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Radially polarized beams with an output power of 275 W, M2 = 2.3 and an efficiency of about 52.5% were generated from an Yb:YAG thin-disk laser. An intra-cavity circular resonant waveguide grating was used as a polarization selective mirror inside the laser cavity. We report on the design and the fabrication using a scanning beam interference lithography system and discuss the calculated and measured performances of the presented polarizing grating mirrors.
©2011 Optical Society of America
1. Introduction
The benefits of axially-symmetric (radially and azimuthally) polarized beams have often been reported in the last few years. For instance, radially polarized beams are advantageous for particle acceleration [1], lithography, data storage, resolution-enhanced microscopy [2], particle trapping or guiding [3], orientation of single molecules and optical tweezers [4]. At high powers, the most interesting application is metal processing, i.e. metal sheet cutting [5–7] or welding [8] as well as drilling [9–11]. During the last decades different extra- and intra-cavity approaches for the generation of radially and azimuthally polarized beams have been developed and reported by several scientific groups [12–19].
In this paper, we report on the highly efficient intra-cavity generation of beams with radial polarization in an Yb:YAG thin-disk laser. The basic principle of the polarizing mechanism has been reported earlier [20,21]. However, we focus here on the extension of the principle towards high laser output power. For this, optimized design and novel fabrication principles have been implemented and experimentally demonstrated.
2. Polarizing principle and grating design
To control the polarization of laser emission, a substantial reduction of the reflection coefficient for the undesired polarization state is introduced in one of the dielectric multilayer mirrors of the cavity. It is known that the coupling of free-space radiation to waveguide modes caused by a grating is polarization selective since the phase matching condition, also called resonance condition [22], can only be satisfied for one polarization at a time and at a given angle of incidence and wavelength. This coupling condition is expressed by the following relation:
where neff is the effective refractive index of the coupled mode which is depending on the opto-geometrical parameters of the waveguide, θ is the coupling angle of incidence, m is the diffraction order, λ is the wavelength of the incident beam and Λ is the period of the sub-wavelength grating. Hence, using this mechanism to couple the incident free-space beam to leaky waveguide modes of the fully dielectric multilayer mirror can lead to the desired polarization discrimination. In fact, this coupling is accompanied by a power leakage through the ± 1st diffraction order into the substrate as depicted in Fig. 1(a) . Therefore, by a proper design of the structure parameters (layer thicknesses, grating groove depth, and period) an intra-cavity reflectivity difference between the two orthogonal polarization states can be achieved at the wavelength of the laser to polarize [20,21]. In Fig. 1(b), the filtering was applied to TE polarization as an example, but it can be applied to TM polarization as well. Using a fully dielectric structure has the advantage to be very suitable for high-power applications.
Fig. 1 a) Leaky-mode based polarizing mechanism and b) calculated TE and TM reflection coefficient in the case of TE-polarization filtering.
Figure 2 shows the calculated field distributions inside the multilayer waveguide for both TE and TM polarization. The grating parameters were set to fulfill the coupling condition for TE polarization under normal incidence. As expected and can be seen in Fig. 2, a power leakage for the TE polarization occurs through the ± 1st diffraction order inside the substrate whereas for TM polarization the structure is only slightly affected by the grating and therefore remains highly-reflecting. In the case of axially-symmetric (radial and azimuthal) polarization states, the required local reflectivity difference for TE (electrical field parallel to grating lines) and TM (electrical field perpendicular to grating lines) polarized incident radiation can be generated by using a circular grating [23,24]. All the simulation results presented in this paper were obtained with a commercially available modelling code based on the modal method as described in [25,26].
Fig. 2 TE and TM 2D-field-distributions in a standard multilayer in association with a sub-wavelength grating.
