Second harmonic generation in a photonic crystal

Martorell, Jordi; Vilaseca, R.; Corbalán, R.

doi:10.1063/1.118244

Cited by 149 publications

(66 citation statements)

References 17 publications

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“…Full transmission was observed throughout the waveguiding band. The coupled-cavity systems may offer potential applications: (1) guiding of light in optoelectronic components and circuits, (2) the efficiency of the second-harmonic generation process [4,21] can be increased as a result of large optical field amplitude and low group velocity at the waveguiding band edges as pointed out by Yariv and coworkers [17], (3) gain enhancement can be achieved in coupled-cavity waveguiding band edges, analogous to gain enhancement in the photonic band-edge laser which was proposed by Dowling et al [8], (4) the spontaneous emission can be drastically enhanced at the coupled-cavity band edges [22].…”

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confidence: 99%

Propagation of light through localized coupled-cavity modes in one-dimensional photonic band-gap structures

2001

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Abstract. We report on the observation of a new type of propagation mechanism through evanescent coupled optical cavity modes in one-dimensional photonic crystals. The crystal is fabricated from alternating silicon-oxide/silicon-nitride pairs with silicon-oxide cavity layers. We achieved nearly full transmission throughout the guiding band of the periodic coupled cavities within the photonic band gap. The tightbinding (TB) parameter κ is determined from experimental results, and the dispersion relation, group velocity and photon lifetime corresponding to the coupled-cavity structures are analyzed within the TB approximation. The measurements are in good agreement with transfer-matrix-method simulations and predictions of the TB photon picture. 42.70.Qs; 71.15.Fv; 42.60.Da; 42.82.Et In recent years, the intense theoretical and experimental investigations of photonic band-gap (PBG) [1,2] phenomena have generated a trend towards the use of these materials in certain potential applications. In particular, enhancement of spontaneous emission near the photonic band edges [3], second-harmonic generation [4], nonlinear optical diodes, switches, limiters [5][6][7], a photonic band-edge laser [8] and transparent metallo-dielectric structures [9,10] were reported for one-dimensional (1D) PBG structures. PACS:By introducing a defect into a photonic crystal, it is possible to create highly localized defect modes within the PBG. Photons with certain wavelengths can be trapped locally inside the defect volume [11], which is analogous to the impurity states in a semiconductor [12]. Recently, we demonstrated guiding and bending of electromagnetic (EM) waves along a periodic arrangement of defects inside a threedimensional photonic crystal at microwave frequencies [13,14]. It was also observed that the group velocity tends towards zero and the photon lifetime increases drastically at the coupled-cavity waveguiding band edges [15]. In the coupledcavity structures, photons hop from one evanescent defect mode to the neighboring one due to overlapping between * Author to whom correspondence should be addressed. (E-mail: bayindir@fen.bilkent.edu.tr) the tightly confined modes at each defect site, as illustrated in Fig. 1a [13,16,17]. Due to coupling between the localized cavity modes, a photonic defect band (waveguiding band) is formed within the stop band of the crystal. This is analogous to the transition from atomic-like discrete states to the continuous spectrum in solid-state physics. Recently, Bayer et al. observed formation of a photonic band due to coupling between the optical molecules [18].In this communication, we demonstrate the guiding of light through localized coupled optical cavity modes in 1D PBG structures which are fabricated from siliconoxide/silicon-nitride (SiO 2 /Si 3 N 4 ) pairs with λ/2 SiO 2 cavity layers. It is observed that nearly 100% transmission can be achieved throughout the waveguiding band. The dispersion relation, group velocity and photon lifetime of the coupled cavities are investigated within t...

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Propagation of light through localized coupled-cavity modes in one-dimensional photonic band-gap structures

2001

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“…This can be made by means of sol-gel technique, which provides filling of pores with various oxides, e.g., TiO2 [12]. The study of various types of nonlinearities in photonic crystals is rather important and it is a topical problem [13][14][15]. Particularly, it can lead to development of new types of switches [16], media with special conditions for soliton propagation [17], etc.…”

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Light-Induced Modification of 3D Photonic Band Structure Detected by Means of Photoreflection

et al. 1999

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Porous synthetic opal possessing a three-dimensional photonic band structure of semimetallic type was impregnated with polycrystalline CdS. The photonic stop band in (111) direction was examined by means of photoreflection technique. Under cw laser excitation of semiconductor inclusions the reflectance of the system changes indicating a modification of photonic band structure. A possible mechanism is discussed. Numerical simulations within the framework of quasicrystalline approximation are given.

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“…[13][14][15][16] The advantages inherent to a high confinement, however, are partially counterbalanced by a difficult energy coupling into the resonators: well isolated resonant states, in fact, correspond to large (external) quality factors of the cavity.…”

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“…9,10 In particular, in PC microresonators it is possible to obtain extremely high quality factors (Q) in reduced volumes while tailoring their dispersive features, 11,12 characteristics which can be exploited to achieve efficient frequency generation with various schemes. [13][14][15][16] The advantages inherent to a high confinement, however, are partially counterbalanced by a difficult energy coupling into the resonators: well isolated resonant states, in fact, correspond to large (external) quality factors of the cavity.…”

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Impedance matching in photonic crystal microcavities for second-harmonic generation

2006

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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 out-coupled generated second harmonic is maximized by impedance matching the photonic crystal cavity to the output waveguide.In the early sixties the very first experiments in nonlinear optics were Frankens investigations of traveling-wave second harmonic generation.1 It took a number of years to realize that guided-wave optics and resonators could dramatically enhance phenomena requiring high intensities and tuning of critical parameters.2-4 Since then, both the advent of nano-optics and the technological advances have made new solutions available. Among them, microresonators can certainly be considered among the best candidates for nonlinear optics and frequency generations. [5][6][7][8] In the past few years, photonic crystal (PC) microcavities, i. e. periodic (bandgap) structures hosting a resonant defect, have attracted attention for some of their unique properties.9, 10 In particular, in PC microresonators it is possible to obtain extremely high quality factors (Q) in reduced volumes while tailoring their dispersive features, 11, 12 characteristics which can be exploited to achieve efficient frequency generation with various schemes. [13][14][15][16] The advantages inherent to a high confinement, however, are partially counterbalanced by a difficult energy coupling into the resonators: well isolated resonant states, in fact, correspond to large (external) quality factors of the cavity. 17To this extent, impedance matching has been proposed based on a properly designed coupling to/from the microcavities. 18,19 In this Letter we propose and investigate an efficient outsourcing scheme to maximize frequency doubling from a PC defect. Resorting to a second-order nonlinearity in a large Q photonic crystal microcavity, an optical pump is up-converted to a resonant crosspolarized harmonic signal. Since the device is designed to be nearly transparent to the pump wavelength, input coupling losses are minimized while the out-coupled second harmonic can be maximized by impedance matching. The temporal evolution of the resonant mode at the second-harmonic (SH) can be described and related to the cavity parameters by coupled mode theory in the time domain (CMT-TD):where a SH is the mode amplitude at the SH frequency ω SH , τ SH takes into account both internal (1/τ o ) and external (1/τ e ) losses (1/τ SH = 1/τ o + 1/τ e ), κ is the (three-dimensional) overlap integral between the sus-1

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Second harmonic generation in a photonic crystal

Cited by 149 publications

References 17 publications

Propagation of light through localized coupled-cavity modes in one-dimensional photonic band-gap structures

Propagation of light through localized coupled-cavity modes in one-dimensional photonic band-gap structures

Light-Induced Modification of 3D Photonic Band Structure Detected by Means of Photoreflection

Impedance matching in photonic crystal microcavities for second-harmonic generation

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