We present a sidewall patterned shifted Bragg grating based on an add-drop filter in silicon-on-insulator platform with a coating of amorphous titanium dioxide. This particular waveguide grating is equivalent to two identical gratings written across either sides of a waveguide with a longitudinal offset of half of a period. The add-drop operation occurs on the basis of mode conversion due to shifted sidewall structure followed by mode splitting with asymmetric Y-junction. A signal launched through the wide arm (single mode) of an asymmetric Y-junction generates the fundamental mode at the stem of the Y-branch. First order mode is generated at the stem if the signal is launched through the narrow arm. Thus, an asymmetric Y-branch is used as a mode splitter fulfilling proper limiting condition for an adiabatic operation. A signal at the Bragg wavelength launched through the wide arm of asymmetric Y-junction generates fundamental mode at the stem. The fundamental mode converted to first order upon reflection from the shifted Bragg grating. The reflected mode couples into the narrow arm of the Y-junction. The bandwidth of the reflected signal depends on the grating strength. We used 80 nm grating amplitude for 800 nm wide waveguide. The height of the guiding layer is 220 nm. The TiO2 thickness is set to 180 nm. A reflection bandwidth of 2.2 nm with 14 dB extinction ratio is obtained at 1552.5 nm for 300 µm long grating. We further demonstrate the potential of TiO2 recoating with atomic layer deposition as a method of fine tuning the spectrum.
We propose the nonlinear Fourier Modal Method (FMM) [J. Opt. Soc. Am. B 31, 2371 (2014)] as a convenient and versatile numerical tool for the design and analysis of grating based next generation all-optical devices. Here, we include several numerical examples where the FMM is used to simulate all-optically tunable functionalities in sub-wavelength periodic structures. At first, we numerically investigate a 1-D periodic nonlinear binary grating with amorphous TiO2. We plot the diffraction efficiency in the transmitted orders against the structure depth for normally incident plane wave. Change in diffraction efficiencies for different incident field amplitudes are evident from the plots. We verify the accuracy of our implementation by comparing our results with the results obtained with the nonlinear Split Field-Finite Difference Time Domain (SF-FDTD) method. Next we repeat the same experiment with vertically standing amorphous Titanium dioxide (TiO2) nanowire arrays grown on top of quartz which are periodic in two mutually perpendicular directions and examine the efficiencies in the direct transmitted light for different incident field amplitudes. Our third example includes analysis of a form birefringent linear grating with Kerr medium. With FMM we demonstrate that the birefringence of such a structure can be tuned by all-optical means. As a final example, we design a narrow band Guided Mode Resonance Filter (GMRF). Numerical experiments based on the nonlinear FMM reveal that the spectral tunability of such a filter can be obtained by all-optical means.
In this work the split-field finite-difference time-domain method (SF-FDTD) has been extended for the analysis of two-dimensionally periodic structures with third-order nonlinear media. The accuracy of the method is verified by comparisons with the nonlinear Fourier Modal Method (FMM). Once the formalism has been validated, examples of one- and two-dimensional nonlinear gratings are analysed. Regarding the 2D case, the shifting in resonant waveguides is corroborated. Here, not only the scalar Kerr effect is considered, the tensorial nature of the third-order nonlinear susceptibility is also included. The consideration of nonlinear materials in this kind of devices permits to design tunable devices such as variable band filters. However, the third-order nonlinear susceptibility is usually small and high intensities are needed in order to trigger the nonlinear effect. Here, a one-dimensional CBG is analysed in both linear and nonlinear regime and the shifting of the resonance peaks in both TE and TM are achieved numerically. The application of a numerical method based on the finite- difference time-domain method permits to analyse this issue from the time domain, thus bistability curves are also computed by means of the numerical method. These curves show how the nonlinear effect modifies the properties of the structure as a function of variable input pump field. When taking the nonlinear behaviour into account, the estimation of the electric field components becomes more challenging. In this paper, we present a set of acceleration strategies based on parallel software and hardware solutions.
