1. Introduction

High-performance pulsed laser sources emitting in the mid-infrared wavelength region (mid-IR) are rapidly attracting attention because of their numerous potential applications in medicine, material processing, fundamental research and metrology [1, 2]. While the latter exploits the existence of distinct atmospheric molecular absorption bands in the mid-IR, most of the other applications are detrimentally affected by linear absorption. Although the related effects on pulse and beam degradation have been known for decades [3, 4] they have, to the best of our knowledge, not yet been comprehensively studied with respect to their impact on the performance of ultrafast laser systems operating in the mid-IR. Since the development of these sources has seen an enormous progress in recent years [5–8], a thorough investigation including the identification of efficient mitigation strategies is of significant interest for the design of most ultrafast mid-IR laser systems. Figure 1 gives an overview of a typically observed atmospheric transmission spectrum at sea level (after a propagation distance of 10 cm), which is dominated by water-vapor absorption lines around 1.9 µm, 2.7 µm and 6 µm [9].

 

Fig. 1 Typical atmospheric transmission spectrum for a propagation distance of 10 cm at sea level [9]. Vibrational modes and their superposition are exemplarily marked for the most important water-vapor absorption bands.

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The presence of several molecular absorption lines can distort the pulse profile in the time domain after propagation as has been shown in [3]. The temporal pulse distortions due to water vapor are well-known from long-distance propagation of THz radiation [10]. However, their impact on the evolution of the pulse peak power has not yet been the focus of a rigorous investigation (including especially the mid-IR wavelength range). Absorption lines, which are caused by water-vapor typically exhibit a complicated structure with varying separations and line strengths. Due to the increasing complexity of the mathematical problem, model calculations on temporal propagation effects induced by numerous water-vapor absorption lines have not shown a complete, accurate agreement with experimental observations yet. Therefore, a numerical approach describing the linear pulse propagation through humid air was realized within the frame of this work. Such a simulation tool can, within the small signal limit, provide a quantitative statement about the pulse peak power loss after propagation, which is of capital importance for most applications.

A second detrimental effect arising from atmospheric absorption is thermal blooming [4]. Here, the absorbed laser power causes a diverging thermal lens in air leading to a distortion and extension of the beam profile during propagation. This ultimately degrades the stability and quality of the beam emitted by a laser system. Thermal blooming has been studied extensively for high-power, long-distance propagation in atmospheric transmission windows [4, 11]. However, the effect is much more dramatic inside of the strong absorption bands, and it becomes challenging for ultrashort-pulse propagation even at relatively low average power levels and short propagation distances.

In this work the atmospheric water-vapor absorption lines around 1.9 µm serve as a particular example of a molecular absorption band that coincides with the gain bandwidth of thulium-doped silica fibers. We have verified that the presence of several strong molecular absorption lines within the spectrum of an ultrashort pulse causes both a degradation of the pulse shape in the time domain and, for a sufficiently high average power, a distortion of the transverse beam profile in the spatial domain. These detrimental effects represent a significant challenge for the development and power-scaling of ultrashort-pulse lasers operating in the mid-IR wavelength region, e.g. Tm-based fiber lasers [6] and optical parametric chirped-pulse amplification (OPCPA) systems [12, 13]. Such sources are of particular interest for applications in high-field physics and attoscience, which require few-cycle pulses with highly confined temporal profile and excellent beam quality. Those applications would, as well as numerous other examples, obviously suffer from the impact of atmospheric molecular absorption lines in the mid-IR. Consequently, mitigation strategies and guidelines based on experimental observations and simulations will be discussed in this paper.

In the first part of this paper we present an experimental investigation on the impact of atmospheric molecular absorption lines on the temporal shape of ultrashort pulses and introduce a simple, yet accurate, simulation model to quantify the loss of peak power in the small signal limit. In the second part of this work we experimentally investigate the effect of thermal blooming caused by atmospheric molecular absorption lines after short propagation distances and average powers on the order of 10 W.

