Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media

Roppo, Vito; Centini, Marco; Sibilia, C.; Bertolotti, M.; Ceglia, Domenico de; Scalora, Michael; Aközbek, Neşet; Bloemer, Mark J.; Haus, Joseph W.; Kosareva, O.G.; Kandidov, V.P.

doi:10.1103/physreva.76.033829

Cited by 80 publications

(84 citation statements)

References 60 publications

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“…If one of the generated photons is however returned into the pump l by stimulated emission, the process becomes much faster and tends to dominate the nonlinear dynamics in the limit of high-power pulse propagation over short distances. Interestingly, these S K plll A l A l A * l processes produce automatic phase-locking of mode p to the pump mode l, similarly to what happens in non-phase matched second and third harmonic generation processes (Roppo et al, 2007). However, processes S K plll require (i) that modes p and l belong to the same symmetry class, and (ii) that they present a large overlap.…”

Section: Effect Of Modal Symmetries and Launch Conditions On Intermodmentioning

confidence: 99%

Multimode Nonlinear Fibre Optics: Theory and Applications

Horák¹,

Poletti²

2012

Recent Progress in Optical Fiber Research

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Section: Effect Of Modal Symmetries and Launch Conditions On Intermodmentioning

confidence: 99%

Multimode Nonlinear Fibre Optics: Theory and Applications

Horák¹,

Poletti²

2012

Recent Progress in Optical Fiber Research

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“…This inhomogeneous solution to the wave equation co-propagates both in time and space with the fundamental pulse, therefore with an apparent group velocity determined by the dispersion at ω . Thus, this SH pulse separates both spatially and temporally from the interface-generated SH pulse [27,30 ] and its intensity is not affected by changes in the excited volume close to the surface (see Figure 1). These two pulses were separately detected by cross-correlating the total second harmonic radiation emitted from the 5mm thick LiNbO 3 crystal, with a synchronized 800-nm pulse in a β -BBO crystal.…”

Section: Fig 2 A)mentioning

confidence: 99%

Ultrafast Reversal of the Ferroelectric Polarization

et al. 2017

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The ability to manipulate ferroelectrics at ultrafast speeds has long been an elusive target for materials research. Coherently exciting the ferroelectric mode with ultrashort optical pulses holds the promise to switch the ferroelectric polarization on femtosecond timescale, two orders of magnitude faster compared to what is possible today with pulsed electric fields.Here, we report on the demonstration of ultrafast optical reversal of the ferroelectric polarization in LiNbO 3 . Rather than driving the ferroelectric mode directly, we couple to it indirectly by resonant excitation of an auxiliary high-frequency phonon mode with femtosecond mid-infrared pulses. Due to strong anharmonic coupling between these modes, the atoms are directionally displaced along the ferroelectric mode and the polarization is transiently reversed, as revealed by time-resolved, phase-sensitive second-harmonic generation. This reversal can be induced in both directions, a key pre-requisite for practical applications. 2The ferroelectric polarization is typically controlled with static or pulsed electric fields.Switching is in this case an incoherent process, with speed limited to hundreds of picoseconds by the nucleation and growth of oppositely polarized domains [1,2,3]. To overcome these limitations, attempts have been made to drive the ferroelectric mode coherently with light pulses. These strategies, which have been based either on impulsive Raman scattering [4,5,6,7] or direct excitation of the ferroelectric mode [8,9,10] using THz radiation, have not yet been completely successful.Recent theoretical work [11] has analyzed an alternative route to manipulate the ferroelectric polarization on ultrafast timescales. It has been proposed that a coherent displacement of the ferroelectric mode could be achieved indirectly, by exciting a second, anharmonicallycoupled vibrational mode at higher frequency. The underlying mechanism is captured by the following minimal model, which is illustrated in Fig. 1. Consider a double well energy potential along the ferroelectric mode coordinate Q P as shown in Fig. 1Here, ω p is the frequency of the ferroelectric mode for a fixed temperature T below the Curie temperature T C . Take then a second mode Q IR with frequency ω IR , described by the Fig. 1(a), which is anharmonically coupled to the ferroelectric mode with a quadratic-linear dependence of the interaction energy aQ IR 2 Q P . The total lattice potential can then be written asIn equilibrium, Q P takes the value of one of the two minima of the double well potential Fig. 1(b). For finite displacements Q IR , this minimum is first displaced and then destabilized as Q IR exceeds a threshold value (colored lines in Fig. 1(b)).Importantly, the direction of this displacement is always pointed toward the opposite potential well and independent on the sign of Q IR [11].The corresponding dynamics of the two modes for resonant periodic driving of Q IR by a midinfrared light pulse is obtained by solving the equations of motionHere, f t) is the driving pulse ...

