1. Introduction

Beam shaping is the process of redistributing the irradiance and phase of an optical beam [1]. The ability to tailor a beam is beneficial in many applications including material processing, lithography, and laser induced chemistry. Unfortunately current beam shaping methods are complex and/or bulky, thus a simple and compact alternative is desirable. To transform an input field into a desired output field, optical elements such as masks [2], refractive optics [3,4], and diffractive optics [5] are used. The effectiveness of these methods are typically limited by diffraction and/or losses. An alternative method is the use of a single Gradient Index (GRIN) volume. These volumes gradually transform the input irradiance distribution to the desired output distribution, using a variable refractive index profile designed using ray optics [6] or beam propagation models [7,8]. Theoretically GRIN volumes are low-loss, durable, and not limited by diffraction. Current GRIN fabrication methods [9–12] are limited to simple symmetric profiles. Therefore, to fabricate complex refractive index profiles, 3D manufacturing processes such as photo-polymerization [13–15] and 3D printing [16] are being explored. In this manuscript the fabrication of GRIN structures using ultrafast laser inscription is investigated for the first time in bulk glass.

Ultrafast laser inscription uses a femtosecond laser to induce a refractive index change inside a glass substrate. The induced modification is localized to the focal point and the strength of the refractive index contrast is controlled by adjusting either the laser’s pulse energy or the substrate translation speed. Uniform refractive index layers [17] and volumes [18] have previously been fabricated using the ultrafast laser inscription technique. However, only a limited number of devices with a smoothly varying refractive index profiles have been demonstrated [19–22]. Here we fabricate planar waveguides with refractive index profiles in both the transverse and propagation direction, for 2D beam shaping applications. These devices are made with an outlook towards future 3D GRIN beam shaping devices [23].

2. Material modifications

To induce a localized refractive index contrast inside a glass volume, an ultrafast Ti:sapphire oscillator (Femtosource XL 500, Femtolasers GmbH) centred at 800 nm, with 50 fs short pulses and 5.1 MHz repetition rate was used. For all inscription, the laser’s repetition rate was reduced to 255 kHz using an external pulse picker. The $3.9\times 3.4$ mm laser beam was focused into a borosilicate (Schott Borofloat 33) sample using a 0.65 NA focusing objective at a depth of $170$ µm. The sample was mounted on a set of Aerotech 3-axis air-bearing translation stages, enabling the sample to be moved with respect to the stationary focal point. At the focal region nonlinear absorption alters the refractive index to form an athermal modification. The focal region is elongated in the $y$-axis, causing the modification to be approximately $0.8$ µm wide ($x$) by $6.7$ µm high ($y$). The focal volume is then scanned at 15 mm/min in the $z$-direction to form a thin region of index modified material. To form structures sufficiently large to act as a waveguide, the laser’s focal point is scanned 11 times with a 0.4 µm pitch in the $x$-direction, known as the multi-scan technique [24].

To calibrate the refractive index contrast against pulse energy, waveguides with pulse energies ranging from 39–78 nJ in $1.5$ nJ increments were fabricated. The end-on ($x$–$y$) refractive index profile of each waveguide was measured using a refractive index profilometer (Rinck Elektronik, Germany) at 637.2 nm. The maximum refractive index contrast of the waveguide compared to the glass ($\Delta n_{\textrm {max}}$) for each pulse energy is shown in Fig. 1. For pulse energies between 39 nJ and 55.5 nJ, the refractive index contrast of the modified glass is observed to increase while the shape of the index profile remains unchanged (see Figs. 1(a),(b)). For pulse energies 55.5 nJ and above the induced refractive index contrast plateaus and the refractive index profile splits in the $y$-axis, with the upper region moving towards the laser source as the pulse energy increases (see Fig. 1(c)). As the modifications between 39–55.5 nJ have a positive and controllable refractive index contrast they are ideal for 2D and 3D structures that require multi-scanning.

 

Fig. 1. The maximum refractive index contrast ($\Delta n_{\textrm {max}}$) of waveguides written in Borofloat 33 glass using pulse energies of 39–78 nJ, the fit was added to guide the reader. Inserts (a),(b), and (c) are examples of cross-sectional refractive index profiles measured at 637.2 nm using a refractive index profilometer, orientated such that the focused laser beam is incident from the top. Uniform modification between 39–55.5 nJ are used for device fabrication.

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To design 2D graded-index beam shapers the effective refractive index of modifications inscribed with pulse energies between 39–55.5 nJ is required. The measured refractive index profiles and a mode solver (Rsoft BeamProp) were used to calculate the effective index of the fundamental waveguide mode at $980$ nm. Figure 2 shows the effective refractive index change ($\Delta n_{\textrm {eff}}=n_{\textrm {eff}}-n_0$) plotted against the maximum refractive index contrast ($\Delta n$). To simplify the design process, the calculated effective index change of the measured profiles was approximated by the effective index change for an ideal step-index waveguide with dimensions of $4\times 5$ µm (solid line in Fig. 2).

 

Fig. 2. The maximum refractive index contrast ($\Delta n$) and corresponding simulated effective refractive index change ($\Delta n_{\textrm {eff}}$) of uniform modifications inscribed with pulse energies of 39–55.5 nJ, compared to an ideal $4\times 5$ µm rectangular step-index waveguide.

