Three-dimensional Nonlinear Photonic Crystals Research Articles

Second-harmonic flat-top beam shaping via a three-dimensional nonlinear photonic crystal.

We experimentally extend the nonlinear Gaussian to flat-top beam shaping from one to two dimensions through a three-dimensional nonlinear photonic crystal. Employing a near-infrared femtosecond laser, we induce a modification inside lithium niobate to achieve a second-order nonlinear optical coefficient modulation in three dimensions. The flat-topped truncation of wavefront has been adjusted in a mutual perpendicular coordinate separately. Among the generated flat-topped beams, the optimal flatness is 97.1%, and the nonlinear conversion efficiency is 10-2 at the peak power of 37 kW with the interaction length of 630 µm. By adding an extra dimension, our work simultaneously enables full-wavefront flat-top distribution and nonlinear frequency conversion.

A Brief Review on Nonlinear Photonic Crystals Induced by Direct Femtosecond Laser Writing

Direct femtosecond laser writing or inscription is a useful technique, and it has been employed to engineer various materials in many applications including nonlinear photonic crystals, which are of periodically patterned second-order nonlinearity to get and control the coherent light at new frequencies. By manipulation of second-order nonlinearity, either erased or poled, quasi-phase matching has been achieved in several crystals, especially three-dimensional nonlinear photonic crystals have been originally proposed and proved to be truly three-dimensional. Here we shortly review on the recent advances in the research field of nonlinear photonic crystals inscribed by femtosecond laser, as well as look into the future in this field.

Manipulating the orbital-angular-momentum correlation of entangled two-photon states in three-dimensional nonlinear photonic crystals

Three-dimensional (3D) nonlinear photonic crystal (NPC) has recently been realized in experiment, which provides a powerful platform for quantum-state engineering. Here, we propose a fork-grating 3D NPC scheme to manipulate orbital-angular-momentum (OAM) correlations of entangled two-photon pairs. The spiral spectra, bandwidths, and generation rates of counterpropagating and copropagating photon pairs are theoretically analyzed. Our results show that 3D NPC is of practical significance to generate high-dimensional OAM entanglement for quantum precision measurement, quantum computing, and quantum communication.

Localized Ferroelectric Domain: Localized Ferroelectric Domains via Laser Poling in Monodomain Calcium Barium Niobate Crystal (Laser Photonics Rev. 15(9)/2021)

In article number 2100088, Leszek M. Mazur and co-workers fabricate two- and three-dimensional nonlinear photonic crystals in the bulk of a single-domain ferroelectric calcium barium niobate (CBN) crystal by employing femtosecond infrared optical pulses to invert spontaneous polarization in CBN. The structures are used to demonstrate nonlinear diffraction via transverse second harmonic generation. This work constitutes the first realization of optically induced spatially localized ferroelectric domains in the bulk of a single-domain crystal and has the potential for applications in nonlinear light processing and frequency conversion.

Quasi-phase-matching-division multiplexing holography in a three-dimensional nonlinear photonic crystal

Nonlinear holography has recently emerged as a novel tool to reconstruct the encoded information at a new wavelength, which has important applications in optical display and optical encryption. However, this scheme still struggles with low conversion efficiency and ineffective multiplexing. In this work, we demonstrate a quasi-phase-matching (QPM) -division multiplexing holography in a three-dimensional (3D) nonlinear photonic crystal (NPC). 3D NPC works as a nonlinear hologram, in which multiple images are distributed into different Ewald spheres in reciprocal space. The reciprocal vectors locating in a given Ewald sphere are capable of fulfilling the complete QPM conditions for the high-efficiency reconstruction of the target image at the second-harmonic (SH) wave. One can easily switch the reconstructed SH images by changing the QPM condition. The multiplexing capacity is scalable with the period number of 3D NPC. Our work provides a promising strategy to achieve highly efficient nonlinear multiplexing holography for high-security and high-density storage of optical information.

Nonlinear wavefront shaping with optically\xa0induced three-dimensional nonlinear photonic crystals

Generation of coherent light with desirable amplitude and phase profiles throughout the optical spectrum is a key issue in optical technologies. Nonlinear wavefront shaping offers an exceptional way to achieve this goal by converting an incident light beam into the beam (or beams) of different frequency with spatially modulated amplitude and phase. The realization of such frequency conversion and shaping processes critically depends on the matching of phase velocities of interacting waves, for which nonlinear photonic crystals (NPCs) with spatially modulated quadratic nonlinearity have shown great potential. Here, we present the first experimental demonstration of nonlinear wavefront shaping with three-dimensional (3D) NPCs formed by ultrafast-light-induced ferroelectric domain inversion approach. Compared with those previously used low-dimensional structures, 3D NPCs provide all spatial degrees of freedom for the compensation of phase mismatch in nonlinear interactions and thereby constitute an unprecedented system for the generation and control of coherent light at new frequencies.

A new dimension for nonlinear photonic crystals

The first three-dimensional nonlinear photonic crystals have been constructed thanks to the use of femtosecond laser writing in quadratic nonlinear materials.

