1. Introduction

Femtosecond laser processing of transparent materials has an increasing potential to be applied in the fabrication of diffractive optical elements (DOEs). This technology has different advantages that can lead manufacturers of DOEs to choose it as their fabrication technology; first, it provides a straightforward manufacturing process for volume fabrication of DOEs, which can be more adequate than surface-fabricated DOEs in a variety of cases. Some examples include applications in environments where a high risk of surface damage is possible, i.e. industrial applications, or the need to provide DOEs with advanced functionalities, like higher diffraction orders, form-birefringence or high diffraction efficiency Bragg gratings [1,2]. Furthermore, within the fabrication methods of volume DOEs, femtosecond direct writing offers a higher robustness, 3D operation malleability, and variety of substrate materials than other fabrication techniques such as laser interference patterning [3]. Reports concerning femtosecond laser fabrication of volume phase-gratings (VPGs) [4–10], Fresnel lenses [11–13], form-birefringence [14] or optical-holographic imaging [15,16] have increased during the last decades, which contribute to the state of the art in spatial and spectral beam shaping, beam splitting and combining, optical imaging and data storage [17].

The amount of the refractive index change generated in the laser-processed zone is one of the most limiting factors when a DOE is fabricated using femtosecond laser direct writing. When the top index modification is limited below 10⁻³, which is typical in a wide range of materials [18–20], functional DOEs can be fabricated by compensating the low refractive index change with more scanning repetitions. The first approach for increasing the efficiency of the DOEs with this method was the fabrication of cascade multi-layered gratings [5,7,8,10]. The assumption when using this fabrication technique is that the overlapped regions between separated laser scans generate a negligible change that can be treated as a continuous modification [9]. High diffraction VPGs of up to 90% efficiency have been accomplished with this method. Nevertheless, as these VPGs behave like Bragg gratings [21], they have the disadvantage that this high performance is only achieved when the VPG is illuminated at the Bragg condition [22,23]. In particular, this can limit the application of such VPGs in setups where perpendicular illumination is needed, or setups where VPGs are illuminated at several wavelengths.

Some authors have studied a different approach of multilayer fabrication in order to potentially improve the efficiency of VPGs outside the above mentioned specific configuration [10,24,25]. This fabrication approach is based on the fabrication of separated layers where the layer-to-layer distance coincides with the Talbot self-imaging planes. In this manner, when the laser-modified elements are coherently layered with the respective near-field diffraction pattern, an enhancement of the total diffraction efficiency is achieved. In the case of Ng et al. [24], a combined 1^st order diffraction efficiency of up to 35% was achieved when 8 layers were separately inscribed with a distance of 20 µm between them. Some other authors have reported the fabrication of VPGs with even more complex geometrical arrangements, such as the stitching of layers with relative displacement [10], or the variation of grating orientation between the respective layers [25].

To the best of our knowledge, the fabrication method of selectively inscribing a number of separated volume phase-gratings has been only tested with VPGs at a high resolution limit (Λ ${\sim} $ 1 µm period) and small phase accumulation (combined 1^st diffraction efficiency of a single-grating of up to 5.2%). In this work, the fabrication of separated phase elements was investigated in a larger size approach. VPG periods of Λ $= $ 10 µm allowed us to fabricate single-gratings of a combined efficiency of the 1^st diffraction orders up to 42.3%. This regime of single-layer VPGs with a high diffraction efficiency led us to the functional development of double volume phase-gratings (DVPGs) with hundreds of microns of distance between the phase elements. Double-grating systems are usually found in reflective or transmission configuration in applications such as spectroscopy [26], interferometry [27], laser pulse compression [28], or metrology [29], but they are usually found like a combined system of separated elements. In this work, we propose the implementation of a grating pair that is monolithically integrated in a single piece of bulk material. Due to the two dimensional light modulation given in the Talbot effect, the fabrication of the DVPGs was optimized both in the distance and the relative displacement between the gratings. Such structures have been fabricated in a borosilicate glass doped with CdS_xSe_1-x semiconductor nanocrystals (OG530, Schott Glass Inc.), a material known for showing a high refractive index change when processed with femtosecond laser [30].

