Open Access
Add to BibSonomy
Abstract
We study the propagation of coherent broadband light through laser induced periodic surface structures (LIPSS) fabricated on diamond surfaces. 3D finite-difference time-domain (FDTD) simulations were carried out for a variety of experimentally produced LIPSS morphologies, which include the specific nanometer-scale mesoscopic irregularities arising from the fabrication technique. We compare their performance with sinusoidal grating-like structures, showing that the specific features present in LIPSS nanoripples produce a considerable scattering and diffraction when compared to the ideal nanostructures. With a view on determining the scope of the potential optical and photonic applications of LIPSS, we evaluate the effect of these irregularities on the transmitted spatial beam quality and the spatial phase characteristics of the optical wavefront in a broad spectral range.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The direct laser fabrication of micro- and nanostructures in semiconductor materials has recently arisen keen interest in the scientific community. For instance, diamond and silicon nanophotonic devices have been the focus of intense research towards the next generation of integrated photonic circuits and quantum technologies [1–4]. The well-known outstanding properties of diamond, such as its hardness, thermal conductivity, and optical characteristics have turned it into one of the most interesting materials for photonic source development [5,6], integrated photonics [7,8] and quantum applications [3,4,9].
A key interesting aspect is in the fabrication of functional nanostructures on diamond, such as metasurfaces at subwavelength scales since they can lead to effective ways of controlling light propagation. Those include light trapping [10], control of the reflection at specific wavelengths, or to alter the light wavefront in a controlled manner, to name a few [11,12]. The fabrication of such structures can be carried out in different ways, where the main driving force is in the simplicity and convenience of using directly laser-written nanostructures.
The need for specific morphological features depends heavily on the application of interest, and they range from controlled formation of nanocrystals to nanometer-scale patterning. Currently, an important application where diamond metasurfaces are relevant is in their use as optical coatings that can operate at high-power in diamond-based photonic systems [13,14]. Diamond has also shown exceptional capabilities as a Raman-active medium for the construction of high power lasers [5,15–17]. One of the main drawbacks here is that these lasers typically require effective anti-reflective (AR) coatings for the spectral ranges of operation. These AR coatings are also important in terms of minimizing spectral or etalon effects that affect the spectral performance of diamond Raman lasers [18,19].
The need for diamond AR coating technology leads to significant limitations in terms of damage threshold, robustness and cost of these lasers [20]. In this sense, the physical properties that make diamond an excellent material for photonic applications, such as high index of refraction, also make it challenging for multi-layer dielectric coating deposition. Typical approaches rely on the fabrication of multi-layer thin-film optical elements along the propagation path. A possible alternative consists in the nanopatterning of the surface of the active medium, with the aim of producing a moth-eye effect that adds AR properties to the surface at broad wavelength ranges [21]. However, diamond is a demanding material to physically nano-pattern due to its extreme hardness and resistance to modification using conventional chemical etchants [22]. To date, lithographic techniques such as electron-beam lithography, are the main processes in order to fabricate these kind of structures [23]. Moreover, it has already proven its ability to produce convenient nanostructures for the UV range [2].
Alternatively, the LIPSS fabrication technique is a fast, simple and cost-effective manufacturing approach when compared to the aforementioned techniques and allows the direct laser fabrication of nanopatterns ranging from hundreds of nanometers to few tens of nanometers [24]. This strategy has already shown promising results regarding the fabrication of effective diamond metasurfaces [13]. In fact, the production of LIPSS-based nanostructures in diamond and the study of its photonic properties is an emerging field of research [13,14,25–27]. One of the challenges here resides in the difficulty of producing reliably the required aspect ratio to behave as effective AR coatings [28].
The LIPSS technique applicability is not limited to the production of AR coatings. Other applications include the utilization of the diffractive and refractive properties of both the nanostructures and the diamond itself, which remain largely unexplored. Examples of applications include light trapping devices [10], energy harvesting [29] or ultra-low power sensing [30,31]. Recently, light trapping nanostructures have been considered for assisting quantum state manipulations in nitrogen-vacancy (NV) centers in diamond [32,33]. Some of these applications not only require of challenging structures with high aspect ratios, but also low scattering losses. The effects of LIPSS on the beam quality remain to be explored.
