Maximum-exponent scaling behavior of optical second-harmonic generation in finite multilayer photonic crystals

Scaling laws of second-harmonic generation (SHG) in nonlinear Bragg stacks (or finite one-dimensional photonic crystals) as a function of the number N of periods are explored. While it is known that SHG scales like the sixth power of N when phase matching is achieved, we find maximal scaling like the eighth power of N under appropriate non-phase-matching conditions with the pump and harmonic waves being resonant with band-edge states. In this framework we introduce the concept of self-adaptive coherence length that scales with the system length. An analytical treatment based on coupled-mode equations clarifies the conditions for obtaining different scaling laws as a function of filling factor in the photonic gap map.     

Bragg polaritons: strong coupling and amplification in an unfolded microcavity

Periodic incorporation of quantum wells inside a one-dimensional Bragg structure is shown to enhance coherent coupling of excitons to the electromagnetic Bloch waves. We demonstrate strong coupling of quantum well excitons to photonic crystal Bragg modes at the edge of the photonic band gap, which gives rise to mixed Bragg polariton eigenstates. The resulting Bragg polariton branches are in good agreement with the theory and allow demonstration of Bragg polariton parametric amplification.     

Nonlinear photonic crystals as a source of entangled photons

Nonlinear photonic crystals can be used to provide phase matching for frequency conversion in optically isotropic materials. The phase-matching mechanism proposed here is a combination of form birefringence and phase velocity dispersion in a periodic structure. Since the phase matching relies on the geometry of the photonic crystal, it becomes possible to use highly nonlinear materials. This is illustrated considering a one-dimensional periodic Al0.4Ga0.6As/air structure for the generation of 1.5 microm light. We show that phase-matching conditions used in schemes to create entangled photon pairs can be achieved in photonic crystals.     

Enhanced Čerenkov second-harmonic emission in nonlinear photonic structures

We study experimentally and theoretically the ?erenkov-type second-harmonic generation in a one-dimensional nonlinear photonic crystal. We demonstrate that the power of emitted second-harmonic can be enhanced 270 times by varying the angle of incidence of the fundamental beam such that the reciprocal lattice vector of the crystal can be used to compensate for the phase mismatch in the transverse direction enabling interaction in the nonlinear Bragg diffraction regime.     

Parametric generation of light in arbitrary directions of a biaxial KTP crystal pumped by an Nd:YAG laser

The conditions for collinear phase matching in the parametric generation of light in arbitrary directions of a biaxial KTP crystal pumped by an Nd:YAG laser were investigated with the use of invariant expressions for the refractive indices of isonormal waves. The tuning curves, effective nonlinear coefficients, spectral and angular phase-matching widths were calculated. B. I. Stepanov Institute of Physics, National Academy of Sciences of Belarus, 68, F. Skorina Ave., Minsk, 220072. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 2, pp. 177–184, March–April, 1999.     

光子晶体光纤四波混频光谱中相位匹配特性的研究

与传统光纤不同,光子晶体光纤可以具有多个零色散波长,在四波混频光谱中,具有更丰富的相位匹配特性。目前很多文献报道了光子晶体光纤非线性光学特性的实验结果,但对其产生机理及光谱的变化规律缺乏详细的理论分析。为此对光纤中四波混频原理进行了分析,给出了高增益的相位匹配条件。利用多极法计算了光子晶体光纤的非线性系数及色散特性。对具有多个零色散波长光子晶体光纤的相位失配特性进行了分析,得到了相位匹配波长随泵浦波长及泵浦功率的变化规律。给出了相位匹配曲线,分析了不同色散曲线的相位匹配波长特点,两个零色散波长光子晶体光纤,在四波混频光谱中将激发出四个新的波长。实验得到了两个零色散波长光子晶体光纤的四波混频光谱,与理论分析一致,验证了相位匹配理论的可靠性。多个零色散波长光纤,能产生丰富的相位匹配曲线,会出现更多的四波混频波长,可以有效的控制光孤子及超短脉冲的四波混频及共振散射产生的光谱特性。为光子晶体光纤中基于四波混频的波长变换及超连续谱的研究提供了理论指导。     

One-dimensional quadratic walking solitons

The properties of one-dimensional quadratic walking solitons were investigated in planar lithium niobate waveguides near the type I phase-matching condition for second-harmonic generation. Wave propagation was studied under different conditions of phase matching, walk-off angle, and incident fundamental power.     

