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Abstract
High-rate direct femtosecond (fs) laser writing is a well-established technology for fabricating various micro-optical elements in bulk dielectrics. In this technology, the “heat accumulation” effect, occurring during high-repetition rate (∼ 1 MHz) exposure in dielectrics by a fs laser, enables ultralow-energy micro-modification via cumulative heating. Meanwhile, in this work in the transient multi-photon A-band photoluminescence studies, we demonstrate that this effect underlies dynamic thermal lensing even in diamond with its high thermal conductivity, dynamically shifting the laser focus upstream. Our study paves the way for more precise, accurate and robust direct fs-laser writing of advanced three-dimensional structures in diamond and other dielectrics for a variety of photonic applications.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Direct femtosecond laser writing is well-established as a key-enabling, versatile technology for fabricating micro-optical and micro-fluidic elements in bulk dielectrics [1–3]. Depending on laser fluence and exposure, related material micro-modification regimes and the resulting embedded microstructures vary from 1) nanoscale plasmonic chemical segregation, yielding in transparent bulk birefringent nanogratings [4]; 2) homogeneous melting/recrystallization, producing densified regions of phase-contrast waveguides without material disruption [5]; till 3) local ablation and lateral densification, making hollow voids and channels for optical storage [6] and microfluidics [7], respectively.
Generally, minimal heat-affected zone (HAZ) around fs-laser focus in dielectrics, emerging due to their low thermal conductivity (∼ 0.01 W/cmK [8]), was considered as the main prerequisite for high-precision and resolution in direct fs-laser writing [9], and also as the main reason for marginal energy transport off the focal region. Practically, some time ago one important regime of oscillator-only direct laser writing in bulk dielectrics was found [10], supporting their ultralow-energy modification via multi-shot cumulative heating at multi-MHz repetition rates [10,11]. Due to such multiple cumulative heating, it has been possible to date to modify optically-active point defects in diamond [12–14]. Moreover, waveguides were fabricated in a few studies in bulk silica materials in this regime, exploring the repetition-rate effect in the MHz-range [10–11, 15–17].
Meanwhile, the related issues of inhomogeneous temperature distribution during cumulative fs-laser heating and related thermal lensing effect were not considered so far, comparing to, e.g., local modification of refractive index via generation of self-trapped excitons [18]. Furthermore, potentially these thermal cumulative effects could strongly emerge in crystalline dielectrics as anisotropic wave-front distortions (“thermal lensing”), thermal birefringence etc., which could transiently shift or modify the laser-heating source and thus are highly important for well-controlled and precise direct fs-laser writing in bulk dielectrics.
In this study we observe dynamic displacement of fs-laser focus in bulk natural diamond, the highly-transparent material with very high thermal conductivity, under its sub-MHz exposure on a millisecond timescale, which is visualized by transient laser-excited photoluminescence and appears to be reversible upon switching the laser off for a few milliseconds. This observation rises a question of robust spatial focusing of high-rate fs-laser pulses in bulk dielectrics and direct writing of continuous buried micro-structures while changing writing regime.
2. Experimental details
In this experiment, 1030-nm, 300-fs fiber laser pulses, coming at 100-kHz repetition rate and variable pulse energies E = 4-63 nJ (peak powers of 13-140 kW, sub-filamentary focusing regime for 1030-nm peak laser-pulse powers < 2 MW [19]), were focused at each pulse energy into a new 3-micron wide (1/e-level diameter 2w) and 25-micron long (1/e-level Rayleigh length 2l) region inside a diamond (refractive index n0 (λ = 1030 nm) ≈ 2.4 [20]) by 0.25-NA micro-objective (10×) (Fig. 1(a))
Fig. 1. (a) Schematic of the experimental setup. (b) Photoluminescence spectra at variable fs-laser pulse energies.
At the maximal 500-kHz exposures and reduced pulse energy of 35 nJ, side-view imaging of the bluish emission region, spatially evolving far beyond the waist range 2l, was performed by the color CCD camera as a function of millisecond-scale exposure times, interrupted from time to time to explore the reversibility of its sub-millimeter upstream (back to the laser) displacements.