Using the Fourier Modal Method for gratings with Kerr media [J. Opt. Soc. Am. B 31, 2371 (2014)] we demonstrate that low energy Optical Bistability for normally incident light field can be observed by strong nonlinear light-matter interactions in a Silicon Nitride waveguide-grating with 2-D periodicity. Finite divergence of the incident light beam has been taken into account in our numerical study and the gratings are designed to observe bistable behavior in direct transmitted light inside the optical telecommunication C-band (1520 nm-1570 nm). The waveguide grating structures are fabricated from PECVD synthesized Silicon Nitride thin film on top of quartz with standard electron beam lithography and reactive ion etching techniques. We aim to demonstrate this phenomenon experimentally using a tunable narrow line-width pulsed laser. Our resonant nanostructures may find applications in free space all-optical information processing and all-optical switching.
We demonstrate that the integration of graphene strongly influences optical properties of the subwavelength gratings, opening a way toward nanophotonic devices. By using the Fourier-expansion modal method, we demonstrate that graphene–titanium dioxide nanostructures can be used for designing polarization-insensitive absorbers and biochemical sensors.
A basic recipe for spatial shaping of spectrally and temporally partially coherent broadband pulsed fields like supercontinuum pulses is discussed. To shape these pulsed beams from Gaussian to flat-top shape, a shaping element is designed using the optical map transform method. The spatial profiles show a high quality flat-top region and the time integrated intensity profile is also of high quality flat-top shape. The spatiotemporal target field distribution is shown to bend, which is of practical importance in time-resolved experiments in ultrafast optics.
A polarization independent band-pass filter is created by combining a silicon cross-slot waveguide and a Bragg grating cavity. By theoretically investigating different types of cavities we show how the sensitivity to polarization of the device can vary, and how we can strongly confine light in a two-dimensional slot waveguide. This kind of structure, where a slot waveguide, a photonic crystal and a nanowire waveguide are merged together, may find applications in the field of sensing. Indeed, a slight variation in the surrounding refractive index breaks the device symmetry. One polarization can thus be used to monitor the fluctuation of the other one. We describe here the principle of a Bragg grating merged with a cross slot waveguide in which a cavity is placed. We discuss the advantage of using different geometries of cavity and how this choice may affect the response of the device.
Light pipes are key optical components used in projection systems to transport and homogenize light from the source towards the light valve. They can provide a uniform light distribution at their output as a result of multiple internal reflections. In laser projection systems, such light pipes are useful in combination with a laser-light module consisting of one or more single-mode lasers and a rotating diffuser. The partially coherent light emanating from the rotating diffuser is transported and homogenized towards the end of the light pipe. Consequently, propagation through the light pipe will also modify the coherence properties of the laser light. In this paper, a computationally efficient simulation model is presented to propagate partially coherent light through a homogenizing rectangular light pipe. The resulting coherence function clearly differs from that of free-space propagation over the same optical path length. The implications of these results on, for example, the appearance of speckle are discussed in further detail. The simulation results are experimentally verified using a reversing wavefront Michelson interferometer. The approach described in this paper can be extended further to investigate other types of light pipes, such as tapered light pipes or even more complex ones.
We propose the Fourier Modal Method (FMM) as a convenient numerical tool for the design and analysis of nonlinear optical waveguides. The scope of this work includes the design of a polarization-independent nonlinear cross-slot waveguide for telecommunication applications at the wavelength of 1550 nm. The FMM method has been implemented, obeying the proper Fourier factorization rules, within a MATLABTM environment. The influence of the modal field intensity on the transverse refractive index distribution due to the optical Kerr effect is modeled with FMM for a propagation invariant scheme of the waveguide. The waveguide is geometrically optimized for an enhanced nonlinear light matter interaction. A silicon-inorganic hybrid material platform based on hydrogenated amorphous silicon (a-Si:H) and amorphous titanium dioxide (TiO2) is considered for the mentioned waveguide. With the optimized design of the waveguide, the achieved value of the nonlinear waveguide parameter (γ) is 4.678 × 104 W-1Km-1.
