Enhanced Čerenkov second-harmonic emission in nonlinear photonic structures

Nonlinear generation of an optical bottle beam in domain-engineered ferroelectric crystals

Nonlinear wavefront shaping in periodically poled ferroelectric crystals has received great attention because it offers a convenient way to generate a structured light beam at new frequencies. In contrast to structurally uniform beams like Laguerre-Gaussian or Hermite-Gaussian modes, here we demonstrate the possibility to generate a spatially varied optical bottle beam via a frequency doubling process in a domain-engineered Sr0.61Ba0.39Nb2O6 (SBN) crystal. The nonlinear holography method was employed to design the modulation pattern of the second-order nonlinear coefficient χ(2), and the femtosecond laser poling was used to imprint the χ(2) pattern into the SBN crystal via ferroelectric domain inversion. The second harmonic bottle beam with zero intensity in its center that is surrounded in all three dimensions by light was observed with the incidence of a fundamental Gaussian beam. These results are useful for nonlinear generation and control of structured light at new frequencies, which has important applications in nonlinear photonics and quantum optics.

Research development on fabrication and optical properties of nonlinear photonic crystals

Since the lasers at fixed wavelengths are unable to meet the requirements of the development of modern science and technology, nonlinear optics is significant for overcoming the obstacle. Investigation on frequency conversion in ferroelectric nonlinear photonic crystals with different superlattices has been being one of the popular research directions in this field. In this paper, some mature fabrication methods of nonlinear photonic crystals are concluded, for example, the electric poling method at room temperature and the femtosecond direct laser writing technique. Then the development of nonlinear photonic crystals with one-dimensional, two-dimensional and three-dimensional superlattices which are used in quasi-phase matching and nonlinear diffraction harmonic generation is introduced. In the meantime, several creative applications of nonlinear photonic crystals are summarized, showing the great value of them in an extensive practical area, such as communication, detection, imaging, and so on.

Broadband enhancement of Čerenkov second harmonic generation in a sunflower spiral nonlinear photonic crystal

We present an experimental study on the Čerenkov second harmonic emission in a novel sunflower spiral array of ferroelectric domains in LiNbO₃ crystal. The spiral patterns offer a diffusive, circularly symmetric distribution of reciprocal lattice vectors, thereby enabling enhanced emission of the Čerenkov beam in a broad spectral range. Instead of the traditional electric field poling, the sunflower spiral patterns are fabricated here by using our pioneering method of ferroelectric domain engineering with ultrafast light. This all-optical method gives access to high quality domain structures with short periods, which is beneficial for efficient Čerenkov harmonic generation.

Nonlinear Raman-Nath second harmonic generation of hybrid structured fundamental wave

We numerically and experimentally investigated the nonlinear Raman-Nath second harmonic generation of hybrid structured fundamental wave whose phase modulation combined periodic and random structure. The second harmonic generation of both one- and two-dimensional hybrid structured fundamental wave were investigated in this paper. The results show that more diffraction spots can be obtained in these hybrid structures than the pure periodic modulation cases. Besides, the total intensity of the second harmonic not only can be dramatically enhanced without altering the diffraction angles, but also is increasing with the degree of randomness of the structure. This study enriches the family of second harmonic generation of structured fundamental wave and has potential application in dynamically controlling second harmonic wave in arbitrary directions.

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.

Enhanced fourth harmonic generation via nonlinear Čerenkov interaction in periodically poled lithium niobate crystal

We introduce a custom-cut periodically poled ferroelectric crystal for the phase matching of multistep cascading frequency conversion processes. Our approach involves combination of collinear second harmonic generation and transverse sum frequency mixing via the total internal reflection of the fundamental and collinear second harmonic beams. As a proof of concept we demonstrate multiple frequency generation with an enhanced fourth harmonic signal in a one-dimensional periodically poled LiNbO₃ crystal.

Nonlinear Raman-Nath second harmonic generation with structured fundamental wave

We proposed and experimentally demonstrated that nonlinear Raman-Nath second harmonic can be achieved in real time when a fundamental wave with the phase periodically modulated, termed as structured fundamental wave, incident in a homogeneous nonlinear medium. The diffraction of second harmonic originates from the structured fundamental wave, rather than the grating of a nonlinear photonic crystal. Nonlinear second harmonic generation, in forms of both one- and two-dimensional, was investigated in our experiment. This method circumvents the limitation of nonlinear photonic crystals in some extend and has potential applications in nonlinear frequency conversion, optical signal processing and beam shaping, etc.

Simultaneous type I and type II Čerenkov-phase matched second-harmonic generation in disordered nonlinear photonic structures

We observe simultaneous type I and II Čerenkov-phase matched second-harmonic generation in a disordered nonlinear photonic crystal. The mean width of the disordered ferroelectric domains and the laser beam width are adjusted to be on the same length scale. We analyze the polarization properties, emission angles and intensities of each process.

