Complete pump depletion by autoresonant second harmonic generation in a nonuniform medium

Abstract

In this paper, we develop for the first time to our knowledge an analytical theory of second harmonic generation (SHG) in a generic nonuniform χ 2 medium. It is shown that by varying the properties of the medium gradually enough, the system can enter an autoresonant state in which the phases of the fundamental pump and of the generated second harmonic wave are locked. The effect of autoresonance allows efficient transfer of energy between the waves and, due to the continuous phase-locking in the system, all the energy of the pump could be converted to the second harmonic. Simple closed-form expressions for the waves amplitudes as a function of the longitudinal coordinate are derived, and an explicit criterion for the stability of the autoresonant state is obtained. Our analytical theory is compared to the numerical solution of the coupled mode equations, which are found to be in excellent agreement with each other. The analytical closed-form expressions that we derive could be very useful for practical design of SHG devices with increased performances, such as highly efficient, wideband frequency converters.

Design constraints of optical parametric chirped pulse amplification based on chirped quasi-phase-matching gratings

“…We can define an OPA bandwidth as the range of frequencies which experience complete amplification according to Eq. (10). Assuming for simplicity a linear, unapodized chirp profile and approximating γ p (Ω) ≈ γ p0 for peak coupling coefficient γ p0 , we find the following for the range of material phase mismatches that are fully amplified:…”

“…For small ρ, the amplification corresponds closely to Eqs. (9) and (10). For larger ρ, the interaction approaches the adiabatic frequency conversion case [8,9], and for ρ 1 (corresponding to DFG or SFG rather than OPA), correspond to the case considered in [7].…”

“…Their main role historically has been to broaden the phase-matching bandwidth compared to conventional periodic QPM gratings, without the need to use short crystals with reduced conversion efficiency, tighter focusing, higher intensities, operation close to the damage threshold, or other potential drawbacks. Quite recently, new applications of chirped QPM gratings have emerged, in particular high-gain optical parametric amplification (OPA) [1][2][3][4][5][6], and high-efficiency adiabatic frequency conversion (AFC) [6][7][8][9][10][11]. Together, these processes reveal the possibility of achieving essentially arbitrary-bandwidth, high-efficiency optical parametric chirped pulse amplification (OPCPA) within the transparency window of QPM media, while simultaneously suppressing gain-narrowing effects [12].…”

Broadband and efficient adiabatic three-wave-mixing in a temperature-controlled bulk crystal

“…Building upon this effect, adiabatic TWM in a nonlinear crystal can result in high conversion efficiencies over a remarkable bandwidth [24,25]. For this process to occur, the phase mismatch (Δk) between the mixed waves is slowly tuned from Δk < 0 to Δk > 0 (or vice versa) along the propagation axis, allowing the adiabatic conversion to adapt to these (slow) changes [26].…”

Broadband and robust adiabatic second-harmonic generation by a temperature gradient in birefringently phase-matched lithium triborate crystal

“…In order to achieve wider bandwidths, we can utilize the concept of adiabatic conversion, which can be realized by a thermal gradient: At the entrance to the crystal, the temperature will be below the phase matching temperature, hence the process is not phase matched and the two harmonic waves (fundamental and second harmonic) are uncoupled. The temperature will increase slowly (adiabatically) along the crystal, passing the phase matching temperature at the middle of the crystal, and rising towards the exit of the crystal to a temperature which is much higher, hence decoupling again the two [20] for the case of SHG in the context of auto-resonant processes [11,12] and recently also measured by a thermal gradient in MgO:LiNbO 3 [21], but these reports included only the conversion efficiency vs the pump power, without a detailed study of the acceptance bandwidth and the required thermal profile. More recently, broadband adiabatic optical parametric amplification was reported using a 4-point temperature profile [22].…”