Measurement of the optical dielectric properties of thin-film materials by ultrafast time-resolved interferometry

Results in Physics 16 (2020) 102958

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Measurement of the optical dielectric properties of thin-film materials by ultrafast time-resolved interferometry

T

Hai-Ying Songa,b, Peng Wanga,b, Qi-Ni Gea,b, Ya-Chao Lia,b, Elshaimaa M. Emaraa,b, ⁎ Mei-Rong Lua,b, Shi-Bing Liua,b, a Strong-field and Ultrafast Photonics Lab, Key Laboratory of Trans-scale Laser Manufacturing Technology, Ministry of Education, Institute of Laser Engineering, Beijing University of Technology, Beijing 100124, China b Beijing Engineering Research Center of Laser Technology, Beijing University of Technology, Beijing 100124, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Thin film material Refractive index Femtosecond time-resolving

We report a time-resolved optic interferometry (TROI) that enables to straightway probe the optical properties of traditional and special thin-film materials by feat of a phase delayed-interference between double beams of femtosecond laser synchronously traveling through vacuum (air) and sample, respectively. As a verification of measurement accuracy created by the TROI, the group and phase velocities as well as the refractive index of noncrystal thin-film HfO2, the crystal thin-film materials YAG (isotropic cubic system), and LiNbO3 (aeolotropic rigonal system), are measured by femtosecond laser pulse with 800 nm central wavelength. The data exhibit a satisfactory consequence in which even a subtle change of measurand can be ascertained by manipulating the resolution in temporal and spacial domains via the delay-line, whether the films are isotropic or aeolotropic and any different orientations of sample. Unambiguously, the presented TROI is conspicuous to the precision measurements of environment-dependent and phase-sensitive optical parameters especially involved in specific nanoscale optical devices and structured layers or coatings.

Introduction Usually, the optical properties of materials (matters) are light-wavelength dependent and associate closely with the dielectric constant (function) of the materials, ε = n + iηa in the linear approximation, where n and ηa describe the indexes of refraction and absorption, respectively. With the rapid emergence of new materials, the ascertainment of dielectric properties and protean dynamical responses for some special functions of optical materials have become more and more important in the diagnostics. For instance, the measurement of refractive index n for the organic materials (nanocomposites) incorporated by high refractive index inorganic materials like as ZnS [1,2], ZrO2[3], TiO2[4,5], PbS [6,7] etc., and the confirmation of optical response property for the amorphous (anatase phase) TiO2 nanostructured thin films[8–10] are essential for their wide applications in the future. Especially for some micro/nano scale structured layers [11–14]or coatings (such as metamaterials) [15–17]integrated into the micro-devices (or microsystems), the achievable measurement precision of optical parameters is difficult to hit the spot by employing the traditional optical interferometry, although it has been used for almost

a hundred years as a laboratory measurement technique. Accidentally, one may find that the final exhibited functions of the devices or systems composed of the film structural parts usually are related unexpectedly with responses to the optical parameters, and even governed by various properties of the extreme nonlinear optics or photonics. As thus one might be likely to acquire surprise observations by capturing some counterintuitive physical phenomena via the subtle changes of optical parameter caused by the light propagation through the complicated film materials. However, the conventional methods that ascertains the dielectric properties are well known diversified optical interferometric measurements with traditional coherent light sources[18,19]. The representative one of that is based on the change of the interference fringes when the coherent lights propagate through two well designed discrepant media (or nanosized systems). But it is usually not competent for the measurements of extreme nonlinear optical property or ultrafast dynamical response in micro/nano scale structured thin films (systems). Since the advent of femtosecond (fs) laser pulse, the accurate measurement of subtle changes of optical parameters such as the dielectric constant, absorptivity, and refractive index etc., becomes

⁎ Corresponding author at: Strong-field and Ultrafast Photonics Lab, Key Laboratory of Trans-scale Laser Manufacturing Technology, Ministry of Education, Institute of Laser Engineering, Beijing University of Technology, Beijing 100124, China. E-mail address: [email protected] (S.-B. Liu).

https://doi.org/10.1016/j.rinp.2020.102958 Received 25 December 2019; Received in revised form 17 January 2020; Accepted 17 January 2020 Available online 30 January 2020 2211-3797/ © 2020 Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).

