We milled a sub-wavelength diffraction grating on the facet of a large mode area fiber. The diffraction grating had different reflectivities for TE and TM polarized light. It was tested in a thulium-doped fiber laser where it functioned as a low reflectivity output mirror integrated with an intracavity polarizer. Compared to the laser with a perpendicularly cleaved output fiber, the laser with diffraction grating had a slightly increased threshold power and the same slope efficiency. The beam quality factor M2 was not impaired. Polarization extinction ratios of about 20 dB that were observed at low laser powers dropped to 10 dB at high powers.
© 2016 Optical Society of America
High-power polarized laser beams are needed in nonlinear optics to pump optical parametric oscillators [1, 2], generators of second harmonics , etc. In materials processing, the polarization dependence of laser cutting efficiency was discussed by Niziev and Nesterov . Polarization-dependent, laser-induced periodic surface structures are formed on the laser-treated surfaces as a result of interference between the incident laser beam and surface scattered waves . Polarization multiplexing is used to scale the power of fiber lasers .
Several approaches are used to achieve a stable and defined polarization state at the output of fiber lasers. Polarizing isolators, polarizers, and other hybrid elements are included into low-power fiber lasers made from polarization-maintaining (PM) fibers. The σ-laser configuration is used to mix PM and non-PM elements in resonators with defined output polarization .
Any passive intracavity element negatively influences the threshold, slope efficiency, reliability and cost of high-power fiber lasers. Active PM fibers were combined with a bulk polarization beam splitter in the resonator of a 300-watt ytterbium-doped fiber laser . Cross-axis wavelength-matched fiber Bragg gratings were used to define the wavelength and linear polarization in a 100-watt ytterbium-doped fiber laser . A linearly polarized output was achieved by inducing differential bending loss between the light polarized along the slow axis and fast axis of the PM fiber. Due to a lower effective index of refraction, light polarized along the fast axis of the fiber has higher bending loss when the fiber is wound into a coil of appropriate diameter. The technique was demonstrated for a 100-watt ytterbium-doped fiber laser .
One of the emerging technologies in fiber optics is the fabrication of microoptical elements directly on cleaved or polished end fiber facets through etching, milling or additive manufacturing. To date, interference lithography , photolithography , electron-beam lithography , focused ion-beam milling , nano-imprint technology [15,16], two-photon polymerization 3D printing [17–19], and laser micromachining were demonstrated as tools for fiber-facet patterning. The polymers are not yet suited for high-power applications and their exploitations is tricky due to polymerization inhomogeneities and nonuniform deformations occurring during the exposition and development processes . The best suited technique of micro-patterning for high-power applications is etching or milling the microstructures directly on silica fiber facets.
In this paper, we present a polarizing diffraction grating etched directly on the fiber facet serving as a laser output reflector. We assume that light propagates in the fiber core towards the perpendicularly cleaved fiber end, which serves as a low-reflectivity mirror. The diffraction grating milled on the surface of the fiber facet modifies the reflection coefficient of the mirror. A focused ion beam was used to mill the grating grooves perpendicularly to the slow axis of the PM fiber. The grating parameters were optimized in a way ensuring that difference in reflections between the TE and TM modes was achieved, the reflection of the TE mode was close to optimum, and loss caused by diffraction into higher modes was low. The grating was tested in a thulium-doped fiber laser with a wavelength of 2040 nm at moderate powers.
Design and fabrication of diffraction gratings are described in Section 2 and 3, respectively. The grating performance in the laser at moderate powers is given in Section 4.
2. Diffraction grating design
The diffraction gratings properties were analyzed and optimized by means of a rigorous coupled-wave analysis (RCWA), finite-difference time-domain (FDTD) method, and Fourier modal method (FMM). The RSoft DiffractMOD, MIT MEEP , and UFE FMM  simulation software were used for RCWA, FDTD, and FMM analysis, respectively. The RCWA method allows fast optimization of grating parameters. The FDTD and FMM methods were used to evaluate the reflectivity of optimized gratings for guided mode, and the FDTD method additionally provided estimation of the modal loss.
Light diffraction is limited to zero order in sub-wavelength diffraction gratings. Optical properties of such gratings can be explained by the effective-medium theory . The sub-wavelength grating behaves roughly as a homogeneous birefringent layer. Its reflectivity varies periodically with grating thickness with period depending on the polarization of incident light. The maximum reflectivity can not exceed a value given by Fresnel’s equations for an unstructured fiber facet in the effective-medium model.