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3. Quadratic planar waveguides

Planar waveguides with quadratic profiles in the transverse direction resize Gaussian beams in a predictable manner. Therefore, quadratic planar waveguides are designed and fabricated to validate the manufacturing process. The effective refractive index profile across a quadratic planar waveguide in the $x$-axis can be defined as

Three quadratic planar waveguides were designed to resize a $160$ µm wide Gaussian beam. Each waveguide has a different quadratic coefficient: strong ($Q=0.03022$ mm$^{-2}$), medium ($Q=0.00945$ mm$^{-2}$), and weak ($Q=0.00159$ mm$^{-2}$). The effective index profile of each waveguide is shown in Fig. 3. To avoid beam distortion, the quadratic waveguides are designed to be twice the width of the input beam ($360$ µm). The effective index of planar waveguides approximately depends on the mode confinement in the $y$-axis since the mode confinement in the $x$-axis is negligible. For fabrication the results from the theoretical step index waveguide model shown in Fig. 2, were used to map the designed effective index values of the quadratic planar waveguides to a laser pulse energy, shown in Fig. 1.

 

Fig. 3. Designed effective refractive index profiles of quadratic planar waveguides. (a) Differential interference contrast image across a strong quadratic planar waveguide. The individual multi-scans are inscribed top-down. The gray-scale intensity resembles refractive index change.

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The fabricated quadratic planar waveguides are $360\pm 1$ µm wide in the $x$-axis and $9.13\pm 0.01$ mm long in the $z$-axis. Each multi-scan is offset by $0.4$ µm in the $x$-axis and is inscribed with a different pulse energy to form the designed quadratic refractive index profile. A differential interference contrast image of a strong quadratic planar waveguide is shown in Fig. 3(a). The observed striations in the $z$-axis are due to variations in inscription power and position errors for each multi-scan. To characterize the quadratic planar waveguides, an elliptical ($155.7\times 6.2$ µm) Gaussian beam with a wavelength of $980$ nm was injected into each device. The diameter of the output intensity profile in the $x$-axis measured at the $1/e^2$ intensity point is recorded in Table 1. An output profile is shown in Fig. 4.

 

Fig. 4. Beam shaping of a Gaussian beam by the strong quadratic planar waveguide.

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Table 1. Theoretical and measured $1/e^2$ output beam diameters after a $155.7$ µm wide input Gaussian beam propagated through a $9.13$ mm long quadratic planar waveguides with different quadratic index profiles.

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4. Gaussian to flat-top beam converters

Using the method outlined in [7], a device was designed to transform an input Gaussian beam ($I_{in}(x) = exp[{-2(2x/w_{in})^2}]$) to a super-Gaussian ($I_{out}(x) = exp[{-2(2x/w_{out})^{10}}]$), where $w_{in}$ and $w_{out}$ represent the diameter of the input and output beam, respectively. The designed $w_{in}$ is $160$ µm while the designed $w_{out}$ is $200$ µm. The GRIN beam shaper is $297$ µm wide in the $x$-axis and 6 mm long in the $z$-axis, as shown in Fig. 5. A minimum refractive index contrast of $1.1\times 10^{-3}$ was applied to ensure good mode-confinement in the $y$-axis. The refractive index contrast ($\Delta n$) was then varied by $6.34\times 10^{-4}$.

 

Fig. 5. Designed refractive index profile of a Gaussian to flat-top beam converter at $980$ nm. The material’s refractive index of n=1.4637 and a base step index change of $1.1\times 10^{-3}$ has been removed to show the spatially varying index contrast of the design.

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To fabricate the GRIN volume, 6 mm long modifications were inscribed in the $z$-axis. This was then repeated 743 times with each scan being offset $0.4$ µm in the $x$-axis. While scanning in the $z$-axis, the pulse energy was varied to form the designed refractive index profile. This was achieved by sampling the design refractive index contrast every $15$ µm, and mapping this to a specific pulse energy. The laser pulse energy was then linearly interpolated between each sample point. The total device fabrication time was approximately 6 hours. A stitched differential interference contrast image of the device is shown in Fig. 6.

 

Fig. 6. A stitched differential interference contrast image of a Gaussian to flat-top mode converter. The gray-scale profile resembles the designed refractive index profile.

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The mode converter was tested by injecting an elliptical Gaussian beam ($162.8\times 12.3$ µm) into the GRIN volume and measuring the output intensity profile, as shown in Fig 7. The output super-Gaussian has a fitted width of $143\pm 1$ µm. This is 29% less than the designed width of $200$ µm. The flat-top output has the desired beam shape at the left-hand side, and a uniform intensity at the centre of the beam. However, the right-hand side stops earlier than designed. The multi-scan direction is from left to right.

 

Fig. 7. The measured output beam profile compared against the theoretical super-Gaussian output from a GRIN mode converter.

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Using a refractive index profilometer and a mode solver, the effective refractive index was calculated for slices in the $y$-axis across the device’s input surface. The calculated effective index was then compared against the designed profile in Fig 8. The effective refractive index is shown to decrease across the device from left to right corresponding to the multi-scan direction. Due to the effective refractive index being larger on the left side of the structure, guided light bunches to the left causing the output profile to truncate. The reduction in the fabricated refractive index contrast is attributed to an accumulation of stress in the glass caused by the one directional multi-scan. To avoid the formation of non-uniform stress fields in the glass, an alternative scanning process known as the half-scan method [26] could be employed for future devices.

 

Fig. 8. Designed and measured effective refractive index of the input of a Gaussian to flat-top beam shaper. The refractive index of the material has been removed to only show the effective index contrast. The multi-scan direction is from left to right.

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5. Conclusion

Using the ultrafast laser inscription technique, two-dimensional gradient-index beam shapers were fabricated in borosilicate glass. Resizing of Gaussian beams and the transformation to super-Gaussian (flat-top) beams was demonstrated in planar waveguides with varying refractive index in not only the transverse dimension but also the light propagation direction. It has been shown that to optimise the output profiles alternative scanning patterns are required. This process can be expanded to create 3D volumes [18] that include GRIN profiles [23].