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We report a wavelength-locked cladding-pumped ytterbium-doped fiber laser that can simultaneously emit radially and azimuthally polarized beams based on Pancharatnam-Berry phase optical elements. Multi-wavelength free running operation of the radially and azimuthally polarized laser beams can be switched to a single-wavelength one assisted by volume Bragg grating, with wavelength locked at around 1053.4 nm and spectral linewidth of 0.06 nm (FWHW). By rotating the glan-taylor polarizer, we can obtain switchable radially and azimuthally polarized beams output. The radially and azimuthally polarized beams mode purity can maintain 97.3% and 96.3% at maximum output power, and the polarization extinction ratio (PER) can reach 97.8% and 95.9% for the radially and azimuthally polarized laser, respectively.
© 2017 Optical Society of America
1. Introduction
Radially and azimuthally polarized beams, the sub-class of cylindrical vector beams with nonhomogeneous polarization, have drawn considerable attentions for their unique properties and applications [1], such as high resolution imaging [2,3], materials microfabrication [4,5], optical particle trapping [6], surface plasmon excitation [7], optical data transmission [8, 9] and so on. Inspired by the desired applications, radially and azimuthally polarized beams have been produced through passive and active methods [10, 11]. Among these methods, fiber laser that can produce vectorial output modes is particularly attractive due to its potential to generate high output power and extreme flexibility [12–31]. However, the conventional generation methods suffered from low polarization purity, degraded beam quality and low transformation efficiency. Moreover, the spectral characteristics and stability have been paid less attention, which is very important for some specific applications requiring narrow spectral width and high wavelength stability [1].
Various polarization-dependent optical elements and spectrally controlling components have been investigated and successfully applied in different systems [32]. Researchers have manifested that polarization can be effectively manipulated through the Pancharatnam-Berry phase (PBP) [33–36], which results from the space variant polarization manipulation, not the optical path difference. By writing nanostructure gratings in silica glass with femtosecond laser, a kind of cylindrical vector beams converter, S-waveplate, could induce PBP [37]. The polarization evolution can be manipulated via PBP outside or inside the laser cavity, which has exhibited impressive performances [38, 39]. For the spectral counterpart, some wavelength selectors, such as etalons, dispersive prism, and gratings, have been widely used in various scalar laser systems. However, the above methods suffer from the large loss, being bulky, and limited spectral narrowing ability. Volume Bragg grating (VBG), recorded in photothermal refractive glass, can provide an ideal solution for narrowing the spectral linewidth and locking the operation wavelength, and the optical component has been successfully applied to select laser wavelength and narrow the spectral linewidth in solid-state or fiber lasers [40, 41].
In this paper, we investigated the wavelength-locked polarization modes behavior of the vectorial fiber laser cavity modulated by the dielectric S-waveplate intracavity. The radially or azimuthally polarized beams output can be conveniently delivered and switched with laser central wavelength located at 1053.4 nm and spectral linewidth of 0.06 nm. For the free-running operation, the output power and slope efficiency are 3.03 W and 36.9% for radially polarized laser, 2.98 W and 35.8% for azimuthally polarized laser. To the best of our knowledge, the slope efficiency of this switchable vectorial fiber laser is the highest one at 1 μm wavelength up to now. In the wavelength-locked regime, the output power and slope efficiency are 2.75 W and 33.5% for radially polarized laser, 2.68 W and 32.7% for azimuthally polarized laser. The mode purity of the vectorial modes could maintain 97.3% and 96.3%, and the polarization extinction ratio (PER) are 97.8% and 95.9% for radially and azimuthally polarized beams at the maximum output power.
2. Experimental setup
The S-waveplate fabricated by the femtosecond laser writing nano-grating technique can act as an artificial uniaxial crystal, which leads to homogeneous phase retardation δ at the wavelength λ. By manipulating the local nano-grating orientation and geometrical parameters of the birefringence of the artificial uniaxial crystal, we can effectively manipulate the polarization state of light [42–45]. The direction of optical axis can be represented by the following expression:
where the polar coordinate representation is adopted, and α0 is a constant angle representing the initial orientation of optical axis for ϕ = 0, and q is the topological charge of S-waveplate, as shown in Fig. 1(a). The orientation of the nanostructure is spatially varying at different locations, and a coordinate-dependent matrix can be used to describe the optical axis [42]:Here, J is the Jones matrix of a uniaxial crystal, M (r, φ) is the rotation matrix, and So the Jones matrix T (r, ϕ) can be obtained as:The Gaussian beam can be converted to radially or azimuthally polarized beams when it sequentially passes the GLP and S-waveplate (q = 1/2, δ = and α0 = 0), as shown in Fig. 1(b). By the transfer matrix method [39], it can be calculated that the E4(r, φ) will be equal to E1(r, φ) and E3(r, φ) will be equal to E2(r, φ), which means that a non-polarized beam can be converted to radially polarized or azimuthally polarized beams after every round trip.