2. Methods

The fabrication of the DVPGs [ Fig. 1(a)] was made with an Amplitude Satsuma Laser, consisting of a 500 kHz diode-pumped ultrafast fiber amplifier system of λ = 1030 nm and 280 fs pulse duration. The laser beam at the output aperture of the amplifier is a Gaussian of M²= 1.2 and 2.7 mm of diameter. A beam expander of 3x was used to expand the diameter of the beam and fill the total aperture of the focusing objective, which is a high power NIR laser objective with an entrance aperture of 8 mm and a NA of 0.4. In the focus of the objective lens the spot size is 2.5 µm, according to the specifications of the suppliers. Then, a computer controlled scanning system of motorized linear stages was used to fabricate structures along the 3-axes x, y and z inside the bulk material. DVPGs were fabricated following the fabrication strategy in the scheme Fig. 1 b); both VPGs in the DVPG were fabricated simultaneously by making a two depth inscription in each lateral step. Every VPG and DVPG presented in this work was fabricated with a period of Λ = 10 µm.

 

Fig. 1. a) Cross-section microscope image (10x) of a double volume phase-grating fabricated in the nanostructured glass with a femtosecond laser. b) Scheme of the laser fabrication strategy followed in this work. c) Droplet shape approximation taken for the simulation with the RCWA numerical solver. The definitions of the widths a and thickness L, together with the relative displacement $\Delta x$ and the distance between the gratings $\Delta z$ are illustrated.

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A borosilicate glass doped with a 1% volume fraction of embedded CdS_xSe_1-x semiconductor nanocrystals of 3.9 nm radius (OG530 Schott Glass Inc.) was used as the substrate material. Its refractive index in the range from 550 nm to 850 nm is 1.51. This material is extensively use as an optical cut-off color filter, and for that reason has an orange colored appearance.

A numerical rigorous coupled wave analysis (RCWA) software (GSOLVER) was used in order to simulate the far-field diffraction generated by the DVPGs. The profile shape of the phase element was approximated by a droplet shape [Fig. 1(c)] formed with a triangle and a semicircle. The refractive index change Δn is assumed to be homogeneous inside the structure. This value can be interpreted as the averaged value of the actual Δn distribution [30,31] in the laser modified zone. This approximation is expected to be adequate as long as the thickness parameter Q of the gratings is less than unit [32]. In order to fit with the experimental measurements, the losses generated from reflections and absorption were introduced in the model by multiplying the simulated efficiency results by a factor of 0.8. This value can be approximately subdivided in scattering and absorption losses of 12% and surface reflection losses of 8%.

Laser processed areas were characterized by an optical microscope with magnifications of 10x and 40x. The images presented in the work have been taken after cleaving the sample in a direction transversal to the laser inscribed lines. In order to distinguish the cross-section image from the roughness of the surrounding material, oil was applied to fill the roughness of the surface. A HeNe λ = 633 nm and a supercontinuum white light laser were used to measure the far-field diffraction efficiencies. Diffracted beam intensities were measured by both a manual potentiometer (for the monochromatic laser) and a spectrometer Oriel MS257 with an integrating sphere.

3. Results

3.1 Single volume phase-grating fabrication

Laser processing conditions were optimized in order to fabricate single layer VPGs. Microscope images of the laser-processed cross-sections at different pulse energies are presented in Fig. 2(a). A repetition rate of 500 kHz was selected at a scanning speed of 2 mm/s. Widths a ranging from 2.5 µm to > 10 µm and thicknesses L from 14.6 µm to 41.9 µm are measured (widths are taken in the equator of the droplet). Measurements of laser modified zones wider than the laser spot size (${\sim} $ 2.5 µm) suggest that heat accumulation is occurring [33–35]. An overall droplet shape is observed, which gets more pronounced as the pulse energy increases, with the shape size increasing with laser pulse energy. This indicates a larger area of multiphoton ionization [36,37]. Microscope images of the laser modified zone appear homogeneously dark, which could be explained by the redshift in the absorption spectra of the nanocrystals [38]. The surrounding grey region suggests that an overlapped molten region has been generated as VP Gs of Λ $= $ 10µm were fabricated. This means that the refractive index that surrounds the droplet shapes could be different [39] from the rest of the bulk, which in principle could affect the amplitude of the phase modulation.

