1. Introduction

In the last two decades, material processing with ultrashort pulse lasers (with pulse durations in the pico- and femtosecond range) has become increasingly important. Compared to short pulse lasers (in the nanosecond range), ultrashort pulse lasers allow very precise and efficient material removal [1–3]. Application examples are the micro processing of bulk material surfaces [4,5] and the selective structuring of thin films [6–8]. Thereby, the laser pulse acts as ultrafast heat source inducing phase changes and mechanical stress in the material. For a deeper understanding of the laser-matter-interaction, knowledge of the time-resolved full optical complex dielectric function ε, which can be expressed as complex refractive index N = n-ik [9], on an ultrafast time scale is inevitably necessary. The imaginary part k of the complex refractive index gives additional information about the optical absorption in the material. In many cases the pulse absorption can be described by Beer’s law including the optical absorption coefficient α_abs calculable by the imaginary part k (section 3.3). The corresponding optical penetration depth d gives the depth value at which the intensity of the radiation inside the material decays to 1/e (about 37%) of its original value at the surface. The ultrafast time-resolved absorption coefficient is the crucial optical parameter to understand the absorption of the laser pulse during the pulse irradiation or to understand subsequent physical mechanisms for longer times after the laser excitation.

Knowledge of the transient α_abs during the pulse irradiation can reveal origins for the pulse duration dependent ablation efficiency of metals [10–15] and dielectrics [16]. The temporal evolution of α_abs to later times can resolve the absorption behavior of subsequent pulses during double-pulse [17,18], pulse bursts [19,20], temporally shaped pulses [21,22] or high repetition rate material processing [23–25]. Additionally, measurements of the full complex refractive index could improve the understanding of ultrafast phase transitions occurring in the first tens of picoseconds after the pulse impact [26,27].

Despite these multiple fields of application, ultrafast measurements of optical properties in highly absorbing materials like metals have mostly been limited to the measurement of laser induced reflectivity changes. In transparent materials like dielectrics transient transmission measurements allow the generation of additional information about the absorption behavior [28,29]. For metallic substrates such measurements are only possible for very thin films of typically a few tens of nm, where the film thickness lies in the range of the absorption length [30]. Reflectivity measurements were performed for a wide range of metals [31–35]. However, the complex refractive index and in conclusion the optical penetration depth is not directly calculable from the reflectivity. To obtain that data, ellipsometric measurements are necessary.

Such measurements without using ultrashort laser pulses have been performed on laser irradiated silicon and germanium [36], on TlInSe₂ [37] as well as on silver and gold [38]. In these cases, a continuous wave laser was used as pump source and in consequence ultrafast phenomena could not be observed.

Other pump-probe ellipsometric studies focused on ultrafast effects but far below the threshold fluence for irreversible material changes or even ablation. For example, the plasma density in germanium was investigated at a fluence of 10 mJ/cm² [39], the relative refractive index change in gold at a fluence of 0.047 mJ/cm² [40] and the evolution of the dielectric tensor in CrO₂ was investigated at maximum fluences of 20 mJ/cm² [41]. These measurements were performed on a fixed position on the sample and by averaging a large number of reflected probe pulses (10 – 1000). If measurements close to or above the ablation threshold fluence are carried out this measurement mode is not applicable, because the sample has to be moved to an untreated position from pulse to pulse. Averaging over a large number of pulses is hardly practicable because it is directly associated to the measurement duration and to the needed area on the sample.

There have been further approaches to collect ellipsometric data or data about dielectric function changes above ablation threshold fluences with sub-ps temporal resolution. In this case irreversible incubation effects or ablation prohibit multi-pulse experiments on a fixed sample position and demand single pulse experiments: A dual-angle reflectometry setup was used to detect the dielectric function dynamics in laser excited GaAs [42] and ZnO [43]. An interferometric approach, also using two incident probe-angles, was used to investigate shock waves in polycarbonate [44] and ablation dynamics of thin Ti films [45]. A 4-detector setup was used to measure the velocity of laser generated gold vapor [46] and the plasma expansion in bismuth [47]. Different probe angles or several detectors require complex adjustment leading to unneeded sources of errors compared to true ellipsometric techniques [42]. To our knowledge, the transient complex refractive index of laser irradiated materials was not determined by the previous alternative techniques.

Summarizing state of the art, the transient complex refractive index change initiated by ultrashort laser pulses has not been measured by ellipsometric techniques on an ultrafast time scale at fluences relevant for material processing. A simple and straightforward ellipsometry setup that directly determines time-resolved absolute values of the real and imaginary part of the complex refractive index is still missing.

By combining the advantages of the above described methods a simple and straightforward ellipsometry setup is presented in this paper that directly determines time-resolved absolute values of the imaginary and real part of the complex refractive during material processing on an ultrafast timescale:

Firstly, a sub-ps temporal resolution for the observation of ultrafast phenomena is achieved by utilizing an ultrafast laser source matching today’s common pulse durations of about 500 fs and wavelengths of 1056 nm and 528 nm used for material processing on an industrial scale (section 2.4).

Secondly, time-resolved measurements close to or above the ablation threshold fluence (in the order of 1 J/cm²) are feasible. In pump-probe mode, fully ellipsometric measurements are carried out for every delay time. For this, single pump pulses are placed on a new and unprocessed position on the sample for every measurement step (section 3.1). Detailed information on the required measurement procedure and data processing is given in section 2 and 3.

Thirdly, a minimum of optical components, detectors and beam paths is used to keep the measurement setup as simple and robust as possible (section 2.4).

