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Structured Illumination Microscope allows resolutions of 120 nm or 100 nm when combined with TIRF. Here we present an elegant and simple way of further increasing this resolution to

In this work we propose a method for reconstructing the profile of rough surfaces with superresolution from far-field scattering measurements obtained with Tomographic Diffractive Microscopy (TDM). The inversion algorithm used in the reconstruction, where the optimization is performed with TE and TM data simultaneously, does not require any regularization step and accounts for multiple scattering.

International audience; We have developed a reflection tomographic microscope in which the sample is reconstructed from different holograms recorded under various angles and wavelengths of incidence. We present an iterative inversion algorithm based on a rigorous modeling of the wave-sample interaction that processes all the data simultaneously to estimate the sample permittivity distribution. We show that using several wavelengths permits a significant improvement of the reconstruction, especially along the optical axis.

Within Silicon-based waveguide arrays, we demonstrate that sub-λ, below band-gap nanostructured waveguides can provide a robust control and a fine tuning of the coupling coefficient, which is considered for an optical isolator integrated on Silicon.

International audience; Tomographic diffraction microscopy is a three-dimensional quantitative optical imaging technique in which the sample is numerically reconstructed from tens of holograms recorded under different angles of incidence. We show that combining the measurement of the amplitude, the phase, and the polarization of the field scattered by the sample with an approximate knowledge of the sample permittivity allows reconstruction of spatially complex samples up to 50 nm resolution. This technique should be particularly useful for imaging objects made of known materials.

While the resolution of fluorescence microscopy has undergone a significant improvement in the recent years, reaching a few tens of nanometers, that of marker-free microscopes remains stuck at several hundreds of nanometers.

International audience; Total internal reflection microscopy is mainly used in its fluorescence mode and is the reference technique to image fluorescent proteins in the vicinity of cell membranes. Here, we show that this technique can easily become a phase microscope by simply detecting the coherent signal resulting from the interference between the field scattered by the probed sample and the total internal reflection. Moreover, combining several illumination angles permits generating synthetic aperture reconstructions with improved resolutions compared to standard label-free micro-scopy techniques. Total internal reflection fluorescence (TIRF) microscopy is the reference technique to study the membrane dynamics and organization in biological cells [1,2]. Its main advantage is the ability to illuminate with a high axial sectioning the sample, typically over a thin slice of about 100 nm, by taking benefit from a total internal reflection (TIR) configuration. The sample is deposited on a glass substrate, and by illuminating through the substrate above the critical angle, an evanescent wave is created at the interface to locally probe the sample. Compared to standard wide-field fluorescence microscopy, images with highly improved contrast are provided, since the background signal stemming from the volume of the sample can be suppressed. The preferred TIRF configuration nowadays uses a high numerical aperture (NA) immersion objective both to illuminate above the critical angle and collect the fluorescence signal. Using fluorophores as contrast agents, however, presents some drawbacks, as their addition is invasive and induces the increased risk of photobleaching and phototoxicity to the cell [3]. Long-term studies are thus difficult to achieve. The spe-cificity of labeling is, moreover, at the same time the main advantage and the main limitation of fluorescence imaging, since the lack of structural images can be detrimental to the interpretation of the results. Therefore, there is a clear need for a high-resolution technique able to probe cell membranes without the constraint of incorporating a fluorescent label. Two main approaches have been used so far to perform label free imaging in TIR with a high NA objective. The first approach uses a spatially incoherent source (such as a light bulb or LED) to illuminate the sample simultaneously with all angles above the critical value imposed by the glass substrate and the sample immersion medium (usually water) [4,5]. As the sample refractive index is higher than that of water, TIR is frustrated at locations where the sample is close to the interface, which modulates the reflected intensity and is the source of contrast in the resulting image. The second approach uses a laser beam focused in the back focal plane (BFP) of the objective at the edge of the NA [6,7]. The focused beam is scanned along a circle in the BFP, so that the sample is illuminated in TIR by a rotating collimated beam, and the integration time of the camera is set to match the rotation period of the beam. The totally reflected beam is blocked in a plane conjugated with the BFP to detect only the scattered intensity and obtain dark-field imaging. Both approaches have a high temporal resolution, and the second one claims an improved resolution at the price of some sample distortions in the image. In this Letter, we propose a label-free TIR microscopy technique that keeps the same setup simplicity as the previous approaches, but permits besides to perform phase imaging and improve the resolution through synthetic aperture generation. The core idea of the technique is that the intensity detected in TIR microscopy can directly give access to the phase and the amplitude of the field scattered by the probed sample. Assuming the scalar approximation, the detected intensity I can be written as I ˆ jE r ‡ E s j 2 ˆ jE r j 2 ‡ jE s j 2 ‡ E r E s ‡ E r E s , (1) where E r is the field reflected by the interface in TIR, and E s is the field backscattered by the sample. As in TIR the sample is illuminated over a very thin slice and is usually of very weak contrast in biology, we can assume E r is very strong compared to E s , and neglect jE s j 2 in Eq. (1). Since E r is close to the edge Letter Vol. 43, No. 9 /

