The effect of intra-cavity phase anisotropy on polarization flipping induced by optical feedback is experimentally and theoretically investigated. In experiments, we place a polarizer in feedback cavity to induce polarization flipping. The polarization flipping doesn’t occur when the angle between polarizer axis and laser polarization approaches 45°. It is found that the larger the phase anisotropy is, the more easily the polarization flipping happens. As the intra-cavity phase anisotropy is increased, polarization flipping always occurs when the angle between polarizer axis and laser polarization is changed from 0° to 90°. This indicates that the phase anisotropy of the laser cavity contributes to the polarization flipping. It is necessary to keep certain phase anisotropy for the lasers used for polarization control.
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Polarization control has been widely applied in polarimetry, metrology, and photo-communication. Polarization flipping and control has attracted considerable interest [1, 2], recently. Birefringent metal/dielectric (semiconductor) polarizer is used to control the polarization state of vertical cavity surface-emitting lasers by Mukaihara and associates . The effect of thermal lensing on polarization flipping is reported by Panajotov and associates . Choquette and associates  control the laser polarization by using anisotropic transverse laser cavity geometries. The polarization flipping induced by optical feedback was studied by Stephan and associates [6–8]. Sciamanna  also reported the polarization flipping induced by optical feedback. In the prior works listed above, people mainly looked at polarization flipping when the angle between the optical axis of polarizer and the laser polarization is either 0° or 90°, further research is needed when the angle is between 0° and 90°. Meanwhile, people mainly focused on the polarization flipped between the two eigenstates. The intra-cavity phase anisotropy was usually neglected. Hence, the effect of intra-cavity phase anisotropy on polarization flipping induced by optical feedback still lacks of study.
In this paper, the effect of intra-cavity phase anisotropy on polarization flipping induced by optical feedback is experimentally and theoretically investigated. A polarizer is placed in the external feedback cavity forming polarized feedback. When the angle between the optical axis of the polarizer and the laser polarization approaches 45°, polarization flipping doesn’t occur initially. Then, a force is exerted on one of the two cavity mirrors to increase the intra-cavity phase anisotropy gradually. We find that the greater the phase anisotropy is, the more easily the polarization flipping happens. It is realized that the polarization flipping always happens when the angle between polarizer axis and laser polarization is changed from 0° to 90°. The experiment results may help people to design laser system which is used to control the laser polarization easily.
2. Experimental setup
The layout of experimental setup is shown in Fig. 1. The setup consists of three parts: feedback part, laser, and detection part.
The intra-cavity HeNe laser outputs linear polarization with a single longitudinal mode oscillating in resonant cavity, the working wavelength is 632.8 nm. The gaseous pressure ratios in the laser tube are He: Ne = 9:1 and Ne20: Ne22 = 1: 1. The reflectivities of cavity mirrors M1 and M2 are 99% and 99.5%, respectively. The length of resonant cavity formed by mirror M1 and M2 is 140 mm. Resistance coil R is used to tune the cavity length slightly by heating when needed.
One surface of the M1 is coated with anti-reflecting film facing the laser tube; the other surface is coated with reflecting film. There is frequency difference (denoted as |v∥-v⊥|) between the two eigenstates of one longitudinal mode due to phase anisotropy caused by residual stress remaining in M1. The frequency difference between the adjacent longitudinal modes spacing of laser (denoted as Δν) is twice as much as |v∥-v⊥| . Thus, Δν can be used to indicate the phase anisotropy of the laser cavity. Δν can be expressed as Eq. (1), Δν can be tuned by exerting a force F on M1, so does the phase anisotropy of the laser cavity. As is shown in Fig. 1(b), a mechanical structure is designed to exert a force F on M1 along its diameter by twist the screw.
Feedback part is made of piezoelectric transducer (PZT), feedback mirror M3, attenuator AT, and polarizer P1. Feedback cavity length is about 140 mm. M3 moves back and forth pulled by a PZT which is driven by a triangle voltage. The reflectivity of M3 is 99%. The AT is used to reduce the effect of multiple feedbacks. The angle between X axis and the optical axis of P1 is denoted by θ. The light whose polarization is parallel to X axis is denoted by ∥-polarization, and the other one is denoted by ⊥-polarization.
The detection part consists of beam splitter BS1, BS2, Wollaston prism W, photo detectors D1, D2, polarizer P2, avalanche photo diode APD, spectrometer SP, and scanning interferometer SI. The two optical axes of W are parallel to X axis and Y axis, respectively. The ⊥-polarization and ∥-polarization are separated by W, and their intensities (I⊥ and I∥) are detected by D1 and D2, respectively. The P2 is placed to enable a 45° angle between the axis of P2 and ⊥-polarization (or ∥-polarization). The APD and SP are used to measure the frequency difference between the adjacent longitudinal modes spacing of laser. The longitudinal mode of the laser is observed by the SI.