3. Results
3.1 PL spectral assignment and pulse energy yield
The observed photoluminescence spectra in Fig. 1(b) demonstrate a main structureless emission A-band [21], starting at ≈ 350 nm and extending till ≈ 700 nm, with its intensity peak at ≈ 430 nm monotonously raising versus the increasing pulse energy of 4-42 nJ (peak intensity of 0.2-1.8 TW/cm2). Indeed, the uv-vis PL origin can be rather unambiguously identified as A-band with its peak at 415-445 nm [21,22], which is especially very intense in low-nitrogen diamonds because of its strong nitrogen A-center damping [23,24]. The corresponding PL excitation band is known to be symmetric to A-band, occupying the range of 3-4 eV [25]. Importantly, A-bands may have different origins [21], where in the first model the relatively narrow A-band peaked at 440 nm in low-nitrogen type II diamonds is associated with radiative recombination at dislocations (donor-acceptor (D-A) pairs decorating dislocations [22], vacancies bound to dislocations [26,27], dislocations decorated with D-A pairs [28], on pure non-decorated dislocations [29–32]). In the second model, A-band with a maximum at 480 nm observed in natural type I diamonds is intra-center transitions at the B2-centers (platelets). In the third model A-band is also assigned to electron-hole recombination at deep centers, the energy levels of which lie in the middle of the bandgap [33,34]: EA = (Eg/2) ± 0.75 eV, occurring through the formation of free excitons [35] as a two-stage process [36,37]. In our study, the observed A-band extends in the range of 2-4 eV with its peak at ≈ 3 eV at the presence of high (650 ppm) A-center density and marginal B2-center density in the high-nitrogen natural diamond, representing, according to the diamond specification and our recent spectral studies [38], the radiative relaxation in the intra-gap energy set of molecular-like states of the unknown optical center. Additionally, at shorter wavelengths, there is a preceding periodical vibronic progression with the diamond LO/TO-phonon wavenumber of ≈ 1300 cm-1. Meanwhile, at higher pulse energies of 50 and 63 nJ (peak intensity ≈ 2-2.5 TW/cm2) an additional broad photoluminescence band appears just above the second-harmonic position (515 nm) in the spectra (Fig. 2(a)), slightly reducing the main band intensity.
Fig. 2. (a) Laser energy/intensity dependence of PL peak intensity and its dual-range linear fits in lgΦ-lgE coordinates. (b) Schematic spectral structure, explaining the dual-band photoluminescence spectra and dual-slope fitting in (a). The upright red arrows indicate the 1030-nm laser photons, blue and green arrows indicate the corresponding photoluminescence bands, and other arrows indicate radiation and non-radiative (dashed) relaxation processes.
Moreover, the corresponding PL yield versus laser energy/intensity was observed to change its slope (power) in the lgΦ-lgE coordinates from 2.9 ± 0.5 for E ≤ 10 nJ (I ≤ 0.4 TW/cm2) till 1.2 ± 0.1 for higher energies (intensities) (Fig. 2(b)). The low-energy three-photon process can be directly related to the intra-center excitation of the top excited state, radiatively relaxing via the “blue” photoluminescence (Fig. 1(b)). Then, in together with the high-energy appearance of the second, “green” luminescence band in Fig. 1(b), the second, high-energy linear “blue” PL yield could be associated with radiative/non-radiative relaxation of the top excited state into the intermediate one (Fig. 2(a)), yielding further either radiative “green” relaxation, or one-photon laser re-excitation back to the top excited state. In this way, both the linear high-energy PL yield and the high-energy appearance of the “green” PL band can be tied together. This suggestion of the intermediate excited state of this poorly explored A-band-related optical center is consistent with our previous temperature-dependent studies of 515-nm fs-laser excited A-band photoluminescence, showed enhanced damping even at minor heating (<55 °C) [38], as typical for A-band [39,40]. Specifically, 1) thermal activation of dissociation in the excited state, thermal overcoming of an activation barrier from the excited state 2) to the ground state, or 3) to the intermediate state are considered as the main mechanisms of thermal damping of photoluminescence, and the latter one probably takes the place in the optical center of the diamond, similarly to, e.g., NV-center in this material [41].
