1. Introduction

The generation of the fundamental transverse mode of radial polarization in a high power laser has been a subject of vivid interest since Niziev [1] predicted a possible increase of up to 50% of the laser machining efficiency of metals, and Muys [2] confirmed it theoretically. Also in basic research circularly symmetrical polarization states are of growing interest (e.g. focus shaping [3], higher harmonics generation [4]). A number of polarizing mechanisms implemented in one of the laser mirrors have been proposed. In a first category a multilayer subwavelength grating acts as a mirror with a polarization dependent effective index of each layer [5], allowing the design of polarization selective grating mirrors. Such mirrors, conformally replicated in a multilayer structure by an autocloning technique [6], have been used as wide-band, out-coupling mirror of a Nd:YAG ceramic laser creating azimuthal or radial polarization [7]. In a second category of polarization selective mirrors, the grating-mode interplay in a deep high index contrast corrugation leads to the destructive interference of the TM polarization in the transmission medium, therefore to very high TM reflection whereas the TE polarization is weakly reflected [8,9]. In a third category, the polarization selective mechanism is based on resonant grating effects whereby one of the polarizations is given the possibility to tunnel through the multilayer mirror with the mediation of a grating exciting a guided, leaky or lossy mode of the multilayer [10]. Most often the grating corrugation is located in the first or in the last layer of the mirror. It can also be etched in the mirror substrate first, then replicated conformally at each multilayer interface if ion plating or IBS is used for the layer deposition [11,12]. All grating polarizing mirrors aimed at the generation of the radial polarization so far have circular grating lines, the grating coupling the local TE-polarization to the substrate through the multilayer mirror, and the local TM polarization still experiencing a close to 100% reflection. A different polarization mechanism is reported here whereby it is the TM polarization that leaks through the multilayer to the substrate and naturally imposes the generation of the azimuthally polarized mode if the grating lines are circular. The usefulness of such laser mode was highlighted recently for its efficiency in making deep and rather uniform holes in metals [13]. This laser mirror uses a multilayer of high index contrast and a grating of radial period smaller than the wavelength, which permits the TM polarization to leak through the multilayer stack under an angle located between the TE and TM angular band edges of its TE and TM angular reflection spectra. As this diffractive dichroism principle is non-resonant, its bandwidth is wider than the previously reported polarization selective laser mirrors. In the objective of covering a wide wavelength spectrum with the same polarizing mirror, the bandwidth is here further expanded to about 10% of the central wavelength by a specific structure of the multilayer. The 1.0 to 1.1 micrometer range was chosen as an example as a number of lasers emit in this spectral band such as Yb:YAG (1030 nm), Nd:YAG (1064 nm), and neighboring wavelengths depending on the host material, e.g. up to 1078 nm with Yb-doped ceramic lasers or semiconductor disk lasers. The functional demonstration of the lasing of the azimuthally polarized mode is made at the 1064 nm wavelength of a Nd:YAG laser by means of an original grating technology.

2. The diffractive dichroic laser mirror

The rationale of the polarization filtering mechanism will first be outlined on a general basis, then a design will be developed on a specific example of the element which will be fabricated and finally demonstrated experimentally.

2.1 Basic principle

The polarization selective operation of the laser mirror is illustrated in Fig. 1(a) . A corrugation grating is situated at the top of a multilayer mirror. The grating period is chosen so as to give rise to the 0th and ±1st diffraction orders in the layer stack and substrate, as well as to only the 0th order in reflection to prevent any diffraction loss at the side of the active medium. The transmitted 1st orders must have propagating character in the low index layers of the mirror in order to be permitted to leak into the substrate, thus the necessary condition on the grating period Λ is: λ/n_l < Λ < λ. As from now, the polarization discriminating effect is introduced: it is well known that the angular tolerance of a multilayer mirror depends on the polarization and that the width of the TM stopband in the angular reflection spectrum extends to a smaller angle than the TE stopband, thus the sufficient condition for a complete reflection of a normally incident TE polarization and the leak of the TM polarization through the mirror is that the grating directs the first orders in the substrate direction under an angle comprised between the mirror’s angular band edges of the TE and TM polarizations.

