Measurement of the nonlinear coefficient of orientation-patterned GaAs and demonstration of highly efficient second-harmonic generation

Quasi-phase-matched (QPM) GaAs structures, 0.5 mm thick, 10 mm long, and with 61-mum grating periods, were grown by a combination of molecular-beam epitaxy and hydride vapor phase epitaxy. These were characterized by use of mid-IR second-harmonic generation (SHG) with a ZnGeP(2) (ZGP) optical parametric oscillator as a pump source. The SHG efficiencies of QPM GaAs and QPM LiNbO(3) were directly compared, and a ratio of nonlinear coefficients d(14)(GaAs)/d(33) (LiNbO(3))=5.01+/-0.3 was found at 4.1-mum fundamental wavelength. For input pulse energies as low as 50muJ and approximately 60-ns pulse duration, an internal SHG conversion efficiency of 33% was measured in QPM GaAs.     

Waveguide second-harmonic generation device with broadened flat quasi-phase-matching response by use of a grating structure with located phase shifts

We report on a theoretical analysis and experiments for bandwidth broadening in quasi-phase-matched (QPM) second-harmonic generation (SHG).We used phase-shifted segments of a periodic grating to obtain a spectrally broadened, nearly flat response simultaneously with high conversion efficiency. We used an x-cut MgO:LiNbO(3) QPM waveguide in our analysis and experiments. The spectral range of the 850-nm fundamental for which SHG conversion exceeded 0.95 of the maximum value broadened from 0.02 to 0.12 nm when a 1-cm-long grating was divided into three segments with optimum phase shift. SHG conversion efficiency was 300%/W for this waveguide. The SHG efficiency and phase-matching characteristics showed good agreement with theoretical results.     

Competition between SFG and two SHGs in broadband type-I QPM

In this paper, we have studied the characteristics of second-order nonlinear interactions with band-overlapped type-I quasi-phase-matching (QPM) second harmonic generation (SHG) and sum-frequency generation (SFG), and predicted a blue-shift with a band-narrowing of their bands and a sunken response in the SFG curve, which are due to the phase-matching-dependent competition between band-overlapped SHG and SFG processes. This prediction is then verified by the experiment in an 18-mm-long bulk MgO-doped periodically poled lithium niobate crystal (MgO:PPLN) and may provide the candidate solution to output controlling for flexible broadcast wavelength conversion, channel-selective wavelength conversion and all-optical logic gates by cascaded QPM second-order nonlinear processes.     

High conversion efficiency of second harmonic generation in a short nonlinear photonic crystal with distributed Bragg reflector mirrors

Second harmonic generation (SHG) in a short nonlinear photonic bandgap (PBG) structure coated with distributed Bragg reflector (DBR) mirrors is theoretically investigated by means of an iteration approach that fully considers pump depletion. A total conversion efficiency of about 96% can be obtained in an optimized structure with a size scale of about 0.2 mm and at the modest pump intensity of about 0.133 MW/cm², which is four orders of magnitude more than that in a quasi-phase-matching (QPM) structure with the same sample length. Such a high conversion efficiency of SHG will greatly facilitate the success of short frequency conversion devices and all-optical integration in nanostructures.     

Efficiency pedestal in quasi-phase-matching devices with random duty-cycle errors

It is shown that random duty-cycle errors in quasi-phase-matching (QPM) nonlinear optical devices enhance the efficiency of processes far from the QPM peak. An analytical theory is shown to agree well with numerical solutions of second-harmonic generation (SHG) in disordered QPM gratings. The measured efficiency of 1550?nm band SHG in a periodically poled lithium niobate (PPLN) waveguide away from the QPM peak agrees with observations of domain disorder in a PPLN wafer by Zygo interferometry. If suppression of parasitic nonlinear interactions is important in a specific application of QPM devices, control of random duty-cycle errors is critical.     