3.2 Reversible spatial displacements of the PL region during ms-scale cumulative exposures
Using the synchronized color CCD-camera, side-view imaging of the 1030-nm fs-laser excited emission region was performed as a function of ms-scale exposure time (Fig. 3(a)). Specifically, its upstream (back to the laser) monotonic multi-micrometer displacement was observed. Moreover, at the later time instants the main peak drops in its intensity and splits off into two low-intensity peaks (Fig. 3(b)), which could be related to 1) intra-pulse dynamics, including the spatiotemporal transition in the abovementioned three/one-photon A-band photoexcitation mechanism, 2) longitudinal instabilities in PL yield during the fs-laser exposure, etc.
Fig. 3. (a) Upstream evolution of the focal region versus exposure time. (b) Longitudinal profiles of emission intensity at different time instants, showing the double-peak structure separated by the vertical dashed line. (с) Enlarged image of PL in 2.5x with deferred parameters half-lengths and half-widths.
More exactly, the first peak shifts downstream and completely disappears in some point, giving rise to the second peak (Fig. 4(a)). Its simultaneous drop in intensity is more pronounced over the first 10-15 ms (Fig. 4(b)). The PL intensity center-of-mass in the emission regime decreases very rapidly in time from one emission region to another one (Fig. 4(c)). Finally, despite the visible elongation of the emission regions in time, their lengths at half-maximum (half-lengths, Fig. 4(d)) drop twice rather quickly versus time, similarly to the corresponding half-widths.
Fig. 4. Spatial (a) and temporal (b) evolution of the first and second peak intensity in longitudinal profiles (Fig. 3(b)). (c) Velocity of the first and second peak center-of-mass displacements versus exposure time. (d) Half-lengths and half-widths of emission regions (Fig. 3(a)) versus exposure time.
The electromechanical shutter was used to explore the reversibility of the downstream displacement versus the interruption time in laser exposure (Fig. 5). First, Fig.5a indicates the almost complete recovery (upstream displacement) of the emission regime after 12 ms, with the emission region emerging instantaneously again in the same initial position of the focus (Z = 110 µm) upon the start of a new exposure. The next Fig.5b shows that the intermediate velocities of the downstream and upstream displacements are almost identical, as well as the corresponding transient positions (Fig.5c).
Fig. 5. (a) Reverse upstream displacements (recovery of the initial position) of emission region versus interruption time in laser exposure. The horizontal dashed lines indicate the starting point (Z = 110 µm) and the maximal displacement (Z = 210 µm) during the laser heating. (b) Velocity of down- and upstream displacements versus exposure time (“pumping”) and interruption (“relaxation”) time in laser exposure. (c) Downstream and upstream displacements of emission region (center-of mass) during the first 12 ms of exposure time (“pumping”) and interruption (“relaxation”) time in laser exposure.
4. Discussion
Though previously only local heat accumulation was observed in dielectrics during high-rate fs-laser exposures [10–11,15–17], in this work we observed reversible displacement of the PL-tracked fs-laser focal region, which could be related to local modification of the refractive index, Δn, along the laser path in the diamond, resulting in its earlier focusing, i.e., self-focusing. Usually, prompt electronic or delayed picosecond-scale orientational self-focusing mechanisms with the nonlinear index n2 are taken into account [18]
5. Conclusions
Though cumulative heating effect, occurring during MHz-rate direct femtosecond laser modification in dielectrics, is rather well known, dynamic lensing effect during such multi-shot exposures was revealed in our study for the first time. Such reversible upstream displacements of the focal region by almost ten Rayleigh lengths reveals the important details of non-linear “laser-matter” optical interaction and could strongly affect direct fs-laser local nano- and micro-fabrication of various micro-optical elements in bulk dielectrics.
Funding
Russian Science Foundation (21-79-30063).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available from the authors upon reasonable request.
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