First pump-probe ellipsometric (PPE) measurements were performed on molybdenum. Pump pulses at two different industrially important wavelengths λ (fundamental infrared wavelength λ_IR = 1056 nm and second harmonic green wavelength λ_green = 528 nm) were applied. Infrared pump pulses allow the spectral separation from the green (λ = 528 nm) probe pulse enabling measurements with highly suppressed scattered pump light. The infrared excited PPE measurements are necessary for a comparison with the results of a two color pump-probe microscope (PPM) in section 3.2 to perform a consistency check between PPE and PPM with comparable parameters. In contrast, green pump and probe pulses (single color PPE) enable a proper investigation of laser ablation or processing because the influence of a laser pulse on reflectivity and absorption at the same wavelength is studied, e.g. pulse duration dependent ablation efficiency. It has to be emphasized that the probe wavelength stayed constant for both pump pulse wavelengths. Furthermore, if metals are investigated the pump pulse can be regarded as ultrafast heat source in first order approximation. Only the time integrated reflectivity R_IR and R_green of the pump pulse is defining the amount of absorbed energy for both wavelengths (for molybdenum R_IR = 67% and R_green = 59% [48]). If identical amounts of energy are absorbed in the material, the transient PPE signal is also expected to show the same behavior – independent of the pump wavelength.

The accuracy of the ellipsometry setup in steady-state as well as in pump-probe mode is demonstrated in section 2.6 and 3.2. Measurements on molybdenum below and above the ablation threshold fluence show the evolution of the complex refractive index and the optical penetration depth during and after the impact of the pump pulse for the first time to our knowledge (section 3.1 and 3.3).

2. Materials and methods

2.1. Sample description and determination of threshold energetics

Experiments were performed on two different material systems – SiO₂ coated Si samples served as layer system for steady-state measurements and the transition metal molybdenum (Mo) was investigated in the actual time-resolved ellipsometric measurements. For the reference samples, mono crystalline Czochralski-grown wafers (p-doped, (111) crystal orientation) were coated with thermally grown SiO₂ films. The layer thickness of the SiO₂ films varied from 100 nm to 500 nm in 100 nm steps for different samples. This material system can be described nearly ideally by optical material data for Si and SiO₂ available in literature. Therefore, SiO₂ films on Si could be used as reference thin film system to check the accuracy of the presented ellipsometric pump-probe setup in steady-state-mode (section 2.6).

For the actual time-resolved ellipsometric measurements, sputtered molybdenum (Mo) films with a thickness of 430 nm were used. At the applied pump pulse wavelengths of 1056 nm and 528 nm the optical penetration depth of Mo is 19 nm and 11 nm, respectively, the thermal penetration depth is 11 nm [48–50]. The layer thickness d is large compared to the optical penetration depth of Mo. In consequence, the film can be considered as thick substrate.

Investigations below and above the ablation threshold fluence F_thr of the Mo sample were performed. F_thr was determined by a common method described in [51] by Liu expressed by the following formula:

 

Fig. 1 Semi logarithmic plot of the squared ablation diameter D² over the applied pulse peak fluence F₀ for the determination of the ablation threshold fluence F_thr of molybdenum for infrared (λ_IR = 1056 nm) and green (λ_green = 528 nm) pulses. The fitting function is shown in the inlay. Microscopic images show the material modification at fluences under (≈0.3 J/cm²) respectively above (≈0.8 J/cm²) the ablation threshold fluence.

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2.2. Ellipsometric measurement principle

Ellipsometric measurements are based on the analyses of the polarization state of light reflected from a sample surface. For this, the sample is illuminated at a defined incident angle and at a known polarization angle. After the reflection, the state of polarization is changed. From this change, the optical properties of the illuminated material can be derived.

In this work, the rotating analyzer mode was applied as ellipsometric operation mode [55]. The advantage is a relatively simple setup due to a minimum of optical components and the absence of chromatic optics compared with operation modes including compensators [56]. A disadvantage of the rotating analyzer mode is given by the fact, that measurement errors increase at phase differences close to Δ = 0° or 180°. Possible consequences to the here presented investigations are explained in section 3.1. For a rotating analyzer measurement, light is incident to the sample at an angle θ which is chosen close to the Brewster angle (typically ≈70°) for maximizing polarization effects. The incident light is linearly polarized by a polarizing optical element (“polarizer”). The polarization angle φ is usually set to 45° with respect to the incident plane. Thus, identical parts of s- and p-polarized light (perpendicular and parallel to the plane of incidence) are incident on the sample. The reflection behavior of both parts is determined by the complex reflection coefficients r_s and r_p of the sample. Typically, the reflected light is elliptically polarized. In rotating analyzer operation mode, the state of polarization of the reflected light is analyzed by a rotating polarizing optical element (“analyzer”). For this, the analyzer is stepwise rotated and the transmitted intensity I is detected in dependency on the analyzer angle ϕ. The intensity distribution versus the analyzer angle can be fitted by Eq. (2) which describes a harmonic function with a 180° periodicity:

2.3. Ultrafast pump-probe measurement principle

The pump-probe technique offers the possibility to temporally resolve and to investigate ultrafast processes occurring on a femtosecond to nanosecond timescale [58,59]. For this, two ultrashort laser pulses are applied – a pump pulse and a probe pulse. The intense pump pulse initiates a reaction lasting typically much longer than the ultrashort pulse itself [32]. The weak probe pulse, usually a split or transformed part of the pump pulse, illuminates the sample and is then detected by a photodiode or a CCD camera. It has to be emphasized that the temporal resolution of the pump-probe measurement is independent of the averaging time of the photodiode or CCD camera. The temporal resolution is defined by the pulse duration of the probe pulse [60]. Thus, measurements with sub-picosecond resolution are possible, even if detectors with exposure times in the microsecond time range are used [61].

To analyze the temporal reaction process, the probe pulse is stepwise delayed with respect to the pump pulse over the reaction time interval. The delay can be realized for example by an optical delay line [62]. Data points are generated at different delay times Δt and can be combined to a measurement series representing the entire reaction process, provided that the optical delay is long enough. A requirement for the combination is that every single measurement is performed under identical conditions. Every pump pulse has to induce an identical reaction and every probe pulse has to provide an identical illumination. When working above ablation threshold, the processed spot shows an irreversible change from the preceding pump pulse, thus the sample has to be moved between single measurements and has to be homogeneous over the investigated area.

The setup presented in this paper combines the possibility of above threshold fluence measurements with sub-picosecond temporal resolution. Additionally, the ellipsometric data acquisition technique explained in section 2.2 was implemented.

