Ultrafast mid-infrared high harmonic and supercontinuum generation with 2 n characterization in zinc selenide

Polycrystalline ZnSe is an exciting source of broadband supercontinuum and highharmonic generation via random quasi phase matching, exhibiting broad transparency in the mid-infrared ( 0.5 20 m μ − ). In this work, the effects of wavelength, pulse power, intensity, propagation length, and crystallinity on supercontinuum and high harmonic generation are investigated experimentally using ultrafast mid-infrared pulses. Observed harmonic conversion efficiency scales linearly in propagation length, reaching as high as 36%. For the first time to our knowledge, 2 n is measured for mid-infrared wavelengths in ZnSe: ( ) 14 2 2 3.9 (1.2 0.3) 10 / n m cm W λ μ − = = ± × . Measured 2 n is applied to simulations modeling high-harmonic generation in polycrystalline ZnSe as an effective medium. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

RQPM is a promising isotropic approach for broadband three wave mixing applications with a wide spectral range [9] achieved at significantly lower cost compared to nonlinear frequency conversion processes from expensive single crystals cut in specific orientation with tight angular tolerance or even more expensive periodically poled crystals of very limited choice. This is especially true in mid to long wave IR regime, with the availability of poly-ZnSe.
Longer wavelengths lead to increased spectral broadening through self-phase modulation (SPM) and filamentation in poly-ZnSe [11][12][13]. As a result, interest in the MIR nonlinear properties of RQPM and poly-ZnSe has continued to grow [14][15][16][17]. Linear scaling of harmonic efficiency with crystal length has been demonstrated experimentally to lead to high conversion to the harmonics (19% second harmonic, 0.5% third harmonic) [12].
MIR ultrafast nonlinear optics contains a diverse array of applications in ultrafast spectroscopy [17][18][19]. As Cr and Fe doped ZnSe are proving to be exciting laser materials for broadband amplification in MIR, non-linear response to MIR pulses on ZnSe is also relevant from that perspective [20]. Recent progress has also been made in the field of efficient, broadband harmonic generation [21]. MIR RQPM is another way to generate SC/HHG with high efficiency and large spectral bandwidths.
In this work, we observed SC generation and HHG/IHC to 7th order via RQPM using ultrafast MIR pulses in poly-ZnSe, extending previous results [12,17] to longer wavelengths. Contrasting with previous works [6,11,13,14], in this study both the transmitted fundamental and generated harmonics were studied experimentally and theoretically. Sample thickness was varied, with a maximum thickness of 4 cm. This has allowed us to investigate experimentally the interplay between changes in the fundamental and HHG/IHC. By varying the input pulse power, intensity, wavelength, and propagation distance, we explored the conditions under which SC, HHG/IHC, and filamentation occur. In our experiments, we clearly demonstrate these processes occur within a non-perturbative regime of harmonic generation. We explore MIR nonlinear propagation effects with up to 4 cm propagation lengths for the first time. Harmonic efficiency was found to follow a linear scaling with increasing propagation length, leading to harmonic efficiency as high as 36% (2nd through 7th). To the best of our knowledge, this is the highest harmonic efficiency reported in ZnSe. Our experiments were repeated with single crystal ZnSe (single-ZnSe), where harmonics only up to order three were generated, exhibiting a smaller spectral bandwidth for individual harmonics and greater than an order of magnitude smaller harmonic efficiency in a clearly demonstrated perturbative regime. Even though 2 ( ) n MIR may be very different for nearinfrared (NIR) wavelengths, the approximation ( ) 2 2 ( ) n NIR n MIR ≈ is still used in the field as an estimate due to lack of experimental data at MIR wavelengths. In this work, we have measured experimentally for the first time The goal of our simulation work is to shed light on the process of the strong, nonperturbative scaling HHG and SC generation in poly-ZnSe as well as to test whether an effectively scalar medium model can capture the main physics. The model can predict the experimentally observed trends in harmonic generation as a function of input power and propagation distance, which it mainly attributes to cascaded second and third order nonlinearities [22], free carrier generation and random quasi-phase matching.