Second-harmonic generation with a high-index-clad waveguide

Theoretical and experimental analyses of second-harmonic generation (SHG) with a high-index-clad waveguide are reported. It was found that confinement of the propagation modes and the overlap between the fields of fundamental and second-harmonic waves could be increased in this waveguide. This structure was achieved in an x-cut MgO:LiNbO (3) quasi-phase-matched (QPM) waveguide by use of Nb(2)O(5) as a cladding layer. With the QPM SHG device, harmonic blue light of 5.5 mW at the 434-nm wavelength was generated with a normalized conversion efficiency of 1200%/W cm(2).     

Phase matching considerations in second harmonic generation from tissues: Effects on emission directionality, conversion efficiency and observed morphology

We present a heuristic treatment which relates SHG image intensities, signal directionality, and observed morphology to the physical structure of collagen and cellulose fibrillar tissues. The SHG creation model is based upon relaxed phase matching conditions which account for dispersion, randomness, and axial momentum contributions from the media, and includes a mathematical treatment which relates SHG conversion efficiency to fibril diameter and packing through the inclusion of potential intensity amplification resultant from quasi-phase matching (QPM). A direct consequence of this theory is that SHG in biological tissues is not strictly a coherent process, and that the forward directed SHG has a longer coherence length than the backward component, Through this treatment, we show that the emission directionality and also conversion efficiency do not arise solely from the fibril size but also depend on packing density and order of the inter-fibril structure. We demonstrate these principles in comparing the SHG response in normal and Osteogenesis Imperfecta (OI) skin. We show that the observed directionality and decreased relative intensity in the diseased state is consistent with phase matching conditions arising from the decreased fibril size and more random assembly. We further use this theory to explain the differences in morphology seen in forward and backward collected SHG in fibrillar tissues (e.g., collagenous and cellulosic). Specifically, we attribute segmented appearance to destructive interference between small fibrils separated by less than the coherence length. We suggest the approach based on relaxed phasematching conditions is general in predicting the SHG response in tissues and may be broadly applicable in interpreting the SHG contrast for diagnostic applications.     

Vector method for studying the second-harmonic-generation light derived from complex periodic ferroelectric domains

In this Letter, in order to overcome the disadvantages of controlling the second-harmonic-generation (SHG) light derived from the traditional one-dimensional (1D) periodic ferroelectric domains we propose a kind of so-called complex periodic ferroelectric structure (CPFS), which unit cell is composed of even layers of positive and negative domains arranged alternatively following aperiodic sequence. It is found that comparing with the traditional periodic structure, CPFS cannot offer more reciprocal vector compensations for the mismatching phase, but CPFS may provide larger effective nonlinear coefficients (ENCs) in high-order quasi-phase-matching (QPM) and possesses advantages of the amplitude modulation for SHG peaks. In this Letter we study CPFS by use of vector method (VM), where the contribution to ENC for each domain or each unit cell will be treated as a vector and the QPM condition for CPFS and the modulation effect of aperiodic unit cells have been obtained. Without any Fourier transformation VM treats the grating function in real space and will be very convenient and intuitive. Both VM and CPFS would possess potential applications in the field of SHG investigations.     

Collinear second harmonic generation of 20 wavelengths in a single two-dimensional decagonal nonlinear photonic quasi-crystal

We report on the observation of quasi-phase matched collinear second harmonic generation (SHG) at 20 wavelengths in a two-dimensional nonlinear photonic quasi-crystal with decagonal lattice. We show that at some wavelengths the second harmonics are generated via standard quasi-phase matching, namely a reciprocal vector exists that equals the phase-mismatch vector, while at others the SHG is as a result of the projection-based quasi-phase matching in which the momentum conservation is satisfied up to a projection of a reciprocal vector onto the direction of propagation. In spite of different generation mechanisms, the reciprocal vectors (or their projections) involved in the collinear QPM SHG can be described by a generalized equation.     

