Competing Nonlinear Delocalization of Light for Laser Inscription Inside Silicon with a 2-µm Picosecond Laser

The metrology of laser-induced damage usually finds a single transition from 0% to 100% damage probability when progressively increasing the laser energy in experiments. We observe that picosecond pulses at 2-µm wavelength focused inside silicon provide a response that strongly deviates from this. Supported by nonlinear propagation simulations and energy flow analyses, we reveal an increased light delocalization for near critical power conditions. This leads to a nonmonotonic evolution of the peak delivered fluence as a function of the incoming pulse of the energy, a situation more complex than the clamping of the intensity until now observed in ultrafast regimes. Compared to femtosecond lasers, our measurements show that picosecond sources lead to reduced thresholds for three-dimensional (3D) writing inside silicon that is highly desirable. However, strong interplays between nonlinear effects persist and should not be ignored for the performance of future technological developments. We illustrate this aspect by carefully retrieving from the study the conditions for a demonstration of 3D data inscription inside a silicon wafer.

Figure 1

Experimental arrangement for the damage tests with a 2-µm laser at different pulse durations. DM is a dichroic mirror rejecting the pump. FI is a Faraday isolator transmitting linearly polarized pulses. QWP is a quarter-wave plate to create a nearly linear polarization after exiting the fiber. HWP is a half-wave plate on a motorized stage added to control the FI transmission and the laser pulse energy used in the experiments. CVBG is a chirped volume Bragg grating to compress the pulse down to 2 ps and can be bypassed with an inserting mirror (M). The residual divergence of the beam after L1 is exploited to collimate the beam with L2 at the position where it reaches an appropriate diameter to fill AL, the aspheric focusing lens. Sh is a mechanical shutter. For high-sensitivity modification detection, an infrared dark-field microscope is implemented. OL,TL, and QTH are, respectively, an objective, a tube lens, and a Quartz-Tungsten Halogen lamp for imaging with an ($\mathrm{In},\mathrm{Ga})\mathrm{As}$ camera.

Figure 2

Energy dependence of the damage probability with 2-ps pulses focused (NA = 0.85) at 150 µm below the surface of silicon. The sample is irradiated with gradually increasing energies on fresh sites separated by 50 µm. All measurements result from statistics over 10 identical irradiations corresponding to lines observed by dark-field IR microscopy as shown by the inserted images. The spatial scale applies to all inserted images. Several transitions between 0 and 100% damage probability (color regions) evidence a nonmonotonic change of the delivered fluence due to the nonlinearities.

Figure 3

Energy flow analysis by nonlinear propagation simulations of focused picosecond pulses. Nonlinear propagation simulations for 2-ps pulse at 2-µm wavelength are performed to map the energy flow inside the material near the focal region (NA) at a depth of 150 µm. The insets show the fluence distribution and energy flow lines obtained by retrieving the wave vectors from the wavefront of the pulse at each propagation distance for incoming energies of 0.01, 0.1, and 0.5 µJ. The graph gives the number of energy flow lines reaching a zone of 1 µm at the vicinity of the focus as a function of the input pulse energy. A minimum corresponding to a lower angular component contributing to the focus is found when varying the pulse energy. The structured fluence distribution originates from diffraction for a beam overfilling the entrance pupil of the lens. The Supplemental Material [19] provides a more complete energy flow analysis under various assumptions on the spatial characteristics of the beam.

Figure 4

Influence of the pulse duration on the bulk damage response with pulses focused (NA = 0.85) at 150 µm below the surface of silicon. All measurements result from statistics over 10 identical irradiations to report the damage probability as a function of the incoming pulse energy (b). Only the shortest pulses (2 ps) exhibit multiple transitions. For comparison, the damage threshold as a function of the tested pulse durations is shown (b). The vertical bars stand for the energy range between the highest tested energy without any modification and the lowest energy exhibiting 100% modification. The lowest threshold for modification is found for the intermediate pulse duration of 9 ps.

Figure 5

Bulk-surface two-plane data inscription by laser machining. The sample is observed by (a) SEM and (b) IR dark field microscopy (NA = 0.45) focused at the surface and (c) at the bulk-written plane below the surface. The bulk text is first inscribed with consecutive irradiations of sites with tightly focused pulses (2 × 10⁵ pulses at 100 kHz) at a fixed pulse energy above the bulk damage threshold (320 nJ). Machining of the surface text is performed in a second step using the same procedure with pulses at reduced energy (50 nJ). The two planes are clearly distinguished with IR microscopy and there is nothing related to the bulk inscription revealed by SEM imaging of the surface. The same scale bar applies to all images.