2.4. Pump-probe ellipsometry (PPE) setup

An overview of the experimental PPE setup is shown in Fig. 2. Laser pulses at a center wavelength of λ_IR = 1056 nm with a pulse duration of τ_p,IR = 680 fs (FWHM) emitted by a Nd:glass laser source are divided into pump and probe pulses by a polarizing beam splitter (ratio of 90% to 10%). An optional second harmonic generation module on the pump path allows the green conversion of the pump pulse to λ_green = 528 nm with a pulse duration τ_p,green = 540 fs). The respective wavelength is filtered by subsequent dielectric mirrors reflecting only the applied wavelength. A mechanical shutter (VincentAssociates^® Uniblitz LS6, total opening time 2.3 ms; pulse delay Δt_pulse from pulse n-1 to pulse n + 1 Δt_pulse = 4 ms at laser repetition rate f_rep = 500 Hz) in the pump path separates a single pump pulse, used for initiating the ablation. The pump pulse is focused with a f = 100 mm lens on the sample (Gaussian beam radius = 30 ± 0.5 µm at e⁻² intensity measured as described in section 2.1).

 

Fig. 2 Pump-probe ellipsometry (PPE) setup: laser pulses (τ = 680 fs, λ = 1056 nm) are divided into pump and probe pulses. The pump pulse adjustable in wavelength (λ_IR = 1056 nm or λ_green = 528 nm) is focused at the sample and initiates the reaction. The probe pulse is frequency doubled (SHG) for illumination. It is coupled in the ellipsometric branch of the setup (incident angle θ = 70°). The polarization of the probe beam on the sample is adjusted by the polarizer (φ = 45°); the polarization of the reflected probe light is analyzed by the analyzer. The locally distributed reflected intensity is detected by a CCD-camera. To temporally delay the pump against the probe pulse a delay line (Δt ≤ 300 ps) is used.

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The probe pulse is frequency doubled (SHG) (probe pulse: λ = 528 nm, τ = 540 fs (FWHM) measured by an APE PulseCheck autocorrelator) and weakly focused by a f = 1000 mm lens for illuminating an area of about 700 µm in diameter on the sample (measured by a Coherent LaserCam-HR^TM). The probe pulse is coupled into the ellipsometric branch of the setup. The incident angle is fixed at θ = 70° (see section 2.2). The linear polarization angle φ of the probe pulse on the sample is adjusted by a Glan-Laser-Prism (“polarizer”) (extinction ratio 10⁶:1) to φ = 45° with respect to the incident plane. The process area is imaged by a 20x magnification stress-free and thus polarization maintaining microscope objective with numerical aperture NA = 0.42 (optical resolution = 0.61 λ/NA = 0.8 µm). Polarization changes that might originate from tilted angle incident beams due to the relatively high NA were analyzed by performing ellipsometric measurements with reduced NA. By mounting a variable iris in front of the objective the NA could be reduced from NA = 0.42 to 0.15. The obtained ellipsometric angles ψ and Δ describing the state of polarization were independent of the adjusted NA over the investigated range. A further validation of the polarization conservation in the objective is given by the fact that measurements without pump pulse on reference samples show a good agreement with measurements by a commercial ellipsometer and with literature (section 2.6). Therefore polarization effects originating from the high NA can be excluded. The polarization of the reflected probe pulse after transmission through the objective is analyzed by a rotatable thin film polarizer (“analyzer”) (extinction ratio 2·10⁶:1). A band-pass filter (530 ± 10 nm) in front of the CCD detector (pco. Pixelfly USB) blocks ambient light and plasma emission or scattered pump light from the sample when 1056 nm pump pulses are applied (see section 3.1). Noise of scattered pump light is also reduced by the relative angle of 70° between incident pump and probe pulses – also in the case of 528 nm pump pulses. The CCD camera (pixel size = 6.45x6.45 µm²) is triggered to the laser frequency and the camera exposure time is set to 2 µs which leads to the detection of a single probe pulse. The implementation of only one probe path and one detector into the setup allows keeping the measurement setup as simple and robust as possible. Additionally, the necessity of calibrating different probe paths or detectors against each other is avoided.

To optically delay the pump against the probe pulse, the pump pulse is guided over a variable linear translation stage (Δt ≤ 300 ps). The delay time zero is defined as the point in time when the overlap of pump and probe pulse are maximal. It is measured by an ultrafast reflectivity increase on a Si sample. The increase is caused by the excitation of electrons and is assumed to occur instantaneously with the incident pump pulse compared with the temporal resolution of the setup [26]. The maximum overlap of pump and probe pulse is reached when the reflectivity increase reaches 50% of its maximum value. The uncertainty of the determination is estimated to be ± 200 fs. The uncertainty due to the exchange of samples is negligible (<50 fs).

To take a series of images covering the whole ablation process, the sample is irradiated by a new single pump-probe-pulse combination at a new position for every delay time Δt and for every analyzer angle ϕ.

2.5. Data post processing

Every image in a PPE measurement series has to be post processed because of two reasons. Firstly, every image contains background signals as for example ambient light, noise of the CCD camera or radiation of the heated sample. Secondly, illumination fluctuations due to pulse to pulse fluctuations on the probe path can be compensated. Hence, two additional measurement series are carried out in addition to the actual PPE measurement to correct these influences.

At first, a series is recorded only with pump pulse where the probe pulse is blocked. Images for every analyzer angle are recorded. The set delay time is irrelevant because the probe pulse is blocked. The images of this series contain only the background signal. In a first post processing step, from every PPE image (Fig. 3(a)) the background image at the corresponding analyzer angle (Fig. 3(b)) is subtracted. The resulting image (Fig. 3(c)) is then corrected from background signals and contains background free information about the reflected probe pulse.

 

Fig. 3 Data post processing procedure for PPE measurements: 1. Step: a background image (b) recorded without probe pulse is subtracted from the raw PPE image (a) to eliminate background signals – image (c) is obtained; 2. Step: illumination fluctuations are compensated by calculating the mean gray scale values (MGSV) of an unprocessed area on the PPE image (blue area image (c), with an exemplary MGSV of 23493) and the MGSV of the corresponding area on an averaged reference image without pump pulse (blue area image (d), with an exemplary MGSV of 23285). The PPE image (c) is normalized by multiplying it with the quotient of the two MGSV – the final image (e) is obtained. For further transient ellipsometric analyses an area of 12x4 pixels in the center of the laser irradiated spot is chosen (green rectangle in image (f)).

