Waveguides with arbitrary cross sections are written in the volume of Al2O3-crystals using tightly focused femtosecond laser radiation. Utilizing a scanning system with large numerical aperture, complex cladding geometries are realized with a precision around 0.5 µm and a scanning speed up to 100 mm/s. Individual beam and mode shaping of laser diode radiation is demonstrated by varying the design of the waveguide cladding. The influence of the writing parameters on the waveguide properties are investigated resulting in a numerical aperture of the waveguides in the range of 0.1. This direct laser writing technique enables optical devices which could possibly replace bulky beam shaping setups with an integrated solution.
© 2011 OSA
As a laser source with high compactness and large electrical-to-optical efficiency, laser diodes provide a suitable device for integrated optical applications. Since the availability of laser diodes emitting in the green spectral range [1,2], these highly integrated light sources cover the spectral range from ultraviolet to near-infrared nearly completely.
The wide variety of applications for laser diodes for example in spectroscopy, in laser printers or as a pump source for solid state lasers, is broadened by green laser diodes into the visible spectral range. Compact laser sources based on second harmonic generation emitting red, green or blue light can be replaced by laser diodes. This miniaturizes the setup and enables mobile projection systems in laptops or mobile phones.
Due to the elliptical shape and the large divergence of the laser diode radiation, beam shaping is mandatory for most applications. Optical elements like cylindrical lenses , mirrors  or prisms  are typically used to transform the beam for the particular task. Such elements enhance the complexity of the setup and a further miniaturization is hampered.
A flexible tool for three dimensional microstructuring is offered by direct laser writing with femtosecond laser radiation. Focusing a femtosecond pulse tightly in a transparent material, a refractive index change in the region of the focal volume due to nonlinear absorption is induced . Different kinds of integrated optical devices like waveguide lasers , amplifiers , photonic crystals  and in combination with wet etching microchips for biochemical analysis  have been realized with this fabrication technique.
The basic element in most of these components is a waveguide. Therefore waveguide writing with femtosecond laser radiation has been intensively studied [11–14]. Such a structure is used for beam guiding as well as for beam and mode shaping. Light can be guided around the corner with a curved waveguide . The beam diameter and the shape of the guided mode are influenced by the morphology of the waveguide-core and the waveguide-cladding [16–18]. With these approaches the influence on the optical properties of the resulting waveguide is mainly based on the properties of the structuring laser beam.
A different strategy is demonstrated in this paper. It has been observed for crystalline media, that the index of refraction is reduced in the irradiated volume and increased in the adjacent volume by stress induced birefringence [19,20]. Here we write the waveguide cladding with a high speed scanner with large numerical aperture  in the volume of sapphire thus controlling the development of the core-region indirectly. This enables the fabrication of individual waveguide geometries with low processing time.
We show that fs-direct writing with a scanner provides a flexible method for three dimensional structuring in the volume of transparent dielectrics. This technique could offer an integrated solution for beam shaping of laser diode radiation.
2. Sample processing
The fs-direct laser writing is carried out by a fiber laser (Satsuma, Amplitude Systemes) with a central wavelength of λ = 1030 nm and a pulse duration of τ = 480 fs. The maximum average output power is P = 5 W with a variable repetition rate f = 0.1–5 MHz. The linearly polarized beam is focused by a flatness of field-corrected microscope objective with a numerical aperture of NA = 0.3 which leads to a calculated diameter of 1.7 µm in the focal region. Spherical aberration can be pre-compensated for a depth up to 2 mm by a correction collar of the microscope objective. The sample is moved by the computer controlled positioning stage Microstep (Kugler) parallel to the propagation direction of the radiation. The absolute accuracy of this equipment is Δx = 100 nm and the maximum velocity is vmax = 2 mm/s. While moving the sample longitudinally to the incoming laser beam (z-axis) a scanner deflects the beam in perpendicular direction (x-y plane). The scanner is connected to an acousto-optic modulator which allows to turn the beam off and on while structuring. A scanning velocity up to 100 mm/s is used with a precision of Δx ≈0.5 µm. Starting to move the focus at a point below the sample and moving upwards while scanning a circle, a helical path is generated (Fig. 1 ).
The single crystalline Al2O3-samples have a dimension of 10x10x1 mm3 with an orientation of the c-axis parallel to the 1 mm side, which is adjusted parallel to the z-axis. Both 10x10 mm2-surfaces are polished to optical quality. Regarding the refractive index of Al2O3 the correction collar is set to a depth of 1 mm. As the correction is not changed while translating in z-direction, the elongation of the focal length will vary at different depths. Different geometries like circles or stars are scanned in the x-y plane while moving the sample in z-direction. The various cladding shapes are written in the volume to investigate the amount of stress which is induced in the waveguide core. The stress should be maximized to obtain a high numerical aperture. Repetition rate, pulse energy, scanning and translation velocity are varied to analyze the influence on the waveguide properties. Two parallel tracks with a distance of D = 30 µm and single tracks, written in the usual transversal way without using the scanner , are also structured into a depth of 200 µm. In this case the numerical aperture of the microscope objective is NA = 0.6.
