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Different types of quadratic, radially symmetric, nonlinear photonic crystals are presented. The modulation of the nonlinear coefficient may be a periodic or an aperiodic function of the radial coordinate, whereas the azimuthal symmetry of the crystal may be either continuous or discrete. Nonlinear interactions within these structures are studied in two orientations, transverse and longitudinal, for which the interacting beams propagate either perpendicularly or in the plane of modulation. We show that radially symmetric structures can phase match multiple arbitrary processes in any direction. We study multiple wavelength three-wave mixing interactions and multiple direction interactions and analyze spatially dependent polarization states of the generated harmonics.

A known algorithm for modeling quasi-periodic lattices is used to generate two-dimensional quadratic nonlinear photonic quasi-crystals containing a set of desired discrete spectral components. This allows us to fabricate optical devices in which an arbitrary set of nonlinear optical processes can be efficient. We demonstrate this capability by fabricating two devices: a multidirectional single-frequency doubler and a multidirectional, multifrequency doubler that is capable of nearly collinear doubling of cw radiation in the optical communication C band (1530-1570 nm) through angle tuning.

We propose a novel all-optical, nonlinear mode-conversion scheme based on cascaded three-wave-mixing phase-matched interactions in quadratic nonlinear crystals. We demonstrate the method experimentally by performing all-optical mode conversion of an input 1636 nm Hermite-Gaussian mode from the zeroth order to the first order using two periodically poled LiNbO(3) crystals. Nonlinear mode conversion of an input beam into a higher order, orthogonally polarized output beam can be realized using only one quasiperiodic nonlinear structure. Moreover, it can be enhanced for conversion of complex modes, e.g., Laguerre-Gaussian or Bessel modes.

We demonstrate simultaneous phase matching of two different nonlinear processes, using a noncollinear interaction in periodically poled crystal with single grating. The noncollinear scheme provides phase-matching solutions over continuous regions of the optical spectrum and can be used for multiple-harmonic generation as well as all-optical effects. We have demonstrated experimentally third-harmonic generation of a 3 microm pump wavelength in a noncollinear configuration using a periodically poled LiNbO3 crystal. We observed, in good agreement with theoretical calculation, very broad spectral and thermal acceptance bandwidths, as well as a relatively narrow angular bandwidth.

A bulk of LiNbO3 was periodically poled in two dimensions to achieve noncollinear second-harmonic generation. The sample was fabricated using an electron-beam indirect exposure. This method used a dielectric buffer layer deposited on LiNbO3 Z−-polar face to trap the incident electrons. These localized electrons formed a charge droplet which generated a strong electric field and triggered the domain inversion process in the LiNbO3. Tailored two-dimensional domain configurations enabled quasi-phase-matched frequency doubling of a Nd:YLF laser at 15 different input angles. The measured angular dependence was in agreement with calculations based on the nonlinear reciprocal lattice vectors of the poled structure.

We report the experimental realization of a new type of optical parametric oscillator in which oscillation is achieved by polarization rotation in a linear retarder, followed by nonlinear polarization mixing. The mixing is performed by a type II degenerate parametric downconversion in a periodically poled KTP crystal pumped by a 1064 nm pulsed Nd:YAG pump. A single, linearly polarized beam, precisely at the degenerate wavelength is generated. The output spectrum has a narrow linewidth (below the instrumentation bandwidth of 1 nm) and is highly stable with respect to variations in the crystal temperature.

We have measured the thermal expansion and the temperature dependence of z and y components of the refractive index for KTiOPO4 and KTiOAsO4, in the wavelength range 532-1585 nm and temperature range 25-200 degrees C, using an interferometric technique. The measurements were used to derive temperature-dependent Sellmeier equations for the two materials. These equations predict with good agreement the temperature dependence of quasi-phase-matched nonlinear frequency converters.

We present a cw single-frequency laser source with what is to our knowledge the largest emission range ever demonstrated, from the green to the mid-IR range. It employs a cw optical parametric oscillator with subsequent resonant frequency doubling. Typical output powers are 30–500 mW, with 160 mW at 580 nm. Mode-hop-free oscillation, high absolute frequency stability, 20-kHz-signal linewidth, and up to 38-GHz continuous tuning are demonstrated. Both PPLN and PPKTP are used as nonlinear materials, and their performance is compared.