2. Temporal pulse evolution

The experimental observations that will be presented in the following were enabled by the development of a mode-locked, thulium-based fiber oscillator operating in a stretched-pulse regime. Stable, self-starting mode-locking was achieved by exploiting nonlinear polarization evolution in conjunction with a saturable absorber mirror in a sigma-arm configuration. The setup of the mode-locked laser is similar to the one presented by Haxsen et al. [14], but the oscillator emitted pulses with more than 1 nJ energy at 24 MHz repetition rate. Propagation through 2 m standard single-mode fiber was sufficient to de-chirp the 2.5 ps long oscillator output pulses to about 330 fs pulse duration (assuming a Gaussian pulse shape). The spectrum of the compressed pulses is centered at 1910 nm and has a 10 dB-bandwidth of more than 40 nm (Fig. 2). The oscillator spectrum shows several narrow dips, which are caused by the absorption lines of atmospheric water molecules [15] and can be associated with the propagation through the free-space section of the cavity. A commercially available software [16] based on the split-step Fourier method was used to simulate the spectral power density and the residual phase of the externally compressed oscillator pulses without considering the absorption lines (Fig. 2). These simulation results are the basis for the subsequent discussion of the temporal propagation effects.

 

Fig. 2 Spectrum of the externally compressed pulses, before (red) and after (blue) propagation through a climate chamber filled with air. The simulated oscillator spectrum (without absorption) is also shown (orange).

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In order to investigate the impact of molecular atmospheric absorption lines on the propagation of ultrashort pulses a multi-pass cell was enclosed by a home-made climate chamber (50 cm x 70 cm x 30 cm). The signal was delivered into the chamber by a single mode fiber leading to a free space optical path length of 12 m within the climate chamber. Figure 2 shows the spectrum after propagation through the climate chamber filled with laboratory air (blue curve). It can be seen that the absorption features are strongly enhanced after this free-space propagation of several meters. Different humidity levels can be realized in the climate chamber by progressively filling it with dry nitrogen. We measured the relative humidity in the climate chamber at 22°C and normal pressure with a commercially available temperature and humidity data logger. The effects on the pulse propagation in the climate chamber were characterized by measuring the pulse spectrum and the autocorrelation (AC) at different humidity levels. Figure 3 depicts the measured AC traces for 15% (3.1 g/m³), 30% (6.2 g/m³) and 60% (12.4 g/m³) relative (absolute) humidity, respectively. The measured AC traces indicate that the increased humidity had no significant influence on the FWHM pulse duration. However, it led to the formation of characteristic sidebands in the AC trace and to the appearance of a progressively stronger intensity background relative to the AC peak (with increasing humidity). A significant enhancement of the absolute AC peak value, which is qualitatively equivalent to an increase of the pulse peak power, was detected when decreasing the relative humidity in the climate chamber. However, in order to obtain a quantitative statement about the evolution of the pulse peak power it is necessary to know the pulse profile after propagation.

 

Fig. 3 Measured and simulated autocorrelation (AC) traces after the propagation of 330 fs pulses through 12 m of an air-nitrogen atmosphere with different relative humidity levels. The simulated AC trace at 0% relative humidity is plotted as a reference.

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A simulation tool was developed to describe the experimental observations and quantify the loss in peak power caused by the free-space propagation. The maximum peak intensity during the experiment was about 500 kW/cm² leading to a pulse area of only 10⁻⁵ rad as can be estimated using the formulas given in [17]. Because of the low peak electric field strength associated to the pulse intensity the simulations were carried out in the small signal limit, i.e. without considering nonlinear propagation effects or any coherent interaction between the light pulses and the absorption lines. Thus, in contrast to the work by Seilmeier et al. [3], we have linearized the pulse propagation and we describe it on a macroscopic level by considering the absorption lines and the corresponding refractive index change of the gas mixture within the propagation path. Our simulation approach is straightforward as it is only based on the well-known Kramers-Kronig relations [18] and on linear pulse propagation in dielectric media.