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“…The amount of energy transferred to each harmonic is dictated by the index mismatch at the interface, and does not vary during propagation. 6 When the pump pulse reaches the exit surface the fields decouple and propagate freely. In Fig.…”

mentioning

confidence: 99%

“…In a recent study the results were generalized to include third harmonic generation ͑THG͒ in both positive and negative index media. 6 When a pump signal traverses an interface into a nonlinear medium it generates SH and/or TH fields. Each harmonic has two parts: ͑i͒ a homogeneous portion that walk-off from the pump field; ͑ii͒ an inhomogeneous component phase-and velocitylocked to the pump, with no energy transfer between the fields except at interface crossings.…”

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confidence: 99%

“…Each harmonic was reflected back through the mirrors and polarizer by a concave aluminum mirror with deep-ultraviolet coating. Therefore, the residual pump light was suppressed by at least eight orders of magnitude and either the TM or TE component of the harmonic was selected with a contrast of at least 10 6 . After passing back through the mirrors and polarizer, the harmonic was focused into an all-silica fiber coupled to a UV-sensitive spectrometer and liquid nitrogen cooled charge-coupled device.…”

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Third harmonic generation at 223 nm in the metallic regime of GaP

Roppo

Foreman

Aközbek

et al. 2011

Applied Physics Letters

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We demonstrate second and third harmonic generation from a GaP substrate 500 m thick. The second harmonic field is tuned at the absorption resonance at 335 nm, and the third harmonic signal is tuned at 223 nm, in a range where the dielectric function is negative. These results show that a phase locking mechanism that triggers transparency at the harmonic wavelengths persists regardless of the dispersive properties of the medium, and that the fields propagate hundreds of microns without being absorbed even when the harmonics are tuned to portions of the spectrum that display metallic behavior. , that the inhomogeneous component of the second harmonic ͑INH-SH͒ signal travels at the group velocity of the pump pulse. In a recent study phase and group velocity matching were demonstrated in lithium niobate in the range of transparency for all fields. The INH-SH was shown to refract at the same angle, and travel at the same velocity, as the pump.5 At the same time, the homogeneous SH component refracts and travels according to the values one expects from material dispersion at that frequency.The inhomogeneous component is generally difficult to observe because it travels locked under the pump pulse, with relatively low conversion efficiencies. In a recent study the results were generalized to include third harmonic generation ͑THG͒ in both positive and negative index media.6 When a pump signal traverses an interface into a nonlinear medium it generates SH and/or TH fields. Each harmonic has two parts: ͑i͒ a homogeneous portion that walk-off from the pump field; ͑ii͒ an inhomogeneous component phase-and velocitylocked to the pump, with no energy transfer between the fields except at interface crossings. The key observation here is that the INH-SH has a k-vector always double that of the pump, even for large phase mismatches. Theoretical findings thus suggest that the INH-SH signal experiences an effective complex index of refraction given by 2k c / 2 = k c / = n , i.e., the same index of refraction as the pump pulse.In Ref. 7, a pump pulse tuned at 1300 nm was launched into a slab of GaAs 500 m thick. Transmitted SH and TH signals were detected at 650 nm and 433 nm, respectively, far below the absorption band edge ͑ϳ900 nm͒. Simulations showed that only the inhomogeneous components propagate. Further experimental evidence 8 shows that the INH-SH is enhanced by several orders of magnitude compared to bulk 7 in an opaque GaAs cavity environment thanks to pump and INH-SH field localization and overlap. 9 The results of more experiments carried out in a high-Q GaAs cavity 10 hint that the INH-SH signal ͑612 nm͒ can achieve conversion efficiencies of order 10 −3 with pumping intensities as low as 0.15 MW/ cm 2 inside the cavity. We now ask the following question: does this phenomenon hold for harmonic fields tuned at frequencies in the metallic range? In other words, will a harmonic field propagate if it happens to be tuned in a region where sign͑͒ sign͑͒, where one expects no propagating solutions? The short answer to this ...

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Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media

Cited by 80 publications

References 60 publications

Multimode Nonlinear Fibre Optics: Theory and Applications

Multimode Nonlinear Fibre Optics: Theory and Applications

Ultrafast Reversal of the Ferroelectric Polarization

Third harmonic generation at 223 nm in the metallic regime of GaP

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