1 Introduction

During the past years it has been demonstrated that femtosecond lasers are excellent tools for the microstructuring of nearly all kinds of solid materials [1–6]. The main features of material processing with femtosecond laser pulses are (i) efficient, fast and localized energy deposition, (ii) low deformation and ablation thresholds, (iii) minimal thermal and mechanical damage of the substrate material. This allows one to produce microstructures with very high precision and reproducibility using compact laser systems.

An example of a 25-µm periodic grid structure produced in a 4-µm-thick Ni film is shown in Fig. 1. This structure is fabricated using a commercial Ti:sapphire laser system (Spectra-Physics, Spitfire) delivering 120-fs laser pulses at 780 nm with a repetition rate of 1 kHz. In general, when no special efforts are applied, the minimum achievable structure size is determined by the diffraction limit of the optical system and is of the order of the radiation wavelength.

In this paper investigations of possibilities to go further and to produce sub-diffraction limited structures are reported. We investigate two types of microstructuring with tightly focused femtosecond pulses - microstructuring on the target surface and in the bulk of transparent materials. Direct ablative writing on the target surface is of great practical importance (e.g. for repair of photolithographic masks). Internal microstructures can be produced by tightly focusing femtosecond pulses in the bulk of transparent materials. We use this technique for the manufacturing of optical waveguides.

 

Fig. 1. Electron acceleration grid for a streak camera fabricated in a 4-µm-thick Ni film.

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It has been suggested [1] that by taking advantage of the well-defined ablation threshold one can overcome the diffraction limit by choosing the peak laser fluence slightly above the threshold value. In this case only the central part of the beam can ablate the material and it becomes possible to produce sub-diffraction limited structures [1]. Another approach for the production of sub-diffraction limited structures (which is not discussed here) is to use femtosecond pulses in combination with a scanning near-field optical microscope (SNOM) [7]. In this case the SNOM works in the so-called illumination mode with femtosecond pulses coupled into a fiber tip. Applications of this technique for nanostructuring and direct ablative writing upon metal surfaces have been demonstrated, recently [7].

In Sec. 2 of this paper, we discuss the physics of ultrashort pulse laser ablation. In Sec. 3 we perform systematic investigations of microstructuring with tightly focused laser pulses. Our motivation is to study how far one can go in an attempt to reduce the structure size using Gaussian laser pulses at 780 nm and to identify the best regime (optimum laser parameters) for the fabrication of sub-diffraction limited structures in 100–200 nm chrome-coated surfaces. This technique has potential applications for the repair of photolithographic masks and other purposes. In Sec. 4 we report on the fabrication of optical waveguides in transparent crystals. By adjusting the laser pulse energy close to the damage threshold of a dielectric material, internal waveguides can be produced by tightly focused laser pulses due to laser induced refractive index modifications. Investigations of the waveguiding properties of the fabricated structures are performed.

2 Femtosecond laser ablation

The physics of ultrashort pulse laser ablation of metals and other solids (semiconductors, dielectrics, polymers, etc.) is essentially the same. The only difference is that in metals the electron density can be considered constant during the interaction with the short laser pulse. In other materials, the electron density changes due to interband transitions, multiphoton and electron-impact (avalanche) ionization followed by optical breakdown.

 

Fig. 2. Schematic of femtosecond laser ablation and electron heat transport in dielectric (left) and metal (right) targets.

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Ablation with ultrashort laser pulses consists of the following steps: (1) absorption of laser radiation inside the surface layer by bound and free electrons (electronic subsystem), (2) energy transfer to the lattice (atomic subsystem), bond breaking, and material expansion. At the focus of an ultrashort laser pulse, one can speak about the formation of a solid density plasma as is schematically shown in Fig. 2. In the case of dielectric materials the electron heat transport into the target is strongly suppressed. Electrons are not able to escape due to the charge separation force keeping the plasma charge neutral. In metals the electron heat transport is allowed, since the hot electrons moving into the target can be replaced by cold electrons from the adjacent region (return current). In spite of this, there exist additional physical reasons (see below) leading to a reduction of the electron heat transport in metals. For laser fluences close to the ablation threshold the electron-ion energy transfer occurs on a picosecond time scale. This results in minimal thermal losses and shock-, burr-, and crack-free material removal.

