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Abstract
Two new random polarization smoothing methods using full-aperture elements are proposed on low-coherence lasers, one using birefringent wedge and one using flat birefringent plate. By designing the crystal axis direction and wedge angle of the birefringent plates, the methods can selectively introduce time delay and spatial displacement, so as to obtain fast random evolution of transient polarization by utilizing low spatiotemporal coherence of the laser focal field. Both methods avoid the near field discontinuity and can be used under high fluence. The method using birefringent wedge can slightly improve focal spot uniformity, and the method using flat birefringent plate can obtain non-polarization with DOP lower than 2%. Theoretical studies show that the resulting focal polarization evolves rapidly on sub-picosecond timescales and rapidly covers the entire Poincaré sphere. The method using birefringent wedge is achieved in experiment. The results show that the degree of polarization of the focal spot is reduced from 1 to 0.27, which proves the effectiveness of the full-aperture random polarization smoothing. The full-aperture random polarization smoothing can generate a focal field very close to unpolarized thermal light, which is expected to suppress the laser plasmas instability.
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1. Introduction
Laser and plasmas interaction (LPI) under high intensity can greatly affect the energy transmission from the beam to the target [1]. For experiment on inertial confinement fusion (ICF), LPI should be suppressed for maximum utilizing of laser power, and avoid further harness effects [2–4]. In order to suppress LPI, various beam smoothing methods have been designed. First, spatial smoothing methods, such as continuous phase plate (CPP) [5,6], lens array (LA) [7,8], can control the envelope of the focal spot, thereby reducing the maximum peak intensity and improve energy deposition. Second, the polarization smoothing (PS) [9,10] and the temporal smoothing methods such as smoothing by spectral dispersion (SSD) [11] and induced spatial incoherence (ISI) [12] reduce the occurrence probability of the LPI transition by breaking the coupling conditions of the LPI process.
The combination of SSD + CPP + PS is most widely used in high-power laser facilities based on the 1053nm narrowband neodymium glass amplifier, such as NIF [13], Shenguang III [14,15]. For an efficient frequency conversion, the SSD modulation bandwidth of these devices is often several hundred GHz, which is much slower than the LPI growth rate. The use of PS on these devices was found to significantly suppress the LPI process. Analysis shows that this is mainly caused by breaking the LPI coupling condition through the change of the focal spot polarization [16]. Simulation results show that the temporal modulation of the polarization state of the focal spot can significantly reduce the stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS) processes in the ICF [17–20]. And the effect is found better with faster polarization modulation.
On the other hand, thanks to the research on spectral compensation [21] and frequency conversion [22], low temporal coherent laser such as super luminescent diodes (SLD) [23] with continuous and broad spectrum have become an optional seed for laser driver [24]. Different from the traditional laser scheme, the low-coherence laser does not need additional modulation bandwidth, and the laser focal spot can be controlled by the combination of ISI + CPP. Such focal spot shows low temporal and spatial coherence, and the electrical field evolution is fast and random, determined by the coherence time and coherence length of the low-coherence laser [25]. On the “Kun-Wu” low-coherence laser, by exploiting the temporal coherence of the laser focal spot, we have obtained non-polarized focal spot with rapid evolution by using a random polarization smoothing scheme. It is realized by a specially designed half-aperture waveplate [26]. The polarization of the focal spot evolves completely randomly both on time and on space. The spatial evolution scale is determined by the speckle scale, and the time evolution scale is determined by the coherence time of the laser.
Random PS aims to obtain rapidly and randomly evolving unpolarized light field, such focal spots are very close to unpolarized random thermal light. Ideally, the degree of polarization (DOP) [27] of the focal spot should be reduced to 0. However, in the experiments reported in the previous article [26], the focal spot of random PS using half-aperture waveplate could have a maximum DOP value above 0.3. This is mainly caused by the uneven mixing of orthogonal polarizations. In addition, the discontinuous distribution of the half-aperture waveplate will cause diffraction, which limits the application under high fluence.