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Secondly, a steady-state-series (see section 2.6) is recorded without pump pulse whereas 30 images are averaged for every analyzer angle (Fig. 3(d)). This series is taken as reference with the aim of compensating for example pulse to pulse fluctuations. In a second processingstep, the mean gray scale value (MGSV) of an unprocessed area on the PPE image is determined (Fig. 3(c), blue area). The MGSV of the same area of the reference measurement series is also determined (Fig. 3(d), blue area). The PPE image is than multiplied by the quotient of the two MGSVs for normalizing the gray scale values of the complete image. By this, probe pulse fluctuations are compensated and the final image is obtained (Fig. 3(e)).

For further transient ellipsometric analyses, only the center of the laser irradiated spot is considered where the fluence of the applied Gaussian shaped pump pulse profile can be assumed as constant. An area of 12x4 pixels is chosen (green rectangle in Fig. 3(f)). The asymmetric aspect ratio is caused by the tilted observation angle of θ = 70°. The pixel field corresponds to an area of 4x4 µm² on the sample.

2.6. Validation of ellipsometric results in steady-state-mode

Ellipsometric measurements in steady-state-mode were performed to test the accuracy of the ellipsometric part of the setup. The SiO₂/Si and Mo samples described in section 2.1 were investigated. In steady-state-mode the shutter in the pump branch (see Fig. 2) stays closed during the measurement. Thus, the sample is illuminated only by the probe pulse – no irreversible material modification is induced. The optical properties of the unprocessed material were determined. Ellipsometric angles ψ and Δ were obtained by data processing according to section 2.2. Besides the blocked pump path the same measurement parameters as in the pump-probe investigations were applied (5 analyzer positions, no averaging, pixel area 12x4, see section 3.1). The results are compared in Fig. 4 to values measured by a commercial available spectroscopic ellipsometer (Ocean Optics “SpecEl-2000”, absolute accuracy ψ ± 1.3° and Δ ± 0.8° based on NIST-traceable 100 nm SiO₂ layer on Si) and to literature values [48]. In both cases values at the probe wavelength of 528 nm were obtained and used for comparison.

 

Fig. 4 Ellipsometric angles ψ and Δ determined by the PPE setup in steady-state-measurement-mode (without pump-pulse) (“experiment”, blue bar), by the commercial ellipsometer Ocean Optics “SpecEl-2000” (“commercial elli.”, light blue bar) and taken from literature [48,49,63] (“calculated/literature”, gray bar) are compared for showing the accuracy of the built setup. SiO₂ films with different thicknesses on a Si substrate as well as a Mo sample were investigated. All values (experimental/commercial elli./literature) were obtained by measurements at λ = 528 nm.

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Deviations between experimental and commercial setup are <1.7° (≙1.9%) for ψ and <3.4° (≙1.9%) for Δ for the SiO₂/Si layer systems and the Mo. Compared to the literature values, the experimental values for the SiO₂/Si layer systems show deviations in the same magnitude (<1.6° for ψ and <2.5° for Δ). The literature values for Mo show slightly larger deviations (1.2° for ψ and 4.3° for Δ). It has to be noted here, that the literature values in reference [48,49,63] where derived from bulk Mo whereas the Mo film for this work was prepared by sputtering. It is well known that the sputtering process can influence the optical properties of Mo and can lead to a variation of optical properties much larger (>10% for ψ and >30% for Δ [63]) than measured in this work. Besides that, values obtained from the steady-state-measurement-mode in the built up experiment show a good agreement withliterature values and values from the commercial setup.

For the following PPE measurements, the Mo sample was used. For this sample, deviations between experimental and commercial setup values amount to 0.01° for ψ and 2.3° for Δ. By calculating the corresponding n and k values (Eq. (8)), the deviation is reproduced to 0.17 for n and 0.10 for k. Related to the absolute values of n and k for Mo (N_Mo = 2.87-i3.61, measured by Ocean Optics “SpecEl-2000”) this denotes a relative error of 5.5% for n and 2.6% for k, respectively. The relation of this absolute error compared to relative fluctuations during the measurement and measured signal changes will be shown in section 3.1.

3. Results

In the following, pump-probe ellipsometric (PPE) measurements are shown at the pump wavelengths λ_IR and λ_green. In section 3.1, the transient complex refractive index change in laser irradiated Mo is measured. The obtained results (n, k) at the pump wavelength λ_IR are converted into relative reflectivity changes (ΔR/R) to enable a comparison with ΔR/R measurements performed on a conventional pump-probe microscope (PPM) also working with infrared pump pulses (section 3.2). This comparison shall prove the consistence between transient measurements of n and k and ΔR/R. Finally, the transient optical penetration depth is calculated by the measured k values in section 3.3.

3.1. Transient complex refractive index determination in laser irradiated molybdenum

In this section, the functionality of the before described ellipsometric setup is demonstrated in pump-probe mode. Complete pump-probe ellipsometric test measurements are demonstrated on Mo. The transient complex refractive index change in Mo is determined for laser fluences below and above the ablation threshold fluence F_thr. For infrared pump pulses at λ_IR = 1056 nm the fluences were chosen to be F₀ = 0.3 J/cm² and F₀ = 0.8 J/cm², respectively (F_thr,IR = 0.42 J/cm², see section 2.1). For green pump pulses at λ_green = 528 nm the fluences were chosen to be F₀ = 0.29 J/cm² and F₀ = 0.85 J/cm², respectively (F_thr,green = 0.38 J/cm²). The entire data acquisition and processing procedure is shown using the measurement series at λ_IR and the fluence of F₀ = 0.8 J/cm² as example.

In Fig. 5, raw images of the CCD detector from the Mo film at λ_IR = 1056 nm and F₀ = 0.8 J/cm² are presented. For recording an image, the sample is moved to an unprocessed position, the delay line is adjusted to the desired delay time, the analyzer angle is set and the sample is illuminated by a single pump and probe pulse combination. This process is repeated for every image. In the first row images for different delay times – indicated in the left upper corner of every image – at a constant analyzer angle of ϕ = 0° are arranged. The laser processed spot becomes visible in the center of the 0 ps image as an elliptical weak bright spot. The ellipticity is caused by the tilted observation angle of 70° against the surface normal.