A theoretical description of femtosecond laser ablation of a metal layer is given below. In this case the laser energy is first absorbed by free electrons due to the inverse Bremsstrahlung. The absorption is followed by a fast energy relaxation within the electronic subsystem, thermal diffusion and an energy transfer to the lattice due to electron-phonon coupling. The spatial and temporal evolution of the electron and lattice temperatures (T_e and T_i , respectively) in a thin surface layer with the subsequent material expansion is described by the following one-dimensional equations

where x is the direction perpendicular to the target surface, d/dt=∂/∂t+u∂/∂x, C_e and C_i are the heat capacities (per unit volume) of the electron and lattice subsystems. The parameter γ is characterizing the electron-lattice coupling, ρ and u are the density and velocity of the evaporated material, P_e and P_i are the thermal electron and ion pressures, P_c is the elastic (or “cold”) pressure which is positive for compression and negative for expansion, Q(x)=-k_e (T_e )∂T_e/∂x is the heat flux, and S=I(t)Aα exp(-αx) is the laser heating source term. Here I(t) is the laser intensity, A and α are the surface absorptivity and the material absorption coefficient, and k_e is the electron thermal conductivity. Eqs. (1) and (2) are energy conservation equations for the electron and ion subsystems. Eq. (3) expresses Newton’s law and Eq. (4) - the continuity equation - describes the conservation of mass.

Unfortunately, there is a lack of reliable information on several parameters, which enter into the above hydrodynamic equations. For example, there is no sufficient information on the equations of state which could describe the evolution of the electron, ion and cold pressures. There are also some uncertainties in the electron-lattice coupling and electron relaxation rates. Therefore, in spite of the obvious simplicity of the above equations, their application for modeling of femtosecond laser ablation remains problematic.

The simplest model for ultrashort pulse laser ablation can be obtained by neglecting the material expansion completely and declaring that one needs a definite amount of energy to initiate ablation. In this case the last terms in Eqs. (1) and (2) (containing ∂u/∂x) can be omitted and the hydrodymanic equations reduce to the well-known two-temperature diffusion model. Using this model an analysis of femtosecond laser ablation of metals has been performed earlier [5].

Since the electronic heat capacity is much less than the lattice heat capacity, electrons can be heated to very high transient temperatures. When k_BT_e remains smaller than the Fermi energy E_F =${\mathit{\text{mv}}}_F^2$/2, the electron heat capacity and the electron thermal conductivity are given by [8] C_e ≃π²(k_BT_e/E_F )N_ek_B /2 and k_e =C_e$v_F^2$ τ/3, where N_e is the electron density and τ is the electron relaxation time, which is determined by the electron-phonon and electron-electron collisions 1/τ=1/τ_eph +1/τ_ee . When the lattice temperature is larger than the Debye temperature, T_i ≥Θ=ħω_D/k_B , where ω_D is the Debye frequency (the maximum phonon frequency), all oscillation modes of the lattice are excited, and a good approximation for the electron-phonon collision frequency is given by [9] 1/τ_eph ≃k_BT_i/ħ. The electron-electron collision frequency can be estimated by [9] 1/τ_ee ≃(k_BT_e )2/ħE_F .

In case of material processing with long laser pulses the electronic and atomic subsystems are in equilibrium T_e =T_i , and the condition τ_eph <τ_ee or τ≃τ_ph is fulfilled. With ultrashort laser pulses a strong overheating of the electronic subsystem occurs T_e ≫T_i , and τ_eph >τ_ee becomes possible. In this regime the electron relaxation time is determined by the electron-electron collisions τ≃τ_ee ∝^{T -2} _e and the following dependencies of the thermal conductivity k_e ∝$T_e^{-1}$ and of the thermal diffusivity D=k_e/C_e ∝$T_e^{-2}$ are valid. This corresponds to a rapid decrease of the thermal diffusivity and of the electron thermal losses with increasing electron temperature (and laser fluence)[10]. This effect is responsible for the successful application of ultrashort pulse lasers for the processing of metals.