Fig. 1 (a) Schematic diagram of S-waveplate with q = 1/2 and (b) the conversion between Gaussian beam to radially or azimuthally polarized beams and the PR represent the partial reflection mirror.
With the above considerations, the experimental setup was elaborately designed to generate wavelength-locked radially and azimuthally polarized beams, as shown in Fig. 2. A 2.3-m-long ytterbium-doped double-clad fiber is used as the gain fiber, which has a core diameter of 10 µm with a NA of 0.08 and an inner cladding diameter of 125 µm with 0.46 NA. The V number of this fiber is calculated to be around 2.37 for 1060 nm, which manifests that only the fundamental mode can be propagated. The absorption coefficient of this fiber inner cladding is around 4 dB for pump light at 976 nm, and the two fiber ends are cleaved at an inclined angle of 8° to suppress any reflection back into the fiber. The pump source is a fiber-coupled wavelength-locked 976 nm laser diode, and its pigtail fiber has core diameter of 105 µm and NA of 0.22. The pump light was collimated by L1 (N-BK7, coating-B, f = 30 mm) and focused by L2 (N-BK7, coating-B, f = 25.4 mm). The cavity of fiber laser consists of the optical round trip between the laser mirror M2 and M3, where M3 is a dielectric HR mirror or VBG and M2 is the output coupler lens with partial reflection (R = 15%) at 1000-1100 nm. M1 is a 45° dichroic mirror with 98% reflectivity at the lasing wavelength of 1060 nm and 86% transmission at 976 nm. A reflective VBG (OptiGrate Corp.) with a center wavelength of 1053 nm and spectral selectivity of 0.26 nm was selected to lock the operating wavelength. The VBG used in our experiments was 4.75 mm thick with a clear aperture of 5 × 5 mm and anti-reflection coating (R< 0.3%) at 900-1100 nm. The laser could emit out from the both fiber ends. The laser from one end was collimated by L2 and reflected to M2 through dichroic mirror M1, and the laser from the other end was collimated by L3 (N-BK7, coating-B, f = 25.4 mm) and totally reflected back into fiber by M3. A GLP and S-waveplate were placed in the internal cavity between the partial output coupler lens M2 and dichroic mirror M1. When the laser passed through the GLP, it would be converted to linear polarized beam. Radially or azimuthally polarized beams could be generated when linear polarized Gaussian beams passed through the S-waveplate. Radially or azimuthally polarized beams could be switchable by reasonably adjusting the direction of GLP in the transverse plane (xy). Because the M2 is a partial reflection mirror, a part of radially or azimuthally polarized beams would be directly delivered out the cavity, and the rest of light would be reflected into the cavity. From the above analysis, it is easy to know that the radially or azimuthally polarized beams can be converted into original linear polarization state after sequentially through the S-waveplate and GLP based on the Jones matrix.
Fig. 2 Experiment setup of Yb-doped fiber laser with radially and azimuthally polarized beam output by use of S-waveplate.
3. Experimental results and discussions
At first, free-running characteristics (i.e., without wavelength selection) of fiber laser have been investigated, and the output performance has been shown in Fig. 3. For radially and azimuthally polarized laser, the maximum output power reached up to 3.03 W and 2.98 W and slope efficiency are 36.9% and 35.8% with respect to launched pump power. In order to compare the performance of the wavelength-locked Yb-doped fiber laser with free-running Yb-doped fiber laser, the dielectric mirror M3 was replaced by VBG. The maximum output power is 2.75W and 2.68 W and slope efficiencies with respect to launched pump power are 33.5% and 32.7% for radially and azimuthally polarized laser, as can be seen in Fig. 3. The slope efficiency decreased mainly attributed to the unabsorbed launched pump power (about 91% launched pump power was absorbed). When we used the VBG to lock the laser wavelength, the unabsorbed launched pump light would transmit VBG with low reflectivity (R< 0.3%). The output spectrum of free-running and wavelength-locked Yb-doped fiber laser has been shown in Fig. 4. We can see that the free-running operation Yb-doped fiber laser has multi-wavelength oscillation. However, the output wavelength is locked at 1053.4 nm with spectral width (FWHW) of 0.06 nm when introducing the VBG as the wavelength selection elements.
Fig. 3 Output power versus launched pump power for the fiber laser with radially and azimuthally polarized beams output.
Figure 5(a) shows the intensity pattern of the radially polarized beam. We can see that beam show the typical donut-shaped profile. Figure 5(b)-5(e) illustrate corresponding intensity pattern of radially polarized beam transmitted through a polarization analyzer when the polarization analyzer was rotated at different angles. As shown in Fig. 5(b)-5(e), the double-lobe intensity patterns of transmitted radially laser beam was always parallel to the corresponding optical axis direction of polarization analyzer, which indicates that the laser beam output from this fiber laser is radially polarized beam. Figure 6(a) shows the intensity pattern of the azimuthally polarized beam. Figure 6(b)-6(e) illustrates the corresponding intensity patterns of azimuthally polarized beam transmitted through a polarization analyzer when the polarization analyzer was rotated at different angles, and the double-lobe intensity pattern of transmitted azimuthally laser beam was always perpendicular to the corresponding optical axis direction of polarization analyzer and these indicate that the laser beam output from this fiber laser is the azimuthally polarized beam.