Photonic-crystal waveguide for the second-harmonic generation

The possibility of efficient second-harmonic generation in the optical range in a planar dielectric waveguide with the active region in the form of a one-dimensional photonic crystal has been theoretically shown. The true phase matching can be achieved by controlling wave dispersion in the photonic crystal. The dispersion equations for the photonic crystal and three-layer waveguide have been self-consistently solved. It is shown that the coherence length may exceed 10 mm.     

新型光学晶体KABO的非线性频率变换特性

简述了新型非线性晶体KABO的光学特性.根据相位匹配角公式、非线性有效系数公式、走离角公式和允许角公式,详细计算了KABO晶体倍频时的相位匹配角、非线性有效系数、倍频时谐波走离角、允许角随波长变化的理论曲线.特别是对LD泵浦掺钕的全固态激光器532 nm输出时,得到了KABO晶体采用I类相位匹配进行四倍频的相位匹配角、非线性有效系数、倍频时谐波走离角、允许角分别为:58.1°、0.254×10^-12m/V、2.8°、1.8233 mrad·mm;并将该晶体与目前可应用于紫外倍频的晶体比较,在考虑走离效应的情况下,研究了四倍频转换效率随KABO晶体长度、基频光光斑半径的变化规律.     

Omnidirectional reflection from the one-dimensional photonic crystal containing anisotropic left-handed material

We study the transmission properties in the one-dimensional photonic crystal containing alternate anisotropic left-handed material (LHM) layers and regular isotropic right-handed material (RHM) layers. For such an anisotropic case, the dispersion relation from the Bloch theorem is derived and the Bragg gaps of the periodic structure are observed. It is found that in the m=0 Bragg gap, there is an omnidirectionally reflectional (ODR) region, which is also invariant with a change of scale length, similar with the [`(n)]=0\bar{n}=0 gap in isotropic one-dimensional photonic crystal. With the aid of effective medium theory (EMT), the analytic expressions of all six elements of the effective electric permittivity tensor and magnetic permeability tensor are obtained. By using these results, we investigate the ODR region in the m=0 Bragg gap in all the possible cases of both TE and TM modes. We find that with different choices of parameters, the m=0 Bragg gap has different transmission properties, and the ODR region in it changes, consequently. The edges of the ODR region are given out in these cases. To one's interest, these results predict a complete reflection region in the m=0 Bragg gap, which is able to omnidirectionally reflect waves in both TE and TM modes.     

Efficient second-harmonic generation in birefringently phase-matched GaAs/Al(2)O(3) waveguides

We report efficient second-harmonic generation of femtosecond pulses in birefringently phase-matched GaAs/Al(2)O(3) waveguides pumped at 2.01mum. By use of pump pulses of ~200-fs duration and type I interaction, practical second-harmonic average powers of up to ~650muW were obtained, with an average input power of ~50muW. Waveguides of four different widths and two different lengths were investigated, and a normalized conversion efficiency of greater than 1000%W(-1)cm(-2) was obtained for a 1-mm waveguide. Measurements of pump and second-harmonic spectra provided clear evidence of phase matching and depletion of the pump spectrum. The measured bandwidth of the second harmonic was ~1.3nm. From the measurements of transmitted pump power at the phase-matching wavelength, pump depletions of more than 80% were recorded.     

Impedance matching in photonic crystal microcavities for second-harmonic generation

By numerically integrating the three-dimensional Maxwell equations in the time domain with reference to a dispersive quadratically nonlinear material, we study second-harmonic generation in planar photonic crystal microresonators. The proposed scheme allows efficient coupling of the pump radiation to the defect resonant mode. The outcoupled generated second harmonic is maximized by impedance matching the photonic crystal cavity to the output waveguide.     

Phase matching in ?erenkov second-harmonic generation: a leaky-mode analysis

Use of leaky modes allows us to demonstrate very simply that ?erenkov second-harmonic generation is not free of phase matching. The ?erenkov phase-matching condition is derived for what is to our knowledge the first time. The way to overcome the difficulty linked with the divergence at infinity of the leaky modes is discussed.     