First of all, the spectral absorption coefficients for different humidity levels were estimated from the measured spectra after propagation through the climate chamber and the initial oscillator spectrum. The absorption coefficient of the strongest absorption lines could not be retrieved accurately due to the limited signal to noise ratio of the spectrometer. Because of this, the well-resolved weaker absorption lines were used to scale available high resolution data of atmospheric transmission to match the experimental measurements. The raw data for this fit were supplied by a modelling tool, which is freely available [9, 19]. The parameters used in this modelling tool were a temperature of 22°C, a pressure of 1 atm, Voigt line profile for the individual absorption lines and a resolution of 5∙10⁻³ cm⁻¹. The typical linewidth of the retrieved spectral absorption coefficient was about 0.18 cm⁻¹. As a second step the fitted high resolution data for the atmospheric absorption coefficients were numerically integrated to obtain the spectrally-resolved refractive index variation as governed by the Kramers-Kronig relations [18] (where P represents the principle value)

The numerical treatment was facilitated by Mclaurin's formula as it delivers accurate results without requiring extensive computational time [20]. The resulting complex refractive index spectrum was subsequently used to simulate the linear pulse propagation in humid air with a Fourier transform formalism. This calculation was based on the description of the electric field evolution in the spectral domain according to

In the equations above, ω represents the angular frequency, c the speed of light in vacuum, n the refractive index (real part), κ the absorption term (imaginary part of the refractive index) and z the propagation distance. The initial data used for the calculation, i.e. the spectrum and phase of the compressed oscillator pulses, were provided by the aforementioned simulation of the compressed oscillator output (Fig. 2).

It can be seen in Fig. 3 that the simulations reproduce the measured AC traces accurately at all relative humidity levels. The numerically retrieved temporal pulse profile after propagation in the climate chamber at 60% relative humidity is shown in Fig. 4. Post pulses and a long pulse tail generate the characteristic side-features and the intensity background of the AC traces at high relative humidity (Fig. 3(d)). Our simulation results confirm that the observed pulse quality degradation is caused by the presence of multiple narrow atmospheric molecular absorption lines. These absorption lines lead to a refractive index profile consisting of multiple sharp Fano-shaped features with varying strength and separation as exemplified in the inset of Fig. 4. The refractive index profile causes quasi-periodic sharp spectral phase distortions across the spectrum after propagation, i.e. dispersive terms. This leads to the formation of post-pulses and a rather long pulse tail, which carries a significant amount of the pulse energy. Both the experiment and simulation indicate, that the temporal separation between the individual post-pulses and the main pulse peak (e.g. about 1.7 ps) is related to the mean spectral separation of the strongest water absorption lines across the spectrum (e.g. about 7 nm, see Fig. 3 and 4).

 

Fig. 4 Simulated pulse profile after 12 m propagation in the climate chamber with 60% relative humidity. Inset: Excerpt of a spectral region with strong absorption lines as retrieved from [9, 17] and the measured spectra. The corresponding calculated refractive index profile is also shown.

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Based on the simulation results the loss in peak power after propagation through the climate chamber can be calculated for any arbitrary humidity level. The initial pulse energy for this simulation was 750 pJ, which corresponds to about 1.95 kW of peak power for the compressed pulses prior to propagation. Figure 5 shows the evolution of the relative peak power with increasing humidity as well as the relative change in average power after propagation through 12 m of air. It can be seen that the pulse peak power decreases dramatically with increasing relative humidity levels. The comparison of both curves reveals that the peak power after propagation is affected by both the average power absorption and the degradation of the pulse quality caused by the dispersive terms of the refractive index profile. It can be further deduced that these dispersive terms have a significant influence on the pulse peak power after propagation. In particular, the relative loss in peak power and the relative absorbed average power after propagation differ by a factor of approximately two for the highest considered humidity level.

 

Fig. 5 Simulated peak power and average power loss after 12 m of propagation at varying humidity levels.

