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. 2020 Jan 30;5(5):2458–2464. doi: 10.1021/acsomega.9b04026

Highly Efficient Super-Continuum Generation on an Epsilon-Near-Zero Surface

Wendong Tian †, Fei Liang †, Shumeng Chi †, Chang Li †, Haohai Yu †,*, Han Zhang ‡,*, Huaijin Zhang †,*
PMCID: PMC7017490  PMID: 32064405

Abstract

graphic file with name ao9b04026_0004.jpg

The efficient super-continuum (SC) generation on a surface via a high-order photo–electron interaction is a great challenge for integrated optics because the surficial nonlinear optical efficiency is usually limited by finite light–matter interaction length and electric field intensity. Nowadays, epsilon-near-zero (ENZ) materials, showing infinite enhanced electronic field in theory, provide a kind of new platform to obtain a giant nonlinear response on the surface. Here, under the irradiation of a multiwavelength laser, an exotic and efficient SC generation from 406 to 1100 nm on the ENZ aluminum-doped zinc oxide surface was experimentally demonstrated by diversified nonlinear processes, including second harmonic generation, third harmonic generation, four wavelength mixing, and cascading stimulated Raman scattering. Particularly, an unprecedented nonlinear conversion efficiency of 3.94% W–1, 16 orders of magnitude higher than the common surface case (about 10–16% W–1), was presented.

1. Introduction

The inherent spirit of nonlinear optics is the generation of light sources with the new optical frequency and broadened spectrum by the nonlinear optical effects including sum-frequency, rectification, compression and amplification, and so forth. Remarkably, the super-continuum (SC) generation is a fascinating but challenging process with broadband spectrally continuous output via a high-order photo–electron interaction in nonlinear media under the irradiation of an ultrahigh-intensity pulsed laser.1−3 Until now, the SC generation ranging from ultraviolet to infrared and even terahertz region has been realized4,5 and has been successfully applied in many interdisciplinary areas from the classical to quantum science, including the high-resolution spectroscopy,6 optical coherence tomography,7 multiwavelength telecommunications,8,9 optical clocks,10 and so forth. In particular, it is also considered as a key for opening up new perspective to investigate the limits on the drift of fundamental physical constants.11 In nonlinear optical theory, the nonlinear response is dependent on the interaction length in the nonlinear medium and considerable nonlinearity, which boosts the SC generation in photonic fibers with meter-level length or plasmas with huge optical nonlinear coefficients in recent years.12,13 The present condition indicates that the SC generation on the surface is still a challenge because the atomic–thick interaction length determines the low efficiency of 10–16% W–1 or less14 in the nonlinear frequency conversion on the surface, despite that the surface is indeed favorable for modern integrated photonics and optics.

Recently, the epsilon-near-zero (ENZ) materials, in which both the real and imaginary parts of the epsilon approach zero, have drawn enormous interests in nonlinear optics and photonics.15−18 In Maxwell’s equations, the continuity of electric displacement on the interfaces provides the possibility for enhancing the applied light intensity by reduced epsilon of the medium.19 In view of nonlinear optics, the ENZ materials should have exotic properties because the infinitely boosted light-field intensity could be generated in theory, and it has been partially identified in single-wavelength,20 such as colossal nonlinear refractive index,15 second harmonic generation (SHG),21 ninth order harmonic generation,22 and so on.23 Here, we experimentally demonstrated the SC generation on the surface of an aluminum-doped zinc oxide (AZO) film with near-zero epsilon around 1500 nm. With a simultaneously multiwavelength (1130–1750 nm) mode-locked femtosecond laser, the SC generation spanning the range from 406 to 1100 nm was realized with the unprecedented nonlinear conversion efficiency of 3.94% W–1. The rich nonlinear optical processes were unambiguously identified to involve SHG, third harmonic generation (THG), four wavelength mixing (FWM), and cascading stimulated Raman scattering (SRS) (Figure 1a).

Figure 1.

Figure 1

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(a) Schematic diagram of SC generation on the AZO surface under 1.5 μm mode-locked femtosecond laser illumination; (b) atomic force microscopy (AFM) characterization of the as-prepared AZO film; (c) SEM graph of the AZO film surface; (d) XRD pattern of the AZO film and the standard diffraction of ZnO are plotted as comparison; (e) Raman spectrum of the AZO film; (f) linear relative epsilon of the AZO film calculated by the Drude model. The condition Re(ε) = 0 occurs at λ0 = 1503 nm. The shaded region shows the spectral range with Re(ε) less than 1.