Results in Physics 16 (2020) 102958

H.-Y. Song, et al.

possible for intricate film materials and surprisingly achieved rapid development by time-resolved ultrafast processes. To perform a satisfactory high resolution in the measurements, for instance, the fs laser was used for optical coherence tomography by way of either low-coherence interferometry[20] or complex spectral signal processing[21]. By means of fs open aperture Z-scan technique and transient absorption spectroscopy technique, recently, the ultrafast nonlinear optical properties and corresponding relaxation time of AI:InSe thin film were investigated[22]. Furthermore, for tracking a fs laser beam propagating in phase-sensitive photonic structures, the heterodyne detection and time-resolved photon scanning tunneling microscope was successfully developed to pinpoint the spatial position at which the fs pulse arrives at a particular moment by changing the reference branch timely[23]. The ultrafast time-resolving measurements (UTRM) of refractive index (RI) or dielectric constant of materials by means of fs laser propagating features has become an important approach, by feat of which one can obtain the unknown optical properties that conceals in some especial nanosized systems[24] (such as artificial structured materials or intricate surface layers). Both for practical application (online inspection) and scientific exploration, the UTRM is of potential advantages, and has come into using such as the microscopic detection of biomolecular interaction (receptor molecules with active binding sites)[25] and quantum interference in plasmonic waveguides[26], and so on. In this article, we report an ultrafast TROI by which a subtle change of optical parameters such as phase and group velocities as well as the refractive index can be conveniently detected via fs laser propagation through nanoscale film materials at random structural orientations. Besides the unambiguous high-precision, the presented TROI is of high time-dependent and high phase-sensitive features due to its distinctive timeresolving ability, and thus suits well to the detection of subtle changes about the anisotropic optical properties concealed in nanoscaled systems, such as the exact control of incorporated trace oxygen quantity over the optical and dielectric properties of high-κ hafnium-oxide thin films in the radio frequency reactive magnetron sputtering technique [27].

nondispersive medium vg = vp or dvp/ dk = 0 which means vp nothing with k ; (2) for dispersive medium vg ≠ vp or dvp/ dk ≠ 0 which involves two probable cases i.e., vg < vp implying the normal dispersion and vg > vp the anomalous dispersion. One can also find that, for given ω (or wavelength λ ), the light wave is interrupted or reflected since n = 0 or k → 0 and the light wave is absorbed due to the resonance when n = ∞ or k → ∞. It should be noted that, in general, the direction of group velocity vg is different from that of wave vector k for the anisotropic media in which it is identical to the normal direction on the isosurface of RI. The relevant dispersion relation, in this case, is written as ω = ω (k) = ω (k , θ , ϕ) and the RI vector is defined as n (k) = c k/ ω. Furthermore, the relationship of group velocity with RI meets the equation

