Rigorous theory of the diffraction of Gaussian beams by finite gratings: TE polarization

A rigorous modal theory for the diffraction of Gaussian beams from N equally spaced slits (finite grating) in a planar perfectly conducting thin screen is presented. The case of normal incidence and TE polarization state is considered; i.e., the electric field is parallel to the slits. The characteristics of the far-field diffraction patterns, the transmission coefficient, and the normally diffracted energy as a function of several optogeometrical parameters are analyzed within the so-called vectorial region, where the polarization effects are important. The diffraction pattern of an aperiodic grating is also considered. In addition, one diffraction property known to be valid in the scalar region is generalized to the vectorial region: the existence of constant-intensity angles in the far field when the incident beam wave is scanned along the N slits. The classical grating equation is tested for incident Gaussian beams under several conditions.     

Use of a Fabry-Perot interferometer to isolate pure rotational Raman spectra of diatomic molecules

We propose to use a Fabry-Perot interferometer (FPI) as a comb frequency filter to isolate pure rotational Raman spectra (PRRS) of nitrogen molecules. In making the FPI's free spectral range equal to the spectral spacing between the lines of nitrogen PRRS, which are practically equidistant, one obtains a device with a comb transmission function with the same period. However, to match the FPI transmission comb completely with the comb of nitrogen PRRS lines one should tune the wavelength of the radiation used to excite the PRRS of nitrogen exactly to the position of any minimum in the FPI transmission comb. Thus to achieve this task for the case of nitrogen PRRS one must take the FPI's free spectral range Dnu(f)= 4B(N(2)) and the wavelength of the exciting radiation such that (1/lambda(exc)) = 4B(N(2))(k + 1/2), where B(N(2)) is the rotational constant of the nitrogen molecule and k is an arbitrary integer number. In this case all (odd and even) pure rotational Raman lines of nitrogen will pass through the FPI while the line of exciting radiation is being suppressed. Additionally, a FPI cuts out the spectrally continuous sky background light from the spectral gaps between the PRRS lines.     

Two-dimensional point spread matrix of layered metal-dielectric imaging elements

We describe the change of the spatial distribution of the state of polarization occurring during two-dimensional (2D) imaging through a multilayer and in particular through a layered metallic flat lens. Linear or circular polarization of incident light is not preserved due to the difference in the amplitude transfer functions for the TM and TE polarizations. In effect, the transfer function and the point spread function (PSF) that characterize 2D imaging through a multilayer both have a matrix form, and cross-polarization coupling is observed for spatially modulated beams with a linear or circular incident polarization. The PSF in a matrix form is used to characterize the resolution of the superlens for different polarization states. We demonstrate how the 2D PSF may be used to design a simple diffractive nanoelement consisting of two radial slits. The structure assures the separation of nondiffracting radial beams originating from two slits in the mask and exhibits an interesting property of a backward power flow in between the two rings.     

Polarization-dependent Talbot effect

The term "polarization-dependent Talbot effect" means that the Talbot self-imaging intensity of a high-density grating is different for TE and TM polarization modes. Numerical simulations with the finite-difference time-domain method show that the polarization dependence of the Talbot images is obvious for gratings with period d between 2 lambda and 3 lambda. Such a polarization-dependent difference for TE and TM polarization of a high-density grating of 630 lines/mm (corresponding to d/lambda=2.5) is verified through experiments with the scanning near-field optical microscopy technique, in which a He-Ne laser is used as its polarization is changed from the TE mode to the TM mode. The polarization-dependent Talbot effect should help us to understand more clearly the diffraction behavior of a high-density grating in nano-optics and contribute to wide application of the Talbot effect.     

Measurement of duty cycles of metal grating masks formed on dielectric substrates

A nondestructive method for measuring the duty cycles of metal grating masks formed on top of dielectric substrates is proposed. For a near-normal angle of incidence, the zeroth diffracted order transmission efficiency curves for both TE and TM polarized probe lights, as a function of duty cycles, behave linearly in the duty cycle ranging from 0 to 1. By comparing the measured efficiencies, or the ratio of zeroth-order transmission efficiency for TM polarization to that for TE polarization, with that of the rigorous-coupled wave analysis (RCWA) method for a fixed grating period and depth, one can determine the duty cycle of the grating. By selecting the probe light appropriately, the measurement errors originating from deviations of the incident angle and grating depth can be negligible. This method is applicable for all metal gratings, which are not easy to measure nondestructively due to fine grooves smaller than the wavelength. This method is simple, accurate, nondestructive, and low-cost. The results of experimental verification are presented and show excellent agreement with scanning electron microscope images.     