In this paper, we present a full-aperture random PS method based on low-coherence laser. The new method avoided the problems of uneven polarization mixing and hard-edge diffraction, and can achieve lower DOP under high fluence. Full-aperture random PS can generate unpolarized focal spots by exploiting the spatial or temporal coherence of the laser focal spots. In section 2, the focal spot polarization of the random PS is analyzed by simulation. In section 3, by using a home-made single-shot polarimeter, the focal spot DOP of the random PS on the “Kun-Wu” laser is studied. The improved full-aperture random PS is expected to experimentally obtain laser focal spots similar to unpolarized thermal light, which will be helpful for the control of the LPIs.
2. Full aperture random polarization smoothing
In order to obtain non-polarized thermal like focal spot field, random PS needs to use low-coherence light to ensure rapid random evolution of the light field, and reduce the DOP of the focal spot to 0 by polarization control [26]. DOP is defined as the ratio of polarized to total radiance, it can be calculated from coherency matrix as follows:
There are fundamental differences between the random PS and the traditional PS on focal spot intensity. Generally, random PS need to satisfy Jxx = Jyy to obtain random polarization. However, traditional PS rely on Jxx≠Jyy to improve the focal spot uniformity. As a result, to make random PS effective, the improvement of focal spot uniformity by uneven mixing of polarization should be avoid.
In the random PS by using half-aperture waveplate or incoherent beam combination [26], x- and y-polarized laser come from different regions of the near field. Since the waveplate introduces a path difference far exceeding the coherence time between x- and y-polarization, Jxy = 0 is obtained. Jxx and Jyy is only approximated equal after using temporal and spatial smoothing method of ISI + CPP. The difference between Jxx and Jyy cause uneven mixing of polarization. Ideally, uneven mixing won’t change the focal spot intensity distribution since x- and y-polarized near field was already incoherent after using ISI. But it will cause residual DOP values. With ISI division of 8 × 8, the residual DOP is averaged about 0.12, and the maximum can reach more than 0.3 [26].
Different from random PS of half-aperture waveplate or incoherent beam combination, two new full-aperture random PS schemes which use full-aperture birefringent plate are proposed to realize random PS on single beam. The full aperture birefringent plate divides the incident linearly polarized laser into orthogonal polarizations of ±45 degrees. Decoherence can be achieved by introducing spatial displacement on focal plane to utilize the spatial coherence of the focal spot [25], or by introducing delay to utilize the temporal coherence of the focal spot. Spatial displacement or time delay can be selectively achieved by designing the shape and crystal axis direction of the full-aperture birefringent plate. Discontinuity is avoided by full-aperture optics for high fluence application. Figure 1 presents two types of the full-aperture random PS designs.
Fig. 1. (a), full aperture random PS by birefringent wedge, which exploits spatial coherence of the focal spot. The laser beam is divided into orthogonal polarized beam 1 and 2 with different direction, this will cause spatial displacement on focal plane, and reduce Jxy by the spatial coherence of the focal spot. (b), full aperture random PS by flat birefringent plate, which utilizes temporal coherence. The laser beam is divided into orthogonal polarized beam 1 and 2 with same direction of wavevector, temporal delay is introduced by the difference between refractive index of o- and e- light, and Jxy is reduced by temporal coherence.
