difference between slow and fast axes along the fiber. (c) Poincare sphere: input and output polarizations.
Figure 2(a) shows the power transfer between the fast and slow axes during the propagation of the light through the fiber. It can be seen that for the Y polarized light, that was introduced to the fiber, half of the power was transferred to the X axis after 19.5m, which means ~16 fiber’s turns. It also can be seen from Fig. 2(b) that the phase difference between the two axes for this fiber length is zero, which means that we get a 45° rotation of the linearly polarized light at the end of the fiber. The Poincare representation at the input and output of the system can be seen at Fig. 2(c).
In order to demonstrate the non-reciprocal behavior of our system, the simulation was run again. This time the sign of the magnetic field was replaced from B to -B, and 45° linear polarized light was introducing into the fiber. The obtained results can be seen in Fig. 3.
Fig. 3 Simulation results of the reversed direction. (a) Power transfer between the slow and fast axes along the fiber. (b) Phase difference between slow and fast axes along the fiber. (c) Poincare sphere: input and output polarizations.
It can be seen that for the same fiber's length, the reverse operation of the system gives full power transfer to the X axis. The accepted phase difference was not equal to zero. However, from the Poincare representation it can be seen that the output polarization is almost horizontal.
4.3 Wavelength dependence
Since the bend induced birefringence is wavelength dependent, there is a need to understand the wavelength dependence of such a rotator. Figure 4 illustrates the amount of power transfer from to of the above mentioned fiber coil setup, for different wavelengths around the value of 1064nm.
It can be seen that this device can be operated at small wavelength range around the center wavelength to which it was designed for (1064nm). This behavior illustrates the capability of such device to perform as an optical filter, in addition to its main use as an optical isolator, which is quite useful in fiber amplifier, mainly for reducing the accompanying amplified spontaneous emission (ASE) noise.
4.4 Systems sensitivity analysis
We also have tested the sensitivity of the system to the coiling radius. For wavelength of 1064nm, a radius of 4cm was required, while the direction of the field is changed every 6 loops. Figure 5 shows simulation results for the amount of energy being transferred by an optical isolator, which is based on the suggested Faraday rotator, as function of the coiling radius. From this figure one may see that there is a high sensitivity to the radius and deviation of even a few mm may significantly affect the efficiency of the proposed system.
5. Experimental results
5.1 Experimental setup
The experimental setup can be seen in Fig. 6.
Fig. 6 Experimental setup: 1064 nm polarized fiber optic source connected to optical polarimeter via single mode fiber which coiling in two electro-magnetic toroids.
In our system two electro-magnetic toroids with radius of 4cm were used. The fiber was coiled within the toroids in accordance with the phase matching condition. The total fiber length is about 6 meters. A polarized fiber optic source with a wavelength of 1064nm was connected to one end of the fiber, while the other end was connected to an optical polarimeter, in order to measure the Faraday rotation.
Different current values were used for each toroid, since there is a difference in their wire thickness. The wire thickness of the first toroid was 0.8mm, so maximum current of 11.5A was used, while the wire of the second toroid had thickness of 0.4mm, so only 2.6A could be used. In order to work with high current values for long period of time, a cooling mechanism was designed, as can be seen in Fig. 7. The toroids were placed inside an aluminum box and immersed in a transformer oil for conducting the heat to the aluminum box envelope. Cooling fins were placed inside the aluminum box in order to improve the heat conduction to the box. The box itself was attached to an air cooled heat sink for evacuating the accumulated heat.
5.2 Results
The rotation angle dependence on the magnetic field of each toroid separately was measured. The magnetic field intensity was controlled by the current passing through each toroid. The results can be seen in Fig. 8.
Fig. 8 The rotation angle as function of the magnetic field: (a). 0.8mm wire toroid and (b). in 0.4mm wire toroid.
The maximum rotation angle received by the first toroid is about 6° degrees, while for the second toroid, with the lower current value, rotation of 7° was achieved. Although the current through the second toroid is lower, the rotation angle is higher, since it has larger number of loops than the first toroid (5000 loops compared with only 1000 in the first toroid). When the two toroids were activated simultaneously, total Faraday rotation of about 13° degrees was measured relative to the input angle of polarization.
In order to demonstrate the improvement in the angle of rotation, attributed by the phase matching between Faraday rotation and the bend-induced birefringence, we compared between the case in which phase matching was present to several other cases without its presence. The above configuration, corresponds to phase matching at wavelength of 1064nm. We measured the total polairization rotation in our system for three other wavelengths of: 780nm, 1310nm and 1550nm. The results can be seen in Table 1.
Table 1. Rotation angle as function of wavelength
Since each wavelength has different Verdet constanst, we need to divide the angle of rotation in the appropriate constant, for each wavelength, in order to get the relation between them. The Verdet constant for different wavelengths in standard silica fiber was measured in previous works [23]. Its value dependence on wavelength can be seen in Fig. 9.
So the angles of rotation versus the wavelength dependent Verdet constant are given in Table 2.
Table 2. The angles of rotation in relation to the wavelength dependent Verdet constant.
Figure 10 shows the graph of this relation as function of wavelength.
From the data above one can see that the phase matching between the bend induced birefringence and the Faraday effect, at wavelength of 1064nm, significantly improves the polarization rotation. The improvement factor is between 4 and 10.
We also compared between several cases with different fiber rounds number, at the same wavelength. A 1310nm laser source was used for that experiment. At this wavelength, and for fiber diameter of 125um and toroids radius of 40cm, we should replace the current direction every 8 rounds in order to get phase matching. We compared three cases: (1) changing the current direction every 8 rounds. (2) changing the current direction every 6 rounds (3) constant current direction. The results can be seen in Table 3.