@S0003-6951~99!05418-2#Due to our misprints, there were some errors in the la-bels of some of the curves in Figs. 1 and 2, as well as in thefigure captions. In Fig. 1, the longer QPM period should be36.3 mm ~and not 36.6 mm!. The first sentence of the figurecaption should read:‘‘Measurement of normalized DFG power as a functionof the signal wavelength, near room temperature, for twograting periods: 35.7 mm ~circles! and 36.3 mm ~triangles!.’’In Fig. 2, both curves correspond to the same QPM grat-ing period of 36.3 mm. The corrected figure caption shouldread: ‘‘Measurement of normalized DFG power as a functionof the PP-KTP crystal temperature with a grating period of36.3 mm, for two signal wavelengths: 1591 nm ~circles! and1595 nm ~squares!.’’Also, on p. 915 ~lines 4–6 on the right column!, thecorrected sentence should read:‘‘The DFG power as a function of the crystal tempera-ture is shown in Fig. 2 for a grating period of 36.3 mm.’’

The frequency stability of a 1560-nm diode laser, whose second harmonic was locked to (87)Rb sub-Doppler lines, was characterized by measuring the beat frequency relative to a 780-nm reference laser that was locked to sub-Doppler lines of another rubidium cell. The square root of the Allan variance reached a minimum value of 7.5 x 10(-12) in 1 s, which corresponded to frequency variations of 1.44 kHz for the 1560-nm laser. The frequency reproducibility of the system was approximately 1 x 10(-9). These values are better than those that can be achieved by locking to Doppler-broadened transitions at the 1550-nm wavelength band.

An external cavity 1540-nm diode laser was frequency doubled in a 3-cm-long periodically poled LiNbO(3) waveguide doubler with 150% W(-1) conversion efficiency, thereby generating more than 3 muW at 770 nm. Second-harmonic light was used to detect and lock to sub-Doppler lines of the (39)K D(1) transition.

Sub-Doppler lines of Cs2 were investigated with a Nd:YAG laser. Modulation transfer spectroscopy and FM spectroscopy were applied to yield error signals that were used for absolute stabilization of the laser frequency. The frequency stability was characterized with an I2-locked dual-wavelength Nd:YAG frequency reference. The root Allan variance of the beat frequency reached a minimum of 1.3 × 10−11 (beat frequency fluctuations of 3.65 kHz) for a measurement time of 20 s. Absolute frequencies of several Cs2 lines were determined with an accuracy of ∼1 MHz. Further improvement in sensitivity was demonstrated by insertion of the absorption cell into a Fabry–Perot cavity. While the laser was locked to the cavity, the cavity length was modulated and the transmitted probe beam was detected at the third harmonic of the modulation frequency.

Two diode-pumped tunable Nd:YAG lasers locked to sub-Doppler transitions of (127)I(2) and (133)Cs(2) are used as a source for two-wavelength interferometry. The synthetic wavelength is highly stable and accurate, owing to the frequency stability of the locked lasers and the precise determination of the frequency difference between Cs(2) and I(2) transitions. The dense spectra of the two molecular absorbers allows selection of synthetic wavelength A over a wide range, between 8.5 mm and more than 1 m, thus enabling distance measurements with a large nonambiguity range. Fringe contrast and phase-shifting methods are used to measure the synthetic phase. An accuracy of 70 µm is achieved for synthetic wavelength Λ ~ 19 mm, corresponding to a phase interpolation accuracy ofΛ/260.

Two frequency-doubled diode-pumped Nd:YAG lasers are used to study the hyperfine spectrum of 127I2 near 532 nm by heterodyne spectroscopy. Eight rovibrational transitions between the lowest vibrational level in the ground (X) state to vibrational levels 32–36 in the B state are observed. The measured frequency splittings are used to determine the difference in the hyperfine constants for these transitions. The standard deviation of the theoretical fit to the measured spectra is better than 10 kHz. The root Allan variance of the beat frequency between the I2-locked lasers follows a 1.1×10−2/τ dependence for measurements times τ > 0.002 s and reaches a minimum value of 2.5 × 10−13 (two-sample beat frequency of 70 Hz) at τ = 32 s. A method for accurately determining the absolute frequency of the iodine lines near 532 nm is proposed.

We have frequency doubled a 1319-nm Nd:YAG laser in a quasi-phase-matched LiNbO(3) waveguide and used the asymptotically equal to1-mW second-harmonic output to investigate the (127)I(2) transitions near 660 nm. We reached submegahertz laser-frequency stability at a (vacuum) wavelength of 1319.098 nm by locking the second harmonic to the center of the P(48)6-6 transition.

Diode-laser-pumped Nd:YAG lasers were frequency stabilized by locking their frequency-doubled output to Doppler-free absorption lines of the (127)I(2) molecule. The successive two-sample deviation of the beat frequency between two independent iodine-stabilized lasers is less than 650 Hz, or 2.3 x 10(-12) of the laser frequency, for averaging times between 24 and 80 s.

