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Non-linear photonics and quantum information > Nonlinear microgenerators based on photonic crystals
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Structures fabriquées au LPN.

This project aims at the conception, the fabrication and the use of efficient and compact sources based on the exploitation of second order nonlinear effects. The investigated approach consists in using semiconductor materials structured at a sub-wavelength scale. These materials exhibit very large nonlinear quadratic susceptibilities ( 1 or 2 order of magnitude larger than usual materials). A periodical structuration in such materials enables the compensation of the chromatic dispersion (phase-matching achieved) and to slow down the waves interacting nonlinearly.
Recently, we have demonstrated in 1D stratified structure second harmonic generation exhibiting efficiency conversion that varies with the sixth power of the length (L6). On another hand, we have developed a software in order to forecast the second harmonic generation in 2D photonic crystals. Please check our current projects.

1 - 1D Microsources based on AlOx/AlGaAs Bragg mirrors

Using microstructures presenting a periodic modulation of the refractive index was proposed as soon as the first steps of second order nonlinear optics in order to achieve phase-matching and as a consequence to obtain large conversion efficiency. To apply experimentally this proposition called quasi-phase matching, a solution consists in using a periodical distribution of the second order nonlinear susceptibility (nonlinear property of the material) in a medium with an uniform refractive index (linear property of the material) (See R.L. Byer et al). This periodicity put back in phase the nonlinear polarization with the generated waves.

Alternatively, phase matching can be obtained by taking benefit of the dispersive properties of a medium that presents a periodical distribution of the refractive index. In these very particular conditions, the periodicity leads to a decrease of the group velocity of the interacting waves. This property has been exploited to enhance second harmonic generation. 1D stratified structures (refractive index periodical in 1 dimension) have been proposed by Scalora et al. to obtain very efficient second harmonic generation, the structure enabling phase matching as well as enhancement of the field. These 1D structures exhibit a "stop-band" that prevents the light from propagating in a spectral range centered on the Bragg wavelength in a similar way to photonic band gap materials. They are called 1D photonic crystals (1D-PCs) or Bragg mirrors. On the borders of the spectral region of the stop-band (band edges), narrow resonances are observed. In these resonances, the reflectivity is null and transmission is maximum. The zero reflectivity corresponds to a total dephasing of Pi for the transmitted beam.
Structures fabricated at LPN.

This characteristic of 1D-PC dispersion make phase-matching possible for second harmonic generation if the 2nth lateral resonance of the second order stop-band is exactly at 2 times the frequency of the nth resonance of the first order stop-band. The electromagnetic field is also enhanced when its frequency is set to these "distributed Bragg resonances" ones.
It can be shown by a simple analytical calculation based on the coupled modes theory that, in a Bragg structure sufficiently long (L is the length), the field enhancement is proportional to L and the intensity (IF) goes like L2. Because the SHG (ISH) intensity varies like L2 and IF2, we find: :


This constitutes a spectacular difference when it is compared to the second harmonic generation efficiency in a bulk medium which goes like L2. We have also recently demonstrated such an over-quadratic dependence of second harmonic generation efficiency in a 1D-PC made of AlOx/ GaAlAs (cf. figure below).

2- 2D nonlinear microsources

We have developed a 2D finite difference time domain (FDTD) software able to take into account second harmonic generation (SHG) in 1D or 2D structured materials. We applied this code to a semiconductor defective photonic crystal (PC) waveguide where phase-matching is obtained by engineering the Bloch modes dispersion. This nonlinear FDTD (NLFDTD) method constitutes an intuitive alternative solution able to analyse the SHG in an arbitrary 2D structure with a reasonable time consumption at expend of loosing generality. In particular, the method works in the non-depleted pump approximation and neglects intra-pulse chromatic dispersion. It is based on the implementation of two parallel linear FDTD codes. The first operating at FF wavelength and the second at SH wavelength. The quadratic nonlinearity is only taken into account for the SH, which is not coupled back at the FF wavelength. Chromatic dispersion is considered simply by taken the actual refractive index at FF and SH wavelength. This artificial separation of FF and SH propagation allows to easily identify FF and SH distribution and other relevant physical parameters.


3-Current Projects

L6 law in guided optics:

We propose to adapt the approach we chose to achieve large second harmonic generation efficiency in vertical Bragg mirrors (use of the anomalous dispersion at the photonic band-edges) to a waveguide configuration. Here, the 1D-PC is deeply etched in a ridge waveguide. The advantage of this configuration is double: strong spatial confinement and availability of the maximum nonlinear tensor component. However, this needs state-of-the art technology like it is shown in the picture below.


2D photonic crystrals:

We are exploring also 2D PCs in second order nonlinear regime. Two configurations are being investigated: the small line-defect optical waveguides (see figure) and the perfectly periodic structures that behave like 2D distributed resonators.

Guide 2D
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Puce Members


 Levenson Ariel  (+33) 1 69 63 61 87  
 Raineri Fabrice  (+33) 1 69 63 63 92  

And also...

 Monnier Paul  (+33) 1 69 63 61 83  
 Raj Rama  (+33) 1 69 63 61 95  

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Puce Publications

Publication in journals
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Puce Contracts and projects

    Puce International Projects

      PHC PICASSO : Active non diffractive light propagation through non-linear photonic crystals

      Reference contract : Binational project supported by the Egide between Spain and France
      LPN leader(s): Rama Raj, Fabrice Raineri
      Main goals : The motivation of this project is to combine non diffractive propragation in photonic crystals and non-linear optics. (2009-2010)

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Puce Past and current Internship Training



  • Nonlinear optics in III-V semiconductor-based photonic crystals

  • F. Raineri-(2001-10-01 / 2004-10-31)
    Contact : A. Levenson
    Group : Nonlinear Photonic and Quantum Information (PHOTONIQ)
    This work concerns both theoretical and experimental studies of nonlinear optics in photonic crystals based on III-V semiconductors. Photonic crystals, with their lattice dimensions of the order of the wavelength of the light, offer efficient ways to control the propagation of the electromagnetic fields. For instance, by adjusting the opto-geometrical parameters of these structures, it is possible to engineer the dispersion of the matter such as the light propagation is forbidden in every directions of the space. The aim of this PhD thesis is to demonstrate that this possibility to engineer the dispersion can also be advantageously used to enhance nonlinear interactions between light and matter. We will see that 1D and 2D photonic crystals are adequate structures to obtain efficient frequency doubling because they enable phase matching in very nonlinear materials such as AlxGa1-xAs and the slowing down of the light as well. We will also show that, by combining the nonlinear properties of III-V semiconductors to 2D photonic crystals, it is possible to realize the basic active functionalities for all-optical data processing such as laser sources, amplification, ultrafast switching…

  • Integrated optical circuits based on hybrid photonic crystal structures in InP / Silicon optical waveguide

  • Y. Halioua-(2007-10-01 / 2011-10-01)
    Contact : F. Raineri , R. Raj
    Group : Nonlinear Photonic and Quantum Information (PHOTONIQ)

  • Study of hybrid structures: Nonlinear III-V semi-conductor photonic crystals/ silicon waveguide

  • A. Bazin-(2009-09-01 / 2012-10-01)
    Contact : F. Raineri , R. Raj
    Group : Nonlinear Photonic and Quantum Information (PHOTONIQ)
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