Second-harmonic generation in resonant waveguide gratings incorporating ionic self-assembled monolayer polymer films

Experimental results on resonantly excited second-harmonic generation (SHG) in a periodic ionically self-assembled monolayer (ISAM) film are reported. A double-layer guided-mode resonance filter (GMRF) structure is coated with 40 bilayers of pyrlium-based chi(2) ISAM thin film and excited with the fundamental of a Nd:YAG laser. Enhanced second-harmonic conversion in the ISAM film is achieved because of the local field enhancement associated with the fundamental resonating leaky mode. This method of SHG is particularly promising, as the ISAM films under investigation exhibit anomalous dispersion that may be applied for phase matching to improve nonlinear conversion efficiency.     

Coupled mode analysis to study cascading in the QPM Cerenkov regime in waveguides

In this paper we use the coupled mode analysis to study nonlinear phase shifts of the fundamental beam caused by cascaded second order nonlinear effects in the Quasi Phase Matched Cerenkov (QPMC) configuration in waveguides. Under the no-pump depletion approximation which is valid for low conversion efficiencies, we obtain the nonlinear phase shift as a function of length of interaction and grating period. It is observed that the nonlinear phase shift of the fundamental beam can be maximized by choosing a grating period for which the phase matched second harmonic radiation mode is radiated parallel to the film-substrate interface, i.e., for zero Cerenkov angle. Although the phase shifts are smaller than in the case of all guided geometry, QPM Cerenkov configuration is expected to have greater tolerance towards various waveguide parameters and the fundamental wavelength.     

Theoretical Study on Intra-Cavity Distributed-Bragg-Reflection Quasi-Phase-Matched Second-Harmonic Lasers

The characteristics of intra-cavity distributed Bragg reflector (DBR) quasi-phase-matched (IDQPM) second-harmonic-generation (SHG) lasers are theoretically studied. In the IDQPM-SHG laser, a QPM device and a DBR for feedback are separately fabricated on the same substrate with the QPM device placed between the DBR and a semiconductor laser. The threshold current of the IDQPM-SHG laser depends on the coupling efficiency between the laser diode and the QPM waveguide and the reflectivity of the DBR. The SH output of the IDQPM-SHG laser is strongly dependent on the generalized SHG conversion efficiency, x. This laser has the potential to attain an SH output over a 30-mW using a currently available 50-mW semiconductor laser for the fundamental light source, when highly efficient QPM device (x=2.2 W⁻¹) is used. Its tolerance for various deviations from the initial design and the problems to develop a commercially available IDQPM-SHG laser are also discussed.     

Using a grating structure for phase compensation in achieving an efficient round-trip optical parametric process in periodically poled lithium niobate with an incomplete quasi-phase-matching period

An incomplete period of the last quasi-phase-matching (QPM) segment in a periodically poled nonlinear crystal represents a key problem in implementing a nonlinear wavelength-conversion device with round-trip or oscillating waves of interaction. Such a segment at the crystal end implies broken QPM periodicity for the reflected waves of interaction. We demonstrate numerically that with a grating structure at the crystal end for the reflecting signal the wavelength-dependent phase shift at Bragg reflection can compensate for the phase mismatch of the reflected signal, idler, and pump of an optical parametric process. Therefore, by slightly shifting the signal wavelength we can maintain the phase-matching condition with any length of the last QPM segment. It is shown that with a grating structure the conversion efficiency of the round-trip optical parametric process can always be optimized.     

Efficient 340-nm light generation by a ridge-type waveguide in a first-order periodically poled MgO:LiNbO3

Quasi-phase-matched (QPM) UV second-harmonic generation (SHG) in a periodically poled MgO:LiNbO3 waveguide is presented. A ridge-type waveguide with high nonlinearity and strong resistance to photorefractive damage was achieved by use of an ultraprecision machining technique. By use of this waveguide in 1.4-microm periodically poled MgO:LiNbO3, a first-order QPM SHG device for 340-nm UV radiation was demonstrated. In a single-pass configuration, continuous-wave 22.4-mW UV light was generated for a fundamental power of 81 mW, corresponding to a normalized conversion efficiency of 340%/W.     