3. Experiment and analysis
The laser polarization is parallel to X axis originally. Firstly we observed the laser outputs under optical feedback, without the force F exert on M1. The Δν is 8.8 MHz with the absence of F, measured by the SP. When the optical axis of P1 is parallel to X axis, i.e. θ equals to zero, flipping phenomenon happens, as is shown in Fig. 2(a). The laser still output one longitudinal mode then, observed with the SI (after lighten for two hours, the laser frequency is stable). So this was polarization flipping between the two eigenstates of one longitudinal mode.
Then we gradually enlarge the θ value by rotating P1. The transmittance of AT doesn’t change in this process. It is found that the laser outputs vary greatly with the change of θ value. Parts of experiment curves are shown in Fig. 2.
In Fig. 2(a), θ equals to 0°, the optical axis of P1 is parallel to ∥-polarization. The polarization flipping occurs. When ∥-polarization oscillates, I∥ is modulated by feedback. While ⊥-polarization oscillates, I⊥ is stable because of the presence of P1. The situation is reversed in Fig. 2(f). In Figs. 2(b) and 2(e), the polarization flipping occurs. I⊥ and I∥ are both modulated because the P1 is not parallel to either X axis or Y axis. In Figs. 2(c) and 2(d), the polarization flipping doesn’t happen, and only one polarization oscillates.
We found that the closer to 45° the θ value was, the harder the polarization flipping happened. While the θ approached either 0° or 90°, it was easy to observe the polarization flipping. Under the experiment condition mentioned above, we can’t get polarization flipping with the θ value bigger than 26° and smaller than 65°, as is shown in Fig. 3 below. It is notable that Fig. 3 is symmetric at the 45°.
4. Theoretical analysis and discussion
Here, a theoretical model based on self-consistency of the laser is presented. We consider the situation of no polarization flipping first. ∥-polarization is supposed to be resonant initially. We divide the laser beam into two parts with the presence of the optical feedback. The first part travels within the laser cavity, and the other one is reflected into the laser cavity by feedback mirror. These two parts superimpose in the laser cavity and the feedback effect comes into being.
The initial electric vector within laser cavity without feedback is denoted as, while the electric vector with feedback is denoted as. According the self-consistency of the laser, we can get thatEqs. (4) and (5), and are both modulated by θ and feedback cavity length l. Furthermore, there is phase difference between and due to the frequency difference between and. Suppose that is larger than, we denote as, which can be expressed as Eq. (6),Fig. 4.
The Fig. 4(a) shows that G changes along with θ. The figure is symmetric at the 45°. If θ<45°, the smaller the θ is, the greater the G is. On the contrary, the G increase along with θ, when θ>45°. If G is greater than polarization flipping threshold (denoted as GPFT), polarization flipping occurs. Hence, we can observe polarization flipping when θ is close to either 0°or 90°, while the polarization flipping doesn’t happen when θ approaches 45°. This agrees well with the experiment results.
As is shown in Fig. 4(b), for different θ value, G increases with the increasing of Δν. Although, only five θ values are shown in Fig. 4(b), the result is similar for θ among 0°and 90°. Δν can be tuned by the F exert on M1, so does the G. This indicates that if we increase the Δν by increasing the F, we may observe polarization flipping when θ is close to 45°.
We gradually increase the force F. The θ is changed from 0°to 90° each time the F is varied. The critical θ value of polarization flipping happens or not is recorded. The experiment results are shown in Fig. 5.
From Fig. 5, we can see that the θ range of no polarization flipping is getting smaller with the increase of Δν. Especially, when Δν equals to 58.1 MHz, polarization flipping happens for all the θ value among 0° and 90°. Parts of the experiment curves are shown in Fig. 6.
It is experimentally demonstrated that the phase anisotropy of the laser cavity has great effect on polarization flipping of the laser. The greater the phase anisotropy (or Δν) is, the more easily the polarization flipping happens. This offers a potential way to control the polarization flipping of the laser.
We have demonstrated that the polarization flipping induced by optical feedback is greatly affected by the phase anisotropy of the laser cavity. A theory model based on self-consistency of the laser is presented to explain the experiment results. The theory model indicates that the polarization flipping may happen easily by enlarge the phase anisotropy of laser cavity. It is experimentally proved that the greater the phase anisotropy is, the more easily the polarization flipping happens. Theoretical results agree well with the experiments. This indicates that the phase anisotropy of the laser cavity contribute to realize the polarization flipping. It is necessary to keep certain phase anisotropy for the lasers used for polarization control. The experiment results may help people to design laser system which is used to control the laser polarization easily.
This work is supported by the key project of the National Natural Science Foundation of China (Grant No. 61036016).
References and links
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