Experimental setup
A continuously tunable, multistage ultrafast Extreme MIR (EMIR) optical parametric amplifier (OPA) ( 2. 5  Transmitted MIR pulses were collected and collimated in a second CaF 2 100 mm focal length lens (L2 in Fig. 1(a)). In the filter plane, filtering was applied, and any relevant filter transmission was applied to the data in post processing. MIR pulses were then coupled into a calibrated MIR spectrometer (Acton Research with FLIR cooled focal plane array) via a third lens (L3 in Fig. 1(a)), which was found to be opaque to the harmonics. The observable spectral range for the spectrometer was 3 5 m λ μ = − , with a variable spectral observation window.
In another configuration, L2 is replaced with a 10X Mitutoyo Plan Apo NIR Infinity Corrected Objective, found to be opaque to MIR pulses. This objective is used to collect the harmonics, and its response curve was included for the spectral calibration of harmonics in post processing. In this case, no filtering is applied, instead the light is collected by L3 and coupled into a fiber before being sent to either a visible (VIS) or NIR spectrometer (together spanning the spectral range 0.5 1.7 m λ μ = − ), replacing "Detector" in Fig. 1. The fiber position relative to the harmonic pulses is kept fixed while switching spectrometers. The VIS and NIR spectrometers are cross-calibrated using the overlap between their spectral windows combined with relative irradiance calibrations.
In a similar setup for near field intensity distribution measurements of the harmonics, the detector in Fig. 1 is replaced with a NIR camera, and neutral density filtering (F) is applied. The filter transmission is considered in post processing. L1 and L2 are configured such that the back surface of the sample is imaged onto the camera.
For determining the efficiency of harmonic generation, the MIR input pulse energy is measured at position E 1 in Fig. 1(a). The harmonic energy is measured at position E 2 , since the objective L2 is not transmissive to MIR wavelength to any level detectable by our energy meter, even without a sample present. The known transmission curves for each optic (L2, L3) are accounted for when calculating harmonic energy.
For the 2 n characterization of ZnSe, we used the conventional Z-scan technique [25] at the U.S. Army Research Laboratory's Adelphi Laboratory Center (ALC). The schematic of the experimental setup is shown in Fig. 1(b). A Ti:sapphire laser system (Coherent, Hidra-F-100) pumped an OPA (Light Conversion, TOPAS-Prime-HE), which was then used for DFG (2 mm thick Type II KTA) to obtain 3.9 m λ μ = pulses. The DFG pulses were spatially filtered by focusing into a 180 µm diameter single-diamond pinhole using an all-reflective geometry. A ZnSe wedge was used as a pickoff for the reference detector. The pulses were subsequently focused into the sample via a 150 mm ZnSe focusing lens.
To determine the energy used in the Z-scan runs, the reading from a spectrally flat broadband THz radiometer with linearity ranging from 0.1 µW to 20 mW was calibrated with a pyroelectric detector (Ophir, PE10) near the output of the DFG where the energy is relatively high (~0.5 mJ). The radiometer was then placed directly in front of the sample (after the spatial filter and pickoff wedge) without the presence of any filters and a reading was taken to obtain the actual energy. Attenuation was achieved by using calibrated Ge neutral density (ND) filters having a spectrally flat response from 2 to 18 µm. The minimum beam waist was measured to be 48 µm gaussian waist radius by one-dimensional knife-edge scans. The pulse width was measured by second-order intensity autocorrelation in a 400 µm thick Type I AgGaS 2 crystal and determined to be 260 fs (FWHM).

Numerical modeling of optical filamentation
We use the gUPPEcore simulator implementing the unidirectional pulse propagation equations (UPPE) [26]. In a scalar and/or semi-vectoral approximation motivated above, the optical field evolution satisfies UPPE, which incorporates nonlinear response of the medium in polarization and current density.
The nonlinear polarization includes both the second-order and third-order nonlinearity. The latter is implemented as usual and parameterized by the nonlinear index for which we use