Gratings with longer periods allow achieving zeroth order diffraction efficiencies beyond the Fresnel reflection limit at the expense of introducing loss due to the diffraction into higher reflected orders. In this work we optimized the grating with the aims as follows: a) achieving the reflectivity of the fundamental fiber mode close to the Fresnel reflection for unstructured fiber facet and avoiding diffraction into higher reflected modes in order to keep the laser threshold sufficiently low and slope efficiency high, b) designing the grating as shallow as possible to facilitate its fabrication, c) maximizing the difference between the grating reflectivity for TE and TM polarizations. The oscillation direction of electric field vector is parallel to the direction of grating grooves for TE polarization, and perpendicular for TM polarization. Our gratings were designed for a wavelength of 2040 nm. The product , where and are zeroth order reflectivities for TE and TM polarized light, respectively, was adopted as a figure-of-merit (FOM).
The results of the RCWA optimization are shown in Fig. 1. The zeroth order reflectivity for TE-mode has oscillatory character as expected from the effective-medium model. The reflectivity is given by Fresnel’s equations for zero depth of the diffraction grating. The reflectivity decreases with increasing grating depth until the quarter depth is achieved. Almost complete suppression of the reflection is possible for appropriately chosen fill factor, which is approximately 0.3 for silica/air interface. Then the reflectivity grows again until the first maximum is achieved and the whole process repeats. The FOM closely follows oscillations of the zeroth order reflectivity with amplitude growing as a result of increasing difference in the zeroth order reflectivity of TE and TM modes. The FOM achieves its first maximum for a grating depth of 590 nm and fill factor of 0.6, and the second maximum at a grating depth of 1415 nm and fill factor of 0.55. The results of optimization are summarized in Table 1. The RCWA results were obtained for plane wave diffraction and were verified by 2D FDTD method for the diffraction of the guided mode of a slab waveguide with a thickness and numerical aperture matched to the fiber (Fig. 2). To complete the optimization, a 3D analysis of fundamental fiber mode reflection was performed by using FMM. Similar results are obtained by the FDTD and FMM methods, while the RCWA method allows interpretation of loss as a diffraction of light into ±1 orders. The ±1 reflected diffraction orders have angles that are far away beyond the total internal reflection angle of the weakly guiding core of single mode fiber and are source of loss. The FDTD simulations reveal a smoother onset of modal loss resulting from the onset of higher order diffraction in reflected light, as can be seen in Fig. 2b. The dashed curves in Fig 2b are obtained as a sum of diffraction efficiencies into the ±1 orders in reflection calculated by RCWA. Smoother onset results from low spectral resolution of the grating caused by low number of grooves irradiated by fiber mode. Further evidence of the source of loss is shown in Fig. 3, where ±1 orders are clearly visible in the diffraction pattern calculated by FDTD method.
3. Fabrication of the diffraction grating
The designed grating was fabricated using the focused ion beam (FIB) milling. This single-step and maskless process is a very convenient technique for rapid prototyping. The milling was carried out using our FIB machine (Tescan LYRA3) with an ion source of liquid gallium, integrated with a scanning electron microscope (SEM), gas injection system (GIS), and secondary ion mass spectroscope (SIMS). The ion beam spot size of our FIB device for fine milling is about 70 nm. The limitations of our device are in the transversal dimensions of the structure 400 μm × 400 μm, the aspect ratio of the holes or trenches because the beam should be focused onto the bottom of the structure, and accumulation of the electric charge on the surface of the dielectric, which repels ions. In situ calibration was performed sufficiently far from the fiber core before inscribing the grating. A small-size test grating was milled close to the perimeter of the fiber, platinum strip was deposited across the grating grooves using GIS, and finally, a trench was etched to measure grating’s depth and fill factor. Based on the calibration data, a grating with dimensions of approximately 35 μm × 35 μm was fabricated centered at the fiber axis with grooves oriented along the fast axis of the PM fiber. The fiber facet with the diffraction and test gratings is shown in Fig. 4. The fabricated grating has a groove depth of approximately 550 nm and a fill factor of 0.7 which differs slightly from designed parameters. The difference from optimum parameters should have small effect on results as can be seen from Fig. 1.