The above described approach was applied to a thin-disk laser to generate beams with radial polarization. For this, two different design structures, as shown in Fig. 3 , have been studied and their performances with respect to the spectral bandwidth of the damped polarization, the reflectivity difference between the two polarization states, and the reflection coefficient of the lazing polarization (see Table 1 ) were compared theoretically. Whereas in the first design [Fig. 3(a)] the grating is defined in the top high-index layer of the mirror, in the second design [Fig. 3(b)] it is defined at all layer interfaces. In the following, we will call the first design “top-etched” and the second one “multiple-corrugated”. The same coating sequence, consisting of 29 alternating Ta2O5/SiO2 quarter-wave layers (at 1030 nm wavelength and 0° angle of incidence) was applied for the modeling of both approaches. The nominal refractive indices n (as communicated by the supplier) and thicknesses w of the layers are nh = 2.185 and wh = 118 nm for Ta2O5 and nl = 1.48 and wl = 174 nm for SiO2 at the 1030 nm wavelength. The multiple-corrugated structure is obtained by first etching the grating into the substrate and then applying the multilayer coating [20].
Fig. 3 Cross-section of the a) top-etched and b) multiple-corrugated structures. H and L demote High and Low index respectively.
Table 1. Calculated reflection coefficients and spectral bandwidth of the two developed polarizing leaky mode mirrors
The top-etched design seems, at a first glance, to be easier to fabricate, since it uses a standard multilayer coating, while the multiple-corrugated design requires a coating technique that reproduces the grating structures of the substrate over many layers. However, given that a suitable coating technique exists, the multiple-corrugated design has several potential advantages: The use of a standard etching process in the case of SiO2 substrates, lower scattering losses [27] and significantly broader fabrication tolerances [20]. In fact, if the grating is etched into the substrate instead of the top layer of the mirror it is for instance possible to obtain the same spectral band-width and the same reflectivity difference as for the top-etched structure but with a 4 times shallower grating. This is illustrated by Fig. 4(a) , which compares the performance of a 10 nm deep grating in the substrate (solid line) to the mirror where a 40 nm deep corrugation grating is applied to the top dielectric layer only. In addition, Fig. 4(b) shows that with the multiple-corrugated concept half the groove depth leads to a nearly 2 times broader bandwidth at a reflectivity difference of ~5%. Additionally, a 2 times larger reflectivity difference between radial and azimuthal polarizations at 1030 nm wavelength can be reached with the multiple-corrugated design approach. In these examples the reflectivity for the lasing radial (TM) polarization is very slightly affected by the presence of the grating and still exceeds 99.7% for the top-etched and 99.8% for the multiple-corrugated design. This broad spectrum significantly improves the fabrication tolerances which were found to be critical in previous work based on the top-etched de-sign approach [28,29].
Fig. 4 Comparison of the calculated reflection coefficients for the top-etched and multiple-corrugated structures. a) top-etched and multiple-corrugated structures with 40 nm and 10 nm grating depth respectively; b) top-etched and multiple-corrugated structures with 50 nm and 25 nm grating depth respectively.
Taking advantage of the multiple corrugation interfaces caused by the grating etched into the mirror substrate as shown in Fig. 4(b) leads to an enhancement of the coupling efficiency [22]. Since the polarizing mechanism is based on a coupling mechanism that leads to power leaking into the substrate as described in ref [20,21,28,29], the amplitude of the effect is significantly larger than in the case where the grating is applied to the top layer only.
At the Yb:YAG thin-disk laser wavelength, i.e. 1030 nm, the calculated reflection coefficients as well as the spectral bandwidth for both design structures i.e. the top-etched design with a period of 947 nm and a depth of 50 nm and the multiple-corrugated design with a period of 925.5 nm and a depth of 25 nm are summarized in Table 1.
Hence, we have chosen to use the multiple-corrugated design approach for the generation of beams with radial polarization in the Yb:YAG thin-disk laser. We additionally investigated the effect of the refractive index tolerances of the coated Ta2O5 and SiO2 layers on the spectral band-width of the polarizing effect for this structure. The refractive index tolerances given by the coating supplier are ± 0.01. Figure 5 gives the calculated reflections coefficients spectral for the extreme high and low refractive indices combination C1 = (nTa2O5 = 2.195, nSiO2 = 1.49) and C2 (nTa2O5 = 2.175, nSiO2 = 1.47) and for the nominal values C0 = (nTa2O5 = 2.185, nSiO2 = 1.48) given by the coating supplier. The grating parameters are those given in Table 1 for the multiple-corrugated structure. As can be seen, the reflectivity spectra are shifted by ~5 nm to higher (resp. lower) wavelength for the combination C1 (resp. C2). However, at 1030 nm wavelength, the reflectivity difference between radial (TM) and azimuthal (TE) polarization remains higher than 7% to ensure a large enough polarization discrimination inside the Yb:YAG thin-disk laser resonator. In all cases the reflection coefficient for the radial polarization is not changed and is as high as 99.8%.