Table 3. The angles of rotation as function of the number of rounds of the fiber. Case (1) current direction is changed every 8 rounds. (2) current direction is changed every 8 rounds. (3) constant current direction
As we expected, the highest value of Faraday rotation was recived in the first case, in which there was phase matching between the Faraday rotation and the bend induced birefringence. In this case, total Faraday rotation of about 5° was measured (lower than the previouse value, since the Verdet constant is wavelength dependent), while in the two other cases very small rotation value of 1.1° and 0.2° (respectively) were obtained. So, it can be clearly seen that the phase matching between Faraday rotation and the bend induced birefringence improves the rotation effect.
5.3 Improvement of the Faraday rotator
In order to investigate the ability of the above illustrated setup to achieve the desired 45° Faraday rotation, the next experimental step was to build a fiber based Fabry-Perot (FP) feedback. Consider a CW radiation polarized along the x axis that is directed into a FP resonator in which a magneto optic material is placed. The field complex amplitude function at the exit of the device, assuming that the resonance condition is fulfilled, is given by [24]:
where α is the rotation angle created by the magneto optic medium in one pass. r and t are the amplitude of the reflection and transmission coefficients, respectively. We assumed that the FP is in resonance.According to Eq. (10), if the reflectance intensity is chosen to be 0.95, 45° rotation of the output polarization is achieved, with less than 1.6° polarization rotation induced by the magneto optic rotator. If 10° rotation is induced by the magneto optic rotator, than 88.5° rotation of the output polarization is achieved. This shows that the magneto optic resonator has contributed a significant effective increment to the magneto optic effect [24]. Thus, since the FP based feedback can significantly enhance the polarization rotation effect, we tried to incorporate this concept into our novel experimental configuration. The experimental setup can be seen in Fig. 11.
Fig. 11 Experimental setup: Improved Faraday rotator by using two optical polarization maintaining (PM) couplers.
Two polarization maintaining couplers were used in a way that the output of the basic Faraday rotator illustrated above routed back to its input. The two couplers have coupling relation of 98/2. In that way, the incident light passes through the Faraday rotator for about 50 times so that the accepted total Faraday rotation increases. The measured rotation as function of the current can be seen in Fig. 12.
Fig. 12 The rotation angle as function of the magnetic field at the feedback system in: (a). 0.8mm wire toroid and (b). in 0.4mm wire toroid.
It can be seen that in this configuration, the measured rotation angle was about 20° degrees related to the input polarization, which means that the proposed system has a potential to get the desired large angle rotation.
5.4 Terbium doped glass
In order to decrease the influence of possible non-linear effects in a long fiber device, which have high significance in high power fiber amplifiers, we would like to build a system with the shortest possible fiber length. For that, we examined a special silica glass with low terbium concentration (11.4% Tb4O7). The glass was manufactured by Collimated Holes Inc. Since its Verdet constant should be higher than that of ordinary fused silica fiber, an optical fiber will be drawn out of it. We got a sample disk with thickness of 5mm and diameter of 30mm. In order to measure its Verdet constant, we built the setup presented in Fig. 13.
Fig. 13 Experimental setup: Sample glass disk in magnetic solenoid. Polarized fiber optic source at wavelength of 1310nm being collimated into the glass and directed to the polarimeter input.
The sample disk was inserted into magnetic solenoid with N = 500 loops. The current in the solenoid was 6.4A and its length was 9.5cm. Thus, the magnetic field inside the solenoid was 0.042T. A polarized source at wavelength of 1310nm was collimated and transmitted through the glass and into the polarimeter input. The length of the glass was 30mm. The polarization rotation was measured to be 0.1° which means that the Verdet constant of this glass for wavelength of 1310nm is about 1.38Rad/Tm, which is twice larger than in standard silica fiber. So, making an optical fiber out of this glass can help us in shortening the total fiber length in our system, by half.
6. Discussion
The experimental results that were illustrated above demonstrate the ability of our new configuration to be a basis for compact all fiber Faraday rotator. The final design of such a device should be able to achieve a rotation angle of 45° in order to be able to construct an all fiber isolator. The results show that in the current configuration, 20.7 meters of single mode fiber with cladding diameter of 125um is required. It is possible to use low current value of 2.8A for the two toroids, if we use the same number of loops (5000) in both of them. Another option is to use passive magnets instead of the electro-magnetic toroid by arranging alternating magnet segments around the fiber coils. The assumption is that these magnets will apply a constant magnetic field with an intensity of 0.5Tesla on the fiber coil, in the coiled sections only. In that way we can achieve high value of constant magnetic field without the usage of any current source/external power.
In addition, we would like to use the shorter fiber length, in order to decrease the influence of non-linear effects in high power applications. For achieving this goal we need to increase one of the next parameters: fiber Verdet constant or, alternatively, the magnetic field. Increasing the Verdet constant may be achieved by adding low Terbium percentage to the fiber's core. Higher value of magnetic field can be achieved by larger toroid and by adding more loops for the toroid. Further options to shorten the fiber's length in this system will be examined in the future as e.g. further testing of the presented FP based concept.
7. Conclusions
In this paper we proposed novel configuration for compact all fiber Faraday rotator. Numerical analysis of the capabilities of the proposed device was presented, and its sensitivity to different parameters such wavelength and coiling radius was investigated. The new concept was experimentally tested. A polarization rotation of 13° was measured in six meters of single mode silica fiber (HI1060) and with a magnetic field of about 0.06T, at a wavelength of 1064nm. Several options to increase the Faraday rotation in the proposed device were also examined, such as using Fabry-Perot resonator or doping the fiber with low Terbium concentration. The results clearly show that the phase matching between Faraday rotation and the bend induced birefringence improves the rotation effect. Such a device can be used for the realization of many optical components for optical communication system and high power fiber lasers and amplifiers.
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