 

Fig. 1 (a) sketch of the polarization selective multilayer grating mirror illustrating the polarization selective 1D photonic crystal character of the multilayer mirror (the zigzagging 1st order path in the layers is not represented); (b) Brewster angle and angular position of the TE- and TM-bandedge for a λ/4 stack with an infinite number of layers as a function of the refractive index contrast IC (angles measured in medium with low layer-stack index n_l)

Download Full Size | PDF

The reflection band edge angle Θ_e of a periodic multilayer can be determined by using a 2x2 transmission matrix approach as proposed in [14], resulting in the definition of the band edges by the implicit equation:

Equation (1) is different from the derivation in [14] as the right hand member of Eq. (1) accounts for the number N of layer pairs and also for the order of the transmission maximum m across the multilayer, which in the present case is m = 1. This expression was derived by diagonalizing the transmission matrix of one pair of low and high index layers, discriminating between the propagative and evanescent behavior of the eigenvalues, and using the Sylvester theorem for summing up the contribution of N pairs of layers. The analysis of Eq. (1) confirms that Θ_e,TE is always larger than Θ_e,TM, and permits a straightforward analytical and normalized design of the polarization discriminating structure. Note that in Eq. (2) the angle Θ_e is defined in an incidence medium of index equal to the index n_l of the low index layers.

The leakage rate of the TM first orders cannot be anticipated phenomenologically as it is the result of a complex multiwave coupling between the up- and down-propagating 0th and ±1st orders in the multilayer with possible excitation of multilayer guided and leaky modes. However, a favorable factor facilitating the TM leakage is that the Brewster angle between the mirror’s layers is in the region of the multilayer band edges depending on the index contrast IC = n_h/n_l. It is a specific characteristic of the present wide-band element to possibly have the TE and TM band edges placed at either side of the Brewster angle, thus essentially suppressing the said TM multiwave coupling in the multilayer mirror as will be shown in the next section. It is therefore interesting to determine the relative angular position of the TE and TM band edges of a highly reflective quarter wave stack with infinite number of layers and of the Brewster angle Θ_B in the medium of low index versus IC as illustrated in Fig. 1(b). The TE band edge curve stops at IC = 1.90, meaning that beyond this index contrast value the multilayer is a complete photonic crystal for the TE polarization; such case can be encountered where the high index layer is made of a semiconductor or a chalcogenide glass, and the low index layer is a low index metal oxide or a fluoride glass. The TM angular bandedge is always smaller than Θ_B and always smaller than the TE band edge. The Brewster angle is located between the TE and TM band edges for index contrast values larger than 1.73. This favorable situation is encountered in the far IR, for instance in CO₂ laser mirrors made of ThF₄ and ZnSe where IC = 1.82. It can only be achieved in the visible and near-IR with MgF₂ low index layers and high index layers such as TiO₂, ZnS or diamond having an index larger or equal to 2.4. Most metal oxide layers systems currently used in low loss, high damage threshold multilayer mirrors like SiO₂, Ta₂O₅, HfO₂, exhibit an IC smaller than 1.73. This does not prevent a diffraction grating from diffracting the ±1st TM order efficiently into the mirror substrate through the multilayer between the TE and TM band edges, but it would be advantageous to proceed to a specific design of the multilayer that would shift the TE and TM band edges to the Brewster angle neighborhood so as to flatten the sub-peaks of the TM angular spectrum. This is what will be achieved in the present design where one aims at a particularly wide band polarizing mirror.