The interaction of ultrashort laser pulses with solids can be characterized by two thresholds: the deformation (damage) $F_{\mathit{\text{th}}}^d$ and ablation $F_{\mathit{\text{th}}}^a$ thresholds. For metals, these thresholds are determined by the laser fluence, i.e. by the amount of absorbed energy per cm². The damage threshold $F_{\mathit{\text{th}}}^d$ corresponds to the onset of melting. Ablation occurs at a larger laser fluence F≥$F_{\mathit{\text{th}}}^a$ >$F_{\mathit{\text{th}}}^d$ . For ablation the absorbed laser energy should exceed the kinetic energy of the removed material which can be roughly estimated by $F_{\mathit{\text{th}}}^a$ ~ρ ₀ ${\delta c}_0^2$/2, where ρ ₀ is the solid density, c ₀ is the speed of sound, and δ is the skin depth. Using typical values for metals ρ ₀~10 g/cm³, c ₀~5×10⁵ cm/s, and δ~10 nm, we get $F_{\mathit{\text{th}}}^a$ ~100 mJ/cm².

Close to the ablation threshold, the ablation depth per pulse is determined by L≃δ ln(${F\mathit{/}F}_{\mathit{\text{th}}}^a$ ). Considering the ablation depth per unit laser fluence L/F, one can define an optimum ablation regime by F=F^opt =${\mathit{\text{eF}}}_{\mathit{\text{th}}}^a$ , where e=2.718.

As is demonstrated below, the damage and ablation thresholds depend on the number of pulses which are used to produce a certain structure. Successive laser pulses lead to a growth of the number of laser-induced defects due to multiple heating and cooling processes (local melting and recrystallization). Dependencies of the damage and ablation thresholds on the number of laser pulses can be described by $F_{\mathit{\text{th}}}^{d\mathit{,}a}$ =F_d,a (1/N, τ_p )≃F_d,a (0, τ_p )+F′_d,a(0, τ_p )/N, where F_d,a (0, τ_p ) are the true ultimate damage (melting) and ablation thresholds for an infinite number of pulses, τ_p is the pulse duration, and F′_d,a(0, τ_p )=lim_N→∞[∂F_d,a/∂(1/N)]>0 are material-dependent constants.

Analogous effects for transparent materials have been observed in [11]. They have shown that during multiple laser irradiation of transparent materials the surface damage threshold drops dramatically due to “incubation effects”, i.e. growing density of color centers.

3 Microstructuring of metals

In this section, results on the fabrication of sub-diffraction limited structures in 100–200 nm chrome-coated surfaces are reported. For the experiments, we used the principle setup shown in Fig. 3. 120-fs laser pulses at a wavelength of 780 nm and a repetition rate of 1 kHz (provided by a Spectra-Physics Spitfire laser system) are tightly focused with a 100× microscope objective. The microscope objective has a numerical aperture of 0.75 and a 1.65 mm focal length.

 

Fig. 3. Schematic setup used for sub-diffraction limited microstructuring.

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Fig. 4. SEM photographs of damage (left) and a sub-micrometer hole (right) produced after 1,000 laser shots with a pulse energy of 2.5 nJ and 3 nJ, respectively. Schematic distributions of the laser fluence and corresponding melting and ablation thresholds are shown below.

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In Fig. 4 a SEM photograph of a bubble-like surface damage, which appears after 1000 laser shots with a pulse energy of 2.5 nJ, is shown (left picture). At this energy level, no surface modification has been observed for smaller numbers of pulses. Between the laser pulses the material in the irradiated area is not able to relax to the initial state completely. Local defects and small temperature changes are accumulated with the increasing number of pulses. This manifests itself as a volume-increased bubble-like surface damage. In this case the laser pulse fluence is in between the ultimate damage (melting) and ablation thresholds (as shown in the schematic picture below the SEM photograph). When the pulse energy is increased to 3 nJ, after 1000 laser shots a small sub-micrometer hole appears at the beam center (right picture). In this case the peak laser fluence is slightly above the ablation threshold. Around the hole a doughnut-like deformation of the chrome surface can be observed.

 

Fig. 5. SEM photographs of holes produced with different pulse energies after 1,000 shots.