Effects of MIR pump parameters
In Fig. 2, Fig. 3 , are shown. With these central wavelengths, regimes of 8-and 9-photon absorption are probed. In Fig. 2(a) Figure 3(a) clearly shows two distinct pump power regimes in spectral broadening of the harmonics, despite a relative lack of broadening dynamics in the fundamental. Potential reasons for the lack of broadening dynamics in the fundamental include: energy losses from linear absorption, free carrier absorption [27], depletion from harmonics generation, or inaccuracy of cr P due to lack of MIR data [12]. For 1 5 E J μ  no spectral broadening is observed in the harmonics. While for 1 broadening occurs like the single filamentation regime in [12]. As an example, the critical power for self-focusing of the third harmonic ( ) , much lower than that of the fundamental. With total harmonic conversion efficiencies reaching up to 36% (see section 3.3), it is reasonable that this power threshold is exceeded by (for example) the 3rd harmonic. It is possible, supported by the evidence presented in Fig. 2, Fig. 3, and Fig. 4 and by near field intensity profiles (discussed in section 3.4), that filamentation and resulting IHC generation can occur in the harmonics, without SC generation also occurring in the fundamental. IHC is therefore not necessarily caused by XPM, as has been suggested [6]. Application of these results include generation of broadband VIS/NIR light while retaining the spectral profile of the MIR fundamental pump for use in pump-probe or broadband spectroscopy experiments. The spectra of Fig. 2    Δ =Δ [28]. Table 1 outlines the FWHM spectral broadening of the spectra shown in Fig. 2, Fig. 3, and Fig. 4. For the fundamental, spectral broadening is defined as the positive change in FWHM spectral bandwidth compared to that of no sample. For the harmonics, spectral broadening is defined as the difference (positive change) between observed and ideal bandwidth. The ideal bandwidth is calculated using the spectral bandwidth of the modulated fundamental. We see that for the 3.4 m λ μ = case the 5 mm poly-ZnSe sample yields a third harmonic with a FWHM spectral bandwidth within 1 nm of the ideal case. In stark contrast, in the 3.8 m λ μ = case, the 5 mm poly-ZnSe yields a third harmonic with a FWHM spectral bandwidth which is 52nm larger than the ideal case. This shows that under these conditions, a large portion of the harmonic spectral bandwidth is not due to cross phase modulation. This ultra-broadband harmonic generation is an indication of RQPM due to relaxed phase matching conditions in polycrystalline materials [9,10,12].
Despite the lack of blue-shift in the fundamental (and at times even a slight redshift), significant blue shifting occurs in the harmonics, as can be seen by Fig. 2(a) In Fig. 4(b), the effect of increasing input pump intensity while keeping the pulse power fixed can be seen. Here, the 100 mm focal length lens (L1 from Fig. 1) is replaced with a 20 mm focal length lens. The intensities shown with the 100 mm case varied from Here, we note that although the pulse power is still roughly the same relative to cr P , the FWHM spectral bandwidth of the transmitted fundamental increases to 486 nm, generating a SC spectrum spanning from 2.9 to 4.2 m μ (Fig. 2d.).
In Fig. 4(a), the transmitted fundamental and generated harmonics in a 1 mm single crystal ZnSe sample are shown. Modulations to the fundamental result in spectral broadening, although to a lesser extent than for the poly-ZnSe case, as can be seen from Table 1 for 3.8 m λ μ = . Only 2 nd and 3 rd harmonics were generated when using the single crystal ZnSe sample, and no IHC was observed. Furthermore, the FWHM spectral bandwidth of the harmonics generated by single crystal ZnSe is smaller than the poly-ZnSe case (Table 1) and falls short of the ideal theoretical case. This is because the ideal case assumes perfect phase matching ( Fig. 4(a). Using a 5 mm thick single crystal ZnSe sample would not necessarily be a fair comparison to a 5 mm thick poly-ZnSe sample, since generated harmonics in a thicker single crystal ZnSe sample would undergo further pulse splitting due to group velocity mismatch [29]. In our case, the choice of 1 mm was based primarily on availability. In contrast, poly-ZnSe samples are widely available, cost effective, and do not require considerations relating to phase-mismatch.
Power scaling analysis was performed on both single-ZnSe and poly-ZnSe for the case of 3.3 m λ μ = . The results are displayed in Fig. 5. The input MIR pump pulse energy was varied In the 1 mm thick single crystal case ( Fig. 5(a)), the power scaling is perturbative for both SHG and THG. SHG and THG for 1 mm thick poly-ZnSe deviates from the respective scaling laws once the pulse energy exceeds 1 10 E J μ ≈ (Fig. 5(a)). Higher order harmonics generated in poly-ZnSe (4 th , 5 th , and 6 th order) all deviate from the respective power laws. For comparison, the experiments were performed with 1 cm thick poly-ZnSe ( Fig. 5(a)). With the longer propagation distance, even the SHG and THG was found to vary from the respective power law for all input MIR pulse energies. Figure 5(b) shows that for higher input energies harmonic orders begin to scale the same way, in this case exhibiting a linear increase with the pulse energy. This type of behavior is typically attributed to nonperturbative physics in bulk crystals [30].
While har are clearly ac the pulse ene harmonics bey in the visible. by eye in refl greatly attenu