3. Results and discussion
A single line, written in the transversal way with Ep = 1400 nJ, f = 100 kHz and NA = 0.6, is examined with transmission electron microscopy (TEM). Therefore a longitudinal cut with a thickness of 50–100 nm is prepared. The width of the directly modified line is approximately 1.1 µm, which corresponds to the calculated focal diameter of the laser beam (Fig. 2 ). In the directly irradiated volume the single crystalline sapphire turns amorphous-like and periodic sub-wavelength structures occur. These structures are orientated parallel to the polarization of the laser radiation and parallel to the translation direction of the laser beam. They have a periodicity of around 0.5 µm and could be related to ripples which appear after femtosecond laser irradiation of Al2O3 . Stress-induced lines develop in the vicinity of the modified region (Fig. 2). The lines spread out into the bulk material for more than a micrometer.
Cylindrical structures with different cross sections are obtained by varying the scanning strategy. Circular, elliptical, starlike and shapes with an open cladding geometry are realized (Fig. 3 ). An open cladding depicts a structure, which is not completely enclosed around the core region of the waveguide. A pair of lines also demonstrates an open cladding geometry. Such double-structures, written in the transversal way, are also analyzed to compare them to the waveguides with closed cladding geometry. The diameter of the core is varied between D = 20-50 µm. An exception is used for the semiminor axis of the ellipse with a minimal diameter of 5 µm.
The irradiated sample exhibits a permanent modification along the path of the focal volume above a pulse energy of Ep = 140 nJ and f = 1 MHz, vz = 1 mm/s, vxy = 25 mm/s. The cladding of the structures can be modified by changing the translation velocity in z-direction. Applying a velocity of vz = 0.2 mm/s, a homogeneous cladding is obtained for a circular cross section written with D = 50 µm, Ep = 390 nJ, f = 1 MHz and vxy = 25 mm/s (Fig. 4 left). Increasing the velocity to vz = 1 mm/s, no overlap along the z-axis between the track occurs and the helical path of the focus is observed in a longitudinal cut (Fig. 4 right). Enhancing the pulse energy above Ep = 400 nJ and vz = 0.2 mm/s, crack formation occurs. Thus writing the cladding in a pulse energy regime between modification threshold and crack formation threshold, a uniform modification is obtained, which encloses a defect-free core.
This regime is shifted with the applied parameters of the laser radiation and the geometry of the modification. For tapered shapes, like the spikes of the star or the vertex of the ellipse, the threshold for crack formation is diminished by a factor of 2. Locally a large amount of stress is induced at the spikes and the vertex. Crack formation occurs initially in these regions. But the effective refractive index change is lower than for cylindrical cross sections. Using open cladding geometries like the separated lines, the crack formation threshold is increased to higher pulse energies. An increased pulse overlap, induced by a higher repetition rate or a reduced velocity, reduces the threshold for crack formation. Since the modification threshold is only slightly changed in these cases, the width of the processing window for waveguide fabrication is narrowed for higher repetition rates and lower velocities as well.
The stress-induced lines, observed with TEM (Fig. 2), result in stress-induced birefringence which is detected by polarization microscopy. The birefringence emerges in the region outside of the cladding and in the core region inside the cladding (Fig. 5 ). A single cladding with circular cross section exhibits a stress distribution with radial symmetry. An adjacent cladding distorts the symmetry (Fig. 5a). The conoscopic interference patterns create a dark cross (isogyres) in the middle of the micrograph. The stress distribution is influenced by varying the cladding geometry. An elliptical cross section for example generates local maxima at the vertices (Fig. 5b).