In this work, we fabricate diamond nanostructures utilizing the LIPSS technique and simulate their photonic response for a broad spectral range in the near-IR. In addition, we compare the generated LIPSS to ideal sinusoidal nanostructures, aiming at the analysis of the effect of the LIPSS morphology, including nanoparticle formation, shape imperfections, irregularities and roughness. In addition, we study the aspect ratio dependency on their effectiveness as AR coating. The simulations were carried out using 3D FDTD simulations. Our results show that the suitability of LIPSS as AR coatings is strongly dependant on the aspect ratio and the scattering and diffractive effects. Therefore, strategies to improve the geometrical mesoscopic features of the nanoripples are still needed.
2. Experiments
The nanostructures analyzed by FDTD simulations were based on experimental measurements performed to the fabricated LIPSS. The nanoripples where produced by a frequency doubled Ytterbium-doped solid state laser generating ultrafast pulses (380 fs) at 520 nm with a 1 MHz repetition rate. The majority of the fabricated nanopatterns were produced with an average of 20 pulses per spot and fluence values slightly above the ablation threshold. This value was found to be approximately 2 J/cm2, while the laser fluence was varied from the ablation threshold to a maximum value of 6 J/cm2. The morphology of the generated structures do vary within that range, and in order to produce high quality nanopatterns the total impinging cumulative fluence was in the order of 25–85 J/cm2 [14]. The manufactured sample consisted on a single synthetic diamond crystal Type IIa (Electronic grade, Element6), with growth direction in the <100> crystallographic axis, so the manufacturing laser light was collinear to this axis. Additionally, the roughness was $R_a$ < 5 nm for all the diamond faces, the absorption was < 0.005 cm-1 at 1064 nm and the birefringence was $\Delta n$ < 2$\cdot$10-5 along the entire length of the crystal. Meaning that our sample presented low absorption and could be considered birefringence free.
The fabricated structures showed a periodicity of 470 nm as indicated by the field-emission gun scanning electron microscopy (FEG-SEM)) (see Fig. 1 [a, c]), although the 3D model of the structures was created based on the measurements with the atomic force microscope (AFM) (see Fig. 1(b)). This was done in order to preserve the accurate depth information provided by the AFM. There was however a discrepancy of up to 20% between AFM and FEG-SEM results, and so the structures simulated herein correspond to the measurements performed with the AFM. The study is then completed with altered versions of the actual LIPSS morphology in which the aspect ratio is artificially adjusted.
Fig. 1. a) SEM photography of the fabricated LIPSS. b) Profile of the region of interest (ROI) indicated in a) showing each of the different AFM traces performed with a separation distance of 1 µm and represented in different colours (yellow to purple). c) Average spatial Fourier transform of the ROI indicated in a) and (inset) 2D Fourier transform of the same ROI.
In the following section we show simulations of the experimentally measured nanostructures with adjusted aspect ratios by a factor of 2, 4, 6 and 8. In the same way, we study the light propagation characteristics through sinusoidal structures with the same periodicity and aspect ratios as for the previously described ripples, to compare ideal surfaces with realistic ones presenting nanoparticles and other features consequence of the fabrication process.
3. Simulations
The transmission through the nanostructured surface has been described based on the concept of "fill factor". That is, when the average spacing among the peaks and valleys of the LIPSS is small compared to the wavelength in the medium, the transmitted light will experience an average refractive index of the two materials, which gradually varies from the index of the incident material (usually air or vacuum) to the index of the substrate. This approach is known as effective medium theory (EMT), and even though is a powerful method for calculating the response of highly regular nanostructures, it is not directly applicable to LIPSS. This is in part because of the spatially variable structure pitch and morphology arising from the fabrication process. Our goal here is to study the transmission and reflection waves through realistic LIPSS nanostructures with a more precise outcome. In the following, we evaluate the spectral response in terms of transmission and reflection of light through the LIPSS and compare it with a sinusoidal design.