In Fig. 1 (a), a birefringent wedge is used to divide the linearly polarized laser into o-light and e-light with orthogonal polarizations, and introduce spatial displacement between them on focal plane. Except for the difference in the propagation direction, the o-light and the e-light have the same near field, so their focal spot is the same field with displacement of Δ:
Δ is usually several times the speckle scale. The small-scale inhomogeneity of the ISI + CPP focal spot is eliminated by using ISI, so the focal field displacement of Δ will not cause significant difference between Jxx and Jyy except at the edge of the focal spot. So the uneven mixing is weakened. Under Eq. (5), Jxy equal to the spatial coherence function of the focal spot without random PS. The spatial coherence of the focal spot without random PS is related to the position of the two observation points and the number of the laser’s spatial modes [25]. Two points with a distance smaller than the speckle size have a high degree of coherence. As the distance increases, the coherence function eventually fluctuates randomly with an expected value. Ideally this expected value is 1/N0.5, where N is the number of spatial modes of the laser. For ISI, N is equal to the number of ISI sub-blocks. For SSD, N depends on the amount of angular dispersion. According to the analysis, if Δ is larger than the speckle size, the correlation between the two polarizations can be greatly reduced, and further increasing the value of Δ will not bring lower Jxy. The residual DOP of the focal spot mainly comes from the residual spatial coherence caused by finite spatial mode, which is expected to be 1/N0.5. Compared with the random PS of the half-aperture waveplate, this scheme can greatly reduce uneven mixing, and slightly improve focal spot uniformity by the polarization superposition induced by the wedge.In Fig. 1 (b), a flat birefringent plate is used to introduce time delay and exploit temporal coherence to reduce focal spot DOP. Linearly polarized laser is divided into o-light and e-light with same propagation direction by the birefringent plate. Since the propagation directions and near fields of o-light and e-light are the same, Jxx = Jyy is strictly satisfied, which completely avoids uneven mixing. As a result, this type of random PS will not affect the focal spot intensity in theory. Jxy = 0 is achieved by exploiting temporal coherence. There will be a time delay between o-light and e-light due to the difference in their refractive indices. The refractive index difference of birefringent materials (such as KDP, BBO…) is often in the order of 0.01, and a flat birefringent plate with a thickness of 1 cm can introduce an optical path difference of several hundred femtoseconds. This is sufficient for low-coherence “Kun-Wu” lasers facility [24], but not suitable for lasers with bandwidths of only a few hundred GHz. When using ISI, special design of the ISI stair plate is required to avoid interference, otherwise the DOP of the focal spot cannot be reduced to minimum. The birefringent plate introduces a time delay Δt greater than the laser coherence time between o-light and e-light. Then the time delays introduced by different blocks of the ISI stair plate should be designed such as 0, 2Δt, 4Δt… After passing through the PS crystal, the polarization with additional retardation will have a delay such as Δt, 3Δt, 5Δt… In this way, correlation between different polarizations and different ISI blocks can all be avoided. Theoretically, with enough time delay, Jxy = 0 and DOP = 0 can be achieved with very high precision. But in practice, the time delay Δt is limited by the thickness of the PS crystal and ISI stair plate. As shown in Section 3, when Δt is about 1.4 times of the coherence time (433fs delay on a 3.28THz laser), the maximum DOP can be less than 2%. Compared with other type of random PS, this scheme can reduce the focal spot DOP more effectively.
3. Simulation
In order to fully reveal the characteristics of full-aperture random PS, the focal spot polarizations in four cases are compared by simulation. The four cases are: case 1, birefringent wedge combined with ISI (BW + ISI), case 2, flat birefringent plate combined with ISI (BP + ISI), case 3, birefringent wedge combined with 2D-SSD (BW+2D-SSD), case 4, flat birefringent plate combined with 2D-SSD (BP+2D-SSD). The first two cases are using random PS based on low-coherence lasers, and the latter cases are traditional PS based on modulated coherent lasers. Same CPP with 200-micron diameter focal spot was used in all cases. 2D-SSD is used in the simulation to obtain uniform focal spot, which is beneficial for the reduction of DOP when using the wedge. The laser near field width is 0.17 m, and the focal length of the main lens is 1 m.
The spectrum of the low-coherence laser is the same as the final output spectrum of the second harmonic of the “Kun-Wu” device, its spectral center is at 530nm, and its bandwidth is 3.28 THz [25]. The coherence time is about 0.3 ps. To be used with birefringent wedge, the stair plate of ISI in simulation contains 8*8 = 64 stairs distributed in two dimensions. As a result, the number of spatial modes is 64. The step difference is 0.25 mm, corresponding to a time difference of 433 fs, and the full range between the thinnest to the thickest steps is about 16 mm. To avoid the correlation between orthogonal polarizations, when used with flat birefringent plate, the step difference of ISI is increased to 0.5mm. The discontinuity of ISI limited its application under high fluence, but it is the only two-dimensional temporal smoothing method on large bandwidth low-coherence laser currently.