ω

Experimental description To measure the group velocity of a fs laser propagating in optical medium by TROI method, we set up an experimental configuration as shown in Fig. 1. One can see from the appearance point of view that it basically is an extended Mach–Zehnder interferometer. A commercial ultrafast light source, Ti: sapphire fs pulse laser (micra-10, Coherent Inc.) with repetition frequency of 80 MHz, central wavelength of 800 nm and 50 fs duration, is splitted into two light beams i.e., one as a reference beam and another as a probe beam by a beam splitter BS1 in 1:1. In experiment, the probe beam passes through a sample stage and the reference beam through a TDL which is constituted by a motorized translation stage (Sigma, SGSP26) and a PZT (Sigma, SFS-60XYZ) with the resolution of 4 μm and 1 nm, respectively. This built-up time-delay platform is of an optimized adjust precision of 20 nm, and obviously it corresponds to a time-resolving precision of 0.13 fs. The reference and probe beams recombine in another beam splitter BS2 and the phase difference between these two beams can be adjusted by TDL, and eventually, the interference information will be collected and exhibited by a laser beam analyzer (LBA, USB-SP620U). The experiment can be carried out either in vacuum or in air. If the time difference (i.e., delayed time adjusted by TDL) between the equi-phase surfaces of two pulse beams arriving at LBA is δt0 , the corresponding OPD is cδt0/2 reading from TDL, where c is the light velocity. Therefore, before measurement let two beams meet the interference condition in the absence of sample in air or vacuum by subtly adjusting TDL, so that the clearly interference fringes arise gradually in LBA (here called as background interference, BI) as shown in Fig. 2(A) that observed from our experiment, by which the reference coordinate x 0 (=cδt0/2) written from TDL can be calibrated such as that relates with Fig. 2 [A(d)]. In addition, we also can observe the signal of interference intensity which associates with the incident pulse envelope by so called the method of first order autocorrelation function and the change of intensity signal along with the delay time can be obtained as shown in Fig. 2(B), where the corresponding Gaussian fit curve for the autocorrelative intensity is labeled by the red solid line. In the experiments, the parallel approach used for x 0 calibration is also involved in the first order autocorrelation method. After calibration, insert sample in the probe light-path as shown in Fig. 1 and then readjust TDL to a coordinate x at which the interference signal (fringe or pulse envelope) shown up on the LBA reemerges clearly due to the change of OPD resulted from sample (here called as

A beam of pulse laser (ω0 , k 0 ) propagating in x direction through an optical medium can be usually considered as a wave packet superposed by a series of plane waves (ω, k ) and their wave vectors of these plane waves are limited to change in a small range near the wavenumber k 0 i.e.,

∫δk

A (k )exp ⎡i ⎛⎜kx − ωt ⎞⎟ ⎤ dk. ⎢ ⎥ ⎣ ⎝ ⎠⎦

(1)

The phase and group velocities are defined as vp = ω/ k and vg = dω/ dk , respectively. Taylor expansion of the dispersion relation ω (k ) at k = k 0 writes

dω ⎤ ω (k ) = ω (k 0) + ⎜⎛k − k 0⎟⎞ ⎡ + ⋯. ⎣ ⎝ ⎠ dk ⎦k = k 0

(2)

Substituting Eq. (2) into Eq. (1), yields

ψ ⎛⎜x , t ⎞⎟ = exp ⎡i ⎛⎜k 0 vg − ω0⎞⎟ t⎤ ⎢ ⎥ ⎝ ⎠ ⎣ ⎝ ⎠⎦

∫ A (k )exp ⎡⎢ik ⎛x − vg t ⎞ ⎤⎥ dk ⎜

⎣ ⎝

= exp ⎡i ⎜⎛vg / vp − 1⎟⎞ ω0 t⎤·ψ ⎛⎜x − vg t , 0⎞⎟, ⎢ ⎥ ⎣ ⎝ ⎠ ⎦ ⎝ ⎠

(4)

where n = n (ω) is the real part of complex RI n͠ (ω). The experimental implementation in this paper is based on fs laser interferometry, by means of which the interference signal produced by reference and probe lights propagation through different channels will exhibit by adjusting a time-delay-line (TDL) to change their optical path difference (OPD).

Basic principle

ψ ⎛⎜x , t ⎞⎟ = ⎝ ⎠

dn c +n− = 0, dω vg

⎟

⎠⎦

(3)

where ψ (x − vg t , 0) is the packet at t = 0 and ω0 = ω (k = k 0) . It indicates that the waveform of the packet ψ at position x and time t is same as that of initial packet ψ (x − vg t , 0) and the only change is that the phase is delayed for (k 0 vg − ω0) t . In general, the relation between vg and vp gives vg = dω/ d k = vp e k̂ + k (dvp/ d k) , where e k̂ is the unit vector of propagating direction of light. It presents two implications: (1) for 2

Results in Physics 16 (2020) 102958

H.-Y. Song, et al.