2.2. Multilayer engineering

From what precedes it is clear that it is the multilayer which determines the angular and wavelength spectra of the polarization selective element, the grating acting as a virtual source for the ±1^st order, its period determining the diffraction angle in the multilayer. The multilayer mirror can be a simple quarter-wave stack, each layer having a thickness d given by:

The multilayer is assumed to be composed of ion plated SiO₂ (n_l = 1.48) and HfO₂ (n_h = 2.11) layers on a fused quartz substrate. With this index contrast IC = 1.42 the Brewster angle of 55° in the low index layer is beyond both TE and TM band edges as illustrated in the angular reflection spectra of Fig. 2(a) (black lines) calculated at the wavelength of (1030 + 1064)/2 nm with a number of 39 quarter wave layers of 177 and 124 nm thickness.

 

Fig. 2 (a) Angular dependence of the reflection from a SiO₂/HfO₂ λ/4 stack of 39 layers, with layer-thicknesses set for perpendicular incidence (black) and 25° incidence (grey), (b) wavelength dependence of the reflection of the layerstack, optimized for 25°, with a 970nm period aSi grating on top (thickness 50nm, ridge width 485nm).

Download Full Size | PDF

An angle of 36° between those two band edges could be chosen where the TM reflection is close to zero; however, a grating coupling the 1st orders under such angle in the low index layers would have a period of about 1200 nm which would therefore also give rise to a propagating ±1st order at 1050 nm wavelength into the incident medium. This is not acceptable since the laser polarizing mirror must not cause losses at the side of the laser resonator. The present index contrast IC = 1.42 is therefore too small to give rise to the leakage of the TM polarization without losses for the TE polarization. To forbid the TE 1st order propagation into the air cover, their propagation angle in the low index layers must be larger than the critical angle between the low index layer and the air, i.e. 42 degrees in the considered case of ion plated SiO₂ layers. Besides, to forbid the diffraction of the said orders into the substrate through the multilayer, their propagation angle in the low index layers must be smaller than the TE band edge. The TE band edge must therefore be larger than the critical angle which, by looking up in Fig. 1(b), TE curve, defines IC = 1.5 as the lowest index contrast limit. This is amply satisfied with the TiO₂/SiO₂ and the Ta₂O₅/MgF₂ system for the visible and near IR range and also with the ZnSe/ThF₄ system for high power CO₂ lasers. If IC < 1.5, as is the case with the present choice of layer materials and multilayer deposition technology, it is necessary to shift the band edges to larger angles. This can simply be made by setting the layers to a quarter-wave thickness corresponding to slightly off-normal incidence keeping in mind that the TE reflection under normal incidence must remain close to 100%. The corresponding layer thicknesses are given by

The objective is here however to further widen the spectrum of the polarization function to the 1.0 to 1.1 µm range. To that end, the angular offset described above will be developed so as to bring the Brewster angle between the TE and TM band edges, and to maintain close to 100% reflectivity for the TE polarization over the full range by splitting the double role of the multilayer into two functions: to generally reflect the 0th order transmitted light, and to reflect the 1st order diffracted light polarization dependently; and to attribute these two sub-functions to two adjacent multilayer sections having initially a quarter-wave thickness for normal incidence and the Brewster angle direction, respectively. This function splitting does not lead to the desired TE and TM spectra at once, but represents the physically based starting point of an optimization.

2.3. Design example

The general principle outlined above will now be applied to the design of a specific example of a polarization selective mirror for the wavelength region of 1.0 µm to 1.1 µm. First, the calculation of the multilayer will be outlined, followed by the design of the grating.

The multilayer is made of the same low and high index materials SiO₂ and HfO₂, deposited by reactive low voltage ion plating onto a fused silica substrate, resulting in a Brewster angle of Θ_B = tan(n_h/n_l) = 55°. The first sub-mirror, aimed at achieving a reflection larger than 99% under normal incidence for the 0th order, comprises at least 18 quarter-wave layers. The second sub-mirror, aimed at giving a high TE reflection in the neighborhood of the Brewster angle was limited to a number of 10 layers, owing to a limitation of the total multilayer thickness of about 4 µm to prevent the internal stress characteristic of ion plating to become too disturbing for the stability of the whole stack. Figure 3(a) illustrates the TE angular reflection spectra at 1050 nm wavelength of a sub-mirror comprising quarter wave layers for 0 degree incidence only, a sub-mirror comprising quarter wave layers for 40 degrees only, and a complete reflector comprising the two quarter wave submirrors. The graphs show that the sub-mirrors are capable of creating either a high reflectivity for 0°, or for the Brewster angle, whereas only the combined stack does provide high reflectivity for both angles at the same time.