Traditional coherent source with 2D-SSD is used in case 3 and 4. The 2D-SSD modulation frequency on x-dimension and y-dimension is 6.6 GHz and 20.8 GHz, with modulation amplitude of 49.2 rad and 110.4 rad on second harmonic, and the wavevector of the modulation is kx = 7.03 m-1 and ky = 2.94 m-1. The center wavelength is 530 nm. For a more intuitive comparison, large modulation amplitude in the 2D-SSD is used to match the 3.28 THz bandwidth of the low-coherence laser [25], and it is many times larger than the SSD bandwidth reported in experiment [28,29]. The total angular dispersion is about 60 × 60 µrad2. The angular resolution is 0.53/0.17 = 3.12 µrad. It can be calculated that the number of spatial modes is approximately 370.
For the wedged KDP plate, the center thickness is 24 mm, the angle of the wedge is 3°, the angle between the crystal axis and the surface normal is 3.7°, and the azimuth angle is 45° to equally divide the energy to o-light and e-light. The optical path difference between o- and e-light is about 15 fs, much smaller than the coherence time. The angular difference between the o light and the e light is 9.6 µrad. After focused, a displacement of 9.6 µm will be introduced on the focal plane. The wedge plate also introduces angular dispersion, which is about 3.18urad/nm.
For the flat KDP plate, the thickness is 30 mm, the angle between the crystal axis and the surface normal is 18.36°, and the azimuth angle is 45° to equally divide the energy. The refractive indices of o-light and e-light are 1.5125 and 1.5082, respectively, and the introduced optical path difference is 433 fs, which is larger than the 300 fs coherence time.
Based on the Fresnel approximation, the DOP distribution and the transient polarization evolution of the focal spot is calculated. The orthogonal polarization states Ex(r, ω) and Ey(r, ω) of the light field is calculated independently. The focal spots of different frequency are directly calculated by Fast Fourier transform (FFT) [30]. The near-field resolution used in the calculation is 0.322 mm, the number of sampling points is 2048 × 2048, and the corresponding focal plane resolution is 0.803 µm. In the calculation of the low coherence laser (case 1 and case 2), the sampling interval is 12.5 GHz on frequency, and the total sampling number on frequency is 4096 [31]. For 2D-SSD laser (case 3 and case 4), the spectrum is discrete, and the calculation is strictly calculated on every frequency component. The DOP distribution and the coherency matrix can be calculated by Eq. (1) to (4). Angular dispersion is also included in the simulation.
To calculate the transient polarization evolution, Fourier transform is performed on the Ex(r, ω) and Ey(r, ω) to obtain Ex(r, t) and Ey(r, t). For low coherence source, the calculation is carried out by FFT, and the window on time is limited to be 80 ps. For 2D-SSD, the spectrum sampling is not equally spaced so FFT cannot be used, so, the calculation is based on adding all frequency components, and the width of window on time is set to be 3 ns. By the information of Ex(r, t) and Ey(r, t), variation of the ellipse of the transient polarization and its trajectory on Poincaré sphere can be calculated. It should be noted that x and y here are only used to represent a pair of orthogonal directions. Replacing x and y with +45° and -45° will not affect the whole process.
3.1 Long-term statistical properties of focal spot polarization
The DOP distribution of the focal spot reflects the cumulative effect of polarization evolution under long integration time, and it is completely determined by the spectral distribution of the field. Figure 2 shows the simulation results of DOP distribution in different cases. The total intensity distribution of the focal spot is shown in the upper right corner of each figure. When using birefringent wedge, the edges of the focal spots of the two polarizations do not coincide, which results in the inability to control the DOP in the margin. In order to avoid the influence of the focal spot edge, only the area within the radius containing 70% of the energy is used during the analysis for DOP, which is marked with red dashed lines in the intensity distribution.