Optical transmission through double-layer compound metallic gratings with subwavelength slits

Optical transmission through a double-layer compound metallic grating (DCMG) composed of two identical compound metallic gratings (CMGs) with two subwavelength slits filled with different dielectrics inside each period is investigated by using the finite-difference time-domain method. The results show that the transmission properties of the DCMG are dependent on both the separation G between the two metallic layers and the phase configurations of the electromagnetic waves at the exits of adjacent slits of each layer. When a suitable separation (G?～?300?nm) is chosen, for the DCMG a notable transmission peak emerges at a certain wavelength, at which phase resonance appears for the corresponding CMG, while the transmission spectra of the corresponding double-layer simple metallic gratings (DSMGs) with the separation (G?～?300?nm) exhibit unexpected transmission suppression in a broad spectral region. When G?>?340?nm, the intensity of the transmission around the wavelength for the DCMG gradually decreases down to almost zero as G increases, while the high transmission is nearly maintained for the corresponding DSMGs.     

Polarization dependence of the coupling ratio in LiTaO3 directional couplers

The effect of design and fabrication parameters on the polarization dependence of the splitting ratio in directional couplers produced in LiTaO3 by Zn diffusion has been investigated experimentally at a wavelength of 1558 nm. The directional couplers featured various combinations of waveguide width, separation gaps between waveguides, bending angle, and diffusion conditions. In each case the coupling region was 3.5 mm long. Of particular interest was the identification of parameter sets for which the sum of power splitting ratios from TE and TM inputs equals unity at the output, as needed for electro-optic tunable filters with relaxed beam-splitter requirements.     

Contrast in the evanescent near field of lambda/20 period gratings for photolithography

Light propagation through gratings with periods as small as lambda/20 is investigated computationally by use of the multiple multipole method in two dimensions. High image contrast is evident close to the grating. Strong evanescent decay of the high spatial frequency components is observed with the region of high contrast shrinking linearly as the period of the grating is decreased. Simulations were performed for TE and TM polarizations with the TM polarization providing the dominant contrast compared with TE, which is strongly attenuated owing to the polarizing effect of the gratings. These results show good promise for optical contact lithography in the evanescent near field of a shadow mask to attain feature sizes smaller than lambda/20.     

Modeling, fabrication, and characterization of tungsten silicide wire-grid polarizer in infrared region

We designed and fabricated a tungsten silicide wire-grid polarizer. To examine its polarization characteristics, the transmission spectra of the polarizer were simulated using the effective medium theory. The polarizer was fabricated based on the simulation results. The transverse magnetic (TM) polarization transmittance of the fabricated polarizer was greater than 50% over the 5 mum wavelength, and the ratio of TM and transverse electric transmittance was greater than 100 (20 dB) in the infrared range. This fabricated polarizer has higher durability and better compatibility with microfabrication processes than conventional infrared polarizers.     

Color separation of high-density dielectric rectangular grating in the Fresnel diffraction region

A high-density dielectric rectangular grating is designed for color separation in a Fresnel diffraction field. The Fresnel field distribution is analyzed and the optimization conditions for color separation are given. The process of the modes propagating and energy exchanging with the diffraction orders are expressed by modal method. The color separation for different polarizations can be realized. The energy efficiency is 96.3% at the 633 nm wavelength and 86.9% at the 488 mm wavelength for both TE polarizations, while the energy efficiency is theoretically 96.3% at the 633 nm wavelength for TE polarization and 90.6% at the 488 nm wavelength for TM polarization. The field distributions are scanned by the near-field scanning optical microscopy, and the efficiency is 71.2% for the 633 nm wavelength and 67.3% for the 488 nm wavelength for both TE polarizations experimentally.     

TM Wave Resonant Peaks in Defect-Free Multilayer Structures Containing Nano-Scale Y123 Superconductors

In the ultraviolet region and by using transfer matrix method, the transmission spectra of electromagnetic waves through one-dimensional quasiperiodic photonic structures consisting of high-temperature yttrium barium copper oxide (Y123) superconductor and strontium titanate (STO) dielectric layers are studied theoretically. It is shown that for TE polarization at oblique incidence two band gaps are created, while for TM polarization three band gaps are produced. The edges of both polarizations shift to higher wavelengths by increasing incident angles. Also, for angles of incidence greater than 78^°, the second gap for TM-polarized light is eliminated. It is also found that in the supposed structure the number of PBGs can be modulated by the thickness of dielectric layer, while it is nearly insensitive to the thickness of superconductor layer. Interestingly, for the incidence angles other than normal incidence the structure can exhibit some narrow resonant peaks near wavelengths where the electric permittivity of the superconductor layer changes sign. These resonant peaks are only for TM polarization and not present for TE polarization. This structure can act as a very compact polarization sensitive splitters and defect-free multichannel narrowband tunable filters.     