 

Fig. 5 Data acquisition for a pump-probe ellipsometric measurement. Images show a Mo sample irradiated by a F₀ = 0.8 J/cm², τ = 680 fs, λ_IR = 1056 nm pump pulse and a τ = 540 fs, λ = 528 nm probe pulse. In the first row, the delay time Δt is varied at a fixed analyzer angle ϕ = 0°. The second row shows images at a fixed delay time of Δt = 80 ps for different analyzer angles. The defocused spot at the bottom of every image results from previous measurements where different delay times or analyzer angles were investigated.

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In the following, the reflectivity in the spot center decreases. A dark central area is visible on the 10 ps image. This area is expanded on the 80 ps image. The final state shows the ablation crater. A quantitative reflectivity analysis and an explanation of the reflection behavior will be given in section 3.2. Additionally to the images at ϕ = 0° four further images are recorded for every delay time in angle steps of 36°. Thus the range between 0° and 180° is covered by five equidistant angles. Corresponding images at different analyzer angles are shown for the delay time of Δt = 80 ps in Fig. 5 second row. The defocused spot at the bottom of every image results from previous measurements where different delay times or analyzer angles were investigated.

For calculating the ellipsometric angles ψ and Δ, the mean gray scale value of the central pixel area described in section 2.5 is evaluated over the analyzer angle ϕ. Examples for different delay times Δt are plotted in Fig. 6. Due to the elliptical polarization of the analyzedlight, the plots describe harmonic curves with different amplitudes, offsets and phases. The plots can be fitted by Eq. (2).

 

Fig. 6 Transmitted intensity to the CCD detector in dependency on the analyzer angle ϕ for different delay times (−10 ps to 80 ps). Data are obtained by evaluating the reflected light by a Mo sample irradiated by a F₀ = 0.8 J/cm², τ = 680 fs, λ_IR = 1056 nm pump pulse and a τ = 540 fs, λ = 528 nm probe pulse. For reasons of a clearer visualization, 18 analyzer positions are plotted whereas actual measurements are performed with only 5 analyzer positions.

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The obtained α and β values were converted into the ellipsometric angles ψ and Δ by applying Eqs. (3) and (4). The results for the higher fluence of 0.8 J/cm² are presented in Fig. 7. The amplitude ratio ψ shows a slight increase from ψ = 30° to 31° at the delay time zero until it decreases again to its initial value after about 20 ps. After 50 ps, ψ increases again and reaches values of ψ = 40° at Δt = 100 ps. The phase difference Δ describes a continuous decrease starting at the delay time zero at a value of Δ = 130°. At 5 ps, Δ has a value of 100° and at 100 ps a value of 25°. Heating and phase changes are described in literature to occur in the first 10 to 50 ps [27,53,64]. It can be concluded that the heating of the electrons and the lattice as well as phase transitions are mainly influencing the phase of the reflected probe pulse Δ and less the amplitude ratio ψ. Values for delay times higher than 100 ps could not be calculated for the fluence of 0.8 J/cm². From this time on the reflectivity of the sample is too low to obtain proper ellipsometric signals (section 3.2). The low signal level combined with possible reflection fluctuations at a created gas-liquid mixture surface (see section 3.1) lead to invalid Δ values (Eq. (4): β/(1-α²)^0.5 > 1). A further reason for the invalid Δ values can be found in increased measurement errors of the used rotating analyzer mode at phase differences close to 0° or 180° (section 2.2).

 

Fig. 7 Ellipsometric angles Psi ψ and Delta Δ in dependency on the delay time Δt. Data were obtained by evaluating the reflected light from a Mo film sample irradiated by a F₀ = 0.8 J/cm², τ = 680 fs, λ_IR = 1056 nm pump pulse and a τ = 540 fs, λ = 528 nm probe pulse.

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The ellipsometric angles ψ and Δ were converted into the transient complex refractive index by applying Eq. (8). Results are presented in Fig. 8. The data for the above threshold fluence of 0.8 J/cm² at the infrared pump wavelength described so far are shown on the right. Additionally, a measurement series at a fluence below the ablation threshold fluence at F₀ = 0.3 J/cm² is shown on the left. Analog measurements at the green pump wavelength are added at the fluences of F₀ = 0.29 J/cm² < F_thr and F₀ = 0.85 J/cm² > F_thr. Two additional values are indicated. Firstly, reference values measured by the Ocean Optics “SpecEl-2000” ellipsometer are plotted (Fig. 8 n reference = 2.9 (purple triangle); k reference = 3.6 (turquois circle)). Secondly, complex refractive indices measured with the PPE setup at the final ablation state after around 3 s are marked (Fig. 8 n final = 3.0 (green rectangle); k final = 3.3 (blue triangle)).

 

Fig. 8 Transient complex refractive index N = n-ik of laser irradiated Mo. The Mo sample is irradiated either by an infrared (τ_IR = 680 fs, λ_IR = 1056 nm) or a green (τ_green = 540 fs, λ_green = 528 nm) pump pulse. Left: applied fluence F₀ < F_thr (infrared: F₀ = 0.3 J/cm²; green: F₀ = 0.29 J/cm²); Right: applied fluence F₀ > F_thr (infrared: F₀ = 0.8 J/cm²; green: F₀ = 0.85 J/cm²). Probe pulse parameters are τ = 540 fs, λ = 528 nm. Reference values (“reference”) obtained by an Ocean Optics “SpecEl-2000” ellipsometer are indicated to the left of the transients (n reference = 2.9 (purple triangle); k reference = 3.6 (turquois circle)); values of the final state after about 3 s (“final”) to the right (n final = 3.0 (green rectangle); k final = 3.3 (blue triangle)). The gray shaded area marks the delay time region where a phase explosion should occur. Under this condition, calculating the complex refractive index by Eq. (8) may not be valid. Values in the shaded area have to be considered under reserve.

