Phase retrieval from the spectral interference signal used to measure thickness of SiO<Subscript>2</Subscript> thin film on silicon wafer

A new method of phase retrieval from the spectral interference signal is presented, which is based on the use of a windowed Fourier transform in the wavelength domain. The phase retrieved by the method is utilized for measuring the thickness of SiO₂ thin film on a silicon wafer. The numerical simulations are performed to demonstrate high precision of the phase retrieval. The feasibility of the method is confirmed in processing experimental data from a slightly dispersive Michelson interferometer with one of the mirrors replaced by SiO₂ thin film on the silicon wafer. We determine the thin-film thickness for four samples provided that the optical constants for all the materials involved in the experiment are known. We confirm very good agreement with the previous results obtained by the fitting of the recorded channelled spectra to the theoretical ones. PACS 07.60.Ly; 42.30.Rx; 68.55.Jk; 78.20.Bh     

Total absorption of TM polarized light in a 100 nm spectral band in a nanopatterned thin a-Si film

We report a leaky-mode resonant absorber fashioned as one-dimensional nanopatterned ultra-thin films. This simple structure exhibits optical absorbance of ～66% in the 300-750 nm wavelength band, which is an ～60% increase relative to a comparable planar reference structure. The transverse-magnetic (TM) polarized light in the ～460-560 nm band is nearly totally absorbed. Applying a backside metal reflector raises the absorbance farther to ～73%.     

A spectral interferometric method to measure thickness with large range

We present a spectral interferometric method to measure the thickness of an optical plate or a film with a single layer. The system is based on the Michelson interferometer configuration, and the spectral interference signal of a broadband light source is recorded by a spectrometer. The optical path difference (OPD) between two interfering beams can be obtained by Fourier transform from the spectral interferogram. Gaussian fitting is used to find the exact peak of fringe to enhance the precision of the measurements. When the sample is inserted into the sample beam, the film’s thickness can be calculated by comparing the change of OPD, provided that the sample group refractive index is known. Only a single measurement is needed to determine a film’s thickness after the initial OPD of the system is calibrated. As no moving parts are required, the system has good stability. In particular, a large range of thicknesses, from micrometers up to several millimeters, can be measured. Such a large range is valuable for optical measurements. For demonstration, we measured the thicknesses of preservative film, cover glass and carrier glass, which were 9.6 ± 0.55, 156.1 ± 0.75, 1008.44 ± 0.96 μm, respectively.     

Spectral interferometry and reflectometry used to measure thin films

A new method for a precise measurement of the oscillatory part of phase change on reflection (interferometric phase) from a thin-film structure is presented. The method, which is based on phase retrieval from the spectral interferograms recorded at the output of a slightly dispersive Michelson interferometer, is combined with reflectometry. The interferometric phase of the thin-film structure is measured precisely using a reference sample of known phase change on reflection. The spectral reflectance of the thin-film structure is also measured in the interferometer. The feasibility of the method is confirmed in processing the experimental data for SiO₂ thin film on a silicon wafer of known optical constants. Four samples of the thin film are used and their thicknesses are determined. We confirm very good agreement between the thicknesses obtained from the interferometric phase and reflectance measurements. PACS  07.60.Ly; 68.55.Jk; 78.20.Bh     

Determination of thin film refractive index and thickness by means of film phase thickness

A new approach for determination of refractive index dispersion n(λ) (the real part of the complex refractive index) and thickness d of thin films of negligible absorption and weak dispersion is proposed. The calculation procedure is based on determination of the phase thickness of the film in the spectral region of measured transmittance data. All points of measured spectra are included in the calculations. Barium titanate thin films are investigated in the spectral region 0.38–0.78 μm and their n(λ) and d are calculated. The approach is validated using Swanepoel’s method and it is found to be applicable for relatively thin films when measured transmittance spectra have one minimum and one maximum only.      

Forced capillary waves in the pool covered with a thin film

Forced capillary waves are investigated in the pool of finite dimensions within the framework of linear dynamics of an incompressible liquid. Analytical expression for the velocity potential of the liquid in such waves is derived. It is demonstrated that amplitude poles of the forced capillary waves determine the frequency spectrum of free capillary waves. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 3–6, March, 2008.     