 

Fig. 2. a) Optical microscope images of the cross-sections of the laser inscribed lines at different pulse energies (40x magnification). b) Experimental and simulated far-field diffraction efficiencies of VPG fabricated at different pulse energies. Simulations were done by taking the dimensions of the laser modified zones observed in the microscope cross-sections. The refractive index changes implemented in the simulations for each pulse energy are Δn = 0.003, Δn = 0.0055, Δn = 0.006, Δn = 0.0065, Δn = 0.0075 and Δn = 0.0055. The combined efficiency is shown meaning that both sides ${\pm} $ for each diffraction order have been summed. Experimental and simulated results were obtained at λ = 633 nm and perpendicular illumination.

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Far-field diffraction efficiencies of single layer VPGs fabricated at different pulse energies are presented in the Fig. 2(b). In the image, measured efficiencies (points) are compared with RCWA simulated efficiencies (lines). In order to simulate the efficiencies, the droplet like structure in Fig. 1(c) was adapted to the measured widths and thicknesses in Fig. 2(a). Refractive index changes Δn going from 0.003 to 0.0075 give a good agreement between simulations and experiments. A maximum combined 1^st order efficiency of 42.3% is achieved when the pulse energy is 1.6 µJ (L = 34.2 µm and Δn = 0.0075). The 2^nd order diffraction efficiency remains small comparing with the 1^st order efficiency as expected for a VPG. This value is equivalent to a VPG of Δ$\varphi $ =π/2 using the planar grating approximation [21]. The increasing widths of the laser modified zone can lead to a reduction of the diffraction efficiency of the non-zero orders efficiency [35] for the VPG fabricated at 1.8 µJ.

3.2 Double volume phase-grating fabrication

The cross-section images of DVPGs fabricated at 1.2 µJ and 1.6 µJ are presented in Fig. 3. The sections of both DVPGs are well-defined. The fabrication strategy that we have followed is depicted in the scheme in the Fig. 1(b). In the Table 1, thicknesses of the DVPGs cross-sections have been compared with separated VPGs fabricated at the same exact conditions, i.e., the same depths, pulse energies and scanning speeds. The measured distances between the gratings are Δz = 242.4 µm and Δz = 244.2 µm respectively. A small deviation is observed between the VPGs fabricated in the deeper layer (VPG2) when fabricated separately and assembled in DVPGs. This is produced because the upper structures in z ${\sim} $ 200 µm (VPG1) fade the focusing of the pulse during the fabrication process thus leading to a smaller laser modified zone.

 

Fig. 3. Microscope images of the cross-sections of two DVPGs fabricated at 1.2 µJ and 1.6 µJ pulse energies, 500 kHz, 2 mm/s, at depths of ${\sim} $ 200 µm and ${\sim} $ 440 µm. Images were taken at 10x and 40x magnification. Experimental and simulated combined diffraction efficiency of separated VPGs and DVPG at 1.2 µJ and 1.6 µJ are shown. RCWA simulations were done by taking the dimensions measured from the microscope image (listed in Table 1) and Δn = 0.006 and Δn = 0.0075, respectively. Experimental and simulated results were obtained at λ = 633 nm and perpendicular illumination.

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Table 1. Thicknesses of separately fabricated VPGs and DVPGs

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Measured and simulated diffraction efficiencies of the separated VPGs and DVPG are shown in Fig. 3. VPGs individually fabricated at the same conditions were separately characterized and then fabricated and characterized assembled into DVPGs. A good agreement between the experimental and simulated results are obtained, both for the separated VPGs and the DVPGs. The dimension sizes for the simulations were taken from the cross-section images in Table 1 and the refractive index changes are those used in Fig. 2(b) for 1.2 µJ and 1.6 µJ, i.e., Δn = 0.006 and Δn = 0.0075. The experimental results obtained in DVPGs with these refractive index changes are in good agreement with the results of the simulations, further validating the chosen values. First order diffraction efficiency of single VPGs fabricated at 1.2 µJ and 1.6 µJ are respectively 20.4% and 40.8%, which are equivalent to a phase accumulation of Δ$\varphi $ =π/3 and π/2, respectively. It is observed that the diffraction efficiency is improved when both VPGs are assembled into the DVPG. A higher loss is observed in the 1^st diffraction order efficiency for the DVPG fabricated at 1.2 µJ comparing with the simulated theoretical value. Regarding the 0^th diffraction order, theoretically almost a total vanishing of the 0^th order can happen when the phase accumulation in both gratings is Δ$\varphi $ =π/2. Experimentally, a diffraction value of 8% was measured with the DVPG fabricated at 1.6 µJ.