Compared to EMT, FDTD and Rigorous Coupled Wave Analysis (RCWA) are the two main alternative techniques for a fast and precise resolving of the propagating optical fields using Maxwell’s equations. We selected full 3D FDTD in order to be able to reproduce the asymmetries and variations of the nanostructures in the different spatial scales. We performed the calculations utilizing the high-performance photonic simulation software Lumerical (ANSYS, Inc). A wide range of wavelengths was covered through all the simulations by resolving the equations in the time-domain [34] and evaluating accurately the effects produced by the material morphology. We performed FDTD simulations to ten different surface morphologies and nanostructure aspect ratios across the spectrum from 840 nm to 2 µm. Which is a particularly interesting range for communications, spectroscopy and sensing applications in the eye-safe region [35,36]. Moreover, achieving high aspect ratios at shorter wavelengths can be challenging [14], increasing the interest on the near-IR region.
The simulation environment was set to be a diamond cuboid implemented in the software by the use of the corresponding Sellmeier equation found in [37]. The dimensions of the diamond were 25 $\times$ 25 $\times$ 42 µm3, while the nanostructures were placed centered on the top of the cuboid with an area of 10 $\times$ 10 µm2. The light source generates a broadband Fourier limited laser pulse as the result of simulating a broad spectral range covering from 840 nm – 2 µm with a spectral phase equal to 0 across the spectrum, resulting in a 5.58 fs pulse at the source. When solving this spectrum in the time-domain we observed the propagation of a dispersive pulse through the nanostructures and the diamond, presenting a transversal Gaussian beam profile with a waist radius ($\omega _0$) of 2 µm. Two complex electric field monitors were used to capture the transmitted and reflected light. The transmission was measured with a 25 $\times$ 25 µm2 monitor at a distance of 45 µm from the light source and at the bottom of the cuboid as depicted in Fig. 2, so the capturing of the entire transmitted beam was guaranteed. And the reflection detector was placed above the light source at a few microns distance. The defined boundary condition for the light source was set to be a completely transparent element, so that it does not interact with the reflected light being able to be captured by the reflection detector. While in the case of both detectors, light does not propagate further since they were set to be perfect absorbers.
Fig. 2. Schematic illustration of the setup utilized for the 3D FDTD simulations, including the size and position of the light source and monitors as well as the transmitted beam propagation.
3.1 Transmission, reflection, and overall losses
Our calculations were performed for an area covering 4$\sigma$ of the input Gaussian electric field spatial distribution $\vec {\mathbf {E}}_0(x,y,z=0) = E_0 \exp {(-(x^2+y^2)/\sigma ^2)} \hat {\bf {x}}$. Here the polarization was selected perpendicular to the nanostructures. The complex electric field readout in the transmission detector ($\vec {\mathbf {E}}_T(x,y,z_0)$) located at $z=z_0$ = 45 µm had an area equivalent to 3$\sigma$ in terms of the input Gaussian profile, resulting in an overall measurement error of less than 1%. The reflected electric field $\vec {\mathbf {E}}_R(x,y,-\delta z)$, in contrast, was obtained from a 9 x 9 µm2 planar field monitor placed just above the light source at a distance $\delta z$ = 6 µm.
Examples of the measured intensity profiles are shown in Fig. 3, in logarithmic scale for visual aid. The results obtained from the aforementioned simulations are considerably different from previous studies in the literature, where the LIPSS morphology is often approximated to a fitting function that resembles the AFM measured nanostructure profiles [13]. The specific irregularities arising from the experimental LIPSS process affect the surface of the material in a unique way, such effect is evident observing Fig. 3. An increment in the aspect ratio has a noticeable effect on the quality of the transmitted optical beam, particularly at shorter wavelengths as can be appreciated in Fig. 3(a) and (d). The effect becomes less prominent for longer wavelengths as shown in Fig. 3 [b, c] and [e, f]. This is an expected result consequence of the wavelength-dependent evanescent wave condition for nanostructures with periodicity $\Lambda$ between media with index $n_1$ and $n_2$ at an angle of incidence $\theta$, which corresponds to ${\lambda }={\rm {\Lambda }}\left [{{\rm {\max }}({n}_{1},{n}_{2})+{n}_{1}(\sin \,\theta )}\right ]$ [14].
