## Equipe : SEMO

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### Research in the SEMO team

**Isotropic Single Objective (ISO) microscopy:Focusing light into a spherical spot with a single objective lens**

- Focusing a light beam with a lens produces a spot that is strongly elongated along the optical axis, because the illumination is not uniformly spherical but comes from only one side of the focal point. This anisotropy has plagued all optical instruments for more than 100 years. In the domain of data storage, it is limiting strongly the density of optical storage media (DVD, Blu-Ray).

- In a recent article, we describe a new and surprisingly simple idea to focus light into a spherical spot using a single lens. Using time reversal concept, we show theoretically and experimentally that isotropic focusing can be achieved by placing a mirror after the focal point and engineering the incident beam.

**References :**

- E. Le Moal, E. Mudry, P. C. Chaumet, P. Ferrand and A. Sentenac,

*Isotropic Single Objective (ISO) microscopy : Theory and Experiment*, J. Opt. Soc. Am. A.**28**, 1586 (2011). - E. Mudry, E. Le Moal, P. Ferrand, P. C. Chaumet and A. Sentenac,

*Isotropic diffraction-limited focusing using a single objective lens*, Phys. Rev. Lett.**105**, 203903 (2010).

**Optical diffraction tomography
**

- Wave diffraction tomography is a digital imaging technique in which an unknown object is illuminated by a monochromatic coherent wave under various incident angles and the scattered field is measured in phase and amplitude along various directions of observation. The intrinsic properties (shape, nature) of the object are reconstructed numerically thanks to inversion algorithms accounting for the wave-object interaction. This approach is widespread in the acoustical, mechanical and electromagnetic domains, where analogical imaging systems do not exist and covers a large range of applications, from non-destructive testing, detection of buried objects or medical imaging. It is also more and more considered in the optical domain as an alternative to classical optical microscopy. The performances of wave diffraction tomography depend on the experimental configuration, namely the number of incidences and observations points, the covered angular range and the noise level. They depend also on the inversion algorithms that are used for the reconstruction. In the SEMO team we develop imaging systems based on Wave Diffraction Tomography. We apply our knowledge in electromagnetism and inversion procedures to micro-wave imaging systems, with a particular interest for the detection of buried objects, optical diffusive imaging systems, and, more importantly, to optical microscopy dedicated to fluorescent or non-fluorescent samples. Most of our theoretical studies are validated by experiments. We have shown theoretically and experimentally that Optical Diffraction Tomography gives the map of permittivity of a sample with a better resolution than that of a conventional microscope with same Numerical Aperture. To ameliorate the resolution up to that of a near-field microscope, we have proposed to deposit the sample on a periodically structured substrate in order to take advantage of the high spatial frequencies of the field generated at the grating surface. We have also pointed out the importance of taking into account multiple scattering in the inversion procedures for samples with moderate dielectric contrast.

**References :**

- G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D.

Konan, K. Belkebir, P. C. Chaumet and A. Sentenac,*Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography*, Phys. Rev. Lett.**102**, 213905 (2009). - A. Sentenac, P. C. Chaumet and K. Belkebir,

*Beyond the Rayleigh criterion : Grating assisted far-field optical diffraction tomography*, Phys. Rev. Lett.**97**, 243901, (2006). - P. C. Chaumet, K. Belkebir and A. Sentenac,

*Superresolution of three-dimensional optical imaging by use of evanescent waves*, Optics Letters**29**, 2740 (2004).

- Optical profilometry is a nondestructive and noncontact surface

metrology technique. Different schemes have been proposed in the literature

for determining the surface topography of the samples restricted to the case of surfaces with small slopes and in that configuration vertical resolution can be of the order of several angstroms, while lateral resolution is limited by diffraction. We have shown that the optical diffraction tomography, whose efficiency has been demonstrated for microscopy applications, can be applied for optical profilometry when high lateral resolutions are required.

**References :**

- S. Arhab, G. Soriano, Y. Ruan, G. Maire, A. Talneau, D. Sentenac, P. C. Chaumet, K. Belkebir and H. Giovannini,
*Nanometric resolution with far-field optical profilometry*, Phys. Rev. Lett.**111**, 053902 (2013). - S. Arhab, G. Soriano, K. Belkebir, A. Sentenac and H. Giovannini,
*Full wave optical profilometry*, J. Opt. Soc. Am. A**28**, 576 (2011).

**Characterization of buried targets**

- The targets are assumed to be buried in one of the two media while the sources and the receivers are located in the other medium (limited-aspect data configuration). When clutter is present, we show that the decomposition of the time reversal operator method can be used to improve the signal-to-clutter ratio, since it allows us to synthesize a wave that focuses on the scatterer.

**Reference :**

- A. Dubois, K. Belkebir and M. Saillard,
*Location and characterization of two-dimensional targets buried in a cluttered environment*, Inverse Problems**20**, S63 (2004).

**Ocean surface remote sensing and wave propagation in random media**

- The propagation of waves in disordered and random media, and more precisely scattering by rough surfaces and volume inhomogeneities, is a phenomenon that occurs in many problems in Optics as well as in the microwave regime. The scattered field may be the signal to retrieve, but it can also be considered as a noise, which level is to be estimated or even reduced. The modelling of the interaction of the wave with the medium corresponds to the direct problem, and is the necessary building block for any inverse method. The so-called rigorous models are numerical solutions of the Maxwell’s equations, while in approximate methods, some simplifying assumptions make the problem more or less analytically tractable.