Fig. 2. Distribution of DOP under four cases of (a), BW + ISI, (b), BP + ISI, (c), BW+2D-SSD, (d), BP+2D-SSD. The total intensity distribution of each case is shown in the upper right corner, respectively. The red dashed lines represent the 70% energy radius. The red pentagrams mark the locations used to calculate the Poincaré sphere probability distribution. (e), normalized power spectra of the focal spot intensity in four cases. The power spectra of 45°-polarization when using birefringent wedge is also shown. Same 200 µm radius CPP is used in all cases.
Flat birefringent plates don’t change the focal spot intensity, so the intensity in Fig. 2 (b) and (d) are also the focal spot intensity of ISI + CPP and 2D-SSD + CPP without polarization control. Use of BW will slightly improve the focal spot non-uniformity. On 2D-SSD + CPP, use of BW will change the detailed pattern, which is the result of BW's angular dispersion. In Fig. 2 (e), the power spectra curves and nonuniformity σrms [32] of the focal spots are given. The envelop power is in the range wavenumber k < 0.01 µm-1, and the power of focal spot non-uniformity is in the range k > 0.01 µm-1. σrms of ISI + CPP in case 1 and 2 is 0.094 and 0.111, which is larger than 0.048, 0.056 of 2D-SSD + CPP in case 3 and 4. This is mainly caused by the difference of the spatial mode numbers. In addition, the σrms of 45°-polarization with using of BW in case 1 and case 3 is 0.101 and 0.059, which is slightly larger than the total σrms. The reduction of σrms with BW is not obvious because the small-scale non-uniformity has been sufficiently suppressed by ISI or SSD. The power around 0.01 µm-1 is the main contribution of σrms, which is hardly affected by polarization control. So, the focal spot uniformity is mainly determined by the spatial mode number of ISI or 2D-SSD. Although random PS cannot significantly reduce σrms, it can still increase the smoothing speed by a factor of √2.
In case 1, the spatial variation of DOP is close to the speckle size of 25 µm, which is the size of speckle from individual ISI blocks. The maximum DOP is about 0.37, and the minimum is close to 0. In case 2, the DOP spatial variation comes from the residual correlation after combining the PS flat plate with the ISI plate. The DOP was less than 0.02. In case 3, there are some strips in the DOP distribution, which is caused by the spatial scanning from the wedge dispersion and 2D-SSD. The DOP in most areas is 0∼0.1, but the peaks in some positions can reach 0.2∼0.3. In case 4, the DOP distribution has nearly horizontal fringes, which come from the spatial scanning of 2D-SSD and the temporal dispersion of the plate. And the DOP is between 0.07 and 0.37. The average values of DOP in the four cases are 0.14, 0.01, 0.11, 0.21, respectively. As a comparison, the average DOP when using half-aperture waveplate is 0.12 [26]. The DOPs of BW + ISI and BW+2D-SSD are estimated to be 1/8 and 1/19.2 according to the spatial mode number, respectively. The average DOP of the BW+2D-SSD by simulation is significantly larger than the estimated value, possibly due to the remained 9.6-micron-scale inhomogeneity. These results show that BP + ISI is far more effective on reducing the DOP of the focal spot than other methods.
Degree of polarization does not fully demonstrate the statistical properties of the polarization. One position with relatively low DOP was selected in each case, to calculate the probability distribution of the instantaneous polarization on the Poincaré sphere, with 80 ps observation window for case 1 and case2 (limited by 12.5 GHz sampling) and with 3 ns observation window for case 3 and case 4. The positions of these points are marked as pentagrams in Fig. 2. The DOP of the four points is 0.050, 0.009, 0.039, and 0.069, respectively. The probability density distribution of an ideal unpolarized thermal light on Poincaré sphere should be uniform, with a value of 1/4pi = 0.80. Figure 3 shows the distribution of each case. The observation window in case 1 and case 2 is shorter. As a result, the pattern in Fig. 2 (a) and (b) contains more small-scale non-uniformity. Since the DOP of case 2 is very close to 0, the probability distribution in Fig. 3 (b) is most uniform, and the non-uniformity is mainly random fluctuation caused by the limited observation window. Obviously strong and weak poles can be discerned in the probability distributions of cases 1 and 3. The distribution in Fig. 3 (c) fluctuates more severely than in Fig. 3 (a). In Fig. 3 (d), there are obvious strong points, which even overshadow the random fluctuations. This shows that although BP+2D-SSD can also reduce the DOP of the focal spot, the probability of the field being in certain polarizations is much larger than others. These results show that polarization evolution in random PS based on low coherence laser can cover Poincaré sphere more uniformly.