2. Results and Discussion

2.1. Characterization and Linear Optical Property of the AZO Sample

The AZO film with doping Al3+ concentration of 1 at. % was prepared by pulsed laser deposition (PLD) on the sapphire substrate to get near-zero epsilon in the near-IR spectral region.24−27 The atomic force microscopy (AFM) was used to characterize the surface roughness, and the corresponding height profiles of the prepared film show an average thickness of 140 nm (Figure 1b). Moreover, the rough surface of the AZO surface consisting of bumps and holes was demonstrated by a scanning electron microscope (SEM) (Figure 1c). As the incident light is perpendicular to the surface, the electric field would be parallel to the air–AZO interface and its component in the z direction perpendicular to the interface would be negligible when the surface of the AZO film is strictly flat, thus leading to greatly reduced interaction strength between the incident light electric field and the surface. Therefore, the rough AZO film with a rough surface was employed in the following experiments. The X-ray diffraction (XRD) pattern (Figure 1d) shows that a strong (002) peak and relatively weak (004) peak are located at 34.95 and 73.13°, respectively, which are slightly larger than that of a standard hexagonal ZnO card (34.45 and 72.62°) because the substitution from Al3+ ions on Zn2+ sites results in the contracted lattices and shorter interplanar distance along the c-axis.

Besides, the Raman spectrum (Figure 1e) of the AZO film depicts significant peaks at 438, 483, 574, and 1147 cm–1, which can be assigned to E2high, 2LA, A1(LO), and 2 × 101(LO) modes of the ZnO,28 respectively, where E2 is high-frequency nonpolar mode and Raman active, LA is longitudinal acoustic modes, and A1(LO) and E1(LO) are both polar modes and Raman and infrared active.

In order to obtain the epsilon ε of the AZO thin film, the carrier concentration n and mobility μ were measured via the Hall effect with n = 2.011 × 1028/m3 and μ = 4.314 × 10–5 m2/V s. Then, the real and imaginary parts of epsilon of the AZO film can be calculated using the Drude model

2.1. 1

where ε∞ is the high-frequency epsilon (ε∞ = 3.85 for AZO), ε0 is the free space epsilon, ω is the angular frequency of incident photon, Inline graphicis the plasma frequency, Inline graphic is the charge carrier collision rate, e is elementary charge, and m* = 0.38 m0 (m0 is the mass of the electron) is the effective mass of electron for AZO. As shown in Figure 1f, it is obvious that both the real Re(ε) and imaginary Im(ε) parts of epsilon become less than that of the air (ε = 1) in the spectral range from 1294 to 1686 nm. Remarkably, the real epsilon part of AZO gradually inclines to become zero around the wavelength of 1503 nm (εAZO = 0.0017 + 0.0620i). The imaginary part of the AZO film decrease below 0.15, close to previous reports.24 To further check the accuracy of the theoretical calculations, the real and imaginary parts of the AZO epsilon from 400 to 650 nm were also measured by an ellipsometer (see Figure S1), in which the experimental results were exactly consistent with theoretical values.

From the boundary conditions of Maxwell’s equations, the electric displacement vector Dz in the z direction perpendicular to the interface between the air (Dair-z) and AZO (DAZO-z) must be continuous with Dair-z = DAZO-z, thereby the perpendicular electric fields in the air (Eair-z) and AZO (EAZO-z) should follow the relation of Inline graphic. Consequently, the intensity of electric field EAZO can be greatly enhanced in the wavelength range from 1294 to 1686 nm. For example, the enhancement factor reaches up to 68 and 588 contrast to Eair at the wavelengths of about 1500 and 1503 nm, respectively.

2.2. Second and THG on the AZO Film

The nonlinear optical responses of the AZO film including second and THG (SHG and THG) were studied with the configuration schematically displayed in Figure 2a. The pulsed fundamental laser with the pulse width of 100 fs and a repetition rate of 1 kHz was focused onto the AZO surface with a spot radius of 40 μm. Six wavelengths were utilized, namely, 1205, 1290, 1350, 1430, 1500, and 1544 nm, respectively. Finally, the spectra of the SHG and THG were collected and analyzed by an optical spectrometer.

Figure 2.

