Optically Induced Nonlinear Cubic Crystal System for 3D Quasi‐Phase Matching

Abstract

Quasi‐phase matching (QPM) is a technique in nonlinear optics for achieving efficient energy exchange among optical waves at different frequencies, by spatially modulating the quadratic nonlinearity (χ (2)) of the medium. To realize the full potential of QPM, 3D spatial modulation of χ (2) is required. This has become experimentally feasible recently thanks to the invention of femtosecond laser‐based nonlinearity engineering in ferroelectric crystals. Herein, the first experimental demonstration of QPM second harmonic generation (SHG) in a nonlinear cubic crystal system is presented, in which χ (2) modulations form simple cubic, body‐centered cubic, face‐centered cubic, and diamond cubic lattices, respectively. The experimental results indicate that these nonlinear cubic structures share the same primary reciprocal lattice vectors (RLVs), but possess different Fourier coefficients (in conventional cells), leading to SHG with similar angular resonances but various intensity distributions in the far field. This work contributes to a comprehensive understanding of nonlinear optical processes in 3D periodic media, and thus sheds light on the development of high‐performance QPM devices.

Frequency doubling of femtosecond laser pulses in three dimensional nonlinear photonic crystals

“…It is obvious that S 2 will be maximum, when all mentioned factors go to 1. Similarly to ( 14) and (15), this is accomplished at the phasematching condition, when the transverse components of vectors K x − mG x = 0, K y − nG y = 0 and their longitudinal components k z − 2k 1 − qG z = 0 are matched by respective reciprocal lattice vectors provided by the lattice.…”

“…The fundamental wavelength has been chosen to be 800 nm, where the maximum output power of femtosecond Ti:sapphire laser is achieved. BND appears when both transverse (14) and longitudinal (15) conditions are fulfilled simultaneously. This can be achieved for an arbitrary diffraction order with the indexes {m, n, q}.…”

“…In the work [4], similar model was applied for describing frequency conversion of monochromatic radiation in 2D NPCs, and, then this approach was adopted to utilize third spatial direction [10]. Recent progress in structuring nonlinearity and invention of femtosecond laserbased nonlinearity engineering techniques have led to the fabrication of 3D NPCs [13][14][15] that inspires new possibilities for nonlinear frequency conversion processes and parametric interactions. 3D NPC may become a good platform for realization of consecutive(coupled) parametric processes and nonlinear structuring of light [16,17].…”

Wavelength-dependent nonlinear wavefront shaping in 3D nonlinear photonic crystal

“…3D nonlinear photonic crystals (NPCs) allow spatial modulation of the second-order nonlinear coefficient χ 2 along arbitrary directions, which is a major advantage for the generation of light at new frequencies and enables new functions that otherwise cannot be obtained with one-or two-dimensional structures [1][2][3][4][5][6][7][8] . For instance, the traditional 2D fork-shaped χ 2 gratings are used for second harmonic vortex beam generation from a fundamental Gaussian wave [9,10] .…”

Cherenkov second harmonic generation of femtosecond laser pulses in a homogeneous nonlinear crystal

“…Cherenkov-type SH microscopy is very sensitive to the inhomogeneity of nonlinear susceptibility, thereby representing a powerful tool for nondestructive and high-resolution 3D ferroelectric domain wall visualization [28,29]. Cherenkov SH microscopy offers a much better spatial resolution and sensitivity than collinear non-phase-matched SHG [30], allowing one to visualize 3D NPCs [26,27,31,32] fabricated using direct laser writing by means of tightly focused femtosecond laser pulses.…”