 

Fig. 3 (a) Incidence angle dependence of the TE reflection of λ/4 layer stacks of SiO₂ and HfO₂ at 1050 nm wavelength, with layer thicknesses optimized for different incidence angles Θ_l;_, (b) Incidence angle dependence of the reflection of the SiO₂/HfO₂ layer stack with 23 layers at 1.00, 1.05 and 1.10 µm wavelength after the numerical optimization for high reflection at Θ_l = 0° and Θ_l = Θ_B

Download Full Size | PDF

Using the combination of sub-mirrors from Fig. 3(a) as a physically based starting point, a numerical simulation was carried out to optimize the whole layer stack: the goal functions were: R = 1 for the TE polarization at 1010, 1045 and 1080 nm wavelength for 0° and 55° incidence angle, as well as R = 1 and R = 0 for the TM polarization at the same wavelengths for 0° and 55°, respectively. This multi-goal optimization was carried out by means of the program MC Grating [15], which uses a gradient search method to look iteratively for a solution fulfilling all conditions. Figure 3(b) gives the final result of the optimization process in the angular spectrum with the wavelength as a parameter showing that the TE reflection is close to 100% at 0 degree and at the Brewster angle incidence from a low index medium whatever the wavelength between 1000 and 1100 nm. The TM Brewster angle is now within the stop band of the TE polarization, resulting in a very low TM-reflection (shown for λ = 1050nm).

For the design of the grating the period is considered first. Figure 4(a) gives the reflectivity of the optimized layer stack versus the wavelength and the incidence angle for the TE and TM polarizations superimposed with the 1st order diffraction angles due to different grating periods. As aimed at, a grating period between 850 and 900 nm results in low reflectivity for the TM and high reflectivity for the TE polarizations. This delimits the permitted variation range of the period as an optimization parameter. The remaining grating parameters, height and ridge width, can be chosen to optimize the leak of the TM ±1st order. The radiation strength of the grating is essentially determined by the phaseshift between the optical path through a groove and a high index ridge since the TM leak is non-resonant and amounts under the Brewster condition to a simple ±1st order beam splitting with best suppression of the 0th transmitted order. This remains approximately true although the wavelength/period ratio is too large to draw accurate quantitative conclusions. The present non-resonant diffraction mechanism leads to a rather deep corrugation of the order of 0.5λ/(n_g-1) where n_g is the ridge refractive index and the incidence medium is air.

 

Fig. 4 (a) Dependence of the reflection of the SiO₂/HfO₂ layer stack with 28 layers (same as in Fig. 3(b)) on the wavelength and the incidence angle for the TE and TM polarization, superimposed with the diffraction angle for gratings with 0.8 to 1.0 µm period; (b) sketch of the optimized polarization selective grating mirror, giving the height of the layers and the grating parameters (left), and the wavelength dependence of the reflection of the element (right).