- We aim at enhancing rigorous and approximate models in general, the study of ones fueling the development of others, and then to tune these models for a specific configuration (retrieval of objects with rough surfaces, deterministic inverse surface scattering). The rigorous tridimensional modelling of the scattering of electromagnetic waves is numerically involving. However, it can produce reference data, as an alternative to experimental measurements. These data can be compared to the approximate models, leading to a better understanding of the complex and intricated phenomena of scattering and polarization. Also, with these data, the validity domain of the approximate methods is outlined.

- The aim of the present project is to develop a simple optical imaging system with sub-100 nm resolution particularly useful for the analysis of living cells. Some optical techniques allowing sub-diffraction imaging have been described. However, they always involve sophisticated equipments and are not readily available. Our optical system rests on two main ideas. The first one is to replace the glass slide of classical microscopes by a sub-wavelength grating substrate. This grating converts the incident beam into evanescent waves with high spatial frequencies that are able to probe the finest features of the sample. The second idea is to control the amplitude and phase of the plane waves forming the incident beam. Depending on the illumination mode, one can shine the sample with a sub-wavelength light grid or scan it continuously with a 100 nm light spot. This system should allow super-resolved wide-field imaging and, in combination with Fluorescence Correlation Spectroscopy reading, should permit the study of dynamic processes at nanometre scales. Our first application will be to investigate phenomena occurring on the plasma membrane of live cells. This fundamental research project results from recent theoretical and numerical works done at the Fresnel Institute. It involves the cooperation of three laboratories with complementary expertise in modelling, instrumentation, nanolithography and cell biology.

- Using spatially non-uniform illumination significantly improves the resolution of light microscopy. Indeed, frequency mixing between the object and the illumination permits the recovery of object frequencies beyond the diffraction-limited detection

band pass. However, the image reconstruction process requires a precise knowledge of the illumination patterns (usually focused or periodic) and therefore sophisticated stable mountings. Here, we show, both theoretically and experimentally, that image reconstruction can be performed without knowing the illumination patterns, provided that their average is roughly homogeneous over the sample. Using blind structured illumination microscopy (blind-SIM), a resolution

about two times better than that of conventional wide-field microscopy is obtained by simply illuminating the sample with several uncontrolled random speckles. Our approach is insensitive to specimen or aberration-induced illumination

deformations, does not require any calibration step or stringent control of the illumination, and dramatically simplifies the experimental set-up.

**Reference :**

- E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain and A. Sentenac,
*Structured illumination microscopy using unknown speckle patterns*, Nature Photonics**6**, 312 (2012). - A. Sentenac, K. Belkebir, H. Giovannini and P. C. Chaumet,

*Sub-diffraction resolution in total internal reflection fluorescence microscopy with a grating substrate*, Opt. Lett.**33**, 255 (2008).

- Since the seminal work of Ashkin on radiation pressure, the possibility to exploit the mechanical action of optical fields to trap and manipulate neutral particles has spawned a wide range of applications. From atomic and nonlinear physics to biology, optical forces have provided a convenient way to control the dynamics of small particles. Optical tweezers, for example, have proved useful not only for trapping particles but also for assembling objects ranging from microspheres to biological cells. We have proposed a novel way to trap and manipulate nano-objects above a dielectric substrate using an apertureless near-field probe where light scattering at the probe apex is used to shape the optical field into a localized, three-dimensional optical trap and then we showed than the nano objects can be selectively captured and manipulated under realistic conditions. More recently we study that a nanoparticle placed in the vicinity of a photonic crystal would experience an optical force which, with a proper design of the near-field optical landscape, can lead to trapping. We also investigate the optical binding and the optical force and torque on magnetic and negative-index scatterers. More recently, we study the optical forces in time domain.

**Références :**

- P. C. Chaumet and A. Rahmani,

*Electromagnetic force and torque on magnetic and negative-index scatterers*,

Opt. Express**17**, 2224 (2009). - A. Rahmani and P.C. Chaumet,
*Optical Trapping near a Photonic Crystal*,

Opt. Express**14**, 6353 (2006). - P. C. Chaumet, A. Rahmani and M. Nieto-Vesperinas,

*Optical trapping and manipulation of nano-object with an apertureless probe*,

Phys. Rev. Lett.**88**, 123601 (2002).

- There exists a plethora of techniques for solving Maxwell’s equations in the time-harmonic regime, but in our team we also develop in the time domain, electromagnetic scattering by an arbitrary 2D and 3D structure : Then we can provide non-invasive characterization of inhomogeneous targets from knowledge of a transient scattered field or studied the effects of time varying field on the optical forces.
- Reconstructions of fluorophores distribution in small animals.
- Study of alteration of the fluorescence lifetime of a molecule.
- Homogenization of random medium.

**Organization of special section :**

- A. Sentenac, O. Haeberle and K. Belkebir,
*Special Issue : Digital Optical Microscopy*, J. Modern Optics**57**, 685 (2010). - K. Belkebir and M. Saillard,
*Special section on testing inversion algorithms against experimental data : inhomogeneous targets*,

Inverse Problems,**21**, S1-S3 (2005). - K. Belkebir and M. Saillard,

*Special section on testing inversion algorithms against experimental data*,

Inverse Problems,**17**, 1565-1571, (2001).

**Different codes are used in SEMO team**

- Code to compute the diffraction by objects with arbitrary shape and permittivity/permeability in 2D and 3D. Objects can be in free space or in presence of a multilayer system (method of moment is used for this forwrad problem).
- Code to solve the inverse problem in 2D and 3D.
- Code to compute the scattering by rough surfaces in 1D or 2D.
- Code to compute the diffraction by a grating (modal method and method of moment).
- Decomposition of the time reversal operator method can be used in inverse problem.
- Code to compute the propagation of a short pulse in 2D and 3D.
- Code to compute the optical forces on arbitrary objects in 3D (anisotropy, permeability, permittivity, shape can be arbitrary) in harmonic field or time varying field.