Propagation and scattering of waves in a strongly nonuniform nonabsorbing medium

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 3, pp. 307–313, March, 1989.     

Single-shot chirped-pulse spectral interferometry used to measure the femtosecond ionization dynamics of air

A novel interferometry technique is presented by which, in one shot, one can measure phase changes with a resolution of tens of femtoseconds while extending the measurement over picoseconds or even longer. The method is based on spectral (frequency-domain) interferometry with a pair of linearly chirped pules as probes. With this technique we obtained single-shot measurements of the rapid phase changes induced by optical field ionization of air. This allowed us to calculate the time profile of the electron density created by an intense short laser pulse.     

Accurate measurement method of the thickness of a quartz pendulous reed by combining polarized reflectance and vision image

The detection of thickness provides important information on the production process of the quartz pendulous reed (QRP). Through real-time detection of QPR thickness, high-quality products can be produced, and defective products can be identified and removed. In order to improve detection accuracy and efficiency, a novel noncontact method for measuring the QPR thickness by combining the polarized reflectance and vision image is presented, which can be automated. Based on Snell’s law of fundamental optics, the image of the laser spot is obtained by a laser vision system. The selection criterion of the laser incident angle is analyzed. An improved edge detection algorithm is proposed to locate the subpixel edge of the laser spot, and the calculation method of the laser spot center is presented based on a set of subpixel edge-point data obtained by defining an error function which is to optimize the distribution of data points and minimize it. Experimental results show that the method proposed has good stability and high measurement accuracy, which can achieve noncontact accurate measurement of QPR thickness.     

Depolarization of backscattered linearly polarized light from ZnO thin film

The depolarization behavior of backscattered linearly polarized light from ZnO thin film was investigated experimentally. The results show that the characteristics are related to both the polarization orientation and wavelength of linearly polarized incident light. When the incident light is s-polarized, the depolarization behaviors are different for different wavelengths. When the incident light is p-polarized, the depolarization behaviors, on the contrary, are similar for different wavelengths. In addition, there is an optimal incident angle for depolarization of linearly polarized light with different wavelengths, which is equal to their effective Brewster angles, respectively.     

用透射反射扫描法检测光学薄膜的激光损伤

 用波长1.06μm的激光透射反射自动扫描装置扫描了激光辐照前后薄膜的反射比和透射比。薄膜样品的工作波长为1.06μm。将扫描结果与相衬显微镜观察到的形貌相对照。实验结果表明，用透射反射扫描法不仅能反映出相衬显微镜所能观察到的损伤，而且也能发现某些显微镜所不能发现的损伤。由于透射比和反射比可以反映出薄膜对激光的传输性能，因此也能反映出薄膜能否继续工作，以此来判定损伤与否。因此用透射反射扫描法可以作为检测损伤的手段，由于简单易行，可以在线检测。避免目前损伤测试工作中繁重的人工操作。     

用透射反射扫描法检测光学薄膜的激光损伤

用波长1.06μm的激光透射反射自动扫描装置扫描了激光辐照前后薄膜的反射比和透射比。薄膜样品的工作波长为1.06μm。将扫描结果与相衬显微镜观察到的形貌相对照。实验结果表明,用透射反射扫描法不仅能反映出相衬显微镜所能观察到的损伤,而且也能发现某些显微镜所不能发现的损伤。由于透射比和反射比可以反映出薄膜对激光的传输性能,因此也能反映出薄膜能否继续工作,以此来判定损伤与否。因此用透射反射扫描法可以作为检测损伤的手段,由于简单易行,可以在线检测。避免目前损伤测试工作中繁重的人工操作。     

Electromagnetic waves in the nonlocal Josephson electrodynamics of a thin film of a magnetic superconductor

An integrodifferential equation describing the dynamics of the phase difference with spatial and temporal nonlocality is derived for a Josephson junction in a thin film of magnetic superconductor. It is shown that the magnetic subsystem renormalizes the spectrum of small-amplitude electromagnetic excitations and leads to their damping. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 2, 132–138 (25 January 1999)     

Nondestructive determination of film thickness with laser-induced surface acoustic waves

The application of surface acoustic waves(SAWs) for thickness measurement is presented. By studying the impact of film thickness h on the dispersion phenomenon of surface acoustic waves, a method for thickness determination based on theoretical dispersion curve v( fh) and experimental dispersion curve v( f) is developed. The method provides a series of thickness values at different frequencies f, and the mean value is considered as the final result of the measurement. The thicknesses of six interconnect films are determined by SAWs, and the results are compared with the manufacturer's data.The relative differences are in the range from 0.4% to 2.18%, which indicates that the surface acoustic wave technique is reliable and accurate in the nondestructive thickness determination for films. This method can be generally used for fast and direct determination of film thickness.     