Fig. 3. The simulated transmitted beam profiles at $z = z_0$ of the light intensity in logarithmic scale for the nanostructures at 840 nm, 1.3 µm and 2 µm (a, b, c) and for the original sample adjusted to a 8 times bigger height for the same wavelengths (d, e, f).
In order to quantify the effect of the nanostructure aspect ratio, the height of the nanostructure profile was progressively increased. Figure 4 shows both the transmission of the zero-order diffractive mode $M = 0$ and the contribution of higher-order diffractive modes $|M|>0$ to the transmitted beam for real and ideal nanostructures. Depending on the application, diffracted light may be useful (such as for light trapping devices), whereas low diffracting beams are necessary in laser applications. This is because diffracted light and scattering is often translated into transmission losses for applications such as AR coatings. It is important to remark that the reduction on the diffraction losses at shorter wavelengths observable in Fig. 4 for the high aspect ratio sinusoidal structures, is attained to the fact that the diffraction angle for $|M| = 1$ is small enough; so that the detector is capturing these modes, as we can also see an increment in the transmitted signal.
Fig. 4. Simulation results of transmission and diffraction for each of the samples at all the different heights, the left side image corresponds to the featured sample and its adjusted heights, while the right side image corresponds to theoretical sinusoidal structures. $T(A)$ corresponds to the transmission through the structures with different aspect ratio $A$, whereas $L(A)$ corresponds to the amount of power loss for different aspect ratios $A$ through higher order diffraction and scattering.
In the simulations, the lateral faces of the diamond cuboid were selected to be an impedance matched absorbing surface without any reflections, whereas the diamond material had negligible absorption. The quantity (per unit) of the cumulative losses due to diffraction and scattering was then calculated by:
Values for $T$ and $L$ for both real and ideal structures are given in Fig. 4 for a broad range of wavelengths. As expected, as the aspect ratio of the structures is increased, a higher transmission is attained at longer wavelengths. It is also clear from this analysis, that real LIPSS nanostructures have considerable high order diffraction and scattering contributions even at long wavelengths when compared to ideal sinusoidal structures. This is probably because of the complex 2D spatial frequency distribution present in the LIPSS structures, which was depicted in Fig. 1(b), meaning that the evanescent wave condition mentioned above is not entirely or appropriately fulfilled.
Likewise, Table 1 summarizes values for the reflectivity factor $R$ for the processed samples with a variety of aspect ratios at three representative wavelengths (840 nm, 1.3 µm and 2 µm). The results show that LIPSS nanostructures exhibit in most cases superior AR behaviour than the sinusoidal structures.
Table 1. Measured reflectivity in the simulation setup for each of the simulated structures, being "LIPSS" the ones referring to the featured LIPSS-like structures and "Sine" the perfectly sinusoidal generated nanostructures. The values are represented for all the simulated aspect ratios at three different wavelengths along the simulated spectrum. Aspect ratio 0 corresponds to a diamond bare surface with no structures.
Further analyzing the propagated light, the results show that even though the transmission of light through LIPSS can be efficient, there is significant distortion originated by small-scale diffractive effects caused by the irregularities in the geometry of the nanostructures. This is analyzed employing the Strehl ratio and studying the transmitted wavefront at the detector position.
3.2 Wavefront analysis
In terms of determining how severely the wavefront was affected by the diffractive and scattering effects, we measured the 3D complex electric field in all of the simulation volume $\vec {\mathbf {E}}(x,y,z)$, for the featured original sample ($A$ = 0.11) and evaluated the wavefront at $z = z_0$ (see Visualization 1 as an example). This measurement was performed in order to calculate the Strehl ratio of the beam at the transmission detector, so a quantitative measure of the beam quality reduction could be performed. The Strehl ratio $S(z_0)$ was calculated following the approximation [38]:
where $\sigma _p$ is the RMS deviation of the difference between the measured phase front $\phi$ at point $(x,y,z_0)$ of the transmission detector and the ideal propagated Gaussian beam phase front ${\phi }_0$ at the same point, so that $\sigma _p^2(z_0)=\langle (\phi (x,y,z_0)-\phi _0(x,y,z_0))^2\rangle$. The spatial wavefront phase in the detector plane at distance $z_0$ is calculated from the 3D electric field $\vec {\mathbf {E}}(x,y,z)$ in the polarization angle parallel to the unitary vector $\hat {\bf {x}}$, that is $E_x(x,y,z_0)$, which is also parallel to the polarization vector of the light source as follows:We study the wavefront distortion of the transmitted beam at a range of wavelengths between 840 nm and 2 µm. Figure 5(a) shows the results for the Strehl ratio for two different scenarios, the first one (blue) is for the region concerning the entire transmission detector surface 25 $\times$ 25 µm2, while the second case (orange) is for a 10 $\times$ 10 µm2 area centered into the beam irradiance peak and contains more than 99% of its energy.