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When the laser pulse energy grows, the size of the hole and of the doughnut structure increases (see Fig. 5). The exact values of the damage and ablation thresholds depend on the surface quality, the metal layer thickness, and the number of pulses.

 

Fig. 6. Structures produced with 5-nJ laser pulses and different numbers of shots.

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For microfabrication purposes it is advantageous to use only a few laser pulses to produce a certain structure (to reduce processing time). This can be realized by applying slightly higher laser-pulse energies. In Fig. 6 SEM photographs of holes produced with 5 nJ laser pulses are shown. As can be seen, results similar to that shown in Fig. 4 can be reached already after 2 (damage) and 10 (hole) laser pulses.

One can produce sub-diffraction limited holes also with one or two laser pulses. This is illustrated in Fig. 7. As can be seen, for two laser pulses the optimum pulse energy is around 6 nJ. The size of the produced hole rapidly grows with laser energy.

 

Fig. 7. Microstructures produced with two laser pulses.

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In conclusion, with tightly focused Gaussian pulses sub-diffraction limited microstructuring of thin metal films and metal coatings is possible. Unfortunately, due to the intensity distribution in the focus, surface deformations at the edge of the produced structures occur. These deformations play a crucial role and can limit possible applications of this technique for the repair of photolithographic masks. How these deformations can be avoided is currently under investigation.

4 Microfabrication of optical waveguides in transparent materials

Recently, it has been demonstrated that by tightly focusing ultrashort laser pulses in the bulk of various glasses optical waveguides can be fabricated [12, 13]. In this case nonlinear absorption of laser radiation and eventually optical breackdown occur inside the material (not at the surface). The damage left in the irradiated region after the laser pulse is responsible for an observed increase of the refractive index. This increase occurs due to the formation of color centers and thermo-mechanical stresses.

Here, we present preliminary results on investigations of waveguide structures produced in crystalline quartz. For the microfabrication of these waveguides, we used an achromatic lens with a 40 mm focal length and laser pulse energies of the order of a few µJ. The pulse duration was 120 fs and the repetition rate 1 kHz. A schematic setup is shown in Fig. 8. The sample has been moved perpendicular to the beam direction with a constant velocity of 0.5 mm/s.

 

Fig. 8. Schematic setup used for the microfabricaton of optical waveguides in transparent media.

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Due to the induced stresses the generated waveguides can be best seen using a polarization contrast optical microscope. Two polarization contrast microscope images of optical waveguides produced in crystalline quartz are shown in Fig. 9. The left image shows a top view of several parallel waveguides and the right image the magnified cross section (end view) of one of these waveguides.

The image of the end view (Fig. 9, right) shows details of the generated modifications inside the material. The dark area corresponds to the laser beam focus. The bright areas correspond to the induced stress. The observed refractive index change of Δn~10^-2 is deduced from interferometric analysis of the waveguiding structures. These waveguide structures are stable up to temperatures as high as 1500 K (for more than one hour).

We observed polarization dependent waveguiding of different modes for 514-nm radiation in 10 mm long structures. Fig. 10 shows two different near-field distributions of the light guided in these structures.

The possibility to produce polarization maintaining waveguides and the demonstrated high refractive index changes open many interesting applications in integrated optics (e.g. fabrication of 3-dimensional optical elements).

 

Fig. 9. Top view polarization contrast microscope image (left) of waveguides produced in crystalline quartz (spacing between the waveguides is 0.5 mm). In the right picture a cross section of one of the waveguides (polarization contrast microscope image) is shown.

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Fig. 10. Near-field distributions of guided radiation at 514 nm. Different modes are guided.

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5 Conclusion

The physics of fs-laser ablation of solids has been discussed. Possibilities to fabricate sub-diffraction limited structures in thin metal films and bulk dielectric materials using tightly focused Gaussian pulses have been investigated. Reduction of the damage and ablation thresholds with increasing number of pulses has been observed. This effect is very important for sub-diffraction limited microstructuring of thin metal films and bulk dielectric materials.

With the laser beam focused inside crystalline quartz, polarization maintaining optical waveguides have been written. Relatively high (Δn~10^-2) and temperature stable (up to 1500 K) refractive index changes have been achieved.