Optical characterization of dielectric and semiconductor thin films by use of transmission data

A method to calculate the optical functions n(lambda) and k(lambda) by use of the transmission spectrum of a dielectric or semiconducting thin film measured at normal incidence is described. The spectrum should include the low-absorption region and the absorption edge to yield the relevant optical characteristics of the material. The formulas are derived from electromagnetic theory with no simplifying assumptions. Transparent films are considered as a particular case for which a simple method of calculation is proposed. In the general case of absorbing films the method takes advantage of some properties of the transmittance T(lambda) to permit the parameters in the two regions mentioned above to be calculated separately. The interference fringes and the optical path at the extrema of T(lambda) are exploited for determining with precision the refractive index and the film thickness. The absorption coefficient is computed at the absorption edge by an efficient iterative method. At the transition zone between the interference region and the absorption edge artifacts in the absorption curve are avoided. A small amount of absorption of the substrate is allowed for in the theory by means of a factor determined from an independent measurement, thus improving the quality of the results. Application of the method to a transmission spectrum of an a:Si(x)N(1-x):H film is illustrated in detail. Refractive index, dispersion parameters, film thickness, absorption coefficient, and optical gap are given with the help of tables and graphs.     

Spectral invariance under daylight illumination changes

We develop a method for calculating invariant spectra of light reflected from surfaces under changing daylight illumination conditions. A necessary part of the method is representing the illuminant in a suitable form. We represent daylight by a function E(lambda, T) = h(lambda)exp[u(lambda)f(T)], where lambda is the wavelength, T is the color temperature, h(lambda) and u(lambda) are any functions of lambda but not T, and f(T) is any function of T but not lambda. We use an eigenvalue decomposition on the logarithm of the CIE daylight standard at various color temperatures to obtain the necessary functions and show that this gives an extremely good fit to CIE daylight over our experimental range. We obtain experimental data over the range 350-830 nm from a range of standard colored surfaces for 50 daylight conditions covering a wide range of illumination spectra. Despite a considerable variation in the spectra of the reflected light, we show only small variations when the transformation is used. We investigate the possible causes of the residual variation and conclude that using the above approximation to daylight is unlikely to be a major cause. Some variation is caused by local daylight conditions being different from the CIE standard and the rest by measurement and modeling errors.     

Spectral characteristics of asymmetric directional couplers in graded index channel waveguides analyzed by coupled-mode and normal-mode techniques

We present a detailed analysis of the spectral characteristics of asymmetric directional couplers (ADC's) formed by K(+) -Na(+) ion exchange in BK7 glass and compare the results obtained by the use of normal-mode theory with those obtained by the use of the coupled-mode approach. Maximum power transfer is observed to occur at the wavelength at which the propagation constants of the perturbed component arms are equal. This is attributed to the strong coupling inherent in these devices. Strong coupling and asymmetry are observed to result in unequal confinement of the normal modes, leading to reduce power transfer, even when both arms of the coupler are synchronized. Additionally, significant polarization dependence is observed because of birefringence induced by both the K(+) -Na(+) exchange process and the chosen device structure. Polarization extinction ratios of 11.9 and 26.1 dB are obtained for the arms of the directional couplers. ADC's are observed to operate as bandpass filters, and by adjustment of structural parameters, the peak transmission wavelength can be tuned, with spectral bandwidths of 25-55 nm and coupling lengths of 6-12 mm. Over 90% of the input power in the TE polarization at 1.07 μm can be transferred to the second arm of the coupler, whereas power either in the TM polarization or at wavelengths outside the passband is relatively unaffected. We also show that within the bandpass, where the two arms are phase matched, exact normal-mode analysis yields the same results as the quasi-normal-mode approach, in which the normal modes are expressed in terms of the individual modes.     

Analytical calculation of the longitudinal electric field resulting from the tight focusing of an ultrafast transverse-magnetic laser beam

A purely time-domain approach is proposed for the propagation of vectorial ultrafast beams in free space beyond the paraxial and the slowly varying envelope approximations. As an example of application of this method, we describe in detail the vectorial properties of an ultrafast tightly focused transverse-magnetic (TM(01)) beam, where special attention is given to the longitudinal electric field component. We show that for spot sizes at the waist comparable to the wavelength, the beam diverges more rapidly than expected from paraxial theory. A consequence of this phenomenon is a faster decrease of the amplitude of the longitudinal field away from the waist and a faster evolution of the axial Gouy phase shift in the vicinity of the focus. It has been observed that the phase of the beam has an overall variation of 2pi from z=-infinity to infinity, independent of the beam spot size at the waist and pulse duration.     