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As a next step the correlation between the relative loss in peak power and the relative loss in average power was numerically studied for a more general case of ultrashort pulse propagation in the mid-IR. As an example the water-vapor absorption band at around 1.9 µm (vibrational modes ν₁ + ν₂ and ν₂ + ν₃, see Fig. 1) was chosen. The absorption is generally influenced by the combination of three factors, which are

The simulations were carried out for a transform limited Gaussian pulse (150 fs FWHM duration, corresponding to approximately 34 nm FWHM spectral width) with various center wavelengths, which resulted in a varying overlap of the pulse spectrum with the absorbing region. It can be deduced from Eqs. (1) and (2) that the concentration of the absorbing molecules, which linearly scales the respective absorption coefficient, and the propagation distance are mathematically equivalent parameters. Therefore, the simulations were conducted at a constant relative humidity of 50% but for varying propagation distances. Thus, in addition to the center wavelength of the spectrum, the propagation distance was changed to obtain different fractions of absorbed power for a constant overlap of the pulse spectrum with the absorption band. The results of this two-dimensional parameter sweep can be seen in Fig. 6. The graph shows the transmitted relative peak power with respect to the absorbed relative average power and the center wavelength.

 

Fig. 6 Transmitted relative peak power (color) depending on the absorbed relative average power after propagation and on the overlap (center wavelength) of a Gaussian spectrum (approximately 34 nm 3 dB-bandwidth) with the water-vapor absorption lines of the vibrational band around 1.9 µm. The dashed white contour lines exemplary depict data points corresponding to a fixed propagation distance.

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The evaluation of the simulation results shown above enables several interesting observations, which are not directly intuitive.

In the case of a constant propagation distance the average power loss varies only through the overlap of the pulse spectrum with the absorption band, i.e. the performed wavelength sweep (as exemplarily depicted by the dashed lines in Fig. 6). Figure 7 shows the relative attenuation in peak power with respect to the transmitted relative average power for three different propagation distances. It can be seen in Fig. 7 that the relative pulse peak power is proportional to the relative average power for a fixed propagation distance. Moreover, the proportionality factors increase with longer propagation distance, which can be interpreted as follows. At the same relative average power loss after propagation the detrimental impact of the accumulated spectral phase distortions on the pulse peak power is enhanced for the case of longer propagation distance and less overlap with the absorption band. This is an interesting finding, which is not intuitive and emphasizes that the impact of the propagation effects described herein has to be considered even for an operation at the edges of atmospheric molecular absorption bands.

 

Fig. 7 Transmitted relative peak power as a function of the transmitted relative average power after propagation of an ultrashort pulse with various overlaps (center wavelengths) of the pulse spectrum with the absorbing region. The data corresponding to 10 m of propagation distance are also represented by one of the dashed lines in Fig. 6. The respective slopes have been retrieved by a linear fit (solid lines).

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In order to generally evaluate the impact of the propagation effect for ultrashort pulses in the mid-IR, the simulation procedure was extended to other water-vapor absorption bands as well. These absorption bands are marked in Fig. 1 and the initial conditions of 50% relative humidity and 150 fs (FWHM) Gaussian input pulses have not been changed for all simulations. Figure 8 shows the retrieved proportionality factor ε (the ratio of the relative loss in peak power and the relative loss in average power after propagation) with respect to different propagation distances. The evolution of ε follows an exponential growth with respect to increasing propagation distance for all considered absorption bands (solid lines).

 

Fig. 8 Proportionality between the transmitted relative peak power and transmitted relative average power depending on the propagation distance for three bands of water-vapor absorption lines around 1.9 µm (ν₁ + ν₂, ν₂ + ν₃), 2.7 µm (ν₁, ν₃) and 6 µm (ν₂) in the mid-IR. The solid lines represent an exponential fit.