Fig. 5. Wavefront analysis of light transmitted through LIPSS structures with an aspect ratio of 0.11: a) Strehl ratio measured for the entire detector (blue) and the reduced ROI (orange) at different wavelengths across the IR spectrum. b) Wavefront of the propagated wave at the transmission detector at 2 µm. c) Wavefront profile of the transmitted wave along the $x$ and $y$ axis (orange) and for the residual wavefront when compared to an ideal Gaussian beam at 2 µm (blue). d) Residual wavefront of the transmitted beam after substracting the wavefront of an ideal Gaussian beam at 2 µm.
As can be seen in Fig. 5(a), the Strehl ratio for wavelengths above 1 µm is $S\approx 1$, being mostly affected by scattering effects just in the outer region of the beam. When it comes to longer wavelengths at 2 µm, due to the periodicity of LIPSS the beam is not exposed to distortion effects, as depicted in Fig. 5(b) and (d) the beam in the entire detector region remains nearly unperturbed. In the case of the image Fig. 5(b) we can observe the phase of the beam at the detector, while image d) shows the residual phase of the beam after substracting the ideal Gaussian beam wavefront. This compensation and the paltry effect of diffraction can be clearly appreciated in the lineout of the profiles represented in Fig. 5(c).
In terms of the phase of the full electric field distribution at the transmission detector, we observe that the transverse field distribution features a quasi-azimuthal angular dependence, which appears to carry orbital angular momentum (OAM), probably as a consequence of the nanostructures defects producing a null intensity point that derives into these kind of phase singularities [39]. Indeed, this OAM phenomena have a grown interest for the scientific community nowadays, mainly due to their applicability in the quantum field [40,41]. Figure 6(a), b) and c) show the wrapped phase front of the transmitted beams at 840 nm, 1.3 µm and 2 µm, respectively. Here, we can observe how at shorter wavelengths, due to their relative size to the period of the LIPSS, the wavefront begins to present strong phase discontinuities in the beam edges (see Fig. 6(a)). A more detailed representation of one of the singularities is shown in Fig. 6(d). These fork-hologram shapes correspond to the type of phase distributions used to produce optical vortexes carrying OAM. It is also straightforward to observe the doughnut shaped field distribution in the diffracted electric field in Fig. 6(e), which represents the aforementioned null intensity point originated by topological defects.
Fig. 6. Wrapped wavefront corresponding to the measured phase in the detector for the wavelengths a) 840 nm, b) 1.3 µm and c) 2 µm, respectively. d) and e) correspond to the measured phase and the electric field of the phase discontinuity highlighted in the doted region, respectively.
4. Discussion and conclusions
In this study, we fabricated and measured LIPSS in diamond surfaces to study their effect on light propagation through a wide range of frequencies in the near-IR spectral region. Results regarding this study shine light into the moth-eye effect capabilities of laser induced nanostructures in transparent semiconductors. When it comes to the comparison with ideal structures, AR coatings based on LIPSS proof to be highly suitable for many applications. However, when measuring less-than-ideal structures, diffraction losses appeared to be a significant problem, so the applicability of these nanostructures can be more challenging than originally presumed. On top of this, we analyzed the wavefront distortion incurred by LIPSS. The obtained results showed that low level of distortion is attainable when the nanostructures are considerably smaller than the impinging wavelength. However, further research should be taken to experimentally demonstrate LIPSS optical and photonic capabilities in diamond.