Nonlinear Raman-Nath diffraction of femtosecond laser pulses in a 2D nonlinear photonic crystal

We study second-harmonic generation (SHG) of femtosecond laser pulses in a rectangular two-dimensional nonlinear photonic crystal (NLPC). Multiple SH beams were observed in the vicinity of the propagation direction of the fundamental beam. It has been verified that the angular positions of these beams obey the conditions of nonlinear Raman-Nath diffraction (NRND). The measured SH spectra of specific NRND orders consist of narrow peaks that experience a high-frequency spectral shift as the order grows. We derive an analytical expression for the process studied and find the theoretical results to be in good agreement with the experimental data. We estimate the enhancement factor of nonlinear Raman-Nath diffraction in 2D NLPC to be 70.

Multiple quasi-phase-matching in nonlinear Raman-Nath diffraction

The method of the superposition of a nonlinearity modulation is employed to design a two-dimensional (2D) nonlinear photonic lattice for efficient multiple quasi-phase-matched second harmonic generation in the process of nonlinear Raman-Nath diffraction (NRND). An analytical solution is proposed to calculate the second harmonic intensity in rectangular 2D lattices. This approach can be useful for the generation of multiple second harmonic beams with the efficiency a few orders of magnitude higher than in the case of nonphase-matched generation via NRND.

Nonlinear Raman-Nath diffraction of femtosecond laser pulses

We study the nonlinear Raman-Nath diffraction (NRND) of femtosecond laser pulses in a 1D periodic nonlinear photonic structure. The calculated second-harmonic spectra represent frequency combs for different orders of transverse phase matching. These frequency combs are in close analogy with the well-known spectral Maker fringes observed in single crystals. The spectral intensity of the second harmonic experiences a redshift with a propagation angle, which is opposite the case of Čerenkov nonlinear diffraction. We analyze how NRND is affected by the group-velocity mismatch between fundamental and second-harmonic pulses and by the parameters of the structure. Our experimental results prove the theoretical predictions.

Effect of the domain shape on noncollinear second-harmonic emission in disordered quadratic media

We study the role of the individual ferroelectric domain shape on the second-harmonic emission in strontium barium niobate featuring a random quadratic nonlinearity. The noncollinearly emitted second-harmonic signal is scanned in the far-field at different incident angles for different domain size distributions. This offers the possibility to retrieve the Fourier spectrum, corresponding to the spatial domain distribution and domain shape. Based on images of the domain structures retrieved by Čerenkov-type second-harmonic microscopy, domain patterns are simulated, the second-harmonic intensities are calculated, and finally compared with the measurements.

Unified approach to Čerenkov second harmonic generation

We discuss the effect of second harmonic generation via the Čerenkov-like process in nonlinear bulk media and waveguides. We show that in both schemes the Čerenkov harmonic emission represents in fact a nonlinear Bragg diffraction process. It is therefore possible, for the first time, to describe the bulk and waveguide Čerenkov emission uniformly by considering the spatial modulation of the second-order nonlinear polarization. This is also experimentally illustrated by studying the Čerenkov second harmonic generation at the boundary of a nonlinear quadratic medium via the total internal reflection inside the nonlinear crystal.

Čerenkov-type second-harmonic spectroscopy in random nonlinear photonic structures

We report on experimental and theoretical studies of Čerenkov-type second-harmonic generation in random nonlinear photonic structures with different two-dimensional distributions of the ferroelectric domains. We utilize Čerenkov-type second-harmonic generation spectroscopy to estimate the average ferroelectric domain size by analyzing the spatial Fourier spectrum of the domain patterns. This is measured by scanning the Čerenkov second-harmonic signal for different angles of incidence and light polarizations of the fundamental wave. By comparing the experimental results with numerically simulated Fourier spectra, the corresponding domain patterns are retrieved, which are in a good correspondence with images obtained by Čerenkov-type second-harmonic generation microscopy.

Role of a localized modulation of χ(2) in Čerenkov second-harmonic generation in nonlinear bulk medium

We study the second-harmonic generation in quadratic nonlinear media with localized spatial modulation of χ((2)) response. We demonstrate that the emission of Čerenkov second-harmonic takes place only when the fundamental beam illuminates the region of χ((2)) variation. This proves that the sharp modulation of the χ((2)) nonlinearity constitutes a sufficient condition for the emission of Čerenkov second harmonic in bulk materials. Our calculations are in excellent agreement with simple analytical approach utilizing the concept of reciprocal vectors representing the Fourier spectrum of the modulation of χ((2)).