Spatio-temporally focused femtosecond laser pulses for nonreciprocal writing in optically transparent materials

Abstract

Simultaneous spatial and temporal focusing (SSTF) provides precise control of the pulse front tilt necessary to achieve nonreciprocal writing in glass. The magnitude of the pulse front tilt may be adjusted over several orders of magnitude. Nonreciprocal writing was observed for a larger range of focal depths within the sample using SSTF, and nonreciprocal ablation patterns on the surface were revealed. Further, the lower numerical aperture (0.04 NA) utilized with SSTF increases the rate of writing. This technique allows channels in microfluidic devices to be prototyped an order of magnitude faster than with current methods.

1. Introduction

Three-dimensional (3D) micro- and nanoscale patterning with femtosecond lasers continues to gain novel applications in fields such as micro- and optofluidics, lithography, and electronics. Recently, surface nanostructuring by irradiation with femtosecond laser pulses improved the absorption efficiency of thin film silicon solar cells [Wang 2010]. Additionally, nanostructuring in doped glass was shown to have optical switching capabilities and, with only 150 nm spacing between bits, has application in compact optical memory storage [Shimotsuma 2007]. The type of modification obtained from femtosecond laser exposure depends on the material composition and laser parameters. It has been suggested that femtosecond laser material modification in transparent materials be divided into three categories. In order of increasing intensity, these are: (type 1) a smooth, positive change in the refractive index; (type 2) formation of birefringence with associated anisotropic scattering; and (type 3 void formation [Chan 2001; Sudrie 2001; Bricchi 2004]. Type 2 modifications are perhaps the least exploited, yet investigations of these modifications have revealed remarkable properties including strong polarization sensitivity. The form birefringence arises from subwavelength periodic variations in the refractive index along the dimension of light propagation and perpendicular to the direction of the electric field [Shimotsuma 2003; Hnatovsky 2005; Yang 2006]. These type 2 modifications were suggested by Cheng et al. as a candidate for a polarization-selective optical router [Cheng 2009]. Using an arrangement of type 2 structures, they selectively guided polarized light with the electric field parallel to that of the writing laser. Beresna and Kazansky created a polarization diffraction grating by writing adjacent lines of type 2 modifications with periodic rotation of the writing laser's electric field [Beresna and Kazansky 2010]. Under some conditions, type 2 modifications have the additional quality that the characteristics of the modification change, in an effect called nonreciprocal or “quill” writing [Kazansky 2007; Poumellec 2008; Yang 2008], when the scan direction is reversed. This even occurs in centrosymmetric materials [ ADD REF]

In an attempt to understand nonreciprocal writing, Yang et al. observed type 2 modification in one laser scanning direction and type 3 modification in the reverse direction [Yang 2008]. This phenomenon is due to pulse front tilt (PFT) [Kazansky 2007; Yang 2008], which sets up a traveling wave at focus that interacts differently with the material, depending on whether the sample is translated with or against it. PFT may be imposed by tuning the laser's grating compressor and quantified by measurements with a GRENOUILLE [Yang 2008]. However, misaligning a double-pass grating (or prism) compressor to produce residual angular dispersion necessarily results in spatial and temporal distortions at focus [Osvay and Ross 1994]. Consequently, the conditions for generating PFT are not easily translated between systems, so that deciphering the effect of PFT on nonreciprocal writing is confounded.

We propose a method to obtain the conditions necessary for nonreciprocal writing in a controlled and reproducible manner by exploiting the PFT inherent to a simultaneous spatial and temporal focusing (SSTF) arrangement. In SSTF spatial chirping is used to form a frequency-distributed array of low numerical aperture (NA) beamlets. A feature of SSTF is that out-of-focus nonlinear interactions are suppressed, allowing femtosecond material modification in the bulk of thick transparent substrates. Importantly, at focus, the frequencies overlap spatially and temporally, and the pulse is transform-limited in time as well as diffraction-limited in space [Zhu 2005; Oron 2005]. PFT is achieved without misalignment of the grating compressor and may be measured using scanning SEA TADPOLE [Coughlan 2009] and simulated using Fourier pulse propagation [Coughlan 2009; Vitek 2010]. The magnitude of PFT is adjusted by changing the beam aspect ratio (i.e., the ratio of the spatially chirped beam dimension to the unchirped dimension). With our SSTF system we examined nonreciprocal writing with several orders of magnitude more PFT than was employed by Yang et al., and we obtained somewhat different dependencies. For example, Yang et al. noted that for focal depths outside of a narrow region, nonreciprocal writing vanishes [Yang 2008]. We observed a relaxed depth-dependence, and with our SSTF system we showed nonreciprocal writing with type 3 modifications on the back surface of the sample where either dots or Chevron shapes (the shape of a ‘V’ character) were patterned, depending on the scanning direction. Finally, working at low NA (0.04) with the SSTF setup, compared to 0.5-0.8 NA used in previous studies, increases the interaction volume and may improve the production rate of these type 2 features.