Fig. 1. Schematic diagram of the experimental setup, where BSi is the beam splitter, Mi the mirror, and LBA the laser beam analyzer. (i = 1, 2, …).

period of the incident laser field so as to ensure that the time delay happens in the same one optical period (~ 2.7 fs) although the timeresolution of this measurement system is up to 0.13 fs. Thus we need to take the smallest one of observed PTDs in the experiments. Furthermore, to estimate the measurement accuracy we define the error of observed value as

sample interference, SI), and hence the time delay can be determined by recording the coordinates x 0 and x successively from TDL as δt = 2 x − x 0 / c = 2δx / c , where the factor of 2 stems from the doublepass geometry in the TDL (see Fig. 3). On the other hand, when the same fs laser probe beam propagates in sample and in air with a same distance (thickness) of d, respectively, the time difference (time-delay) resulted in the phase velocity vp ≠ c is distinctly written as δtp = d/ vp − d/ c which is called as phase timedelay (PTD). In the same way, the group time-delay (GTD) is δtg = d/ vg − d/ c . Thus, the phase velocity and group velocity, in experiment, can be obtained i.e.,

vp, g =

cd , 2δx (p , g ) + d

ηψ =

ψtheor − ψ × 100% ψtheor

(6)

where ψ is the observed value in the experiments and ψtheor is the corresponding theoretical value. Experimental result

(5)

To test the reliability and stability of the measurement system in air, here we chose three different kinds of optical film materials. The LiNbO3 crystal with aeolotropic rigonal system is of periodic

where δx (p) (=cδtp) is the coordinate change that results from PTD and δx (g ) (=cδtg ) is that results from GTD. It needs to indicate that the PTD resulted in the thickness of sample must be shorter than one optical

Fig. 2. Time-resolving fs laser pulse-beams interferogram in air. (A) The interference fringes between the two beams with the time delays of (a) −70.00 fs, (b) −46.70 fs, (c) −20.00 fs, (d) 0.00 fs, (e) 33.00 fs, and (f) 66.70 fs. (B) The observed interference signal with the delay times and its Gaussian fit curve (red solid line). 3

Results in Physics 16 (2020) 102958

H.-Y. Song, et al.

Fig. 3. TSchematic diagram for the measurement of time-delaying in the experiment when the fs laser pulse propagates through the sample, where x − x 0 = δx .

which corresponds to the GTD δtg = 3839.67 fs. Consequently, according to Eq. 5 the group velocity vg = 1.3951 × 108 m/s. From early literatures [28,29], the theoretical value of group velocity for LiNbO3 at 800 nm wavelength presents vg = 1.394 × 108 m/s. Therefore, in accordance with Eq. (6) the error resulted in measurement is 0.08% which obviously exhibits a high measurement accuracy. However, the above observed GTD for such a thickness sample, 3839.67 fs, is far than the incident pulse duration and thus it is impossible to distinguish the interference signals resulted from different optical periods of laser field. Based on this case, therefore, we select non-crystal HfO2 film with thickness of 360 nm as a test sample by which the interference signals of BI and SI due to the changes of pulse envelope and phase are acquired as shown in Fig. 4(b) and 4(c). The OPDs for GTD and PTD reading from TDL are δx (g ) = 165 nm and δx (p) = 173 nm, which corresponds to the GTD δtg = 1.10 fs and PTD δtp = 1.15 fs, respectively. In

polarization on the quasi-phasing technology, it has good nonlinear optical properties, some functions such as electro-optic, acousto-optic, piezoelectric, etc., can be achieved. The YAG film with isotropic cubic system has advantages of optical, good mechanical, and stable chemical properties, it can be used as laser pumped crystal rod. The hafnium dioxide (HfO2) film is non-crystal, its excellent properties, such as high hardness, high refractive index, high laser damage threshold, and high transmittance from near ultraviolet to mid-infrared spectrum make it to be one of the promising high dielectric materials. First, a z-cut LiNbO3 crystal film with thickness of 106 nm is selected. Let the reference light pulse propagating in air and the probe light pulse propagating through sample (O-light) give rise to interference and then the acquired interference signals of BI and SI due to the change of pulse envelope are shown in Fig. 4(a). Evidently, the pulse envelope is broadened. The OPD by reading TDL is δx = 575547 nm from BI to SI,