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The sample th pulse energy propagation l broadening fo A redshift in t Figure 6(b spectrum (no atmospheric C Fig. 4(b) for keeping the in in Fig. 6 Fig. 4(a)). d. ree space be due to at seen in mm while are shown an that of damental, rmonic is e by our s C s . l d -nSe for a materials, the efficiency scales linearly with the propagation distance. Here, we confirm this out to 40 mm propagation distance for the first time. Linear scaling is found for several different MIR pump pulse energies (Fig. 7(a).). For each pulse energy, we found that the shortest propagation lengths were outliers to the linear scaling.
A harmonic efficiency as high as 36% was recorded using the 40 mm poly-ZnSe sample ( Fig. 7(a).). We define harmonic efficiency as the ratio of total harmonic pulse energy to input pulse energy. Large efficiency is expected for RQPM processes due to the relaxation of phase-mismatch conditions. The linear scaling of efficiency with propagation distance makes these materials promising for ultra-efficient harmonics generation in materials. The high efficiency is exhibited in Fig. 7(b). In the image, invisible MIR pulses generate NIR and visible harmonics with 36% efficiency in a 40mm poly-ZnSe sample. In comparison, we note that under identical pump conditions, the harmonic efficiency in single crystal ZnSe was not measurable using our energy meter, which has a pulse energy threshold of around 0.3 Since the harmonic pulse energy was not detectable even with the highest MIR pump pulse energy of 12 J μ , we can say that the harmonic conversion efficiency for single crystal ZnSe is 2.5% ≤ . In other words, the efficiency is more than an order of magnitude lower than the poly-ZnSe case.

Near field intensity profiles: filamentation
Near field intensity profiles were recorded by imaging the back surface of poly-ZnSe samples using the generated harmonics and IHC as the illumination source (Fig. 8). The input pulse energy was kept fixed at 1 The fundamental wavelength was also kept fixed 3.3 m λ μ = . Notch filters were used to isolate the SHG, THG, and IHC intensity profiles. Dot patterns reminiscent of RQPM [8] can be seen in both the THG (Fig. 8(a)-(b)) and SHG (Fig. 6(d)-(e)). In neither the 10 nor 20 mm thickness case does the near field intensity profile indicate the presence of filamentation.
Considering the 40 mm thickness case, both THG (Fig. 8(c)) and SHG (Fig. 8(f)) exhibit multiple filaments of 50 m μ FWHM in size. Multiple filamentation is typically correlated with a large increase in spectral broadening, as was observed for the 40 mm case (Fig. 6(b)). In section 3.1, we discussed the presence of IHC without the corresponding SC generation that would be expected if XPM were the mechanism of IHC generation (Fig. 2(b)). By inspecting Fig. 8(i), we can see that IHC spatial profile is entirely matched with those of the filaments in the 40mm case, indicating that the IHC may be generated by the filaments. With the two shorter propagation distances (Fig. 8(g)-(h)), it appears a single filament is formed, of approximate size 100 m μ FWHM at the back face of the sample. Again, the IHC matches the intensity prof of IHC.      ity of the compared ween the de of the fundamental, where the wavelengths corresponding to the spectral side-band and the minimum at 3.7 µm are nicely reproduced. The spectral broadening on the long-wavelength side also exhibits a band similar to that in the experimental data, though at a lower relative strength. Given the effective nature of the model employed in this work we find this result encouraging. Fig. 13. Temporal and spectral properties of the electric field for a single random poly-crystal realization. (a) Temporal waveform of the real electric field exhibits a strong presence of higher-harmonic components which concentrate predominantly in the long tail of the resulting composite pulse. The inset zooms on the electric field profile near the peak, revealing that harmonics and fundamental together give rise to a "random" waveform with non-sinusoidal oscillations. (b) The corresponding spectrum shows that harmonic orders (marked by labels) show increasing levels of noise.