We introduce a numerically feasible method for rigorous modeling of crossed diffraction gratings with isotropic
third order nonlinear materials. The approach is based on an iterative solution of the crossed grating problem
with anisotropic linear materials. Several numerical experiments are performed to demonstrate the versatility
and numerical stability of our computation scheme. Resonance waveguide gratings made of isotropic cubic
nonlinear materials are investigated numerically using this newly developed technique. A polarization-sensitive
shift of resonance peak with variation of light intensity is numerically demonstrated.
Fourier modal method (FMM) is known as a powerful tool in simulations of periodic micro-structures, e.g., gratings. For an arbitrary plane wave incidence, the Rayleigh coefficients for both reflected and transmitted field can be calculated with the FMM efficiently. When dealing with a general beam incidence, FMM together with plane wave decomposition can still provide solutions. However the needed computational resources increase with the number of plane wave components in the angular spectrum domain. To solve this problem, we put forward an efficient approach which integrates interpolation technique into the method above. For most diffractive thin elements, the complex Rayleigh coefficients distribution is smooth. In this case several well-selected plane wave components are enough to characterize the diffraction property. In our method, only these selected plane wave components are analyzed with FMM while the results of other components are obtained by interpolation technique. Besides that, an efficient approach for especially divergent incident beam is also presented in this article. It enable a parallel FMM analysis which calculates a set of plane wave components in one computational loop.
We present numerical simulations, based on elementary mode method, of field emitted by broad-area laser diodes.
The near field is expressed as a superposition of modes with sinusoidal spatial amplitude inside the laser resonator
and zero outside. The assumed functional form of the modes is used to find the intensity distribution in the
far-zone. This information is then used to construct the elementary-mode decomposition in the near-field. The
validity of the elementary-mode approach was verified by comparing the intensity and the degree of coherence
at various distances from the source.
While the theories of the optical coherence of scalar fields and the polarization of beam fields are well established, a
general theory for the coherence and polarization of true electromagnetic fields appearsmore subtle. With random
vector fields coherence may reside among any or all of the electric-field components, leading to a modulation
of the optical intensity or the polarization state, or both, on two-beam interference. We discuss the recent
formulations of both the polarization and the coherence, and we show that the electromagnetic degree of coherence
is characterized by the modulation of all the four Stokes parameters (representing intensity and polarization state)
in a two-pinhole Young's setup. This also leads to a new experimental interpretation for the degree polarization
of a random electromagnetic beam. Certain important results pertaining to electromagnetic coherence, which
are fully analogous to their scalar counterparts, are emphasized.
We analyze the classic Hanbury Brown-Twiss effect for thermal electromagnetic fields in space-frequency domain.
We compare two different approaches and show that the normalized correlation of intensity fluctuations is fully
characterized by the spectral electromagnetic degree of coherence, a result analogous to scalar analysis of the
effect. Differences between the two approaches are discussed.
We discuss how the rigorous grating theory can be extended to cover also partially coherent illumination such
that the method stays computationally reasonable. We first discuss the S-matrix formalism if the input field
is not a simple plane wave, and then continue the approach to the case of partial coherence. We illustrate the
approach by investigating the imaging of a grating in a classical bright-field imaging setup.
The round robin "measurement of subwavelength diffractive elements" tackles the metrology problems related to the measurement of diffraction gratings by AFM. It aims at quantifying the absolute precision and the uncertainty of the measurement considering some features of such structures like the depth, the period, the fill factor and the shape of the profile. This round robin involved four partners within NEMO. Each partner has measured three different samples: one 2D small depth grating, one 1D small depth grating and one 1D high aspect ratio grating. In order to get rid of the samples inhomogeneity, the measurements were performed exactly at the same location on each sample by all partners. This was achieved by using a multiscale resist pattern transferred on the gratings which precisely defined a 5×5 μm2 area. The paper will sum up the experimental values obtained by all the partners, draw general conclusions and make suggestions to improve the accuracy of AFM measurements.