Fig. 4. GTD and PTD produced by a femtosecond laser pulse at 800 nm wavelength propagating through the crystal samples of LiNbO3 and HfO2, respectively: (a) GTD δtg resulted from BI (red) and SI (blue) through crystal plate LiNbO3 with 106 nm thickness, (b) and (c) GTD δtg and PTD δtp resulted from BI (orange) and SI (violet) through an amorphous film sample HfO2 with 360 nm thickness, respectively. 4

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Table 1 The relevant optical parameters for some crystal materials at 800 nm fs-laser wavelength, where the units of vg and vp are in m/s, δx (g , p) in nm, and δtg, p in fs, respectively. The n and n theor represent experimental and theoretical RI values. Sample

d [nm]

δx (g )/ δtg

δx (p)/ δtp

vg [×108 ]

vp [×108 ]

n

ntheor

ηn [%]

HfO2

360

166/1.10

172/1.15

1.5623

1.5348

1.9546

1.9600 [31]

0.275

x-cut LiNbO3 z-cut LiNbO3

520 520

282/1.89 299/1.99

307/2.05 325/2.16

1.4393 1.3952

1.3759 1.3344

2.1804 2.2482

2.1755 [28,29] 2.2553 [28,29]

0.225 0.315 0.155

00 -cut YAG

720

286/1.91

295/1.97

1.6723

1.6496

1.8186

1.8214 [32]

300 -cut YAG

720

285/1.89

295/1.97

1.6745

1.6498

1.8183

1.8214 [32]

0.170

450 -cut YAG

720

287/1.91

294/1.96

1.6690

1.6499

1.8182

1.8214 [32]