The coherence properties of a laser source are derived from high bandwidth (with respect to the source linewidth) measurements of the instantaneous output intensity at the output of a two-beam optical interferometer. This technique saves the need to compensate for polarisation and wavefront mismatches and for unequal power splitting between the two interfering beams.

The probability-density function (PDF) of the fluctuating output intensity of a two-beam interferometer, illuminated by a semiconductor laser, is described theoretically and experimentally. The PDF, while dominated by the laser phase noise, may be substantially modified both by the laser intensity noise and by the thermal noise and bandwidth limitations imposed by the detection system. Two regimes of operation are explored. In the coherent regime, for which the interferometer ’ s differential delay τ is much smaller than the laser coherence time τc, the form of the PDF is highly sensitive to the mean phase difference between the interfering beams: The PDF is strongly asymmetrical for mean phase differences of 0 and π (experimentally reported here for the first time to our knowledge) but is symmetrical when the interferometer is in quadrature. In the incoherent regime, for which τ ≫ τc, the PDF is insensitive to such phase differences. The experimental results are in excellent agreement with a numerical simulation for which it is assumed that the laser phase noise is a Wiener process and for which the finite bandwidth of the detection system, as well as the effects of laser intensity noise and system thermal noise, is taken into account.

When a fiber-optic recirculating delay line with a mid-loop polarization controller is preceded by another polarization controller and followed by a linear polarizer, the system becomes highly polarization-dependent. The periods of the transfer function and of the power spectrum of the phase-induced intensity noise can be halved, and the latter can also exhibit maximum noise instead of minimum noise at frequencies which are multiples of 1/(loop delay). It is also shown theoretically and experimentally that by proper adjustment of the polarisation controllers, the normally observed filtering notches at frequencies f=(n+0.5)/(loop/delay) disappear, making the device a polarization-controlled RF filter. Possible applications are discussed. >

A fiber-optic differential-delay-line structure converts the phase noise of its short coherence source to intensity noise at its output. If this structure is followed by a similar system, intensity noise is generated as well as filtered by each of the two systems. The power spectrum of the noise at the output of concatenated systems built of Mach-Zehnder and the recirculating delay lines is theoretically studied. The spectral structure of phase-induced intensity noise at the output of these concatenated systems is analyzed, taking into account polarization effects and emphasizing the physical interpretations of the results. An experimental verification is presented for the case of two recirculating delay lines in series. >

Metasurfaces constitute a powerful approach to generate and control light by engineering optical material properties at the subwavelength scale. Recently, this concept was applied to manipulate free-electron radiation phenomena, rendering versatile light sources with unique functionalities. In this Letter, we experimentally demonstrate spectral and angular control over coherent light emission by metasurfaces that interact with free-electrons under grazing incidence. Specifically, we study metalenses based on chirped metagratings that simultaneously emit and shape Smith-Purcell radiation in the visible and near-infrared spectral regime. In good agreement with theory, we observe the far-field signatures of strongly convergent and divergent cylindrical radiation wavefronts using

The effect of a modified cladding on the transmission of light through a step-index optical fiber is investigated using 3-D geometrical optics. Measurements of the light transmission of the optical fiber as a function of the modified cladding refractive index and length are presented for the case of focused illumination and compared with 3-D ray theory. The effect of defocus on the transmission of the modified fiber is also studied. Applications to intensity sensors are discussed.

A method for deriving the angular power distribution of various sources which are used to inject light into an optical fiber is suggested. This distribution can be obtained from the optical power carried by meridional bound rays in a fiber whose cladding refractive index can be modified. The theoretical analysis, which indicates that optical power measurement errors must not exceed 1% in order to obtain reasonably accurate power distributions, is augmented by experimental results. In particular, the case of lens illumination and the estimation of the mode field diameter of a single mode fiber are studied in detail.© (1989) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

By inserting a linear polarizer after a fiber optic recirculating delay line, the system becomes highly polarization dependent. The transfer function and the phase induced intensity noise for different polarization inputs are studied.

In this paper we present results of recent theoretical and experimental investigations of the spectral shape of the phase induced intensity noise at the output of several optical recirculating configurations. These configurations include bulk-optics incoherent Fabry Perots, as well as fiber-optic delay lines. It is shown that whenever the system output consists of an infinite series of time delayed versions of the laser input field (recirculating structures), the RF power spectrum of the phase induced intensity noise is periodic with either notches or peaks at integral multiples of 1/(recirculating time), depending on the specific structure of the device. The relative phases of the output fields are shown to be the important factor which determines the shape of the period.

