The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

Detailed and comparable investigations of the time evolution of the readout erasure of 1D
and 2D annular symmetry photonic lattice structures optically induced by nondiffracting
Bessel beam technique were performed. The lattices were recorded with the use of cw single
mode 532 nm, 17 mW laser beam in photorefractive LiNbO3:Fe and LiNbO3:Fe:Cu crystals, the latter
having also photochromic properties. While the 1D Bessel-like refractive lattice had
micrometric scale modulation in the radial direction, the 2D complex lattices inducted by
Bessel standing wave were a combination of annular and planar refractive gratings with
~10 μm period in the radial and
half-wavelength standing wave 266 nm period in the axial directions. The study of
photochromic properties of LN:Fe:Cu crystal at 532 nm showed 1.6 times increase of
absorption coefficient with increase of illuminating intensity from 12.5 to
96.8 mW/cm2,
which opened a direct way of essential decrease of the erasure of the stored lattices
during readout by weaker probe beam at the recording wavelength. Investigations showed
that the erasure constants for 1D and 2D lattices in LN:Fe:Cu crystal are larger than in
LN:Fe crystal (6150 and 5150 s, and 3080 and 698 s, respectively). The nondestructive
refractive lattices recorded by Bessel beam technique will assist the different
applications in all optical devices and communication systems and have particular interest
for experiments on light localization and spatial soliton formation in structured
nonlinear media.

Nondestructive readout of holograms recorded by Bessel beam technique in LiNbO3:Fe and LiNbO3:Fe:Cu crystals

Azimuthally modulated higher order rotationally symmetric Bessel-like optical patterns were generated by coherent superposition of two co-propagating Bessel beams – either in or out of phase. By changing the distance between the beam centers, a whole variety of transition states can be realized. As one prominent example, a 4-fold symmetry quadrupole-like photonic structure was optically inducted in an SBN crystal and nonlinear beam propagation in such a photonic wave-guiding structure is investigated in both self-focusing and self-defocusing regimes. The proposed device serves as an all-optical 2d 1 × 4 photonic interconnect.

Controlled soliton formation in tailored Bessel photonic lattices.

A novel counter-propagating Bessel beam technique is suggested and realized for optical formation of complex two-dimensional (2D) refractive lattice structures in photorefractive materials. The 2D complex lattices optically induced by the suggested method are a combination of annular and planar gratings with refractive index modulation in the radial direction in the transverse plane and the in axial direction along the optical beam propagation. The recording of the lattices is performed by 532 nm and 633 nm laser beams. The counter-propagating beam geometry builds up the Bessel standing wave with periodic annular structure in each anti-node. The refractive lattices are recorded in Z- and Y-cut 2 mm thick photorefractive lithium niobate crystals singly doped by Fe and doubly doped by Fe and Cu. The readout of recorded lattices is performed by Gaussian red and green probe laser beams. The direct observation of recorded lattices by optical phase microscope is also performed. The formed photonic structures ha...

Bessel standing wave technique for optical induction of complex refractive lattice structures in photorefractive materials

Optical induction of Bessel-like lattices in methyl-red doped liquid crystal cells

We report the first observation of Talbot effect – diffraction grating images self-replications at regular distances, from 1D annular grating with the period of d = 30 ± 1 μm. Up to 20 high contrast revivals of the grating were observed by the green laser beam at λ = 532 nm with Talbot distance ZT = d2/λ = 1.57 ± 0.01 mm. The grating self imaging with half period of the original grating at ZT/2 was also observed. Using the annular grating as a mask, the recording of refractive index photonic lattice in 2 mm thick Fe doped lithium niobate crystal was performed by 532 nm laser beam. The replication of the grating images due to Talbot effect provides the recording of two refractive replicas of the grating with the periods of d and d/2 inside the 2 mm crystal checked by phase microscope depth scan observations. The obtained results show the possibility of the use of 2D masks for the creation of 3D photonic lattices in photorefractive materials, which can be used as photonic crystals.

Talbot Effect from Rotational Symmetry Gratings: Application to 3D Refractive Grating Formation

A novel combined interferometric–mask method for the formation of micro- and nanometric scale three-dimensional (3D) rotational symmetry quasi-crystalline refractive lattice structures in photorefractive materials is demonstrated experimentally. The method is based on micrometric scale spatial modulation of the light by amplitude mask in the radial directions and along the azimuthal angle and the use of counter-propagating beam geometry building up Gaussian standing wave, which defines the light modulation in the axial direction with half-wavelength periodicity. 3D intensity pattern can be represented as numerous mask-generated 2D quasi-periodic structures located in each anti-node of the standing wave. The formed 3D intensity distributions of the optical beams can be imparted into the photorefractive medium thus creating the micro- and sub-micrometric scale 3D refractive index volume lattices. The used optical scheme allows also the formation of 2D lattices by removing the back-reflecting mirror. 2D and 3D refractive lattices were recorded with the use of 532 nm laser beam and rotational symmetry mask in doped lithium niobate crystals and were tested by the probe beam far-field diffraction pattern imaging and direct observation by phase microscope. The formed rotational symmetry 3D refractive structures have the periods of 20–60 μm in the radial directions, 60 μm along the azimuthal angle and half-wavelength 266 nm in the axial direction.

Optical induction of 3D rotational symmetry refractive lattices by combined interferometric-mask method in doped LiNbO3 crystals

A new combined interferometric-mask method is suggested and realized for creation of 3-dimensional (3D) holographic
periodic and quasi-periodic structures in photorefractive materials. The method is based on the preparation of 2-
dimensional (2D) micrometric scale masks with different symmetries and illumination of the photorefractive material
through the mask by Gaussian beam in combination with back reflecting mirror. The counter-propagating beam
geometry builds up Gaussian standing wave, which determines the third half-wave period of the grating in the axial
direction. Thus, the created 3D intensity pattern can be represented as numerous mask-generated 2D quasi-periodic
structures located in each anti-node of the standing wave.
The formed intensity pattern can be imparted into the photorefractive medium via electro-optic effect, thus creating
micro- and sub-micro scale 3D refractive index volume gratings with new symmetries and properties. The gratings were
recorded by 532 nm cw laser beams in Fe-doped lithium niobate crystals taking into account their high photorefractive
properties and possibility of creating the persistent gratings. The gratings formed have ~ 10 μm period in radial and
azimuthal directions and ~266 nm in axial direction. The gratings were interrogated by diffraction of low intensity
Gaussian probe beams from the recorded structures.

Vahram Mekhitaryan

Papers

Nondestructive readout of holograms recorded by Bessel beam technique in LiNbO3:Fe and LiNbO3:Fe:Cu crystals

Bessel standing wave technique for optical induction of complex refractive lattice structures in photorefractive materials

Talbot Effect from Rotational Symmetry Gratings: Application to 3D Refractive Grating Formation

Optical induction of 3D rotational symmetry refractive lattices by combined interferometric-mask method in doped LiNbO3 crystals

Combined interferometric-mask method for creation of micro- and sub-micrometric scale 3D structures in photorefractive materials