Z-scan m
The simulations also reveal several mechanisms that contribute to the harmonic generation that looks very much non-perturbative in the sense that the decrease of the energy in the higher orders is very slow. The first important aspect is that several "paths" of different frequency combinations contribute to any given harmonic order. For example, third harmonic receives second-order contribution from the sum of the fundamental and second harmonic. At the same time, third-order nonlinearity generates third harmonic directly. Other ways to produce this frequency include frequency difference process, such as subtracting the fundamental from harmonic order four. All these processes end up with slightly different phase relations and this decreases the temporal coherence of the resulting multi-color waveform, which in turn is less likely to feed the energy back into the fundamental.
In order to elucidate these conclusions, we show in Fig. 13(a) an example of the electricfield waveform as it evolved over 10 mm propagation in a sample without averaging, over several random realizations of the orientation of crystallites (as was done for the simulation of harmonic spectra shown in Fig. 11). The feature that indicates the loss of coherence is the long tail that consists mainly of the higher-frequency waves, together with the essentially random local structure of the waveform. The latter is illustrated in the inset which zooms onto the peak region-here one can appreciate that the superposition of different spectral components appears random, which in turn is an indicator of incomplete coherence. The large temporal extent of this composite pulse is another reason why the energy from the upper spectral bands cannot be effectively returned to the fundamental, a mechanism that underlines the efficiency of the random quasi-phase-matching. Figure 13(b) adds to this argument, showing that the spectrum also exhibits random noisy fluctuation that arise due to superposition of waves with poorly correlated mutual phases. It is also obvious that the random noise becomes more and more evident in higher harmonic orders, which is in line with many more channels (i.e. combinations of other harmonics) that contribute to them.
The second important aspect is the random quasi-phase-matching due to the randomness of the grain orientation. In our treatment, this leads to random on/off in the second-order processes that in turn destroy the coherence required for the energy to flow back to the fundamental.
The third mechanism that needs to be recognized is the group-walkoff between different spectral components. Because of greatly varying group velocities between different orders, the high-frequency components lag behind the main pulse and thus have little opportunity to return their energy back into fundamental.
Finally, free electron generation contributes in two ways. First, it is the spatial and temporal defocusing adding yet more randomness and subsequent loss of coherence. Second, the fast-increasing electron density imparts blue shift and contributes significantly to spectral broadening of all components, thus opening more and more channels for spectral conversions.
Of course, one possibly important aspect that has not been considered in our modeling is that grain boundaries can also add to phase mismatch as they probably appear like locally single-axis anisotropic medium. A fully resolved vectoral model with "microscopic" modeling of the poly-crystalline nature of the medium is needed to test if grain boundaries contribute in significant ways. Such an investigation is left for a future work.

Conclusion
Ultrafast MIR nonlinear optics is an exciting new field, and much interest has been recently shown in RQPM of polycrystalline materials due to promising applications to SC generation and ultra-broadband HHG. This paper has investigated HHG and SC generation in poly-ZnSe using MIR pulses of two different wavelengths, two focal geometries, and for an array of input pulse powers and propagation lengths. Under these conditions it was shown that IHC can be generated with harmonics out to 7 th order without significant broadening in the fundamental. Harmonics generated this way were found to exhibit non-perturbative scaling laws for all harmonic orders. We found that longer propagation lengths lead to stronger nonperturbative behavior. Spectral broadening of the fundamental could be achieved by increasing the propagation distance (with a fixed pulse power) instead of increasing the intensity due to RQPM. The RQPM nature of the interaction was further confirmed by the observation of linear scaling in the harmonic efficiency with propagation length, as well as by high conversion efficiency (36%). With the same pulse power, broadband SC generation could be induced by using a tighter focus, high intensity setup. Blueshifts observed in the harmonics could possibly be explained by photon acceleration [21], although further study would be needed. We also compared harmonics generated in poly-ZnSe to those generated in single crystal ZnSe and found single crystal ZnSe to have more than an order of magnitude lower harmonic efficiency, and an absence of harmonics beyond the 3 rd . The threshold for multiple filamentation in terms of both pump power and propagation distance was extracted for our conditions. It was demonstrated that IHC comes primarily from filamentation within the material. Z-scans were performed to determine 2 n experimentally for a MIR wavelength, showing good agreement to the existing theory. Z-scan results were used as an input for numerical modeling of filamentation in poly-ZnSe. Our simulations show good qualitative agreement with the experiments and have led to insights about the underlying physics.