Manipulation of effective thermal conductivity of multilayer thin film by varying thickness ratio of layers using Monte Carlo simulation

Using the kinetic-type Monte Carlo method, we have simulated the effective thermal conductivity of multilayer thin film with spectral diffuse mismatch model for interface treatment. The results show a monotonously increasing relationship between the thermal conductivity and the material thickness closer to isothermal boundary with a varied size ratio whereas the fixed material amount in two four-layer thin films. This is explained by relatively more significant size effect of the layer closer to the isothermal boundary than that of the layer apart from the isothermal boundary. The finding in the present work guides a new way for optimization and design of interface structures at micro- and nano-scale.     

激励表面等离子共振的金属薄膜最佳厚度分析

根据电磁场在金属薄膜中的能量分布规律和金属薄膜具有复介电常数的特点,对激励表面等离子共振的金属薄膜的最佳厚度进行了探讨. 指出金属薄膜的最佳厚度与激励光波长和金属薄膜的折射率有关,建立了描述它们之间关系的数学表达式,并用实验方法进行验证. 将理论结果与他人的测量结果进行对比后发现,两者符合较好. 研究结果表明：在角度调制下的表面等离子共振传感器,为了获得更高的灵敏度,可根据激励光波长和金属薄膜折射率的虚部确定所要制备金属薄膜的最佳厚度;在波长调制下,则由中心波长和折射率的虚部确定金属薄膜的最适宜使用厚度. 关键词： 折射率 金属薄膜 全内反射 表面等离子共振     

The effect of reflectance coefficients on the interaction of an H wave with a thin metal film

The interaction between an H wave and a thin metal film is calculated in the case of different values of the angle of incidence θ of the wave and reflectance coefficients q ₁ and q ₂ upon reflection of electrons from the surface of a thin metal layer. The behavior of the reflection, transmission, and absorption coefficients is analyzed as a function of the dimensionless frequency of bulk collisions of electrons X and dimensionless frequency of the external field y. The obtained results are compared with experimental data.     

A method for measuring the complex refractive index and thickness of a thin metal film

A circularly polarized heterodyne light beam is incident on a thin metal film, causing successive reflections and refractions to occur at the two sides of the thin film. The phase difference between p- and s-polarizations of the multiple-beam interference signal can be measured accurately with an analyzer and heterodyne interferometry. The phase difference depends on the azimuth angle of the analyzer, the complex refractive index and the thickness of the thin metal film. The measured values of the phase differences under three different azimuth angles of the analyzer can be substituted into the special equations derived from Fresnels equations and multiple-beam interference. Hence, the complex refractive index and the thickness of the thin metal film can be estimated by using a personal computer with a numerical analysis technique. Because of its common-path optical configuration and its heterodyne interferometric phase measurement, this method has many merits, such as high stability against surrounding vibrations, high resolution and easy operation. PACS 78.66.Bz; 78.20.Ci; 07.60.Cy     

Dyakonov-Tamm waves guided by a phase-twist combination defect in a sculptured nematic thin film

The propagation of Dyakonov-Tamm waves guided by a phase-twist combination defect in a sculptured nematic thin film (SNTF) was studied theoretically by numerical solution of a dispersion equation. The phase defect was fixed at 180°, whereas the twist defect was kept variable as also the direction of propagation. Multiple Dyakonov-Tamm waves that differ in spatial profile, degree of localization, and phase speed were found to propagate guided by the combination defect, depending on the angle between the morphologically significant planes of the SNTF on either side of the defect as well as on the direction of propagation. The most strongly localized Dyakonov-Tamm waves turned out to be essentially confined within one structural period of the SNTF normal to the combination defect.