Matched second-harmonic generation of ultrashort laser pulses in photonic crystals

It is shown that one-dimensional photonic bandgap structures are capable of simultaneously satisfying the phase and group-velocity matching conditions for second-harmonic generation involving extremely short light pulses. When these conditions are satisfied, an optical frequency doubler utilizing photonic bandgap structures provides a means for increasing the rate of growth of the second-harmonic signal as a function of the nonlinear-optical interaction length relative to structures designed for quasi-matched interactions and affords possibilities for enhancing the frequency doubling efficiencies independently of the matching length in the bulk nonlinear material. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 12, 800–805 (25 December 1999)     

Periodically poled potassium niobate for second-harmonic generation at 463 nm

We report on the fabrication and characterization of quasi-phase-matched potassium niobate crystals for second-harmonic generation. Periodic 30-mum -pitch antiparallel ferroelectric domains are fabricated by means of poling in an electrical field. Both birefrigence and periodic phase shift of the generated second harmonic contribute to phase matching when the d(31) nonlinear optical tensor element is used. 3.8 mW of second-harmonic radiation at 463 nm is generated by frequency doubling of the output of master-oscillator power-amplifier diode laser in a 5-mm-long crystal. The measured effective nonlinear coefficient is 3.7pm/V. The measured spectral acceptance bandwidth of 0.25 nm corresponds to the theoretical value.     

Method for single-shot measurement of the carrier envelope phase of a few-cycle laser pulse

The interference between different harmonics of a few-cycle optical pulse in the region of the spectral overlap is sensitive to the phase of the optical carrier inside the pulse envelope. Near-surface third-harmonic generation from Si(001) combined with second-harmonic generation in a 10-mum -thick beta-barium borate crystal produces sufficiently strong harmonic emission for single-shot measurement. We propose using this technique to measure the carrier envelope phase of high-energy 5-fs pulses.     

Surface wave-induced enhancement of the Goos-Hänchen effect in one-dimensional photonic crystals

The excitation conditions of surface electromagnetic waves in one-dimensional photonic crystals (Bragg reflectors) are studied. Surface electromagnetic waves are visualized by the far-field optical microscopy of the surface of the photonic crystal. The enhancement of the Goos-Hänchen effect by surface electromagnetic waves excited in one-dimensional photonic crystals has been experimentally observed. The Goos-Hänchen shift reaches 30λ for a wavelength of λ = 532 nm.     

Two-color nonlinear localized photonic modes

We analyze second-harmonic generation (SHG) at a thin effectively quadratic nonlinear interface between two linear optical media. We predict multistability of SHG for both plane and localized waves, and also describe two-color localized photonic modes composed of a fundamental wave and its second harmonic coupled together by parametric interaction at the interface.     

Acoustooptic interaction in two-dimensional photonic crystals: Efficiency of Bragg diffraction

We obtain equations for the Bragg regime of acoustooptic diffraction of light in two-dimensional photonic crystals. We determine applicability conditions of the single-wave approximation, in which it is sufficient to take into account only one Fourier component of each of Bloch waves involved in the acoustooptic interaction. In the single-wave approximation, we obtain formulas that make it possible to estimate the acoustooptic figures of merit of a photonic crystal. We show that, in a photonic crystal, higher acoustooptic figures of merit can be achieved than in the materials that make up the crystal.     

Phase matching of second-harmonic generation in birefringent porous silicon

Optical second-harmonic generation is investigated in free-standing (110) porous silicon films having strong in-plane birefringence. Based on the measured values of the refractive indices, the conditions of phase matching are calculated and verified in the experiments on angular and polarization dependences of second-harmonic generation. Filling pores with a transparent dielectric liquid allows phase matching to be achieved and the second-harmonic signal to be increased by two orders of magnitude. The results of these experiments suggest an opportunity to form new-type nonlinear-optical media consisting of birefringent porous silicon as a phase-matching matrix for the materials embedded in the pores. Received: 30 April 2001 / Published online: 7 June 2001