Fig. 3. On Poincaré sphere, the probability density distributions of the instantaneous polarization, calculated from the fixed position of the focal spot from (a), BW + ISI, (b), BP + ISI, (c), BW+2D-SSD, (d), BP+2D-SSD. The integral time in (a) and (b) is 80ps, and the integral time in (c) and (d) is 3 ns.
3.2 Short-term evolution of focal spot polarization
To further demonstrate the transient properties of focal spot polarization, the transient polarization evolutions of four cases are calculated and shown in Fig. 4. In Fig. 4 (a), transient polarization in 1.5 ps is shown by every 50 fs. In Fig. 4 (b), transient polarization in 15 ps is shown by every 0.3 ps. When using random PS, such as BP + ISI and BW + ISI, the change of transient polarization is quite random at 0.3 ps intervals (in Fig. 4 (b)), while the details of the evolution process can be seen at 50 fs intervals (in Fig. 4 (a)). This demonstrates that the method can generate random polarizations that evolve rapidly and randomly within one coherence time, and the properties of the laser field are in all respects close to that of unpolarized thermal light. However, in cases 3 and 4 using 2D-SSD and traditional PS, the polarization evolution is slower. Due to the large bandwidth of the 2D-SSD in the simulation, it can also obtain transient polarizations that vary in sub-picoseconds, but there are also 5-10ps long intervals where the polarization is changing slowly. Although the same bandwidth is used in all cases, the polarization evolution with 2D-SSD is obviously slower than ISI scheme on low coherence laser. This is because the complex spectrum distribution of the SSD laser is highly ordered, and its large bandwidth cannot be fully transformed into the rapid evolution of the field [25]. For practically achievable SSD with hundreds of GHz bandwidth, polarization is almost static on pico-second scale.
Fig. 4. Evolution of polarization at selected locations on the focal spot with different beam smoothing combinations within (a) 1.5 ps, (b) 15 ps. The shape of the ellipses represents the transient polarization, and the size of the ellipses represents the instantaneous field intensity.
In addition, the trajectories formed on the Poincaré sphere of the four cases within 15 ps are shown in Fig. 5. Due to the fast evolution of the polarization under random PS with low coherence light, the trajectory formed in 15 ps is sufficient to cover the entire Poincaré sphere. However, due to the slow evolution speed, the traditional PS with 2D-SSD still leaves large blank areas on the sphere. The evolution speed of the polarization can be defined as the average angular speed of the polarization on Poincaré sphere. The evolution speed of the focal spot polarization using random PS is 10.7 rad/ps and 10.6 rad/ps (in Fig. 5 (a) and (b)), while the values of the traditional PS are 2.22 rad/ps and 2.12 rad/ps (in Fig. 5 (c) and (d)). The evolution speeds differ by a factor of 5, which is consistent with the ratio of the effective coherence time of their focal regions [25].
Fig. 5. The trajectories formed on the Poincaré sphere within 15 ps for different conditions: (a) BW + ISI, (b) BP + ISI, (c), BW+2D-SSD, (d) BP+2D-SSD.
4. Experimental results
We implement birefringent wedge type of random PS on the “Kun-Wu” laser. The birefringent wedge and ISI parameters in experiment are the same as those used in the simulation of case 1. For case 3 and case 4, the use of such large 2D-SSD bandwidth is limited by modulators and FM-AM. For case 2, the realization needs specially designed large aperture ISI plate and KDP crystal, which are currently both unavailable in our lab. Considering the time and cost, we have only carried out the experimental study of the random PS in case 1. The theory and experiment in case 2 are basically similar to case 1 and its results can be extrapolated from case 1.