Considering the substantial losses observed in LIPSS (such as in Fig. 4), their use as AR coatings for laser applications could be challenging. Nevertheless, results regarding the obtained Strehl ratio point that the beam quality could be high enough for some applications, particularly those not requiring full aperture transmission. One of the key aspects of using LIPSS to produce efficient AR coatings is in the difficulty of attaining high aspect ratios for the wavelengths of interest. Ideally, the nanostructures should present an aspect ratio close to 1, along with a relation between the periodicity and the wavelength of around 0.4. Moreover, as we mention in this work, the losses are closely related to the irregularities generated during the fabrication process. Alternatively, other laser based fabrication methods such as UV photo-oxidation etching could ameliorate this issue [42,43].
Another interesting potential use of LIPSS nanostructures is in light couplers for photonic integrated circuits. Indeed, it was recently proven that grating couplers are a suitable and simple solution to achieve high power transmission [33]. Results within this paper suggest that grating couplers fabricated through LIPSS could in principle achieve similar efficiency levels to those obtained with lithographically engineered grating patterns. Furthermore, the LIPSS shown here exhibit a reflectivity lower than 2% (at specific aspect ratios), meaning they may be useful as highly efficient optical couplers and light absorbers, such the ones used for NV center technology in diamond. In summary, our simulations suggest that LIPSS are a convenient fabrication technique for low cost and fast manufacturing of metasurfaces in diamond for photonic devices.
Funding
CERN (Knowledge Transfer - Singular Light).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. N. Margalit, C. Xiang, S. M. Bowers, A. Bjorlin, R. Blum, and J. E. Bowers, “Perspective on the future of silicon photonics and electronics,” Appl. Phys. Lett. 118(22), 220501 (2021). [CrossRef]
2. M. Kiss, S. Mi, G. Huszka, and N. Quack, “Diamond diffractive optics–recent progress and perspectives,” Adv. Opt. Technol. 10(1), 19–30 (2021). [CrossRef]
3. A. Gruber, A. Dräbenstedt, C. Tietz, L. Fleury, J. Wrachtrup, and C. v. Borczyskowski, “Scanning confocal optical microscopy and magnetic resonance on single defect centers,” Science 276(5321), 2012–2014 (1997). [CrossRef]
4. G. D. Fuchs, G. Burkard, P. V. Klimov, and D. D. Awschalom, “A quantum memory intrinsic to single nitrogen–vacancy centres in diamond,” Nat. Phys. 7(10), 789–793 (2011). [CrossRef]
5. R. J. Williams, O. Kitzler, Z. Bai, S. Sarang, H. Jasbeer, A. McKay, S. Antipov, A. Sabella, O. Lux, D. J. Spence, and R. P. Mildren, “High power diamond raman lasers,” IEEE J. Sel. Top. Quantum Electron. 24(5), 1–14 (2018). [CrossRef]
6. E. Granados, D. J. Spence, and R. P. Mildren, “Deep ultraviolet diamond raman laser,” Opt. Express 19(11), 10857–10863 (2011). [CrossRef]
7. B. J. M. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, and M. Lončar, “Diamond nonlinear photonics,” Nat. Photonics 8(5), 369–374 (2014). [CrossRef]
8. E. Granados, C. Granados, R. Ahmed, K. Chrysalidis, V. N. Fedosseev, B. A. Marsh, S. G. Wilkins, R. P. Mildren, and D. J. Spence, “Spectral synthesis of multi-mode lasers to the fourier limit in integrated fabry-pérot diamond resonators,” Optica 9(3), 317–324 (2022). [CrossRef]
9. J. P. Hadden, V. Bharadwaj, B. Sotillo, S. Rampini, R. Osellame, J. D. Witmer, H. Jayakumar, T. T. Fernandez, A. Chiappini, C. Armellini, M. Ferrari, R. Ramponi, P. E. Barclay, and S. M. Eaton, “Integrated waveguides and deterministically positioned nitrogen vacancy centers in diamond created by femtosecond laser writing,” Opt. Lett. 43(15), 3586–3589 (2018). [CrossRef]
10. A. Raman, Z. Yu, and S. Fan, “Dielectric nanostructures for broadband light trapping in organic solar cells,” Opt. Express 19(20), 19015–19026 (2011). [CrossRef]