Figure 2

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(a). Schematic illustration of optical experiments, HWP, lens (L), filter (F), spectrometer (S), camera (C), and mirror (M); (b) relative SHG intensity of the AZO film under different wavelength incident laser; (c,d) SHG spectra of the AZO film and TaAs(112) face under the excitation laser of 1500 nm; and (e,f) THG spectra of the AZO film and Si(100) face under excitation laser of 1500 nm.

As shown in Figures 2b and S2, the SHG intensities under different fundamental wavelengths are totally divergent. It is relatively weak at 1205 nm and gradually increases to a peak value at 1500 nm. Then, the SHG intensity decreases when the incident wavelength further improves up to 1544 nm. As aforementioned, the real epsilon part of AZO is close to zero around 1503 nm, corresponding to enhanced electric field strength. Therefore, the SHG intensity of AZO is positively dependent on the strength of the internal electric field (Figure 2b). Furthermore, we compare SHG intensities of AZO and TaAs, the known largest second-order susceptibility χ(2) of 3600 pm/V,29 under the same experimental conditions with an incident power of 2.52 mW (Figure 2c,d). Impressively, the SHG intensity of AZO is still 226.5 times stronger than that of the TaAs(112) face, suggesting colossal nonlinear optical response on the AZO surface. Associated with the SHG theory, the SHG intensity (I) can be determined by30Inline graphic. Here, c is the speed of light, n is linear refraction index (n ≈ √ε), ε0 is the vacuum epsilon, and E is the electric field in the AZO sample. As discussed above, the electric field in the AZO film enhances by 68 times with respect to Eair at a wavelength of 1500 nm, whereas that in TaAs decreases to only 1/12 Eair owing to relatively large epsilon (ε = 12).31 Accordingly, the applied electric field EAZO on the AZO surface is about 816 times larger than that of TaAs under the same excitation conditions. Further, it can be deduced that Inline graphic and the absolute value of χ(2) for the AZO surface is determined to be 0.387 pm/V. Considering the difference between bulk and surface nonlinearity, the calibrated second-order nonlinear coefficient χ(2) of AZO is 0.993 pm/V via the Bloembergen–Pershan correction.19 Clearly, this value is only comparable, even smaller contrast to some commercial NLO crystal, such as BBO (χ11 = 3.2 pm/V), LiNbO3 (χ31 = 9.8 pm/V), and KTP (χ31 = 13 pm/V).32 This also indicates that the colossal second-order nonlinear response on the AZO surface is mainly attributed to the strongly boosted electric field in the ENZ region but not increased nonlinear susceptibility.

The nonlinear THG response on the surface of the AZO film was also studied under the irradiation at the wavelength of 1500 nm, corresponding to the THG wavelength of 500 nm shown in Figure 2e. Meanwhile, Si(100) wafer, with a third-order susceptibility of 1.05 × 10–16 m2/V2, is also utilized as comparison33 under the same experimental conditions (Figure 2f). Remarkably, the THG intensity of AZO is 4.03 times stronger than that of Si. Associated with the THG theory, the THG intensity (I) can be determined30 by Inline graphic with the third-order susceptibility χ(3). Similar to that discussed in the SHG process, the electric field on the Si surface decreases to only 2/3 Eair due to large epsilon of Si (ε = 1.5 at 1500 nm). Therefore, the applied electric field strength E on the AZO surface is about 150 times larger than that on Si under the same excitation conditions, and the third-order susceptibility χ(3) of AZO is determined to be 2.91 × 10–22 m2/V2, further to 4.62 × 10–22 m2/V2 via Bloembergen correction.34 Meanwhile, the third-order susceptibility measured by the closed-aperture Z-scan technique is 1.42 × 10–21 m2/V2 at the wavelength of 1500 nm (Figure S3), also 5 orders of magnitude smaller than that of Si wafer. Therefore, the enhanced THG effect on the AZO surface is also dominantly contributed from the boosted electrical field but not third-order susceptibility.