Fig. 5 Calculated TE and TM reflections coefficients for C0, C1 and C2 structures described in the text.
However, to minimize the losses of the lasing radial polarization its reflectivity should be larger than 99.9%, i.e. the additional losses due to the presence of the grating should not exceed 0.1%. For instance, if we consider a laser resonator with 4% transmission output coupler (corresponding to a typical value for a V-shaped thin-disk resonator configuration with one disk), then 0.2% of additional loss in the grating would lead to a relative efficiency drop of approximately 5%.
After optimization of the grating parameters, the targeted period and depth for the grating fabrication were chosen as 930 nm and 15 nm respectively. This leads, at 1030 nm wavelength, to reflection coefficients for radial and azimuthal polarization of about 99.92% and 88.23% respectively. With this design, the calculated spectral bandwidth is larger than 6 nm at 5% reflectivity difference covering the whole spectral gain bandwidth of an Yb:YAG around 1030 nm.
For the experimental characterization of the described polarizing mirror and the subsequent test in an Yb:YAG thin-disk laser, a linear (to facilitate the measurement of the spectral distribution of the TM and TE reflectivities) and a circular grating with the same parameters were fabricated. For the linear grating we used a standard interference lithography setup whereas for the circular grating a SBIL (Scanning Beam Interference Lithography) system was built and used.
3. Grating fabrication using a Scanning Beam Interference Lithography (SBIL) system
Smooth, highly symmetric grating structures are essential for the application of the fabricated polarization selective mirrors in efficient high power lasers. For the generation of such structures e-beam lithography or nano-imprint are possible solutions. However these techniques suffer from either comparable low throughput or flexibility. Furthermore, since most available raster scanning lithography systems work in Cartesian coordinates, circular structures fabricated with such systems all more or less suffer from stair case artifacts.
The writing system we used is a laser direct writing system that works in polar coordinates [30]. This feature makes it very well suited for the generation of rotational symmetric structures. With common laser sources emitting in the visible spectral range, conventional laser direct writing systems typically achieve smallest feature sizes in the order of 0.6 - 0.8µm [31]. For the generation of the circular grating structures we implemented a novel laser direct writing technique, called scanning beam interference lithography (SBIL) that was already successfully applied to the fabrication of large area, high precision linear gratings [32]. We adapted this technique and optimized it for the fabrication of our circular gratings. It is based on two beam interference that occurs in the focus of a microscope objective. Through upstream beam shaping optics we are able to generate an elliptical writing pattern with interference fringes of variable period. During the writing process the pattern, as can be seen in Fig. 6 , is scanned ring by ring across the surface. Adjacent rings are stitched with a step size that is a whole-number multiple of the fringe period. An integrated fringe locking control system ensures precise pattern placement and stitching. Regarding the positioning error of the fringes with respect to the grating centre we typically achieve values of 1–2 nm rms for fringe periods from 500 nm to 1 µm.
With this technique we are able to achieve very low phase distortion even on large substrates. Through the parallel nature of our approach we reach high writing speeds of up to 250 mm2/min. At the present state, using the blue line (457.9 nm) of an Argon ion laser, the period can be varied between 450 nm and 2 µm. The writing pattern has a size of approx. 3 µm width and 10 µm length. Thus we are able to write fringe patterns even very close to the substrate center. Figures 7(a) and 7(b) show a photo and a 3D AFM scan of a circular grating with a period of 1 µm which has been fabricated with our SBIL system. The latter will be covered in detail in a future publication.