Tomographic diffractive microscopy is a marker-free optical digital imaging technique in which three-dimensional samples are reconstructed from a set of holograms recorded under different angles of incidence. We show experimentally that, by processing the holograms with singular value decomposition, it is possible to image objects in a noisy background that are invisible with classical wide-field microscopy and conventional tomographic reconstruction procedure. The targets can be further characterized with a selective quantitative inversion.

We report in this paper results obtained from characterizations of photonic band gap waveguide, using near field optical microscopy. We will show evidence of a Bloch wave propagating within our W1 photonic crystal waveguides (PCWs) structure, using a 2D Fourier transform approach. The processed image will then be compared to simulations obtained from plane wave method. This comparison exhibits that near-field measurements, using tapered optical fibers as probes, are mainly sensitive to the electric field propagating within the structure.

Lasing of triangular and square lattice photonic crystal, waveguides on InP substrate is investigated around the 1.5-/spl mu/m wavelength by optical pumping. The lattice period of the fabricated structures is varied over a very large scale, thereby allowing a detailed exploration of the laser behaviors in the cases of micrometer width waveguides. A genuine distributed feedback (DFB) laser emission is observed in the gap for W2-3 waveguides in the /spl Gamma/M direction of a triangular lattice. A different behavior is obtained for W3 waveguides in the /spl Gamma/K direction of the same lattice as well as for W1 and W3 waveguides in the /spl Gamma/X direction of a square lattice. The laser emission is found to occur at the /spl Gamma/ point of the Brillouin zone (wavevector k=0) when the emission frequency is outside the gap. The DFB-like laser emission is intrinsically single mode in this case. Plane wave calculations show that the field distributions of the two DFB components are radically different. The emitting mode is well localized in the guide core while the non-lasing mode spreads over the whole crystal.

An heteroepitaxial bonded III-Von Si nanopatterned waveguide is demonstrating a wavelength selective behavior thanks to a super-periodicity added to its sub-wavelength, below band-gap, structuration. Effective Medium Theory has been implemented for modal effective index determination, allowing a quick and nevertheless detailed investigation of the role of a large number of geometrical parameters. Such nanostructured waveguides offer the versatility for designing complex geometries required for hybrid advanced optical functions on silicon.

Step-tuning to widely spaced predefined wavelengths using a single current is demonstrated. A compound distributed-feedback-distributed-Bragg-reflector (DFB-DBR) GaInAsP laser structure including multiwavelength gratings (MWGs) on both sections is proposed. MWGs are fabricated by holographic lithography. Each MWG acts as a spectral comb filter. Using vernier effect between passive and active MWGs, DFB modes are successively selected. As wavelength selectivity is performed on the active medium without help of facet reflectivity, output power remains the same on all wavelengths. Four 4-nm-spaced DFB modes are accessed with constant optical output power. Advantages of such a configuration for integrated components are discussed.

Lasing of W1 square lattice-based photonic crystal lasers on the substrate approach is analyzed. A second-order distributed feedback highly monomode behavior is observed. A comprehensive two-dimensional and three-dimensional finite-difference time-domain computation analysis shows that this characteristic arises from the lattice geometry. Single-mode lasers can be obtained using this geometry, opening the way to the realization of monomode laser arrays.

We present a marker-free microscope that records the phase, amplitude, and polarization state of the field diffracted by the sample for different illumination directions. The data are processed with an appropriate inversion method to yield the sample permittivity map. We observe that the full-polarized information ameliorates significantly the three-dimensional image of weakly scattering subdiffraction objects. A resolution about one-fourth of the illumination wavelength is experimentally demonstrated on complex samples.