Download Full Size | PDF

A concern in the present work is to design an easily fabricable corrugation by resorting to wet etching instead of dry etching. The choice was made of a high-index and still transparent grating material in the considered wavelength range: hydrogenated amorphous silicon with n_g = 3.7. a-Si:H is a low loss optical material down to the red side of the visible spectrum. It is unique in this spectral range for its very high index, is perfectly amorphous, and is chemically stable. An a-Si:H film thickness (and groove depth) of about 200 nm would be needed for a full suppression of the 0th order. This is too deep to enable the wet etching of a 800-900 nm period and, furthermore, so thick a high index layer will lead to spurious waveguide mode excitation in the spectrum of interest. Considering that the polarization selective element is actually an intra-cavity element, the TM/TE reflection differential does not need to be close to zero to privilege the emission of the local TE polarization: in the 1.0µm - 1.1 µm range most high power lasers use a high-Q resonator where a 80%/100% reflection differential suffices as demonstrated experimentally by Ref [12]. This all leads to the request of a rather shallow corrugation achieving both requirements of efficient polarization filtering and low-cost fabricability. Opting for an amorphous silicon grating depth of about 50 nm, the optimization process is resumed on the basis of the optimized multilayer of Fig. 3(b), now including the corrugation. The final polarizing grating mirror is depicted in Fig. 4(b), together with its wavelength dependent reflection.

The final element with 23 layers and an overall height of about 4 µm shows very high reflection of the TE polarization in the desired wavelength range, whereas the TM polarization is partially transmitted resulting in about 40-60% reflection only, which is more than sufficient to select the preferred polarization mode in a high Q laser resonator [12].

3. Fabrication

The fabrication processes are summarized in Fig. 5(a) . The first step is the definition of the grating lines in a Cr-mask. This is done by an electron beam writer SB350 OS (Vistec) for the exposure of the resist, and a transfer of the layout into the Cr-layer by ICP etching. The layer stack consisting of 23 layers of SiO₂ and HfO₂ is coated by a PECVD layer of a-Si:H of 45 nm thickness. This process is well established for the fabrication of solar cells [16]. The layers were measured by ellipsometry to have refractive index of n_aSi = 3.68 at 1064 nm wavelength. The imaginary part was too small to be measureable, which means less than k = 1E-5 for the used setup. The next step is the transfer of the chromium mask into an approx. 500 nm thick layer of Shipley 505A photoresist spin-coated on the a-Si:H layer. The transfer is performed in an ad hoc UV mask transfer setup under vacuum at 360 nm wavelength in a hard contact mode. The usual technology for the subsequent physical transfer into the a-Si:H layer is reactive ion etching. However, a silicon ridge aspect ratio of 45/460 can be fabricated by means of conventional wet etching provided the photoresist has a strong adhesion to the silicon layer, the lateral overetch being limited to about 50 nm. Figure 5(b) shows an SEM picture of the cross-section of the layerstack and grating taken from a focused ion beam slice confirming good adhesion of the a-Si layer on the multilayer and the complete etching of the latter down to the last low index layer. The microscope picture of Fig. 5(c) shows the central grating region with high line smoothness and no discernible defects.

 

Fig. 5 (a) Fabrication steps of the polarization selective grating mirror; (b) SEM-image of a cross-section of the polarizing grating mirror; (c) Optical microscope top view of the central region of the circular-line grating.

Download Full Size | PDF

4. Measurement

The characterization of the grating multilayer mirror was made on a rectilinear line grating test structure fabricated under the same conditions as the circular gratings later used for the generation of an azimuthally polarized mode in a laser cavity.

First, the optical properties of the layerstack were confirmed in a gratingless area under 1064 nm laser normal incidence. The residual transmission at this wavelength was measured to be below 0.5%. All further measurements will be made relative to this gratingless reference. The spectral measurements were made in reflection by means of super-continuum white light source and a grating spectrometer. The visible part of the spectrum was blocked by a silicon plate in order to get a distinct illumination band in the 1.0µm - 1.1µm range. The smallest possible incidence angle permitted by the optical setup without beam splitter was 2.5° in conical incidence (incidence plane parallel to grating lines). The resulting reflection curves are compared with the theoretical spectrum calculated under these conditions (Fig. 6(a) ). The TE polarization remains above (97±2)% between 1030 nm and 1080 nm; the dip below 90% between 1010 and 1030 is due to the incidence angle of 2.5°, as is confirmed by the modeling. Thus a high reflectivity of the grating mirror is preserved. For the exact reflectivity value a Q-factor measurement of a cavity build with such mirror will be necessary.