The effect of a modified cladding on the transmission of light through a step index optical fiber is investigated, using geometrical optics and proper choice of ray cor e-cladding encounters. Measurements and analysis of the light transmission of the optical fiber as a function of the modified cladding refractive index and length are presented for various input illuminations: focused and defocused incident beams, effect of offset, polychromatic illumination and illumination with a single mode fiber. Applications to intensity sensors are discussed.

We show that focusing a laser light onto the boundary between antiparallel ferroelectric domains leads to the non-collinear generation of two second harmonic (SH) beams. The beams are emitted in a plane normal to the domain boundaries at the angles that satisfy the Cerenkov-type phase matching condition. Moreover, these beam disappear when the laser light is focused on a homogenous part of a single domain. We utilize this effect for 3-dimensional visualization of fine details of the ferroelectric domain pattern with a submicron accuracy.

We illustrate the phenomenon of the focusing of a freely propagating rectangular wave packet using three different tools: (1) the time-dependent wave function in position space, (2) the Wigner phase-space approach, and (3) an experiment using laser light.

We observe experimentally a novel type of nonlinear diffraction in the process of two-wave mixing on a nonlinear quadratic grating. We demonstrate that when the nonlinear grating is illuminated simultaneously by two noncollinear beams, a second-harmonic diffraction pattern is generated by a virtual beam propagating along the bisector of the two pump beams. The observed diffraction phenomena is a purely nonlinear effect that has no analogue in linear diffraction.

Nonlinear photonic crystals are materials in which the second order susceptibility is modulated in an ordered fashion, usually in one or two dimensions, while the linear susceptibility remains constant. Here, a general analysis of quasi-phase-matched interactions in a nonlinear photonic crystal is derived for the cases of periodic and quasiperiodic structures. The effects of the lattice, motif and interaction area on the generated electric field and intensity are analyzed in a periodic nonlinear photonic crystal. For the case of a quasiperiodic frequency converter, a systematic procedure is described, enabling to phase match any set of interacting waves. Nonlinear photonic crystals with radial symmetry are introduced. These structures have continuous rotation symmetry, but no translation symmetry, in contrary to the lattice based structures. Finally, several applications of quasiperiodic nonlinear frequency converters are reviewed.

We demonstrate, numerically and experimentally, the generation of self-accelerating surface plasmon beams along arbitrary caustic curvatures by two-dimensional plasmonic phase masks. We examine both paraxial and non-paraxial curvatures accelerating along polynomial and exponential trajectories.

We demonstrate experimentally the generation of unique surface-plasmon beams, which compensate the inherent losses of plasmons without using gain media, and show that these beams can extend the limited propagation length of surface-plasmons.

A method for efficient, broadband sum and difference frequency generation of ultrafast pulses is demonstrated. Using aperiodically poled nonlinear crystals and a single step nonlinear mixing process, conversion efficiencies up to 50% are reported.

A method for efficient frequency conversion of ultrafast pulses is demonstrated using an adiabatic aperiodically poled KTP crystal. We produce broadband blue pulses centered at 450 nm by upconverting 30 fs pulses in the near-IR.

We analyze the emission patterns in the process of second harmonic (SH) generation in χ(2) nonlinear gratings and identify for the first time, to the best of our knowledge, the evidence of Raman-Nath type nonlinear diffraction in frequency doubling processes.

Continuously-driven microresonators, whose nonlinear response is dominated by the third-order Kerr nonlinearity, have proven to be valid alternatives to comb sources based on femtosecond mode-locked lasers [1]. More recenlty, the direct generation of optical frequency combs (OFCs) entirely through quadratic interactions has also been demonstrated in singly resonant cavity second harmonic generation (SHG) and in cw pumped nearly degenerate optical parametric oscillation [2,3]. Interestingly, theoretical studies on doubly resonant cavity SHG predicted the emergence of OFCs with a much lower threshold with respect to the singly resonant configurations, as well as rich nonlinear dynamics [4].

We study the second-harmonic generation via transversely matched interaction of two counterpropagating ultrashort pulses in chi(2) photonic structures. We show that the emitted second-harmonic wave attains the form of spatially expanding toroid with the initial thickness given by the cross correlation of the pulses. We demonstrate the formation of such toroidal waves in crystals with random ferroelectric domains as well as in annularly poled nonlinear photonic structures.

New methods to frequency down-convert a broadband near infrared frequency comb into the mid-infrared by three-wave mixing are studied. Modulation of the second-order nonlinear coefficient based on the concepts of either nonlinear spectral holography or quasi-periodic modulation enables us to obtain different spectral shapes of the mid-infrared comb. It includes flat and broadband single-band or dual-band spectra, or a shape that exhibits two or even three sharp peaks at chosen frequencies. The methods we present can be used to tailor the frequency comb spectra to selected molecular absorption lines in the mid-infrared.