We show experimentally that a resolution far beyond that of conventional far-field optical profilometers can be reached with optical diffraction tomography. This result is obtained in the presence of multiple scattering when using an adapted inverse scattering algorithm for profile reconstruction. This new profilometry technique, whose resolution can be compared to that of atomic microscopes, also gives access to the permittivity of the surface.

A three-section sampled-grating DBR laser has been realised. It presents a 25 nm tuning range with an SMSR greater than 30 dB. For the first time with sampled reflectors, access to 22 wavelength channels is achieved thanks to discontinuous tuning among the five main reflection peaks of the comb-reflection spectra of the sampled gratings. Operation of this device under amplitude modulation is also discussed: an AM bandwidth greater than 2.5 GHz has been demonstrated.

We demonstrate continuous wave with an external efficiency over 0.15W∕A and monomode operation of a full photonic crystal (PhC) laser. The optical confinement and a wavelength selectivity better than 25dB are all ensured by a unique PhC. We take advantage of the feedback on the fundamental mode which exists within the photonic gap for some specific designs of the PhC guide. These designs are calculated using the plane wave expansion method.

This work presents a theoretical and experimental study of the spatial hole burning (SHB) applied to phase-shifted amplitude modulated coupling (AMC) distributed feedback (DFB) lasers. Green's function method is used in our model and a new development of this method allows us to calculate the side-mode power. A transverse model is developed allowing the calculation of the spatially dependent refractive index and coupling coefficient from the designed AMC-DFB laser structures. Modeling results show that the effective index variation, associated with that of the coupling coefficient, plays an important role in affecting the laser's characteristics and has to be balanced to improve single-mode behavior. The SHB is studied experimentally by measuring the spontaneous emission radiated from a transparent window inside the electrode. The results clearly show, for the first time, the existence of a hole in the carrier density distribution due to the /spl lambda//4 phase-shift in a highly coupled laser. Both the measured and the calculated SHB are in agreement. >

An accurate three-dimensional method to calculate the Bloch modes of photonic crystal (PhC) waveguides is proposed. Good agreement with available experimental and numerical data is obtained. The originality of the method lies in the fact that the Bloch modes are seen as the electromagnetic fields associated to the complex poles of an in-plane transversal scattering matrix. In comparison with previous approaches, the computational domain discretized is smaller and a higher accuracy for the losses of PhC waveguides is achieved.

Monolithic integration of InP-based materials on Si will allow lasers as well as optical amplifiers operating at 1.55µm to be efficiently included in photonic integrated circuits. We demonstrate here oxide-free heteroepitaxial bonding of InP-clad GaInAs quantum wells to Si, with an atomic-plane-thick reconstruction across the InP-Si interface. The wells photoluminescence emitted-wavelength demonstrates no shift after bonding. Several InP surface activation procedures have been investigated. This bonding approach is compatible with guiding designs including a nanostructuration, thus enabling specific designs associated to desirable optical functions.

We explain how to design a high Q, polarization independent, angularly tolerant filter, with a "doubly periodic" resonant grating etched in a high index material. Thanks to its broad angular acceptance, the fabricated component shows a Q factor of 5600 with a 580μm diameter Gaussian beam. Performing a detailed theoretical and experimental comparative study, we identify the parameters responsible for the degradation of the performances of the filter.

We report on lasing at room temperature and at telecommunications wavelength from photonic crystal nanocavities based on InAsP/InP quantum dots. Such laser cavities with a small modal volume and high quality factor display a high spontaneous emission coupling factor (beta). Lasing is confirmed by measuring the second-order autocorrelation function. A smooth transition from chaotic to coherent emission is observed, and coherent emission is obtained at eight times the threshold power.

Optical diffraction tomography (ODT) is a recent imaging technique that combines the experimental methods of phase microscopy and synthetic aperture with the mathematical tools of inverse scattering theory. We present here in detail how this technique can be applied to highly scattering samples with a nonlinear inversion algorithm taking into account multiple scattering to reconstruct their permittivity profile. The obtained resolutions are substantially improved compared with wide-field microscopy and ODT performed with standard linear inversion procedures.

We will present a futher understanding of the threshold transition in lasers operating at nanoscale, by measuring the threshold transition from a quantum, statistical and dynamical points of view at room temperature and telecommunication wavelengths.