Figure 4 shows the diffraction efficiencies of DVPGs when Δx and Δz are varied. The distances between the gratings Δz was varied from 215 µm to 280 µm in two configurations of relative displacement; Δx = 0 µm and at Δx =Λ/2 = 5 µm. These values were chosen in order to generate a symmetrical diffraction pattern. Distance from the glass surface to the first grating was kept constant at z = 200 µm, and relative displacement between the gratings was measured from microscope cross-section images. In this case DVPGs were fabricated at 1.6 µJ pulse energy. Experimental results are depicted together with the RCWA simulated results at equivalent conditions.

 

Fig. 4. Experimental and simulated far-field efficiencies at m = 0, m = ${\pm} $1 and m = ${\pm} $2 diffraction orders of DVPGs fabricated at different distances Δz, for a relative displacement of Δx = 0 and Δx =Λ /2. DVPGs were fabricated at 1.6µJ. Distances between the VPGs were measured from microscope images. RCWA simulations were done with the droplet profile and sizes taken for VPG fabricated at 1.6µJ, width of a = 8µm, thickness L = 36µm and the refractive index change was Δn=0.0075. Experimental and simulated results were obtained at λ = 633 nm and perpendicular illumination.

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Figure 4 shows that the 0^th and 1^st diffraction efficiencies are drastically affected by the change of Δx. At the 0^th order, the efficiencies are 59% and 7.3% respectively for Δx = 0 and Δx =Λ/2. Similar but inverse efficiencies are obtained at the 1^st order, where the efficiencies are 14.8% and 55.2% respectively for Δx = 0 and Δx =Λ/2. This behaviour can be explained by the near-field propagation generated between the gratings. Our hypothesis is that, as the light distribution in the second grating is determined by the Talbot effect generated by the first grating, a constructive or destructive interference can be generated. Regarding the distance between gratings, in an ideal case RCWA simulations of almost planar DVPGs of Δn = 0.16 and L = 1 µm show a strong dependence of the diffraction on Δz. For the case of Δx =Λ/2 in particular, a 80% of the combined 1^st diffraction efficiency is achieved when the distance between the gratings is very close to ${Z_T}$/2, where ${Z_T} = 2n{\mathrm{\Lambda }^2}/{\lambda _0}$ = 477 µm is the Talbot distance inside the glass. As the phase element profile gets thicker and less rectangular, the dependency on Δz starts to fade.

3.3 Angular and spectral characterization of DVPGs

The thickness parameter Q [32] of a single VPG fabricated at 1.6µJ [Fig. 2(a)] is less than a unit, and therefore, it is expected to behave like a thin-grating. Experiments have shown that the diffraction efficiency of a single VPG of this kind has a small dependence on the angle of incidence. For a range going from – 4 ° to 4 °, the 0^th order efficiency is maintained almost constant at a ${\sim} $ 50%, and the combined 1^st order efficiency varies around the ${\sim} $ 36%, with small asymmetries between the ${\pm} $ sides of the diffraction pattern. Figure 5 shows the dependence of a DVPG when illuminated with different angles of incidence. In contrast with the diffraction of a single VPG, a strong dependence on the angle of incidence is observed. Furthermore, this dependence is different from dependence of the diffraction on the angle of incidence observed in a Bragg grating [7–9], where the maximum efficiency is achieved at the blazed angle. In the case of DVPGs, a maximum diffraction is achieved when the illumination is perpendicular. A simulated DVPG with the droplet phase profile and a Δn = 0.007 fits well with the experimental results. Snell’s law in the glass interface was taken into account in order to compare with experimental results. New losses in the glass interfaces because of the variation of the angle of incidence have been accounted and are negligible. A 0^th order efficiency of 5.1% and a combined 1^st order efficiency of 53% is achieved at perpendicular illumination. At the same time, a second maximization cycle is observed close to ${\pm} $ 4 °, where minimization is given at ${\pm} $ 2 °. These cycles could be explained by the variation of the Talbot effect when the angle of incidence is not perpendicular. The diffraction in the order m = -1 fits better with the simulated results than the m = 1 order, which could be explained by the asymmetrical behavior already observed in the single VPG diffraction fabricated at 1.6 µJ.