Linearly polarized light of a laser diode with an emission wavelength of λ = 444 nm is coupled into the waveguides. The ellipticity of the beam is reduced by a telescope with cylindrical lenses to a ratio of 2:1 (Fig. 6a ). The collimated beam is focused by a microscope objective (NA = 0.4) and the entrance facet of the waveguide is placed in the focal plane of the microscope objective. The exit facet of the sample is imaged by a microscope objective (NA = 0.8) onto a CCD-camera. Slightly above the modification threshold, waveguiding is observed in the core region of the modified cladding (Fig. 6). The waveguiding occurs due to stress-induced positive refractive index changes in the vicinity of the irradiated volume [19,20,23]. Following the stress-induced birefringence (Fig. 5) the positive refractive index profile can be controlled by the cladding geometry. To determine the beginning of waveguiding between the structures in dependence of the applied parameters a threshold for guiding of light is defined. If the ratio of the confined light in the core region of the structure compared to the amount of light in the surrounding region is at least 3:1 the threshold is exceeded. Depending on the geometry of the waveguide cladding, various mode and beam profiles are achieved (Fig. 6b-f). A circular cross section results in a circular beam profile, even if the intensity distribution of the laser beam at the entrance facet of the waveguide is elliptical (Fig. 6a). The mode profile is varied by changing the diameter of the cladding. Diameters around 20 µm lead to a Gaussian single mode profile, while larger diameters result in higher Laguerre-Gaussian modes (Fig. 6d). For highly irregular stress-distributions in the waveguide core as emerging in starlike shapes, a granulation of the guided light is induced (Fig. 6f). Open cladding geometries, like double structures and separated lines, exhibit a weaker light confinement for the same structuring parameters as for closed geometries (Fig. 6b and c). Those open geometries reveal an increased threshold for the guiding of light. The threshold for waveguides with separated lines as a cladding is increased by a factor of 1.5 in comparison to the closed geometries.
Measuring the far-field divergence of a guided mode, the numerical aperture of a waveguide is determined [23,24]. If crack formation does not occur the defects in the directly irradiated volume are larger for higher pulse energy hence inducing more stress in the surroundings which results in a higher positive refractive index change . Also the negative refractive index change in the irradiated region contributes to the waveguiding mechanism by enhancing the light confinement. In addition to that the cladding probably leads to a higher effective refractive index change because of the refractive index reduction. Thus the positive effective refractive index change is enlarged and the numerical aperture of the waveguide is increasing with higher pulse energy (Fig. 7 ). The numerical aperture is reduced if the threshold for crack formation is exceeded. For circular waveguide cross sections written with D = 30 µm, f = 100 kHz, vz = 1 mm/s and vxy = 25 mm/s a maximum numerical aperture of NA = 0.094 ± 0.013 is obtained with a pulse energy of Ep = 1300 nJ. This corresponds to a positive refractive index change of Δn = 2.5·10−3. The uncertainty results from the overlap of guided modes and radiative waveguide modes. With a starlike cladding a maximum numerical aperture of NA = 0.069 ± 0.01 is achieved with a lower pulse energy of Ep = 390 nJ than for circular cross sections (Fig. 7). A higher pulse energy results in cracks at the spikes and the numerical aperture is reduced. Open cladding geometries e.g. the double-structures do not exceed a numerical aperture of NA = 0.021 for a pulse energy up to Ep = 1400 nJ (Fig. 7).
The overall losses of the waveguides including coupling and propagation losses are estimated by measuring the transmitted power and the incident power in front of the waveguide entrance. For waveguides with circular cross section and a diameter of 50 µm a transmission up to 70% is measured. The coupling losses are estimated to be approximately 30% of these losses. This leads to a damping of roughly 1 dB/cm with an uncertainty of 0.5 dB/cm. Following this estimation a damping < 1.5 dB/cm is achieved with the scanner written waveguides.
4. Summary and outlook
Waveguides with arbitrary cladding geometry are fabricated in the volume of Al2O3. The written cladding induces stress and forms indirectly a core region with positive refractive index change. Beam and mode shaping of a laser diode radiation is demonstrated by varying the cladding geometry and the structuring parameter. The elliptical beam profile of a laser diode is transformed into a shape similar to the scanner-written cladding geometry. It is shown that closed cladding geometries with circular cross section enhance the numerical aperture of a waveguide by a factor of 4 to NA = 0.094 and increase the light confinement in comparison to double-structures with open cladding geometry. The utilized scanner allows fast and precise beam deflection. Individual waveguides adjusted to the directional characteristics of a laser diode could transform and guide light in an arbitrary way. An elliptical cross section at the entrance facet of the waveguide which is tapered into a circular cross section towards the exit facet should transform the elliptical beam profile of the laser diode into a circular beam profile. A microlens, monolithically made from the same substrate as the waveguide to collimate the incoming beam, could be provided by in-volume selective laser etching (ISLE) . Such a complex optical element would be a photonically fabricated device with a high degree of compactness. The demonstrated scanner-written waveguides show an outline for flexible light tailoring and are possibly a first step to integrated optical devices for beam shaping applications.
We would like to thank A. Stephanides from RWTH Aachen University for a lot of help in the laboratory and Falk Dorn of the Gemeinschaftslabor für Elektronenmikroskopie of RWTH Aachen University for the TEM images.
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