4. Test of the diffraction grating as a polarizer and output mirror in a fiber laser
The diffraction grating was tested in a thulium-doped fiber laser. The fiber laser only involves PM fibers and PM pigtailed optical components. The laser scheme is shown in Fig. 5. The resonator consists of an active fiber (PLMA-TDF), pump-signal combiner (PSC), and high-reflectivity fiber Bragg grating (HR-FBG). We used 35-watt 793-nanometer laser diodes from LIMO coupled to 220/280 μm multimode pigtails with a numerical aperture of 0.22 as pump sources. A double-clad thulium-doped PM fiber (PLMA-TDF-25P/400-HE from Nufern) with a large mode area and length of five meters was used as an active fiber. The fiber has a core diameter of 25 μm and an inner cladding diameter of 400 μm. It is coated with a low-index polymer with an outer diameter of 550 μm. The numerical apertures of the core and of the inner cladding are 0.09 and 0.46, respectively. The multimode pump absorption is 12 dB for a five-meters long fiber. The unabsorbed pump power is trapped in a cladding mode stripper (CMS). A laser resonator is created between the HR-FBG spliced to PSC and a low reflectivity mirror in the form of a perpendicularly cleaved output fiber. The HR-FBG has a reflectivity of 99.6% at a wavelength of 2039 nm and reflection bandwidth of 1 nm. The output mirror has a reflectivity of 3.5% given by Fresnel’s equations. The output laser power was measured with a power meter from Gentec. The polarization extinction ratio of the laser was determined using a Glan-Taylor polarizer and the beam quality factor was assessed by pyroelectric camera (Pyrocam III) combined with a linear kinematic stage. The optical spectrum was recorded by a Fourier transform infrared spectrometer (Nicolet 8700). The dependence of the laser output power on the launched pump power is shown in Fig. 6. The power launched into the active fiber was measured at the output of the pump-signal combiner as a function of pump laser diode currents during the construction of the laser before splicing with the active fiber. The laser has a maximum output power of 18 W, threshold of 7.4 W, and slope efficiency of 42%. The slope efficiency is lower than the slope efficiency of lasers pumped directly through the HR-FBG [23, 24], which we attribute to additional insertion loss of pump-signal combiner. We determined the M2 beam quality factor to be about 1.4, which indicates that higher-order modes are present in the large mode area fiber. The polarization extinction ratio of the laser beam was close to 1, which reflects the fact that no elements with significant polarization-dependent loss were included in the resonator.
Once the fiber laser with a perpendicularly cleaved output fiber was characterized, we spliced the laser output fiber with the piece of the fiber where the diffraction grating was fabricated. We observed that the threshold slightly increased from 7.4 W to 9.9 W while the slope efficiency remained at 42% (Fig. 6a). This is in agreement with results of simulations where low diffraction loss is imposed by the grating, while the transmission coefficient of the grating is close to that of perpendicularly cleaved fiber. The measured polarization extinction ratio defined as PER = 10 log(Pmax/Pmin) was about 20 dB at low powers and decreased to 10 dB for the output power of 18 W (Fig. 7). The most probable reason of the PER degradation is excitation of the fast-axis mode in the laser and redistribution of the power between two existing modes because the reflectivity ratio between the TE and TM polarization of the grating is only slightly higher than 3dB. Higher extinction ratio could be expected for deeper output gratings with larger polarization selectivity operating in third or even higher FOM maximum (Fig. 1).
The minimum and maximum powers measured behind the polarizer are shown in Fig. 6b. The measured beam quality factor M2 measured at maximum power was 1.4, which is the same value obtained for the perpendicularly cleaved output fiber end. The measured beam diameter as a function of the camera position is shown in Fig. 8a) for both cases. The optical spectrum of the laser at maximum power is shown in Fig. 8b).
Transmission properties of optical fibers can be modified by nanostructuring of the fiber end. In this paper, we modified the fiber facet reflection properties by milling a sub-wavelength diffraction grating on the facet of a perpendicularly cleaved fiber. The diffraction grating has different reflectivities for TE and TM polarized light and can act as a polarizer in a fiber laser. We tested the grating as an output low-reflection mirror in the moderate-power, thulium-doped fiber laser. The beam quality parameter M2 and slope efficiency were preserved while the laser threshold slightly increased. The output beam was polarized with a polarization extinction ratio of about 20 dB at low powers and 10 dB at high powers. No grating damage was observed up to 18 W of output power limited by experiment setup.
Czech Science Foundation, grant GAP15-07908S.
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