The interferogram of a high index phase mask of 200 nm period under normal incidence of a collimated beam at 244 nm wavelength with substantially suppressed zeroth order produces a 100 nm period grating in a resist film under immersion. The paper describes the phase mask design, its fabrication, the effect of electron-beam lithographic stitching errors and optical assessment of the fabricated sub-cutoff grating. (C) 2010 Optical Society of America

International audience; We study adiabatic mode transformations in photonic-crystal integrated circuits composed of a triangular lattice of holes etched into a planar waveguide. The taper relies on the manufacture of holes with progressively-varying dimensions. The variation synthesizes an artificial material with a gradient effective index. Calculations performed with a three-dimensional exact electromagnetic theory yield high transmission over a wide frequency range. To evidence the practical interest of the approach, a mode transformer with a length as small as λ/2 is shown to provide a spectral-averaged transmission efficiency of 92% for tapering between a ridge waveguide and a photonic crystal waveguide with a one-row defect.

We demonstrate in a single laser diode the simultaneous operation on different wavelengths around 1.55 μm while preserving the spectral distributed feedback selection mechanism for each wavelength. The grating that exists all along the cavity is a multiwavelength grating obtained by the linear transfer of superimposed multiple holographic exposures. Such a grating acts as a reflectivity comb, the action of each reflector being uniformly distributed all along the cavity. Thanks to a clever incorporation of a phase shift, the lasing wavelengths are deterministically placed on the Bragg modes. The equal strengths of the different spatial frequencies of the grating translate into uniform optical output powers on the simultaneous lasing modes.

A 10-wavelength 200-GHz channel spacing emitter was realized by monolithically integrating on InP a 10 distributed-Bragg-reflector laser array and a PHASAR used as a 10/spl rarr/1 combiner. The design of a wide-squared spectral bandwidth for the PHASAR as well as the lasers tunability ensure wavelength matching between the PHASAR transmission comb and the laser array comb. The channel spacing accuracy of the source is better than 25 GHz and the rejection is higher than 32 dB for all bias.

In the wavelength-division-multiplexed transmission framework, we investigate the ability of the distributed phase-shifted distributed-feedback (DFB) structure by enlarging the ridge to fulfil the wavelength accuracy required for array fabrication. Measurements on three different phase-shift geometries indicate that the poor localization of the optical mode along the cavity is detrimental to the wavelength accuracy. This study points out the best solution for DFB structure implementable in arrays, using already validated low-cost and high-throughput technologies in a production environment.

A resonant grating filter can be basically described as a sub-wavelength grating inscribed on a a planar waveguide made of dielectric thin film layers. The reflectiv ity of such a structure pres ents some peaks versus the wavelength that are generated by the coupling and coupling out of different modes of the waveguide. These peaks can be tailored in order to create free-space narrow bandpass inverse (notch) filters, with a very sharp spectral response (typically a spectral bandwidth below 0.5 reflectance nm for a component working at 1550nm). We show an experimental demonstration of a high performances resonant grating filter working in reflectance under a given incidence and wavelength. This filter presents simultaneously a good angular tolerance and polarization independence with a full width at half maximum about 0.4nm. The dielectric stack reflectance configuration is chosen so that the coupling conditions for two TE reflectance guided modes are simultaneously satisfied. Moreover, the grating cell presents a complex structure of four holes with different diameters, optimized for increasing the angular tolerance of the filter while maintaining a narrow spectral width for any polarization. Comparisons with theo retical calculations are provided. Keywords: resonant grating filter, notch filters, leaky guided modes Email: fabien.lemarchand@fresnel.fr

Optical diffraction tomography (ODT) is a recent imaging technique that combines the experimental methods of phase microscopy and synthetic aperture with the mathematical tools of inverse scattering theory. We show experimentally that this approach permits us to obtain the map of permittivity of highly scattering samples with axial and transverse resolutions that are much better than that of a microscope with the same numerical aperture.