Three-dimensional nonlinear photonic crystal in ferroelectric barium calcium titanate

The performance of many optical devices based on frequency conversion critically depends on spatial modulation of the nonlinear optical response of materials. This modulation ensures efficient energy exchange between optical waves at different frequencies via quasi-phase matching1. In general, quasi-phase-matching structures, also known as nonlinear photonic crystals2–4, offer a variety of properties and functionalities that cannot be obtained in uniform nonlinear crystals5–9. So far, nonlinear photonic crystals have been restricted to one- or two-dimensional geometries owing to a lack of fabrication technologies capable of three-dimensional (3D) nonlinearity engineering. Here, we provide an experimental example of a 3D nonlinear photonic crystal, fabricated in ferroelectric barium calcium titanate, by applying an ultrafast light domain inversion approach. The resulting full flexibility of 3D nonlinearity modulation enables phase matching of nonlinear processes along an arbitrary direction, thereby removing constraints imposed by low-dimensional structures. A three-dimensional nonlinear photonic crystal in ferroelectric barium calcium titanate that enables phase matching of nonlinear processes along an arbitrary direction, thereby removing constraints imposed by low-dimensional structures, is experimentally realized.

Universal modeling of second-order nonlinear frequency conversion in three-dimensional nonlinear photonic crystals.

The second-order nonlinear frequency conversion in three-dimensional nonlinear photonic crystals is theoretically studied using coupled wave equations. A universal theoretical model is obtained, with a unified expression combining birefringence phase match, quasi-phase match, nonlinear Raman-Nath diffraction, nonlinear Čerenkov radiation and nonlinear Bragg diffraction. They are demonstrated in the numerical simulation. With the phase-matching conditions in lower dimensions extended to three dimensions, more various phenomena can be seen and corresponding mechanisms can be explained. This research enables the control of second-harmonic generation more efficiently and has potential applications in more complicated nonlinear photonic crystals.

Theoretical study on second-harmonic generation in two-dimensional nonlinear photonic crystals.

We theoretically study second-harmonic generation in two-dimensional nonlinear photonic crystals and obtain a unified expression that combines nonlinear Raman-Nath diffraction, Čerenkov-type second-harmonic generation, and nonlinear Bragg diffraction. The analytical solution is deduced, and the theoretical result coincides well with the nonlinear Raman-Nath, nonlinear Čerenkov, and nonlinear Bragg diffraction phase-matching conditions. This method has potential applications in second-harmonic generation of more complicated two-dimensional and even three-dimensional nonlinear photonic crystals.

A naturally grown three-dimensional nonlinear photonic crystal

Nonlinear frequency conversion via three-dimensional (3D) quasi-phase matching (QPM) process is experimentally realized based on a Ba0.77Ca0.23TiO3 (BCT) crystal. The ferroelectric domains in BCT crystal are observed, and the results reveal that the antiparallel domains distribute in three dimensions and can provide 3D reciprocal lattice vectors for QPM processes. Broadband petal-like second-harmonic patterns are achieved, which are well consistent with the theoretical quasi-cubic model of 3D nonlinear photonic crystals. Our work not only promotes the development of QPM technique but also builds a platform for 3D nonlinear optics and quantum optics.

Generation of conical and spherical second harmonics in three-dimensional nonlinear photonic crystals with radial symmetry

Two types of radially symmetric three-dimensional nonlinear photonic crystals with the cylindrical structure and the egglike structure are proposed, from which the conical and the spherical quadratic harmonic waves can be produced, respectively, by three-dimensional quasi-phase matching. First, the cylindrical structures with periodic and aperiodic modulations of the nonlinear coefficient are both studied, showing their significant advantages compared to the corresponding two-dimensional structures. The dependencies of the transverse and the longitudinal phase-matching periods on harmonic propagating directions are also calculated and analyzed. Then, the egglike structure is designed by programming and the distribution of reciprocal vectors is presented, indicating its ability to generate the spherical harmonic as a point light source. The investigation of the intensity distribution on the spherical wavefront is also performed, showing its strong dependence on the harmonic polarization and the quadratic nonlinear coefficients.

Phase matching in three-dimensional nonlinear photonic crystals

The coupled-wave equations of three-wave interactions are generalized into three dimensions. The reciprocal lattice vectors (RLVs) of three-dimensional (3D) nonlinear photonic crystals (NPCs) which show some unique properties are analyzed in detail as compared to those in one- and two-dimensional cases. It is proposed as an example that the cross-distributing conical harmonic beams can be obtained from the 3D NPC by intentionally using the proper RLVs. Some other possible applications are suggested at the end of discussion.

Subpicosecond optical switching in polystyrene opal

An ultrafast all-optical switching is demonstrated in an organic three-dimensional nonlinear photonic crystal with a response time as short as 120 fs. The operating wavelength of the optical switching is in the visible spectrum. The switching function is realized by a shift of the photonic band gap under optical pumping. It is found that the photonic band gap shifts about 10 nm with the excitation of 27.5GW∕cm2 pump laser.