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The exponential growth of ε with propagation distance is significantly stronger for the bands with vibrational modes ν₁, ν₃ and ν₂ as compared to ν₁ + ν₂, ν₂ + ν₃ due to the difference in the maximum absorption line strengths of the individual bands (see Fig. 1). There are two limiting cases for all data sets shown in Fig. 8, which will be briefly discussed in the following. First, it is clear that for vanishing propagation distances no additional loss in the relative peak power can be caused by the accumulation of spectral phase distortions and, therefore, ε_min = 1. Second, it can be seen in Fig. 8 that the proportionality between the relative pulse peak power and the relative average power after propagation saturates at a certain propagation distance. This occurs when the transmitted relative peak power basically vanishes, i.e. when the main temporal feature of the pulse profile is not anymore distinguishable from the accumulated pulse tail. In that case it was confirmed for all considered absorption bands that the transmitted relative average power is on the order of 60%. Consequently, the corresponding proportionality between the transmitted relative peak power and the transmitted relative average power is ε_max ≈2.4. We believe that the slight deviation in the exact value of ε_max for each considered absorption band is due to the individual structure defined by the line separations and the envelope of the distinct absorption lines.

The identification of a simple, quantitative relation between the remaining relative peak power and the transmitted relative average power after propagation is a very significant result for the evaluation of the pulse peak power from mid-IR lasers operating in a wavelength region featuring several strong and narrow molecular absorption resonances. Accordingly, one has to be aware of the fact that the pulse peak power can be significantly reduced even though the fraction of absorbed average power is relatively small. The effect is enhanced for operation within the atmospheric molecular absorption bands around 2.7 µm and 6 µm wavelength since the individual lines are much stronger as compared to the water-vapor absorption band in the two micron regime. This means that significant pulse degradation has to be expected within these bands even for very short propagation distances and small spectral overlaps between the pulse spectrum and the respective absorption band.

3. Spatial beam profile evolution

In a second, separate experiment the influence of the molecular water absorption lines on the spatial (transverse) beam profile has been investigated. For this purpose we used a tunable, narrow linewidth continuous-wave (cw) Tm-doped fiber oscillator, which was subsequently amplified in a Tm-doped large pitch fiber (LPF) [6]. The output beam was propagated in laboratory atmosphere over approximately 1 m, before a small portion of the power was partially reflected on a fused silica wedge and imaged onto an indium antimonide-based infrared detector. The relative humidity for this experiment was approximately 40%. Different output power levels have been tested and, for each one, the amount of absorbed power has been changed by sweeping the operation wavelength of the cw-laser over certain water absorption resonances. For output power levels on the order of or higher than 10 W the beam profiles depicted in Fig. 9 show a characteristic distortion pattern when the cw-laser was swept over an individual absorption line. The beam distortions, also known as thermal blooming, are characteristic for a diverging thermal lens and arise from the negative thermo-optical coefficient of air (∂n/∂T ≈-10⁻⁶ K⁻¹ [21]). No thermal blooming was observed when the wavelength of the cw-laser was off-resonance (e.g. 1913 nm). The beam distortions can be significantly reduced by blowing air over the propagation path of the beam, which prevents the formation of a stationary atmospheric thermal lens [22]. Thus, a simple fan mitigated the thermal blooming to some extent (see Fig. 9). Nevertheless the best mitigation for the observed thermal blooming is the avoidance of absorption lines, which can easily be done for narrow linewidth signals. More problematic, however, is the mitigation for broad band signals.

 

Fig. 9 Images of the transverse beam profile after propagation through 1 m of laboratory atmosphere. Starting from the left, the first four columns represent a wavelength sweep of the cw-laser. Each operation wavelength is marked in the plot of the retrieved spectral absorption coefficient. The rightmost column shows the beam profiles for a broad band source (ultrashort-pulse oscillator spectrum) after propagation at similar power levels. In the first three rows the beam profiles after propagation at different output power levels (prior to propagation) can be seen. The lowest row represents the beam profiles at the highest average power (24 W) when a fan blows air over the propagation path.

