Fiber pdf polarization

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Fodil, F. Amrani, C. Yang, A. Kellou, and P. Grelu, Phys. A 94 , Peng, L. Zhan, S. Luo, and Q. Shen, J. Paschotta, Opt. Express 18 , Paschotta, Appl. Haus and A. Liu, H. Shi, J. Cui, C. Xie, Y. Song, C. Wang, and M. Hu, Opt. Nicholson and M. Express 14 , Chong, J. Buckley, W. Renninger, and F. A Fig. CW laser power against the operating wavelength: 50 mm FBG is written in the middle of a 55 mm piece Squares are for pump power of 31 mW and circles are for of highly doped Er-Yb single-mode fiber SMF pump power of 40 mW; empty symbols are for one PM and filled symbols are for the other.

This arises from the fact that lasing oc- writing. Because the amount beam [10]. Note that ferent values of the applied tension as can be seen in the spectrum measurement was limited by noise to a Fig. The switch from one PM to the other PM actu- apply a lateral stress over a short section.

The phase ally happens when the applied voltage to the PA modulator is shifted 6 mm away from the FBG cen- crosses The polarization extinction ratios ter, on the pump side, in order to get unidirectional were precisely measured to be at least 25 dB for both output in the counter-pumping direction. This con- PMs. A corresponding spectral linewidth of 31 kHz figuration has been selected because it is known to be was also obtained by measuring its beating with a the most efficient for this type of laser [11].

This value is in agreement cise position of the phase modulator was actually op- with a previous report obtained with similar DFB fi- timized by measuring the maximum output power ber lasers [11]. Note that the residual laser output in tain pulsed laser emission in either of the two PMs the co-propagating direction was barely detectable. It is also possible to sipation. In order to carefully power levels. The voltage applied on the PA provides measure the output state of polarization SOP , the the fine tuning on the operation wavelength for both DFB laser was set in the co-propagating configura- Fig.

This multi-pulse regime appears when the pump side so as to minimize the SOP transformation modulation frequency of the PA is smaller than the by the fiber segment outside the cavity, which is relaxation oscillation frequency of the gain medium.

As for the pulse-to- laxation oscillation frequency are dependent on the pulse polarization switching behavior mode C , it pump power higher pump power leading to shorter was inferred by monitoring in parallel i. For the pulse-to-pulse PM switching offset of the electric modulation was varied so as to mode type C , the laser power did not actually reach pass from one PM to the other. Accordingly, real-time zero between the two pulses as can be understood monitoring of the pulsed emission on an oscilloscope from the transfer function shown in Fig.

At the allows easy and rapid fine tuning of the dc offset volt- highest modulation frequency of kHz that we age, in order to get the desired laser operation. Fig- could reach with this setup, the spectral width of one ure 5 shows the results for the three types of opera- pulse, measured as before with a frequency comb, tion labeled A, B, and C, at the kHz modulation was kHz which corresponds to the transform lim- frequency.

Pulses durations of the order of 0. Finally, it are seen. The observed difference in pulse duration must be noted that for high pump power, i. Also note that, for the kHz modulation switchable Q-switched DFB fiber laser based on a frequency, only one pulse is generated during the rapidly tunable birefringent PS induced in a FBG by modulation period.

At lower modulation frequencies, mechanical stresses. Modulation frequencies as high multiple pulses are visible during one modulation pe- as kHz have been achieved, with an extinction ratio higher than 25 dB. A new regime of pulse-to- pulse switching between orthogonal PMs has also been demonstrated. The authors also wish to thank Dr. References 1. Sahlgren, and R. Stubbe, Electron. Fan, B. Chen, X. Li, L. Chen, and Z. Lin, Opt. The Poincare sphere is a graphical tool in real three dimensional space that allows convenient description of polarized signals and polarization transformations caused by propagation through devices.

Any SOP can be represented uniquely by a point on or within a unit sphere centered on a rectangular coordinates system. Partially polarized light can be considered as a combination of purely polarized light and un-polarized light. Orthogonal polarizations are located diametrically opposite to the sphere. As shown in Fig. There are two angles or degrees of freedom, i. These angles can be interpreted as coordinates in a spherical coordinates system, and each polarization state can then correspond to a point, represented www.

Illustration of: a Jones representation , b Stokes representation. That is; if two vectors are perpendicular in Jones space then the corresponding two vectors in Stokes space are antiparallel. Each of these two spaces gives certain illustrations according to the case of study. For totally polarization, the value of polarization vector is unity, elsewhere, the value differs from unity.

There is a unitary matrix, T , in Jones space which www. In turn, the splitting ratios can be calculated by using Eq. As a consequence of this dependence, Eq. However, both equations are normalized properly. So, Eq. Therefore, according to Eq. Polarization mode dispersion and chromatic dispersion The pulses that propagate through single mode fiber SMF are affected by two types of dispersion which are CD and PMD.

Notice that the effects of the two types of dispersion happen at the same time, so to give a distinct sense of the two types of dispersion we decided to obtain the effects in the frequency domain. Finally, the vector sum of the two components will produce the final pulse H 2 w H 1 w A 0, w.

This represents the extra width that results due to the effects of PMD on the propagated signal. That is enough to assume a random form to one of them to find the other. Now, the reconstructed width after including the effects of CD is T1. That is; the width of pulse will increase due to the existence of www.

The dotted, continuous, and discrete lines refer to the initial pulse, two orthogonal components, and final pulse, respectively. In other words, the time separation between the two orthogonal components will be fixed, both amplitude and width of the pulse will change under the effects of CD.

Substituting the first definition in Eq. Elsewhere, the higher order effects must be included through the determination of PMD vector. Elsewhere, the two vectors are never coincided. Using Eq.

The DGD2 of this case can be obtained using Eq. This means that the higher order effects increase the DGD. This means that the two vectors in the same direction if the higher order PMD is neglected, i. Many approaches have been proposed McCurdy et al. This means that the compensation depends on the first term presented in the right hand side of Eq. To clarify the notation used in this section, we attempt to keep the notation simple and transparent while linking to the notation already established as much as possible.

Obviously, the new eigenvalues in presence of the combined PMD and PDL effects are different from that obtained for each effect separately. The Fourier transform of Eq. Substituting Eq.

To visualize the situation more easily, Eq. There are two www. Second, the PDL vector may by frequency dependent. A fixed input polarization was assumed, i. Now, by differentiating Eq. Remembering that, the absence of PMD will not permit the emergence of two components, as a result there is no PDL but the reverse is not correct. Notice that the tensorial nature is important to account for the PMD effects that have their origin in the birefringence of silica fibers, while its frequency dependence leads to chromatic dispersion.

It is assumed here that the z-axis is directed along the fiber length and The electric field vector lies in the x-y plane. This assumption amounts to neglect the longitudinal component of the vector and is justified in practice as long as the spatial size of the fiber mode is longer than the optical wavelength.