2.3. Efficient SC Generation on the AZO Film

Associated with the giant SHG and THG effects in the ENZ region shown above, a possible SC spectrum is expected on the surface of the AZO film by employing a multiwavelength laser in the ENZ region. Here, a multiwavelength laser with the wavelength from 1130 to 1750 nm is shown in Figure 3a, involving five main peaks, namely, peak I (1254–1303 nm), peak II (1303–1368 nm), peak III (1368–1456 nm), peak IV (1456–1564 nm), and peak V (1564–1654 nm). The laser intensity is the strongest at 1500 nm. As expected, the SHG threshold at the peak wavelength of 750 nm is 0.54 mW and the THG threshold at the peak wavelength of 500 nm is 0.67 mW. With the increase of incident power more than 1.2 mW, the peaks of SHG and THG start to broaden and overlap, thus leading to the appearance of an SC spectrum. As shown in Figure 3b, the bandwidth of the SC spectrum reaches to be 694 nm ranging from 406 to 1100 nm under the incident power of 4.35 mW, relating to a colorful spot depicted in Figure 3c. Moreover, the coverage length of the SC spectrum displays no obvious change by adjusting the incident angle and polarization of laser (Figure S4). Next, the deep mechanism of SC generation was elucidated via theoretical simulations. First, THG and SHG make contributions to the SC spectrum, covering from 401 to 541 nm (Figure 3d) and that from about 569 to 870 nm (Figure 3f), respectively. Besides, the theoretical frequency-summing was calculated by the summing of any two peaks of the incident laser with the results that the frequency-summing covered the wavelength range from 638 to 803 nm.

Figure 3.

Figure 3

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(a) Spectrum of input laser includes five peaks: peak I (1247–1303 nm), peak II (1303–1368 nm), peak III (1368–1456 nm), peak IV (1456–1564 nm), and peak V (1564–1654 nm); (b,c) SC spectrum and light spot extends from 406 to 1100 nm under 4.3 mW input power. In order to observe the spectral details more clearly, the ordinate is logarithmically processed. This spectrum can be divided into cyan region, green region, pink region, organic region, and chartreuse region, representing THG (d), SHG + anti-Stokes (e), SHG (f), SHG + Stokes (g) and FWM + anti-Stokes (h), and FWM (i) process, respectively; (j) relationship between input power and spectral width of SC generation; and (k) relationship between input power and output power.

Considering the giant third-order nonlinear process of AZO, the four-wave mixing was also calculated, as shown in Figures S5 and 3i, which indicates that the four-wave mixing should be responsible for the generation of the SC spectral component in the wavelength range from 422 to 541 and 988 to 1100 nm. However, the SC component in the spectral range from 541 to 569 nm cannot be attributed to the aforementioned effects. In fact, we found that the main SHG peak shifted from 750 to 724 nm in the SC generation process with a frequency shift about 486 cm–1, exactly equaling to the 2LA mode vibration in the AZO thin film (see Raman spectrum in Figures 1e and S6). Therefore, the cascaded SRS is also included in the SC generation. On basis of the SRS theory, the stronger the intensity of the narrowed-width vibrational peak, the larger the Raman gain will be. So, the 2LA mode in ZnO with a vibrational frequency of 486 cm–1 is regarded as the main contributor for the SRS process. As shown in Figure 3e, the coupling between the SHG signal and anti-Stokes process results in a new spectral region from 538 to 814 nm, which covers the aforementioned gap (541–569 nm). In addition, the cascaded SHG-Stokes (Figure 3g) and FWM-anti-Stokes (Figure 3h) process fill the spectral gap from 875 to 980 nm. Thus, we divide the SC generation into various nonlinear optical processes quantitatively. In fact, it is a very intriguing case to observe so diversified nonlinearity in one single material, especially on surfaces. In particular, we did not find obvious broadening in the reflected incident laser spectrum with respect to the incident laser (Figure S7), which may owe to the strong incident laser covering up the nonlinear optical effect in the near-infrared range, although the nonlinear response of the AZO thin film is strong.

Finally, we measured the spectral width (Figure 3j) and output power (Figure 3k) depending on the input laser intensity. The spectral width of SC generation displays an almost linear increase with improved input pump power, in which the spectral width is 660, 674, 680, 686, and 694 nm under illumination power of 1.3, 2.0, 2.8, 3.2, and 4.3 mW, respectively. The spectra generated on the AZO film under different incident power are shown in the Supporting Information (Figure S8 and Table S1). On the other hand, the output power also exhibits a positive relation to increased input laser intensity. When the pump power (Pin) is 4.3 mW, the output power (Pout) reaches up to 728 nW, corresponding to an unprecedented conversion efficiency of 3.9375% W–1 (Pout/Pin2). This value is nearly 16 orders of magnitude higher than the typical efficiency of the nonlinear frequency conversion on the surfaces (about 10–16% W–1). Considering the short interaction length in the ENZ film (only 140 nm), this unprecedented record efficiency suggests the giant potential of ENZ materials in nonlinear conversion applications.