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For the infrared pump wavelength and the fluence of F₀ = 0.3 J/cm² (< F_thr), n decreases in the first 5 ps after delay time zero from the initial value of 3.0 to 2.0 and stays on this leveluntil about 40 ps. To later delay times n increases and reaches values of about 2.7 between 100 ps and 300 ps. The n value in the final state n_final = 3.0 is identical to the initial n value. The imaginary part k describes a temporary increase from its initial value of 3.7 to 3.9 at delay time zero and decreases afterwards to 3.4 at 5 ps delay time. k recovers to a value of 3.8 for delay times between 50 and 300 ps. The final k value of 3.3 is slightly lower than the initial value. Thus, even if no ablation is observed, the optical material properties are irreversibly influenced by the pump pulse irradiation, which could be due to surface changes because of melting or oxidation. In general n and k show a similar temporal behavior with the recovery to initial values between 5 and 300 ps delay time. From 100 ps to 300 ps the values seem to decrease slightly.

For the green pump wavelength and the fluence of F₀ = 0.29 J/cm² (< F_thr), measured n and k values show a nearly identical behavior compared to the values obtained with the infrared pump pulse. As expected, the initial values at negative delay times are identical for both pump wavelengths (n = 3.0 and k = 3.7) and agree well with the steady-state values (Fig. 8 n reference = 2.9 (purple triangle); k reference = 3.6 (turquois circle)). It has to be emphasized again that the probe wavelength stayed constant for both pump pulse wavelengths. Thus, initial ellipsometric values (n, k) in the PPE measurements had to be identical regardless of the applied pump wavelengths. The fact that scattered pump light is not eliminated completely by the band-pass filter or the by the relative angle between pump and probe pulses becomes evident by the increased fluctuations within the measurement series and by possible coherent phenomena of probe light and scattered pump light around delay time zero. These effects and deviations at longer delay times of >100 ps have to be further analyzed to explore their physical origins and to investigate if physical processes differ at later delay times for different pump wavelengths. Possibly these deviations are however simply due to the slightly different applied fluences.

For the infrared pump wavelength and the fluence of F₀ = 0.8 J/cm² (> F_thr), n describes a steeper decrease compared to the fluence of F₀ = 0.3 J/cm². At 5 ps a value of 1.4 is reached. Afterwards a continuous decline down to 0.5 at 120 ps is observed. The imaginary part k shows also an increase around delay time zero as it was observed for the lower fluence of F₀ = 0.3 J/cm². However, the increase is less pronounced, reaches a value of only 3.8 and seems to be superposed by a stronger negative transient than at the lower fluence. In the following k decreases steeply to k = 2.4 at about 5 ps and less steeply to k = 0.2 after about 120 ps. Ablation is expected to occur in this fluence regime by the creation of an inhomogeneous gas-liquid mixture or a phase explosion [65,66]. The timescale for its onset is between 10 ps and 50 ps [64,67]. From this point in time, the investigated sample can be considered as transient multilayer system consisting of a solid substrate covered by the inhomogeneous gas-liquid mixture layer with an estimated layer thickness of a few tens of nm [60]. With increasing expansion of the layer, its density decreases and the layer becomes transparent. A micro Fabry-Pérot interferometer is created. This could explain the concentric rings – Newton’s rings that were also observed in further laser irradiated materials on this timescale [68,69] – with a central ellipse slightly visible for example in Fig. 5, Δt = 80 ps, ϕ = 72°. Unfortunately, under these conditions and assuming that the layer surface gets an increasingly rough surface at later delay times, calculating the complex refractive index with Eq. (8) may not be valid. The respective area is marked in Fig. 8 as gray shaded rectangle. The final n and k values have to be considered with constrictions, because in the final state an ablated hole is generated preventing a correct ellipsometric analysis.

For the green pump wavelength and the fluence of F₀ = 0.85 J/cm² (> F_thr), measured n and k values show again a similar behavior compared to the values obtained with the infrared pump pulse at F₀ = 0.85 J/cm². Identical initial values, increased fluctuations within the measurement series and deviations at longer delay times can be explained analog to the sub F_thr measurements.

The overall accuracy and the resolution of the pump-probe ellipsometric setup can be assessed by evaluating the average and the standard deviation of the data for negative delay times in Fig. 8. In this time interval, no material change is expected. Ideally the baseline should form a straight line and its level and the reference value should be identical. The difference between reference value and the average of the transient baseline is 0.17 (5.5%) for n and 0.10 (2.6%) for k as mentioned already in section 2.6. This deviation can be understood as a systematic error. The standard deviation of date points before delay time zero is yielding the statistical error and calculates to about 0.07 (2%) for the infrared pump and 0.18 (5%) for the green pump. That means that the minimal relative changes of n and k, that can be detected with the here described setup, lie in the order of 2% and 5% respectively.

3.2. Validation of transient pump-probe ellipsometric measurements

The consistency of the transient PPE measurements can be tested by calculating reflectivity from n and k and comparing the results with earlier relative reflectivity change measurements from a PPM setup [70]. For this, the here determined transient complex refractive index N = n-ik was converted into the reflection R for perpendicular illumination (Eq. (9)).

Base reflectivity R_before values were obtained by averaging data at delay times Δt < 4 ps. Then, relative reflectivity changes ΔR/R were calculated with the equation ΔR/R = (R-R_before)/R_before. These pump-probe ellipsometric data are compared to data measured by the conventional pump-probe microscope at the same fluences in Fig. 9.

 

Fig. 9 Relative reflective change ΔR/R in laser irradiated Mo. Comparison of data obtained by pump-probe ellipsometry (PPE) and conventional pump-probe microscopy (PPM). The Mo sample is irradiated by a τ = 680 fs, λ_IR = 1056 nm pump pulse at F₀ = 0.3 J/cm² (PPE: black rectangles; PPM: green rectangles) respectively F₀ = 0.8 J/cm² (PPE: red triangles; PPM: blue triangles). Probe pulse parameters are τ = 540 fs, λ = 528 nm.