A point of crucial importance for the fabrication of multiple-corrugated mirrors is the coating technique. Figure 8 shows a SEM picture of a linear multiple-corrugated structure. It illustrates nicely that the grating etched in the fused silica substrate repeats its geometry in every single layer of the dielectric multilayer coating of the mirror. This is due to the ion plating layer deposition technology which ensures a conformal reproduction of the grating topography [20,33].
4. Spectroscopic and laser characterization
For the spectroscopic characterization of the fabricated structures a reflectivity measurement setup, shown in Fig. 9 , was built according to the DIN EN ISO 13697 with a slight modification for its use under normal incidence [34].
Fig. 9 Spectroscopic characterization setup built according to DIN EN ISO 13697 with a slight modification for its use under normal incidence.
We used a tunable laser diode (1000-1050 nm wave-length range) as a source for our experiments. The collimated laser beam is cleaned up using a single mode polarization maintaining fiber in combination with a polarizing beam splitter with an extinction ratio higher than 10,000:1. An optical chopper is used to modulate the laser signal. The modulation frequency f1 provides the reference signal for the first lock-in amplifier (SR830 Stanford Research Systems). A 50/50 beam splitter redirects the beam which is alternately reflected from the chopper mirror or from the sample under test to the integrating sphere. The frequency modulation f2 of the chopper mirror provides the reference signal for the second lock-in amplifier (SR830 Stanford Research Systems). This differential measurement scheme, which uses a fast alternation between the reference signal reflected from the chopper mirror and the “unknown” signal reflected by the sample to be measured, reduces the sensitivity to the intensity fluctuations of the laser beam. The detection of the signal was accomplished using a large-area Si-photodiode (Hamamatsu S2386-8K) coupled to an integrating sphere.
The TE (corresponding to the azimuthal polarization for the circular grating) and TM (corresponding to the radial polarization for the circular grating) measured reflection coefficients are shown in Fig. 10 . As expected, a decrease of the TE reflection coefficient occurs around the central wavelength of the Yb:YAG disk laser. At 1030 nm, the reflection coefficients for the TE (azimuthal) and TM (radial) polarizations were measured to be (90 ± 0.2) % and (99.8 ± 0.2) % respectively. This is in good agreement with the modeling results (also shown in Fig. 10) and demonstrates the high reliability of our polarizing scheme. The slight deviation of the spectra can be attributed to the fabrication tolerances of the grating and the multilayer parameters. The used SBIL writing system that works in polar coordinates as well as the precise control of the complete process parameters during the production of the structures were the central points that allowed us to reach this high reflection coefficient in comparison to our previous work [20].
Fig. 10 Measured and calculated reflection coefficients for a grating with a period of 930 nm and a nominal groove depth of 15 nm combined with a standard 29 quarter-wave layer dielectric mirror
Since the above described polarizing mirrors are developed to be integrated in high-power laser systems where heating of the element can become significant, we analyzed the spectral behavior of one of the fabricated linear polarizing grating mirrors at high temperatures. A linear leaky mode grating mirror (multiple-corrugated design) with a grating period of 930 nm and a grating depth of about 25-30 nm was heated using a Peltier element at the back side of the substrate. Figure 12 shows the obtained results for temperatures of 21 and 134 °C (resp. 21 and 126°C) for TE polarization (resp. TM polarization). One can see that the dip position of the polarizing effect is affected only slightly.
A shift to higher wavelengths by about 8 pm/K was observed showing the high stability of the present mirror design. Such a small shift can be explained by the compensation between the thermal expansions coefficients and the temperature dependence of the refractive indices of the Ta2O5 and the SiO2 [35]. The wavelength dip position versus the temperature is given in the inset of Fig. 11 . On the other hand it can clearly be seen that the TM reflection coefficient is not affected when increasing the temperature of the sample up to 126°C. Therefore the functionality of the polarizing grating mirror element will not be affected even at the high temperatures occurring in high-power laser systems.
Fig. 11 Temperature dependence of the spectral response of the multiple-corrugated polarizing grat-ing mirror. The inset shows the wavelength dip position versus the temperature.