11. W. Cai and V. M. Shalaev, Optical metamaterials, vol. 10 (Springer, 2010).
12. N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014). [CrossRef]
13. E. Granados, M. Martinez-Calderon, M. Gomez, A. Rodriguez, and S. M. Olaizola, “Photonic structures in diamond based on femtosecond uv laser induced periodic surface structuring (lipss),” Opt. Express 25(13), 15330–15335 (2017). [CrossRef]
14. M. Martínez-Calderon, J. J. Azkona, N. Casquero, A. Rodríguez, M. Domke, M. Gómez-Aranzadi, S. M. Olaizola, and E. Granados, “Tailoring diamond’s optical properties via direct femtosecond laser nanostructuring,” Sci. Rep. 8(1), 14262 (2018). [CrossRef]
15. H. Pask, “The design and operation of solid-state raman lasers,” Progress in Quantum Electron. 27(1), 3–56 (2003). [CrossRef]
16. J. T. Murray, W. L. Austin, and R. C. Powell, “Intracavity raman conversion and raman beam cleanup,” Opt. Mater. 11(4), 353–371 (1999). [CrossRef]
17. S. Antipov, A. Sabella, R. J. Williams, O. Kitzler, D. J. Spence, and R. P. Mildren, “1.2 kw quasi-steady-state diamond raman laser pumped by an m2=15 beam,” Opt. Lett. 44(10), 2506–2509 (2019). [CrossRef]
18. G. Hernandez, Cambridge Studies in Modern Optics 3: Fabry–Perot Interferometers (Cambridge University Press, 1986).
19. K. Chrysalidis, V. N. Fedosseev, B. A. Marsh, R. P. Mildren, D. J. Spence, K. D. A. Wendt, S. G. Wilkins, and E. Granados, “Continuously tunable diamond raman laser for resonance laser ionization,” Opt. Lett. 44(16), 3924–3927 (2019). [CrossRef]
20. D. T. Echarri, K. Chrysalidis, V. N. Fedosseev, B. A. Marsh, R. P. Mildren, S. M. Olaizola, D. J. Spence, S. G. Wilkins, and E. Granados, “Broadly tunable linewidth-invariant raman stokes comb for selective resonance photoionization,” Opt. Express 28(6), 8589–8600 (2020). [CrossRef]
21. A. Muhr, D. Twitchen, and H. de Wit, “Diamond meta-surfaces for high power laser applications,” in 2018 IEEE Research and Applications of Photonics In Defense Conference (RAPID), (2018), pp. 1–4.
22. M. Nagai, K. Nakanishi, H. Takahashi, H. Kato, T. Makino, S. Yamasaki, T. Matsumoto, T. Inokuma, and N. Tokuda, “Anisotropic diamond etching through thermochemical reaction between ni and diamond in high-temperature water vapour,” Sci. Rep. 8(1), 6687 (2018). [CrossRef]
23. A. Muhr and E. S. Greg Mulligan, “New frontiers in nanophotonics: Diamond optical windows show promise for high-power lasers,” (2016).