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In general the results show a good agreement between the measurement series. For the lower fluence F₀ = 0.3 J/cm², an increase to ΔR/R = 0.08 around delay time zero is detected for both series. The increase is followed by a decrease to ΔR/R = 0.03 at 5 ps. The relative reflectivity change remains on this level up to delay times of about 100 ps. To higher delay times, it reaches again the zero level. At 0.3 J/cm² the transients display qualitative and quantitative consistency. For F₀ = 0.8 J/cm², an increase to ΔR/R = 0.05 around delay time zero is detected for both series. The increase is followed by a continuous decrease to ΔR/R = −1.0 at 100 ps. In previous work [53,70,71] very similar results were obtained. The most significant correspondence between the data here and the data in literature is a steady and strong decrease of relative reflectivity after delay time zero to a value ΔR/R = −1.0 at 100 ps.

In literature the pump-probe microscopy transients of metals have been interpreted in the following way [53,70,71]: The incident pump pulse photons are absorbed by free electrons in the conduction band that gain higher energy [26]. The initial reflectivity increase is caused by intraband and interband excited electrons [31] and a fast melting process occurring within 2 ps [72]. The energy transfer from hot electrons to the cold lattice is usually described by a two-temperature model [73]. For fluences below the ablation threshold F_thr, the material is heated or melted and cools down or resolidifies on a timescale depending on the applied fluence (tens of ps to ns) [27]. For a fluence above F_thr, the enhanced heating of the lattice results in an expanding gas-liquid-mixture or a phase explosion [32,67]. The reflection decrease between 10 and 300 ps could be explained by increased scattering of the probe pulse in the inhomogeneous gas-liquid-mixture or by the creation of a Fabry-Pérot interferometer causing destructive interference (section 3.1).

A time delay of about 2 ps at earlier (see inset of Fig. 9) and 5 ps to 10 ps at later delay times (see Fig. 9) is detected between both measurement series in this work. E.g. the PPE values reach the ΔR/R zero level at a delay time of 1 ps whereas the PPM values reach the ΔR/R zero level at a delay time of 3 ps (see inlay of Fig. 9). This time delay may origin from slightly different pump pulse fluences. It has been observed previously that the steepness ofthe ΔR/R-decrease varies with the pump pulse fluence. The data here reaches ΔR/R = −0.5 at 35 ps, for higher fluences that value is reached at earlier delay times [71]. This behavior was addressed to an earlier probe light scattering and absorption in an earlier expanding gas-liquid mixture or phase explosion [32]. An error in the determination of the applied fluences coming from uncertainties in the focal radius determination of the applied pulses at the different setups can explain the observed time delay. E.g. an error of +/−1 µm for the beam radius results in an error of +/−0.06 J/cm² for the fluence, which can lead to a temporal shift of the phase-explosion and the observed ΔR/R time delay of 2 ps to 10 ps here. A further explanation of the discrepancy could be found in the fact that for the PPM measurements the pump beam was incident at an angle of about 35° related to the sample surface normal. The pulse was linearly s-polarized. According to Fresnel equations, the absorbed energy of the pump pulse in the PPM experiment was 5% lower than in the PPE experiment.

Besides these minor deviations, the agreement between both curve progressions indicates that the PPE data are consistent with the PPM data.

3.3. Transient optical penetration depth in laser irradiated molybdenum

An important argument for designing the here presented pump-probe ellipsometric setup was the possibility to determine the transient optical penetration depth d, which can be calculated with the help of the before measured complex refractive index k by Eq. (10).

 

Fig. 10 Transient optical penetration depth d in laser irradiated Mo. The Mo sample is irradiated either by an infrared (τ_IR = 680 fs, λ_IR = 1056 nm) or a green (τ_green = 540 fs, λ_green = 528 nm) pump pulse; applied fluences for F₀ < F_thr are: F₀ = 0.3 J/cm² (infrared) and F₀ = 0.29 J/cm² (green); applied fluences for F₀ > F_thr are: F₀ = 0.8 J/cm² (infrared) and F₀ = 0.85 J/cm² (green). Probe pulse parameters: τ = 540 fs, λ = 528 nm. Literature values [48,49] for d at λ = 528 nm are indicated as red circle. The gray shaded area marks the time interval where a gas-liquid-mixture is created or a phase explosion should occur (section 3.1). Under this condition, calculating N by Eq. (8) may not be valid. Values in the shaded area have to be considered under reserve.

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For infrared pump pulses at F₀ = 0.3 J/cm², d decreases from its initial value of 11.4 nm to 10.7 nm at the delay time zero. This denotes a change of d of 6% already during the pump pulse irradiation. In the following d increases to 12.4 nm at 6 ps and remains on that level until delay times of 40 ps. Between 40 ps and 300 ps values ranging from 11.2 nm to 12.4 nm are detected. At early delay times around delay time zero changes in d should be caused by fast electronic processes [26,31]. A smaller value of the penetration depth d around delay time zero generally means that the pulse energy deposition is taking place closer to the surface. The intraband and interband excited electrons may exhibit a slightly higher absorption. To higher delay times the energy is transferred from the electronic system to the lattice [27,73] and the observed increase of penetration depth may simply be a consequence of thermal expansion and the lower density of the heated molybdenum.

For infrared pump pulses at the higher fluence of F₀ = 0.8 J/cm² in the ablation regime, d describes a slight decrease to 11.0 nm at Δt = −0.75 ps followed by an increase to 11.7 nm at Δt = 0 ps. Up to Δt = 10 ps a further continuous increase is measured to d = 20 nm (≙ increase of 77%). The slight decrease might be again addressed to electronic processes [26,31]. The drastic and continuous increase of d already starting at delay time zero is probably related with ultrafast phase transitions [72] below 10 ps and the creation of a gas-liquid mixture or a phase explosion between 10 ps and 50 ps (gray shaded area [53,67,70,71]). In this time domain the irradiating photons penetrate deeper into the Mo – the material seems to become more transparent. Later d increases further to about 50 nm at 50 ps and to more than 200 nm at 100 ps. The observed strong increase of penetration depth during the laser ablation process may be a consequence of the transient decreasing density of the propagating matter, a gas-liquid mixture creating also a Fabry-Pérot interferometer or a spallation front of the ablated Mo film [53,70,71]. But, as mentioned before, the values for longer delay times have to be considered under reserve.