After this confirmation of the proper behaviour of the developed polarizing grating mirrors the latter were introduced as the end-mirror of a 1.35 m long V-shaped laser cavity. A fiber-coupled pump diode with 525 W maximum power at 940 nm and a 3.6 mm pump spot diameter was used together with a 215 µm thick Yb:YAG thin-disk (the curvature of the disk was measured to be ~4 m at room temperature) and a 4% transmission plan output coupler. The 1.35 m long resonator is depicted in Fig. 12.
The TEM01*-mode operation with M2~2 was obtained by resonator design, namely by matching the diameter of the desired mode on the disk to the pump spot diameter, and the optimization of its length at full power.
Up to 275 W of a radially polarized doughnut-like mode (measured M2 ~2.3 at full pump power) was generated with our polarizing mirror with an excellent optical-to-optical efficiency of 52.5%. This is, to the best of our knowledge, the highest power reached out of a laser oscillator at 1 µm wavelength. The output power of the laser as well as its efficiency are shown in Fig. 13(a) . In comparison to the standard HR mirror within the same laser configuration (one to one replacement), a drop in efficiency of about 7% (at max. output power) was measured. The beam quality factor of the emitted laser beam with the HR mirror was measured to be M2~2.4 at full power. It is, as expected, identical to that with the polarization selective mirror since the resonator parameters (curvatures of the mirrors, and lengths) were not changed. These losses are attributed to several factors:
Fig. 13 a) Comparison of laser efficiency between a circular grating mirror and a standard HR mir-ror; b) Measured intensity distribution of the 275 W radially polarized thin-disk laser beam without (top left) and with a linear polarizer at different orientations; c) Measured polarization distribution over the beam cross-section.
- - The grating itself (still 0.1-0.15% lower reflection coefficient than standard HR mirror). This leads to a relative drop of the laser efficiency of approximately 2.5 to 3.75%.
- - Depolarization effects possibly caused by thermally and/or stress-induced birefringence in the 215 µm thick Yb:YAG crystal, due the soldering of the disk on the heat sink
- - The notably smaller spatial overlap of the pure doughnut-like-mode with the homogenous gain distribution on the disk compared to standard laser configuration with an HR mirror. In fact, the intensity distribution of the emitted beams for the resonator with the HR mirror exhibits a peak in its central area which is not the case with our polarizing grating mirror because of the specific intensity distribution (zero-intensity in the center) of beams with radial polarization.
Even though, we still see room for further improvement both in the design and fabrication process. The efficiency of 52.5% that we achieved with our multiple corrugated polarizing grating mirror for a radially polarized high-power solid-state laser operating at M2 ~2.3 is rather close to that of a non-polarizing oscillator with a standard HR mirror. Additionally, we measured the temperature of our polarizing grating mirror during laser operation to be moderate and around 75°C at full output power. Hence, no additional optical perturbations (e.g. turbulences which lead to a degradation of the beam quality) due to our grating mirror are expected and were observed within the resonator.
Figure 13(b) shows the intensity distribution of the beam without the polarizer at the top left-hand corner and the corresponding intensity distributions after the polarizer. The degree of radial polarization was measured to be higher than (98.5 ± 0.5)% (Fig. 13-c) with a home-made 2D-polarimeter [36], revealing a high purity of the radial polarization of the beams generated with our mirror scheme.
5. Conclusion
To conclude, we reported in the present paper on a high-efficiency, high-power radially polarized thin-disk laser using a circular grating mirror as the end-cavity mirror. A 275 W radially polarized doughnut-like mode (measured M2 ~2.3 at maximum output power) was generated with our polarizing mirror with an excellent optical-to-optical efficiency of 52.5% and a high degree of radial polarization of about 98.5%. This is, to the best of our knowledge, the highest output power reported so far for beams with radial polarization out of laser oscillator at 1µm wavelength. Further experiments are under progress in order to minimize the depolarization losses which are introduced by the disk. The direct writing laser fabrication with a novel scanning interference approach has been proven to be an efficient tool for the production of such low-loss polarizing devices.
Acknowledgements
This research project was financially supported by the Baden-Württemberg Stiftung within the project “PolGit”. The authors acknowledge Mr. H. Wagner and Mr. T. Engelhardt for their support in the lab work.
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