Fig. 5 (a) The experiment far-field intensity distributions of radially polarized beam at the maximum output power. (b)-(e) The radially polarized beam pattern after the passage through the polarization analyzer. The white arrows represent the optical axis direction of polarization analyzer.
Fig. 6 (a) The experiment far-field intensity distributions of azimuthally polarized beam at the maximum output power. (b)-(e) The azimuthally polarized beam pattern after the passage through the polarization analyzer. The white arrows represent the optical axis direction of polarization analyzer.
In order to further make sure the output beam is radially and azimuthally polarized beams, Stokes parameters of the output beam have been measured. The experiment setup is shown in Fig. 2 and the CCD, QWP and GLP were used to measure the Stokes parameters of output beam. The Stokes parameters S1, S2, and S3 are defined as
The CCD recorded the light intensity, where m and n represent the optical axis directions of the QWP and GLP with respect to the x axis, respectively [46]. The theoretical and experiment results are shown in Fig. 7, and we can see that the experimental result is in accordance with the theoretical one, which can validate the output beams are radially and azimuthally polarized.
Fig. 7 The first and third rows show the theoretical Stokes parameters for radially and azimuthally polarized beam, respectively. The second and fourth rows show the experimental Stokes parameters for radially and azimuthally polarized beam, respectively. The three columns show the Stokes parameters S1, S2 and S3, respectively.
We used the same way to measure the polarization extinction ratio (PER) of radially and azimuthally polarized beams as [47]. A mechanical slit with the size of 200 µm was placed into the optical path at the distance of 1 m behind the M2, and the size of the output beam was measured to be about 3.5 mm. The mechanic slit was fixed in a mount connected with a three-dimension manual translation platform and placed in the position which could enable the transmitted light intensity to be maximum. Because the size of mechanic slit was much smaller than the laser beam diameter, the laser beam could be approximately regarded as a linear polarized light when the output beam passed through it. The polarization extinction ratio of the radially and azimuthally polarized beam could be measured by rotating the polarization analyzer at different angles. The relationship between the measured power with the angle for radially and azimuthally polarized beam when the laser passed through the polarized analyzer, as shown in Fig. 8. The polarization extinction ratios of the radially and azimuthally polarized beams are 97.8% and 95.9%, respectively [48].
Fig. 8 The normalized intensity variation of light passed through the mechanic slit when the linear polarizer analyzer was rotated at different angles for radially and azimuthally polarized beams. (a) Mechanic slit was rotated at x-axis and (b) Mechanic slit was rotated at y-axis.
The mode purity (fractional content of radially and azimuthally versus Gaussian mode) of radially and azimuthally polarized beams are estimated by one-dimensional intensity distributions across the beam center along the x-axis [49]. Figure 9 shows the mode purity at the maximum output power, and the measured intensity of radially and azimuthally polarized beams were plotted by black dots and fitted by a linear superposition of Gaussian beam and radially or azimuthally polarized beam. We can obtain that the mode purity can reach 97.3% and 96.3% for radially and azimuthally polarized beams at the maximum output power. The residual Gaussian beam can be mainly attributed to imperfections of nano-grating structures, which cannot completely convert the Gaussian beam to radially or azimuthally polarized beam.
Fig. 9 (a) and (b) The intensity distribution of radially and azimuthally polarized beams along the x axis at the maximum output power. The pink dots and blue curves are the intensity profiles of theoretical radially or azimuthally polarized beam and Gaussian beam. The solid red lines represent the fitting results of superposition of Gaussian beam and radially or azimuthally polarized beams.
4. Conclusion
In conclusion, we have demonstrated a wavelength-locked cladding-pumped ytterbium-doped vectorial fiber laser that can simultaneously emit radially and azimuthally polarized beams by using the S-waveplate as polarization-controlling elements. The radially or azimuthally polarized beams output can be conveniently delivered and switched with laser central wavelength located at 1053.4 nm and spectral linewidth of 0.06 nm. At the wavelength-locked regime, the output power and slope efficiency are 2.75 W and 33.5% for radially polarized laser, 2.68 W and 32.7% for azimuthally polarized laser, respectively. The mode purity of the vectorial modes could maintain 97.3% and 96.3% for radially and azimuthally polarized beams at the maximum output power. For the same conditions, polarization extinction ratio (PER) can reach 97.8% and 95.9% for radially and azimuthally polarized beams, respectively. The work explores the controlling potential of vectorial fiber laser in spectrum domain, and manifests the potential of the micro-structured optical element for structured light manipulation.
Funding
National 973 Program of China (2012CB315701); National Natural Science Fund Foundation of China (NSFC) (61475102 and 11574079).
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