A method for designing high-efficiency paraxial domain diffractive elements working over a broad wavelenght is introduced. These elements are based on polarization gratings that manipulate spacially the local state of polarization using form bifringent subwavelenth diffractive structures. Any scaler transmission function can realized simulataneosly for a wide band of wavelenths using such elements. In some cases it is also possible to design beam splitters that exceed the scalar paraxial-domain upper bounds of diffraction efficienty over a broad wavelength band.
For an electromagnetic beam described by Gaussian statistics the normalized intensity fluctuations are known to depend on the beam's degree of polarization. With general non-paraxial random electromagnetic waves, such as optical near fields, a complete characterization of the polarization state requires a 3 x 3 coherence matrix and a three-dimensional degree of polarization. We demonstrate that, under the assumption of Gaussian statistics, the normalized intensity fluctuations in the three-dimensional case are expressible in terms of the three-dimensional degree of polarization. Since such a general description can be employed even for beams with only a transverse electric field, several important physical results follow from comparison of the three-dimensional and usual two-dimensional formulations. The results are expected to be particularly important in intensity interferometry.
KEYWORDS: Electromagnetism, Visibility, Near field optics, Coherence (optics), Near field, Physics, Electromagnetic theory, Statistical analysis, Signal analyzers, Analog electronics
In this work, we apply a recently introduced electromagnetic
degree of coherence to address the coherence properties of random,
stationary electromagnetic fields. In particular, we consider the
limit of complete coherence in space-frequency and space-time
domains. We show that in both domains the (electric) coherence
tensor is analogous, in its spatial and temporal structure, to the
coherence function of fully coherent scalar fields. The results
are important in the rigorous electromagnetic theory of optical
coherence, as encountered, e.g., in non-paraxial near fields and
diffractive optics.
We introduce a method for designing high-efficiency paraxial-domain diffractive elements working over a broad frequency range. The design method is based on the theory of dielectric polarization gratings, in which the local state of polarization is controlled by means of form-birefringent diffractive structures. We show that any scalar transmission function can be easily converted to a corresponding broadband design.
Electromagnetic theory of open laser resonators is formulated in
the domain of partially coherent optics. The theory is then used
to find out the electromagnetic degree of coherence of the field
in various situations. It is shown that if only one transverse
mode is present in the steady-state condition, then the field is
necessarily completely coherent in view of the recently introduced
degree of coherence for electromagnetic fields [Opt. Express. 11,
1137 (2003)].
KEYWORDS: Diffraction, Polarization, Modulation, Electromagnetism, Dielectric polarization, Jones vectors, Beam splitters, Dielectrics, Interfaces, Chemical elements
Intensity transformation by using paraxial-domain polarization-modulating diffractive elements is discussed. It is shown that taking the electromagnetic nature of light into account may lead to a dramatic increase in the diffraction efficiency also in the paraxial domain, in which the vectorial nature of light is usually ignored. Examples are given for signals for which the full 100% conversion efficiency is possible.
Local Spherical Interface Approximation (LSIA) for modelling the propagation of electromagnetic wave fields through analog interfaces is introduced. The method belongs to a class of Local Elementary Interface Approximation (LEIA) in which the propagation is modelled by decomposing the field into local elementary fields. In the method introduced here both the phase-distribution of the field and the boundary of discontinuity are assumed to be locally spherical, which enables the use of Coddington's equations in the determination of the reflected and transmitted fields. The amplitude reflection and transmission is treated with the help of the intensity law of geometrical optics and the energy conservation law. Convergence comparison between LSIA and Local Plane Interface Approximation (LPIA) is performed for a sinusoidal diffraction grating. The accuracy of the method is illustrated with a numerical example.
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