Whereas microelectronic lithography is heading to the 32 nm node and discussing immersion and double-patterning strategies, there is much which can be done with the 45 nm node in microoptics for white light processing. For instance, one of the most demanding applications in terms of achievable period is the LCD lossless polarizer, which can transmit the TM polarization and reflect the TE polarization evenly all through the visible spectrum – provided that a 1D metal grid of 100 nm period can be fabricated. The manufacture of such polarizing panels cannot resort to the step & repeat cameras of microelectronics since the substrates are too large, too thin, too wavy and full of contaminants. There is therefore a need for specific fabrication techniques. It is one of these techniques that a subgroup of partners belonging to two of the Networks of Excellence of the European Community, NEMO and ePIXnet, have decided to explore together. Keywords: Phase Mask, high Index Material, UV Interference Lithography, Immersion, Grating

A biperiodic nanostructuration consisting of a super-periodicity added to a nanohole lattice of subwavelength pitch is demonstrated to provide both modal confinement and wavelength selectivity within a hybrid III-V on a silicon waveguide. The wavelength-selective behavior stems from finely tuned larger holes. Such biperiodic hybrid waveguides have been fabricated by oxide-free bonding III-V material on silicon and display well-defined stop bands. Such nanostructured waveguides offer the versatility for designing advanced optical functions within hybrid devices. Moreover, keeping the silicon waveguide surface planar, such nanostructured waveguides are compatible with electrical operation across the oxide-free hybrid interface.

A grating dry-etched through the upper wells of a multiquantum-well active layer has been characterized before and after regrowth. TEM observation and carrier lifetime measurements have shown growth-free defects of the epitaxial layers. As a consequence, quasi-100% monomode oscillation on /spl lambda/+1 mode has been achieved on complex-coupled distributed-feedback GaInAsP QW lasers fabricated with such grating.

The group index dispersion and birefringence of guided modes supported by straight photonic crystal (PhC) waveguides are theoretically and experimentally investigated as a function of the waveguide width within various reduced frequency domains. Within the photonic gap and far from the Brillouin zone edges, strongly confined modes supported by narrow PhC guides exhibit both a group index and a birefringence larger than those of a deep ridge. These two results evidence the contribution of the photonic gap to the guiding mechanism in the refractivelike domain.

Six-element absorption-coupled distributed-feedback (DFB) arrays have been fabricated by means of holographic lithography. Using a simple current injection scheme in two-section devices, a standard deviation of 0.11 nm from a uniform wavelength channel spacing of 2 nm has been achieved. This value is easily obtained using standard lithography technologies for fabrication, and coarse current control for operation. It allows the use of complex-coupled DPB lasers as sources in photonic integrated circuits.

The performance characteristics of amplitude modulated coupling (AMC) phase-shifted MQW DFB lasers emitting near 1.55μm are reported for the first time. The AMC is obtained by the holographic double-exposure technique; it provides single longitudinal mode oscillation up to 78mW for I = 500mA. This result confirms that AMC flattens the power distribution along the laser cavity. Linewidths as low as 600kHz have been obtained for cavities as short as 600μm at P = 15mW.

We propose a new reflector approach in order to get the reflectivity comb needed in widely tunable lasers. This reflector is realized by holographic exposure of superimposed multiple Bragg gratings. It provides efficient reflectivity with short guide sections (150 /spl mu/m) leading to improved static laser characteristics. This reflector has been successfully included in 20-nm tuning DBR lasers.

Photonic crystals have seen major advances in the past few years in the optical range. The association of in-plane waveguiding and two-dimensional (2D) photonic crystals (PCs) in thin-slab or waveguide structures leads to good 3D confinement with easy fabrication. Such structures, much easier to fabricate than 3D PCs, open many exciting opportunities in optoelectronic devices and integrated optics. We review the basics of these structures, with emphasis on basic properties and loss performance, as well as modeling tools, which show that 2D PCs etched through waveguides supported by substrates are a viable route to high-performance PC-based photonic integrated circuits (PICs). A companion paper by Benisty et al. in these proceedings illustrates further high performance building blocks and integrated devices.

Practical realizations of 2D (planar) photonics crystal (PhC) are either on a membrane or etched through a conventional heterostructure. While fascinating objects can emerge from the first approach ...

The transverse spontaneous emission is used to characterize the gain suppression in semiconductor lasers during their operation for the first time. The carrier heating and the spectral‐hole‐burning are distinguished by using their different spectral behavior. The measurements show a very strong carrier heating in strained multi‐quantum‐well lasers which do not appear in bulk devices. Moreover, the total nonlinear gain coefficient is measured by using a modulation method; the results show a high value of e=16.10−17 cm3 for the strained multi quantum‐well laser and an usual value of e=2.10−17 cm3 for the bulk, consistent with the measurement of gain suppression spectrum.