Perfect quasi-phase matching for the third-harmonic generation using focused Gaussian beams

We propose a method to realize perfect quasi-phase matching (QPM) for nonlinear optical interactions involving Gaussian beams. Using this method, both the wave-vector mismatching and the Gouy phase shift can be compensated. Numerical simulations for the third-harmonic generation show that conversion efficiency near to 100% can be realized even if the fundamental wave is tightly focused, which is difficult or even impossible with the conventional QPM method.     

Second-harmonic generation in periodically poled nonlinear polymer waveguides

We demonstrate quasi-phase-matched (QPM) second-harmonic generation (SHG) at the optical communication wavelengths with side-chain polymer waveguides. A ridge waveguide structure is designed to support fundamental mode guiding at both the pump and the second harmonics, leading to a high field overlap integral of the guided modes. The nonlinearity contrast in the +/0 type QPM waveguide is maximized under a QPM poling electrode width of nearly half the coherence length. Using these configurations, we record a normalized SHG efficiency of 2.2% W(-1) cm(-2) in the polymer waveguide.     

Quasi phase matching in two-dimensional nonlinear photonic crystals

We analyze quasi-phase-matched (QPM) conversion efficiency of the five possible types of periodic two-dimensional nonlinear structures: Hexagonal, square, rectangular, centered-rectangular, and oblique. The frequency conversion efficiency, as a function of the two-dimensional quasi-phase-matching order, is determined for the general case. Furthermore, it is demonstrated for two basic feasible motifs, a circular motif and a rectangular motif. This enables to determine the optimal motif dimensions for achieving the highest conversion efficiency. We find that a rectangular motif is more efficient than a circular motif for quasi-phase-matched processes that rely on a single reciprocal lattice vector (RLV), and that under optimal choice of motif dimensions, it converges into a one-dimensional periodic structure. In addition, in a few specific cases we found that higher order QPM can be significantly more efficient than lower order QPM.     

Tunable ultraviolet radiation by second-harmonic generation in periodically poled lithium tantalate

We describe electric-field poling of fine-pitch ferroelectric domain gratings in lithium tantalate and characterization of nonlinear-optical properties by single-pass quasi-phase-matched second-harmonic generation (QPM SHG). With a 7.5-microm-period grating, the observed effective nonlinear coefficient for first-order QPM SHG of 532-nm radiation is 9 pm/V, whereas for a grating with a 2.625-microm period, 2.6 pm/V was observed for second-order QPM SHG of 325-nm radiation. These values are 100% and 55% of the theoretically expected values, respectively. We derive a temperature-dependent Sellmeier equation for lithium tantalate that is valid deeper into the UV than currently available results, based on temperature-tuning experiments at different QPM grating periods combined with refractive-index data in the literature.     

Phase matching limitation of high-efficiency second-harmonic generation in both phase- and group-velocity-matched structures

In this paper, we studied efficient second-harmonic generation (SHG) of femtosecond pulses in both phase- and group-velocity-matched structures. Obtained results show that phase matching becomes more critical under conditions required for high levels of conversion efficiency. And the imperfect phase mismatch caused by mismatched group-velocity dispersion (GVD) will limit conversion efficiency as well as bandwidth of generated second-harmonic (SH) pulses. The spectral characteristics of the generated SH pulses and its conversion efficiency in the strong pump regime are investigated in detail. The acceptance bandwidth of nonlinear crystal in the high-efficiency SHG is redefined in the paper, and the definition is much closer to the practical application of design.     

Enhanced second-harmonic generation for multiple wavelengths by defect modes in one-dimensional photonic crystals

We present an effective design of aperiodically stacked layers of nonlinear material and air, sandwiched by two truncated photonic crystals, in terms of the simulation annealing method. The constructed structure can achieve multiple-wavelength second-harmonic generation (SHG) at the preassigned wavelengths. We derive a general solution of SHG in 1D inhomogeneous systems and apply it to evaluate the SHG conversion efficiency. Numerical simulations show that the conversion efficiency of SHG can be significantly enhanced when the fundamental wave frequencies are assigned to the designed defect states.