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In order to investigate the beam distortion for ultrashort-pulse systems we amplified a broad band spectrum (Fig. 2) in a fiber-based chirped-pulse amplification (CPA) system [6]. The pulse propagation experiments have been performed with stretched pulses (~1 ns pulse duration, <77 MW/cm² maximum peak intensity) to avoid any additional nonlinear effects. Significant thermal blooming occurred for an average output power of >20 W after just 1 m of free-space propagation (rightmost column of Fig. 9). The corresponding absolute absorbed average power after propagation was around 2 W. In contrast to narrow linewidth operation it is not possible to avoid the individual absorption lines with the broadband spectrum. As a consequence the absorbed power has to be reduced below 1 W in order to mitigate thermal blooming in this experiment. Based on our investigations it has to be expected that similar challenges have to be faced when operating within other strong molecular absorption bands. To a limited extent beam deformations can be reduced by employing a fan to inhibit the formation of a stationary thermal lens in air. However, this strategy is of limited use for some applications since it affects the pointing stability of the beam and is hard to realize for long propagation distances.

4. Conclusion and mitigation

In this work we have studied the impact of atmospheric molecular absorption lines on the linear free-space propagation of ultrashort pulses in the mid-infrared wavelength region. Our results show that atmospheric molecular absorption bands can seriously limit the performance-scaling of mid-IR ultrafast laser systems and need to be considered in their design. The experimental work has been performed with Tm-doped fibers operating around 1.9 µm, but the simulation results presented herein indicate that our findings can be directly transferred to other wavelength regions.

Strong atmospheric absorption lines degrade the pulse profile in the time domain, which mainly results in a loss of pulse peak power but without any significant change of the FWHM pulse duration. It has been shown that the relative loss in peak power can be more than two times stronger than the relative loss in average power after propagation because of the complicated dispersion profile induced by the presence of multiple absorption lines. Furthermore, it has to be highlighted that absorption-induced spectral phase distortions can accumulate during the propagation in a multi-stage amplification system and can, therefore, affect its output peak power even though no significant average power loss becomes evident (since it has been compensated by amplifiers). For high-performance chirped-pulse amplification (CPA) systems the complicated absorption profile is mapped to the stretched pulse envelope and can significantly increase the detrimental impact of nonlinear effects [23, 24]. Moreover, the experimental observation of temporal pulse degradation can become challenging due to insufficient signal-to-noise ratio or limited temporal delay in an AC measurement. Thus, it can be hard to experimentally evaluate the energy, which is located in the pulse tail. This becomes even more problematic for few-cycle pulses in the mid-IR as the temporal delay of post pulses caused by the spectral phase distortions can be significantly larger than the pulse width.

A second challenge arises for average power-scaling of ultrafast mid-IR lasers due to the onset of atmospheric molecular absorption-induced thermal blooming. It has been experimentally demonstrated that this effect can be observed even after short propagation distances (<1 m) for absorbed average powers above 1 W. For the presented broad band spectrum (centered at 1910 nm with 50 nm bandwidth) this corresponds to a critical average output power of about 10 W.

Clearly, both the spatial and temporal effects are unwanted and have to be mitigated in the design process of mid-IR ultrashort-pulse lasers and OPCPA systems. In order to achieve the best performance of an ultrafast laser system operating in the mid-IR, both the product of the absorbing molecule concentration with the propagation distance as well as the overlap of the pulse spectrum with any molecular absorption band have to be minimized. This can be achieved by shortening the free-space sections of a laser system and, in case of water-vapor-induced absorptions, by operating in an atmosphere with very low absolute humidity (e.g. pre-vacuum conditions or by a dry nitrogen atmosphere). Due to the complicated structure of molecular absorption bands in the mid-IR, it has to be expected that the effects addressed in this paper have to be mitigated a priori and that subsequent elimination is impossible. Alternatively, the spectral profile may be shifted away from these absorption bands, but this can be restricted either by application requirements or by the available gain bandwidth.

We believe that the results presented herein are important for the future scaling of the output peak and average power of ultrafast lasers operating in mid-IR spectral regions affected by molecular absorption bands. In particular, they show that an optimized operation regime for high peak power two micron lasers is located beyond 1950 nm in an atmospheric environment. In the case of Tm-doped silica fibers, this would significantly reduce the effective gain bandwidth. Therefore, the full potential of ultrafast Tm-based fiber lasers can only be exploited by operating in dry atmospheres.