Coherency matrix, which represents the polarization characteristic, has four independent variables. In order to measure it, at least four measurements are required. Thermal distortion and random perturbation lead to unstable details in the focal spot. Therefore, the four measurements need to be performed on the same shot to have reliable result. We have built a single-shot polarimeter using non-polarize beam splitters and beam profilers in our laboratory [26]. The intensity distribution of the focal spot was also measured directly using a microscope objective and a beam profiler.
The focal spot intensity of ISI + CPP without polarization control is shown in Fig. 6 (a), and the focal spot with BW type of random PS is shown in Fig. 6 (c). The middle-low frequency power has decreased by using BW. The σrms with and without BW is 0.108 and 0.127, and it can be seen from Fig. 6 that the strong region in (c) is obviously more uniform than that in (a). The improvement of uniformity is the combined effect of angular dispersion and polarization control by the wedge.
Fig. 6. In experiment, (a) and (b), the focal spot intensity and DOP distribution of ISI + CPP without polarization control. (c) and (d), the focal spot intensity and DOP distribution of ISI + CPP with BW type of random PS. The measurement is performed by a home-made single-shot polarimeter. . A 76 µm radius circle with 50% energy included is shown in (c) as red dashed line, which include the region used to analyze the focal spot DOP.
The focal spot DOP of ISI + CPP with and without random PS is shown in Fig. 6 (d) and (b). As expected, in Fig. 6 (b), the DOP without polarization control is one. In Fig. 6 (d), DOP with BW type of random PS is reduced. The spatial variation of the focal spot DOP in the y direction is agreed with the theoretical expectation, and is about 25 µm. There are equally spaced vertical fringes in x direction, and DOP value in the x > 0 region is obviously higher than those of x < 0. Those phenomena were also observed in previous experiments [26], probably due to the non-parallel transmissions in the light path of the polarimeter and non-idealities of polarization optics used. The DOP is found to be distributed between 1 and 0, with an average of 0.34. Average DOP in the x < 0 region is 0.27. In the experiment, the vertical fringes is on the beam profiler of the fourth light arm in the polarimeter. The strong area of DOP in Fig. 6 (d) is mainly formed by the vertical stripes, which leads to significantly larger DOP value in the measurement. The average DOP = 0.27 when using BW + ISI is slightly higher than the DOP = 0.22 when using the half-aperture waveplate [26], and both are higher than the simulated results (0.14 and 0.12). Even so, those results still confirmed that the full-aperture random PS by birefringent wedge can reduce the DOP of the focal spot, and thus obtain focal spot with random evolving polarization. Further experiment on the flat birefringent plate type of random PS is still in plan. And it is expected to obtain better result on reducing DOP.
5. Conclusion
We propose two types of full-aperture random PS for low-coherence lasers. The methods can selectively introduce time delay and spatial displacement, to utilize the low spatiotemporal coherence of the focal field. Both methods avoid the near field discontinuity and can be used under high fluence. The method using birefringent wedge can slightly improve focal spot uniformity, and the method using flat birefringent plate can obtain non-polarization with DOP lower than 2%. With 3.28 THz bandwidth, the random evolving of the focal spot transient polarization on the Poincaré sphere is averaged to be 10.7 rad/ps. Those results prove that the polarization of the focal spot with random PS evolves rapidly on time and space, and the focal field is close to unpolarized thermal field in all aspects. We experimentally realized the full-aperture random PS using birefringent wedge, and measured the focal spot DOP with a single-shot polarimeter built in laboratory. The average DOP of the focal spot with birefringent wedge is reduced from 1 to 0.27. The focal spot DOP can be further reduced by using flat birefringent plate with special designed ISI. The rapid and random changing focal spot polarization realized by full-aperture random PS are expected to significantly suppress LPIs.
Funding
Science Challenge Project (TZ2018005-02); National Major Science and Technology Projects of China (050312.1-2021HTJ-C-01); National Natural Science Foundation of China (12074353, 62105312).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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