A six-wavelength MQW DFB laser array emitting around 1.55 /spl mu/m realized in a single holographic lithography is described. Fringe-free localized grating isolation is attained using a mask with a novel aperture-edge design. The first-order grating periods as well as the ridge locations can be varied in a large span. The high throughput of holographic lithography is extended to multiwavelength DFB arrays. >

We study adiabatic mode transformations in waveguides that rely on subwavelength holes with progressively-varying dimensions. The variation synthesizes an artificial material with a gradient effective index. Two devices are presented, a microcavity with short tapers incorporated at the four reflector extremities, and a taper between a conventional waveguide and a photonic crystal waveguide.

Wide tuning DFB-type oscillation from a DFB-DBR InGaAsP strained QW laser is reported. DFB modes defined by a multiwavelength grating (MWG) in the active section are selected by tuning the passive section current. Upon tuning, output power remains constant and linewidth remains lower than 5 MHz.

Summary form only given. In this paper a monolithic integration of a laser diode with a polymeric based waveguide is reported as a first step in developing a monolithically integrated multi-wavelength DFB laser array with a passive polymeric optical power combiner. This alternative approach based on polymeric materials offers the advantages of potentially low optical losses and high and easy processability; and the capability of preparation of active and passive components on Ill-V wafers with already processed devices.

A grating dry-etched through the upper wells of an MQW active layer has been characterized before and after regrowth. TEM observation and carrier lifetime measurements have shown growth-free defects of the epitaxial layers. As a consequence, quasi 100% monomode oscillation on /spl lambda/+1 mode has been achieved on complex-coupled DFB lasers fabricated with such a grating.

International audience; Oxide-free bonding of a III-V active stack emitting at 1300-1600 nm to a silicon-on-insulator wafer offers the capability to electrically inject lasers from the silicon side. However, a typical 500-nm-thick silicon layer notably attracts the fundamental guided mode of the silicon + III-V stack, a detrimental feature compared to established III-V Separate-Confinement Heterostructure (SCH) stacks. We experimentally probe with photoluminescence as an internal light source the guiding behavior for oxide-free bonding to a nanopatterned silicon wafer that acts as a low-index barrier. We use a sub-wavelength square array of small holes as an effective " low-index silicon " medium. It is weakly modulated along one dimension (superperiodic array) to outcouple the resulting guided modes to free space, where we use an angle-resolved spectroscopy study. Analysis of experimental branches confirms the capability to operate with a fundamental mode well localized in the III-V heterostructures. " III-V/silicon photonics for on-chip and inter-chip optical interconnects, " Laser Photonics Rev. 4(6), 751–779 (2010). 2. J. K. Doylend and A. P. Knights, " The evolution of silicon photonics as an enabling technology for optical interconnection

Low threshold current DFB lasers have been analysed for burst mode operation in a point to point access network of 8 km. These DFB lasers are zero biased and operate at 155 Mbit/s without any electronic feedback control to compensate threshold, turn on delay and efficiency. The BER measurement at 155 Mbit/s for temperature ranging from 20° up to 80°C show that at 60° the sensitivity degrades by 4 dB and at 80°C by 9 dB.

Tomographic diffractive microscopy (TDM) is a label-free imaging technique that reconstructs the 3D refractive index map of the probed object with an improved resolution compared to confocal microscopy. In this work, we consider a TDM implementation in which the sample is deposited on a reflective substrate. We show that this configuration requires calibration and inversion procedures that account for the presence of the substrate for getting highly resolved quantitative reconstructions.

Tomographic diffractive microscopy is a recent imaging technique that reconstructs quantitatively the three-dimensional permittivity map of a sample with a resolution better than that of conventional wide-field microscopy. Its main drawbacks lie in the complexity of the setup and in the slowness of the image recording as both the amplitude and the phase of the field scattered by the sample need to be measured for hundreds of successive illumination angles. In this Letter, we show that, using a wavefront sensor, tomographic diffractive microscopy can be implemented easily on a conventional microscope. Moreover, the number of illuminations can be dramatically decreased if a constrained reconstruction algorithm is used to recover the sample map of permittivity.