It is worthy that the enhanced nonlinearity is a universal effect in ENZ materials. For example, transition-metal nitrides such as titanium nitride (TiN),35,36 zirconium nitride (ZrN),37 and organic materials38 exhibit near-zero permittivity in the visible regime. Besides, yttrium-doped cadmium oxide (CdO) features ENZ properties in the mid-infrared regime.39 The enhanced nonlinearity should be also available in these material systems.

3. Conclusions

In summary, we demonstrated the SC generation with the highly efficient cascaded nonlinear process on the AZO thin film in the near-zero epsilon range with a multiwavelength femtosecond laser. Both theoretical and experimental studies indicate that the giant SHG and THG response should be attributed to the great enhancement of the electric field strength on the ENZ surface but not unexceptional second and third-order nonlinear coefficients. The widest SC spectrum ranging from 406 to 1100 nm with the high conversion efficiency of 3.9375% W–1 was achieved for the first time. This work not only clears up the mechanism of the nonlinear optical response in the ENZ materials and provides a low-cost but efficient SC source for future medical diagnosis and tissue imaging but may also be helpful for the development of integrated nonlinear optics in the visible, near-infrared, and mid-infrared range.

4. Experimental Section

4.1. Fabrication of the AZO Thin Film

The AZO film was fabricated by the PLD method on a sapphire substrate with the diameter of 20 mm. A KrF excimer laser with a repetition rate of 2 Hz was employed as the deposition source with the optimized pulse energy density 1.5 J/cm2 on the target, the Al3+-doped ZnO polycrystalline with Al3+ doping concentration of 1at. %. During the PLD process, the chamber was filled with pure oxygen with the pressure of 2 Pa, and the substrate was heated to 673 K. During irradiation by the excimer laser on the target, the AZO was deposited on the sapphire substrate, and its thickness could be controlled by the regulating the time of irradiation pulses.

4.2. Experimental Configuration for the Nonlinear Characterization of the AZO Thin Film

The input laser was obtained by the optical parametric amplification technique with a pulse width of 100 fs and repetition rate of 1 kHz. Then, the laser light was focused onto the AZO surface through the L1 lens. A half wave plate (HWP) was placed perpendicularly to the direction of the input laser to change its polarization direction, and a mirror (M1) was utilized to reflect the input laser onto the AZO sample. The selected output signals were imaged by the camera through the mirror (M2), and the other reflected signals were filtered by a filter. The generated SHG, THG, and SC signals collected by the objective lens (L2) were coupled into an optical fiber and the spectrometer (S), which could directly fetch the wavelength and intensity of the output signals quantitatively. The powers of SC were also measured by a power meter with high sensitivity.

4.3. Numerical Simulation of the SC Spectrum

The computational spectra were obtained by theoretical simulations using MATLAB software. Based on the spectrum of input laser and nonlinear polarization intensity formula, the wavelength of simulated spectra was calculated by addition or subtraction of involved frequency of fundamental laser. Then, the intensities of simulated spectra were obtained by the multiplication of square root of intensity (Inline graphic) of input laser.

Taking SHG spectrum as an example, its wavelength spanning and intensity can be calculated on basis of the fundamental wave data (wavelength and intensity) from 1130 to 1750 nm. The second-order nonlinear polarization intensity formula is

4.3. 2

where P2ω is the intensity of second-order polarization (ordinate axis of the computational spectra). Ei and Ej are two sets of electric field intensity of the fundamental frequency spectra. ω is the frequency. Ei, Ej, and ω are input data for SHG simulations. χij is second nonlinear coefficient and treated as a constant for the AZO film. c is light speed. Phase mismatch Δk is treated as zero, and wave vector k2ω can be calculated by simulated doubling wavelength.

Acknowledgments

This work was supported by National Key Research and Development Program of China (2016YFB0701002); National Natural Science Foundation of China (NSFC) (51422205, 51772173, 51890863); H.J.Z. acknowledge the support from Taishan Scholar Foundation of Shandong Province, China.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.9b04026.

  • Experimental setup, simulated methods and additional tables and figures, and measured dielectric constant (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao9b04026_si_001.pdf (1.6MB, pdf)

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