2. Experimental methods

The experimental setup is described and illustrated in Vitek et al. [Vitek 2010]. Briefly, 25 μJ pulses at 1 kHz are supplied from a Ti:Al₂O₃ chirped pulse amplification system centered at 800 nm. The SSTF system consists of two gratings (600 l/mm, Thorlabs, #GR25-0608) that spatially chirp and then collimate the pulses. The angle of incidence (36°) on the gratings and the grating separation (630 mm) are selected to minimize second and third order dispersion. The beam incident on the focusing optic, which was a 25 mm focal length, 90-degree off-axis parabola (Janos Technology, #A8037-175), measured 8.7 mm and 0.81 mm full-width at half maximum (FWHM) in the spatially chirped and unchirped dimensions, respectively. At focus the spot size was 39 μm FWHM. The pulse width at focus was 74 fs FWHM.

Nonreciprocal writing was monitored for variations in the scanning depth, rate, and direction and in the electric field polarization. The sample was a 500 μm thick quartz microscope slide. We scanned the sample parallel to and perpendicular to the PFT at rates of 5, 10 and 50 μm/s. The electric field polarization was oriented either parallel to or perpendicular to the scanning direction.

3. Results and discussion

The PFT for our system was simulated using Fourier beam propagation [Vitek 2010]. The predicted value for PFT was 8.3e3 fs/mm. PFT may also be measured with scanning SEA TADPOLE [Coughlan 2009]. Under appropriate conditions, an approximate value of PFT may be quickly obtained using the analytical relationship for the pulse width stretching factor (PWSF) presented in Zhu et al. in Eq. (5) [Zhu 2005]. This approximation applies to SSTF systems with a large amount of spatial chirp. The PFT is the stretched pulse width (the product of the pulse width stretching factor with the pulse width at focus) divided by the beam width at focus. For our system, this relationship gives 2.1e4 fs/mm, which is within reasonable agreement with the simulated value from Fourier beam propagation.

Nonreciprocal writing was observed for scanning along the axis of PFT (Figure 1(a,b)) but was not observed when scanning perpendicular to the PFT (Figure 1(c)), supporting the claim that PFT causes nonreciprocal writing. Anti-parallel scanning directions revealed type 2 and type 3 features that depend on the sample scanning direction and are largely independent of polarization (Figure 1(a,b)).

Figure 1.

Nonreciprocal writing was observed for scanning directions that were perpendicular to the PFT (a,b) but was not observed when scanning parallel to the PFT (c). Each set of anti-parallel lines was imaged with bright field (top) and cross-polarized illumination (bottom). The electric field direction, E, is marked with arrows. The scanning rate was 10 μm/s, and the focal depth in the sample was 210 μm. Scale bar, 50 μm.

We observed nonreciprocal writing for focal depths ranging from 170 μm to 370 μm in the 500 μm thick sample (Figure 2). This is a much broader range than was seen by Yang et al. [Yang 2008]. Under their experimental conditions (0.8 NA), ≥5 μm movement in either direction eliminated the appearance of nonreciprocal writing.

Figure 2.

Nonreciprocal writing was examined at different depths, z, beneath the surface of the sample. Each set of anti-parallel lines was imaged with (a) bright field and (b) cross-polarized illumination. The scan rates for regions 1, 2 and 3 were 5 μm/s, 10 μm/s and 50 μm/s, respectively. Scale bar, 50 μm.

For focal depths ±40 μm outside of the 170 μm to 370 μm range, type 2 features were no longer observed in the bulk. Instead, ablation occurred on the nearest surface. Interestingly, damage on the back surface showed nonreciprocal behavior (Figure 3). Regularly spaced, 25 μm diameter wells were ablated in one direction. In the opposite direction Chevron-shaped structures were produced. The spacing of the structures showed a small but not proportionate increase when the scan rate was doubled from 5 to 10 μm/s between regions 1 and 2. For the highest scan rate of 50 μm/s, the structures became irregular. Organized surface patterning may find novel applications for femtosecond laser modification such as for microfluidic device fabrication. For example, herringbone or Chevron-shaped structures have assisted with particle alignment in microfluidic channels by modifying the flow dynamics [Hsu 2008; Golden 2009].

Figure 3.

Wells (top) or Chevron structures (bottom) were ablated for anti-parallel scanning directions on the back surface of the sample. The scan rates for regions 1, 2 and 3 were 5 μm/s, 10 μm/s and 50 μm/s, respectively. The laser's electric field was oriented along the scanning direction. Scale bar, 50 μm.

4. Conclusion

With an SSTF system, the PFT necessary in nonreciprocal writing is achieved in a calculable and reproducible manner and without the need to misalign the laser's grating or prism compressor. The numerical aperture of the writing beam used in these studies is an order of magnitude smaller compared to previous work, and the PFT is several orders of magnitude larger. Consequently, we observed nonreciprocal behavior over a range of depths (170μm to 370 μm), including the back surface of the 500 μm thick quartz sample. Notably, the structures we have created here are of sufficient extent that patterned microfluidic channels are created in a single pass. Thus, devices can be fabricated quickly and efficiently.