24. M. Mastellone, A. Bellucci, M. Girolami, V. Serpente, R. Polini, S. Orlando, A. Santagata, E. Sani, F. Hitzel, and D. M. Trucchi, “Deep-subwavelength 2d periodic surface nanostructures on diamond by double-pulse femtosecond laser irradiation,” Nano Lett. 21(10), 4477–4483 (2021). PMID: 33960788. [CrossRef]
25. E. Granados, M. M. Calderon, J. Krzywinski, E. Wörner, A. Rodriguez, M. G. Aranzadi, and S. M. Olaizola, “Enhancement of surface area and wettability properties of boron doped diamond by femtosecond laser-induced periodic surface structuring,” Opt. Mater. Express 7(9), 3389–3396 (2017). [CrossRef]
26. M. Shinoda, R. R. Gattass, and E. Mazur, “Femtosecond laser-induced formation of nanometer-width grooves on synthetic single-crystal diamond surfaces,” J. Appl. Phys. 105(5), 053102 (2009). [CrossRef]
27. P. Calvani, A. Bellucci, M. Girolami, S. Orlando, V. Valentini, A. Lettino, and D. M. Trucchi, “Optical properties of femtosecond laser-treated diamond,” Appl. Phys. A 117(1), 25–29 (2014). [CrossRef]
28. A. A. Bushunov, M. K. Tarabrin, and V. A. Lazarev, “Review of surface modification technologies for mid-infrared antireflection microstructures fabrication,” Laser Photonics Rev. 15, 2000202 (2021). [CrossRef]
29. C. Fei Guo, T. Sun, F. Cao, Q. Liu, and Z. Ren, “Metallic nanostructures for light trapping in energy-harvesting devices,” Light: Sci. Appl. 3(4), e161 (2014). [CrossRef]
30. H. Clevenson, M. E. Trusheim, C. Teale, T. Schröder, D. Braje, and D. Englund, “Broadband magnetometry and temperature sensing with a light-trapping diamond waveguide,” Nat. Phys. 11(5), 393–397 (2015). [CrossRef]
31. Y. Zhang, D. J. Hellebusch, N. D. Bronstein, C. Ko, D. F. Ogletree, M. Salmeron, and A. P. Alivisatos, “Ultrasensitive photodetectors exploiting electrostatic trapping and percolation transport,” Nat. Commun. 7(1), 11924 (2016). [CrossRef]
32. H. Sumikura, K. Hirama, K. Nishiguchi, A. Shinya, and M. Notomi, “Highly nitrogen-vacancy doped diamond nanostructures fabricated by ion implantation and optimum annealing,” APL Mater. 8(3), 031113 (2020). [CrossRef]
33. B. Feigel, H. Thienpont, and N. Vermeulen, “Design of infrared and ultraviolet raman lasers based on grating-coupled integrated diamond ring resonators,” J. Opt. Soc. Am. B 33(3), B5–B18 (2016). [CrossRef]
34. M. K. Callens, H. Marsman, L. Penninck, P. Peeters, H. de Groot, J. M. ter Meulen, and K. Neyts, “Rcwa and fdtd modeling of light emission from internally structured oleds,” Opt. Express 22(S3), A589–A600 (2014). [CrossRef]
35. O. Lux, S. Sarang, R. J. Williams, A. McKay, and R. P. Mildren, “Single longitudinal mode diamond raman laser in the eye-safe spectral region for water vapor detection,” Opt. Express 24(24), 27812–27820 (2016). [CrossRef]
36. J. A. Piper and H. M. Pask, “Crystalline raman lasers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 692–704 (2007). [CrossRef]
37. F. Peter, “Über brechungsindizes und absorptionskonstanten des diamanten zwischen 644 und 226 mµ,” Z. Physik 15(1), 358–368 (1923). [CrossRef]
38. V. N. Mahajan, “Strehl ratio for primary aberrations in terms of their aberration variance,” J. Opt. Soc. Am. 73(6), 860–861 (1983). [CrossRef]
39. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). [CrossRef]
40. D. Bacco, D. Cozzolino, B. Da Lio, Y. Ding, K. Rottwitt, and L. K. Oxenløwe, “Quantum communication with orbital angular momentum,” in 2020 22nd International Conference on Transparent Optical Networks (ICTON), (2020), pp. 1–4.
41. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3(5), 305–310 (2007). [CrossRef]
42. L. Weston, J. E. Downes, C. G. Baldwin, E. Granados, S. A. Tawfik, X. Y. Cui, C. Stampfl, and R. P. Mildren, “Photochemical etching of carbonyl groups from a carbon matrix: The (001) diamond surface,” Phys. Rev. Lett. 122(1), 016802 (2019). [CrossRef]
43. A. M. Berhane, C. G. Baldwin, K. Liang, M. Moshkani, C. Lustri, J. E. Downes, C. Stampfl, and R. P. Mildren, “Morphogenesis of mesoscopic surface patterns formed in polarized two-photon etching of diamond,” Carbon 173, 271–285 (2021). [CrossRef]