 

Fig. 5. Experimental and simulated far-field diffraction efficiencies at the orders m = -1, m = 0 and m = 1 of a DVPG when the angle of incidence is variated. A DVPG with a Δx =Λ /2 and a Δz = 244.2µm was fabricated at 1.6µJ, 500 kHz and a scanning speed of 2 mm/s. Experimental measurements were taken by changing the angle of incidence in steps of 0.5 °. In order to see asymmetrical effects, 1^st diffraction orders are shown for both sides (+1 and -1). RCWA simulations were done with droplet elements with a = 8µm width, L = 30µm thickness and Δn = 0.007. Experimental and simulated results were obtained illuminating at λ = 633 nm.

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In order to study the dependence of the diffraction on the illumination wavelength, DVPGs formed with multilayered VPGs were fabricated at different distances (Δz) between the gratings from 209 µm to 239 µm and a relative displacement of Δx = $\mathrm{\Lambda }$/2. The laser processing conditions were 500 kHz, pulse energy of 1.6 µJ and a scanning speed of 2 mm/s. In order to enhance the phase accumulation for long wavelengths, since phase accumulation should be close to Δϕ =π/2 (as displayed in Fig. 3), each VPG in the DVPG was fabricated by overlapping two layers in the z axis with a step difference of 10 µm. In this manner, the effective thickness of each grating increases by several microns. In order to incorporate this to the RCWA simulations, the thickness of the droplet shape [shown in Fig. 2(a)] was extended to 40 µm. The refractive index change implemented in the simulations was Δn = 0.0075. The illumination white light source was impinged perpendicular to the DVPG. The dependence of the combined 1^st order diffraction generated by a DVPG on the illumination spectrum is shown in Fig. 6.

 

Fig. 6. Experimental and simulated far-field diffraction efficiency of the combined 1^st order of a DVPG when illuminated at different wavelengths. DVPGs were fabricated by overlapping two layers of gratings in each VPG, with a Δx =Λ /2 and varying the Δz. DVPGs were fabricated at 1.6µJ, 500 kHz and a scanning speed of 2 mm/s. The white light source was impinged perpendicularly to the DVPG. RCWA simulations were done with a droplet profile of a = 8µm width, L = 40 µm thickness and Δn = 0.0075.

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Figure 6 shows the combined 1^st efficiency close to the peak of diffraction generated at different wavelengths. It can be observed that the peak wavelength depends on the distance between the gratings. Similar peak efficiencies of ${\sim} $ 63% are measured at λ = 827 nm, λ = 794 nm and λ = 751 nm for Δz = 209 µm, Δz = 224 µm and Δz = 239 µm. Notice that as the distance between the gratings increases, the peak wavelengths is inversely reduced, which could be explained by the inverse dependence of the Talbot distance on the wavelength. As RCWA simulation with almost planar VPGs show that maximum efficiency is achieved when the Δz coincide with the half Talbot distance, control of the peak wavelength can be predicted. In order to do this, the Δn or the L of the phase element has to be optimized for achieving a Δϕ =π/2 at different wavelengths. Thus, almost planar simulations have shown an agreement of ${\pm} $ 20 nm with predicted peak wavelength. In the case of the droplet profile as in Fig. 6, simulations and experimental results show a good agreement for a spectral width of Δλ = 200 nm. Nevertheless, as these VPGs are not planar and phase accumulation Δϕ has not been optimized for the different wavelengths, the correspondence between the peak wavelength and the Δz given by the half Talbot distance is faded.

4. Conclusions

Monolithic fabrication of double volume phase-gratings has been successfully achieved using a femtosecond laser. We have presented a new regime of laser integration of medium-sized volume phase-gratings, where single VPGs of combined 1^st diffraction efficiency of 42.3% were the building blocks to fabricate the DVPGs. Laser induced modifications have been structured with a separation of hundreds of microns, which to the best of our knowledge, is a novel approach that can push further the possibilities of laser fabrication of volume DOEs. By doing this, an improvement of the diffraction effect has been observed with no restriction of blazed angles. The agreement between the simulations and the experimental data have shown that this effect can be optimized when the distance between the gratings coincide with half the Talbot distance. Furthermore, it has been proven that DVPGs can be optimized for different wavelengths if the distance between the gratings is controlled. 1^st order efficiencies of up to 63% were measured at wavelengths in the range between λ = 750 nm and λ = 830 nm. Considering that the number of laser scanning repetitions needed in this method are significantly reduced in comparison with the repetitions needed for the fabrication of cascade multilayered VPGs, we conclude that these DVPGs are a promising alternative for a cost-effective solution to fabricate embedded transmission gratings.