Some properties of the optical resonances in a single subwavelength slit

Diffraction of TM-polarized waves by a slit in a thick screen of infinite conductivity is treated. The case of an arbitrary incident beam wave is considered. We study the resonances that appear when the wavelength of the incident beam wave is larger than the slit width, i.e., the subwavelength regime where a one-mode model for the slit can be considered. High anomalous values (resonances) of the transmission coefficient, the angular diffracted energy, and the magnetic field within the slit are analyzed. A simple linear relationship to determine the resonant wavelengths is proposed. We show that the transmission coefficient, the normal diffracted energy, and the magnetic field within the cavity are linear functions of the resonant wavelength and the thickness of the screen. Additionally and surprisingly, we reveal that under certain conditions the incident beam wave via the diffraction can give a suppressed light transmission; i.e., a minimum in the transmission is obtained where a maximum is expected.     

Investigation in the propagation of non-paraxial TE vector Gaussian beam from vectorial structure

Based on the vectorial structure of non-paraxial electromagnetic beam and the non-paraxial vectorial moment theory of light beam propagation, the beam waists, the divergence angles and the beam propagation factors of TE and TM terms have been presented for non-paraxial TE vector Gaussian beam. The formulae obtained are further discussed at the highly non-paraxial and paraxial cases. Their respective maximum divergence angles are given at the highly non-paraxial case. When reducing to the paraxial case, the beam propagation factors of TE and TM terms are smaller than unity, which results from their special energy flux distribution. As TE and TM terms can be detached in the far field, they can be applied in the optical storage and collimation domains.     

Extended Nijboer-Zernike approach to aberration and birefringence retrieval in a high-numerical-aperture optical system

The judgment of the imaging quality of an optical system can be carried out by examining its through-focus intensity distribution. It has been shown in a previous paper that a scalar-wave analysis of the imaging process according to the extended Nijboer-Zernike theory allows the retrieval of the complex pupil function of the imaging system, including aberrations as well as transmission variations. However, the applicability of the scalar analysis is limited to systems with a numerical aperture (NA) value of the order of 0.60 or less; beyond these values polarization effects become significant. In this scalar retrieval method, the complex pupil function is represented by means of the coefficients of its expansion in a series involving the Zernike polynomials. This representation is highly efficient, in terms of number and magnitude of the required coefficients, and lends itself quite well to matching procedures in the focal region. This distinguishes the method from the retrieval schemes in the literature, which are normally not based on Zernike-type expansions, and rather rely on point-by-point matching procedures. In a previous paper [J. Opt. Soc. Am. A 20, 2281 (2003)] we have incorporated the extended Nijboer-Zernike approach into the Ignatowsky-Richards/Wolf formalism for the vectorial treatment of optical systems with high NA. In the present paper we further develop this approach by defining an appropriate set of functions that describe the energy density distribution in the focal region. Using this more refined analysis, we establish the set of equations that allow the retrieval of aberrations and birefringence from the intensity point-spread function in the focal volume for high-NA systems. It is shown that one needs four analyses of the intensity distribution in the image volume with different states of polarization in the entrance pupil. Only in this way will it be possible to retrieve the "vectorial" pupil function that includes the effects of birefringence induced by the imaging system. A first numerical test example is presented that illustrates the importance of using the vectorial approach and the correct NA value in the aberration retrieval scheme.     

一种低偏振可调谐光滤波器的优化设计

光通信系统要求可调谐光滤波器(TOF)隔离度高,偏振敏感性低,目前基于角度调谐滤光片技术的TOF很难满足这一要求.通过膜系仿真分析了此类TOF透射谱劣化的原因.针对不同偏振态的光束在倾斜入射时中心波长及带宽分离现象,提出一种对称反转光路对TOF透射谱进行优化,可在整个透射范围内(C波段)将TOF的隔离度提高到30dB以...     

Design and optimization of broadband and polarization-insensitive dual-core photonic crystal fiber coupler

In this paper, we propose a novel (to our knowledge) broadband and polarization-insensitive dual-core photonic crystal fiber (PCF) coupler through the introduction of an elliptical-shaped central air hole to offset the slight birefringence arising from the dual core. With a full vectorial finite element method and anisotropic perfectly matched layers as the external boundaries, the impact of several fiber parameters on the coupling characteristics of dual-core PCF is investigated in detail. Through optimizing the main fiber parameters, including core diameter, size and ellipticity of the central air hole, and refractive index difference, broadband and polarization-insensitive characteristics are achieved in the wavelength range from 0.8 to 1.7 μm. The variation of the coupling ratio is stabilized at 50±1%, and the coupling ratio difference between x polarization and y polarization is less than 2% over the wavelength range. This dual-core PCF makes it easier to develop a 3 dB coupler over a wide wavelength for passive optical networks and large optical systems.