In section 3.1 comparable transient k values were measured for infrared and green pump pulse experiments. In consequence the calculated d values in Fig. 10 show also nearly identical progressions for both pump wavelengths – with the restriction that the above mentioned influence of scattered pump light (section 3.1) becomes also visible around delay time zero for the green pump pulses. As described before, when considering processes in metals induced by laser heating, the wavelength of the pump pulse should play a subordinated role, because the pulse acts only as a spatio-temporal heat source to the material.

It has to be pointed out, that experimental values of d at negative delay times < −5 ps (mean value 11.4 nm for both fluences) correspond very well with the literature values taken from [48,49] and [63]. These results show that the pump-probe setup reproduces state-of-the-art measurements and that results for positive delay times may be trusted as long as the “ellipsometric boundary conditions” given at the beginning of this section are met.

4. Conclusion

In this work, an ultrafast pump-probe ellipsometry setup was presented allowing the determination of the complex refractive index N = n-ik on an ultrafast timescale with sub-ps temporal resolution. In comparison with state of the art experiments, the developed setup extends investigations to irradiation fluences F₀ above the ablation threshold fluence F_thr, which are relevant for laser ablation and material processing. For delay times up to several hundred picoseconds full-fledged ellipsometric measurements can be performed. The functionality and accuracy of the setup was demonstrated by test analyses on Mo samples (relative deviation of 5.5% for n and 2.6% for k, compared to measurements by Ocean Optics “SpecEl-2000”). Closing a research gap, measurement series of the transient complex refractive index in a laser irradiated metal slightly below and above the ablation threshold fluence F_thr were presented (F₀ ≈0.75 F_thr and F₀ ≈2 F_thr). Two different pump pulse wavelengths were applied (λ_IR = 1056 nm and λ_green = 528 nm) whereas the probe wavelength was kept constant (λ = 528 nm).

For both pump wavelengths very comparable results were obtained. For the sub-threshold fluences, n and k values decrease by 30% and 10%, respectively, at a delay time of 5 ps (Fig. 8). Final values of n = 3.0 and k = 3.8 showing material modifications without ablation are reached after delay times greater than 300 ps. Measurements above the threshold fluences display a more pronounced decrease of n and k. At a delay time of 5 ps, n reaches a value of about 1.4 and k of 2.4. At later delay times, these values further decrease probably due to the onset of ablation. The creation of a gas-liquid-mixture could cause scattering of the reflected light resulting in decreasing n and k [53,67].

The here presented pump-probe ellipsometric setup can be utilized for a determination of the transient optical penetration depth d. d is calculated with the before measured time-resolved complex refractive index k and Eq. (10). Changes of d between −6% and + 77% in dependency on the applied fluence in the first 10 ps during and after the pump pulse irradiation were calculated and an excellent agreement with steady-state literature data was achieved for negative delay times < −5 ps (Fig. 10).

Overall, the first results from the pump-probe ellipsometer indicate significant absorption behavior changes of the pump pulse or subsequent pulses irradiating the sample on the timescale of picoseconds. The laser pulse can be interpreted as a spatially limited and temporally ultrafast heat source that is defined by the pulse duration and the optical parameters of the irradiated matter [27,73]. These optical parameters determine the quantity of absorbed pulse energy and its penetration depth. They are affected during the pulse duration as well as for longer delay times. Thus the pump-probe ellipsometer will be able to measure previously unknown and exact optical parameters of the ultrafast heat source, which initiates thermo-physical processes in the ultrafast time domain, leads to mechanical motion of matter in the nanosecond domain and finally results in laser structured patterns in the microsecond domain. The precise knowledge of the ultrafast heat source is the starting point for every simulation of laser ablation, which has to consider the main optical, thermal and mechanical processes [15].

During the pulse impact, the transient optical parameters are influencing the ablation efficiency of single pulse ablation processes. Single color PPE experiments (green pump and probe pulse) as well as two color PPE experiments above threshold fluence show a reflectivity increase of the green pump pulse by 5% during the pump pulse duration and an increase of its penetration depth by about 10%. Thus, more pump pulse energy is reflected from the Mo, but is absorbed in greater depth. Repeating this measurement with temporally longer pump pulses (>100 ps) at identical pump and probe wavelengths will enable a comparison of absorbed energies and their absorption distribution. Thus, a deeper understanding of the laser pulse as an ultrafast heat source can be created for different pulse durations. These results can address the question of the pulse duration dependent ablation efficiency as observed by many groups lately [10–14,16].

At advanced delay times, the transient optical parameters control the reflection and absorption of subsequent pulses during double pulse or burst mode experiments and thereby define the temporally structured ultrafast heat source represented by several laser pulses. The research question how such a temporally structured heat source influences and controls ablation efficiency is not completely understood at the moment. For example, results of this work show a reflectivity decrease by 20% and a penetration depth increase by 77% at a delay time of 10 ps. A subsequent pump-pulse irradiating the sample at this delay time is less reflected and absorbed in a larger volume and finally exhibits a changed ablation efficiency [17,18].

Moreover, the analysis of the transient complex refractive index can possibly give additional information – in comparison to transient reflectivity measurements available in literature – about the occurrence of ultrafast lattice changes or phase transitions at fluences relevant for material processing. E.g. the reflection of Mo irradiated at the sub-threshold fluences displays nearly the base reflectivity between delay times of 10 ps and 100 ps. In contrast, the real and imaginary part of the refractive index n and k show a clear resolved decrease of 30% and 10%, respectively, in this time interval. These ultrafast changes in n and k may address questions of laser induced melting or changes of lattice conformation in the material [38].

In future, pump-probe ellipsometric studies at intensities relevant for laser material processing will help to obtain a deeper understanding of the laser-material interaction and of the ultrafast laser pulse as an ultrafast heat source. The presented pump-probe ellipsometer enables the investigation of multiple interesting effects like the pulse duration dependent ablation efficiency, double or burst pulse absorption effects or ultrafast phase transitions. This knowledge is inevitable for further improving the laser ablation efficiency and quality of bulk material and thin films.