 

Fig. 6 (a) Calculated and measured TE and TM reflection spectra; (b)-(c) Intensity distribution in the beam cross section, observed on a fluorescent screen outside of the laser cavity: (b) without analyzer, (c) with linear analyzer having the indicated direction

Download Full Size | PDF

The reflection of the TM polarization is significantly reduced to 60% - 70% within the 1010-1080nm range, which is considered as sufficient to damp the undesired polarization in high power Nd:YAG and Yb:YAG lasers [12]. The remaining deviation to the theoretically predicted reduction to 50% to 65% can be attributed to the imperfect illumination of the element in the spectrometer setup, which uses a slightly focused beam containing angular components up to 1° in conical as well as collinear direction. Under these angles the leaking of TM to the layerstack is reduced, leading to the increased reflection.

The functionality of the element as a laser mirror was demonstrated in a self-made laser where the standard back-mirror was replaced by a polarizing grating mirror with a circular grating of 6 mm diameter. The tests were carried out in a pulsed, optically pumped Nd:YAG laser, used for laser machining, having 7 ms pulse duration and 12 Hz repetition rate at 25 W average power, creating a 6 mm diameter Gaussian beam.

The lasing of a donut shaped mode could be observed (Fig. 6(b)). Filtering the output beam by a linear polarizer led to a bow-tie shaped intensity distribution (Fig. 6(c)), which proves the lasing of a mode of circularly symmetrical polarization distribution. Further experiments for a complete characterization of the emitted beam, the damage threshold and the exact reflectivity of the mirror are in process.

5. Conclusion

A new intracavity polarization-mode selection scheme naturally permitting the emission of the azimuthally polarized laser mode was presented. It uses a circular line grating monolithically associated with a multilayer mirror. Its diffractive polarization dichroism relies upon the reflection band edge difference between the local TE and TM polarizations, the ±1^st order TE diffraction being forbidden within the TE stopband of the mirror, whilst the TM diffraction is off the TM stopband leading to a TM power leakage into the mirror substrate through the multilayer. The reflection differential was increased and its wavelength bandwidth enlarged by a multilayer design shifting the TE and TM angular band edges in the neighborhood of the Brewster angle between the low and high index layer materials.

The developed grating technology also has novel features: the very hydrogenated amorphous Silicon of solar cells is used as the corrugated layer, making the best use for photonics of the regrettably too high gap of a-Si:H as an absorber. The relatively large radial period of the circular grating which this polarization selection scheme permits renders it possible to use mask transfer lithography. Furthermore, the very high index of a-Si:H leads to so shallow a corrugation that wet etching can be used regardless of lateral underetching. Beyond its use in the fabrication of the present laser element, this technological achievement opens the way to the use of cheaply fabricable resonant photonic elements based on amorphous silicon.

The polarization selectivity of the developed element was successfully demonstrated in a moderate power Nd:YAG laser experiment with the emission of the azimuthally polarized mode. The very same element can be used as the mirror of a number of lasers in the 1.0µm to 1.1µm wavelength range thanks to its non-resonant, wide band character. Interestingly, the wideband characteristic of the presently developed azimuthally polarizing mirror can be transposed from the wavelength spectrum to the spatial frequency spectrum of the grating, creating a tolerance on the grating period. This implies that the very same polarization filtering scheme can be used for the generation of the radial polarization by means of a grating with radial lines, the grating being segmented in concentric rings having an azimuthal period varying in this tolerance region. This will be the subject of another paper. The applicability of the a-Si layer, lithography and etching technologies for high power lasers still has to be demonstrated. It is already certain that it can be used in high power lasers with an HfO₂ corrugation in which case high damage threshold is guaranteed with the penalty, however, that high cost RIBE must be used to etch the HfO₂ corrugation.