0.173

Declaration of Competing Interest

terms of Eq. (5), the group and phase velocities can be presented as vg = 1.5623 × 108 m/s and vp = 1.5348 × 108 m/s, respectively. Consequently, for the incident laser at 800 nm wavelength the measured RI value can be acquired, n = c / vp = 1.9546 . The theoretical RI value can be achieved by Sellmeier equation[30,31] which writes n theor = 1.9600 and corresponding measurement error ηn = 0.275%. In addition, one can see from the signals of Fig. 4 that the phase velocity of laser pulse propagation associates with the shift of fast vibrating interference curve and thus the PTD can make the resolution of time domain in small than one optical period, which implies the thickness of test sample can be extended to nanoscale. For more comparison, the YAG film is used. Table 1 presents some optical parameters of noncrystal HfO2, isotropic YAG and aeolotropic LiNbO3 crystal films with different cuts and thickness at 800 nm wavelength of laser light. The data show up the tiny differences following the cuts of various orientations for nanoscale materials (or structured layers) even for the isotropic media. As we know the optical properties of isotropic crystals are the same in all directions, while the optical properties of aeolotropic crystals are imparity in different directions. The time-resolved measuring results are agree well with the actual characteristics, and the accuracy of the TROI equipment is further proved.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements We acknowledge the financial support from the National Natural Science Foundation of China (NSFC) with Grant Nos. 51705009 and 51875006, and the Beijing Education Commission (BEC) with Grant Nos. JC101011201801 and KZ201710005004. References [1] Denisyuk I, Fokina M. A review of high nanoparticles concentration composites: semiconductor and high refractive index materials, in nanocrystals, Y. Masuda, ed. Chap. 5 (Sciyo, 2010). [2] Lu C, Cui Z, Wang Y, Li Z, Guan C, Yang B, Shen J. Preparation and characterization of ZnS-polymer nanocomposite films with high refractive index. J Mater Chem 2003;13:2189–95. [3] Xu K, Hu YQ. Fabrication of transparent Pu/Zro2 nanocomposite coatings with high refractive index. Chin J Polym Sci 2010;28:13–20. [4] Pradana A, Kluge C, Gerken M. Tailoring the refractive index of nanoimprint resist by blending with TiO2 nanoparticles. Opt Mater Express 2014;4:329–37. [5] Cai B, Sugihara O, Elim HI, Adschiri T, Kaino T. A novel preparation of high-refractive-index and highly transparent polymer nanohybrid composites. Appl Phys Express 2011;4:092601. [6] Zimmermann L, Weibel M, Caseri W, Suter UW. High refractive index films of polymer nanocomposites. J Mater Res 1993;8:1742–8. [7] Lü C, Guan C, Liu Y, Cheng Y, Yang B. PbS/polymer nanocomposite optical materials with high refractive index. Chem Mater 2005;17:2448–54. [8] Wang Bin, Hongji Qi Hu, Wang Yanyan Cui, Zhao Jiaoling, Guo Jialu, Cui Yun, Liu Youchen, Yi Kui, Shao Jianda. Morphology, structure and optical properties in TiO2 nanostructured films annealed at various temperatures. Opt Mater Express 2015;5:1410–8. [9] Luttrell T, Halpegamage S, Tao J, Kramer A, Sutter E, Batzill M. Why is anatase a better photocatalyst than rutile? – Model studies on epitaxial TiO2 films. Sci Rep 2014;4043. [10] Kasai J, Hitosugi T, Moriyama M, Goshonoo K, Hoang NLH, Nakao S, Yamada N, Hasegawa T. Properties of TiO2-based transparent conducting oxide thin films on GaN (0001) surfaces. J Appl Phys 2010;107:053110. [11] Buividas R, Mikutis M, Juodkazis S. Surface and bulk structuring of materials by ripples with long and short laser pulses: recent advances. Prog Quantum Electron 2014;38:119. [12] Song HY, Liu SB, Liu HY, Wang Y, Chen T, Dong XM. Subwavelength topological structures resulting from surface two-plasmon resonance by femtosecond laser exposure solid surface. Opt Express 2016;24:012151. [13] Song H, Zhang Y, Dong X, Liu S. Subwavelength ripple formation on planar and non-planar surfaces by femtosecond laser scanning. Chin Opt Lett 2016;14:123202. [14] Meng J, Song H, Li X, Liu S. Influence of femtosecond laser pulse energy on the surface reflection of black silicon in alkaline solution. J Laser Appl 2016;28:012005. [15] Pombo-García K, Zarschler K, Barbaro L, Barreto JA, O’Malley W, Spiccia L, Stephan H, Graham B. Zwitterionic-coated ‘stealth’ nanoparticles for biomedical applications: recent advances in countering biomolecular corona formation and uptake by the mononuclear phagocyte system. J Laser Appl 2016;28:012005. [16] Smith DR, Pendry JB, Wiltshire MCK. Metamaterials and negative refractive index. Science 2004;305:788. [17] Zheng X, Lee H, Weisgraber TH, Shusteff M, DeOtte J, Duoss EB, Kuntz JD, Biener MM, Ge Q, Jackson JA, Kucheyev SO, Fang NX, Spadaccini CM. Ultralight, ultrastiff mechanical metamaterials. Science 2014;344:1373. [18] Hariharan P. Basics of Interferometry. Academic; 2007. [19] Malacara D. Optical Shop Testing. Hoboken: John Wiley & Sons; 2007.

Conclusions In conclusion, as a high-precision detection method with femtosecond time-resolving power, we introduce a temporal domain interferometry to measure the group and phase velocities as well as the refractive index experimentally by fs pulse laser propagating in optical film materials including noncrystal and crystal nanoscale films at 800 nm wavelength. The strict synchronism of probe and reference beams due to which is split by one incident beam is guaranteed, and the ultrahigh time-resolving precision with 0.13 fs provides perfect recognition capability of optical information. Based on this superiority technically, the observations show that the subtle changes of optical parameter at different orientations samples can be ascertained whether the isotropic YAG with cubic system or the aeolotropic LiNbO3 with rigonal system. This method is appropriate well for the accurate measurement of optical parameters for any nanoscale optical media (materials), especially for some specific structured surfaces or layers that traditional measurement is unfulfillable.

CRediT authorship contribution statement Hai-Ying Song: Conceptualization, Data curation, Formal analysis, Writing - original draft. Peng Wang: Data curation, Software. Qi-Ni Ge: Data curation. Ya-Chao Li: Investigation. Mei-Rong Lu: Data curation. Shi-Bing Liu: Conceptualization, Formal analysis, Writing - review & editing.

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