Spectral dependence of the optical absorption coefficient, α, for the chemically reduced nominally pure LiNbO3 crystal (sample #2) annealed in a hydrogen atmosphere at 500 °C for 100 min. The sample notation is given in accordance with Table I.
Kinetics of normalized transmittance, NT = (T(t)/T 0) × 100%, in the chemically reduced sample #6, demonstrating the transient optical damage (photorefractive defocusing), when the 514.5-nm laser beam (Pin = 20 mW) is focused on the +Z-face (I ≈ 260 W/cm2 at the entrance to the crystal surface).
Kinetics of NT in the chemically reduced sample #6, demonstrating both the transient and steady-state optical damage, when the laser beam is focused on the +Z-face, at an input power of 76 mW (I ≈ 990 W/cm2 at the entrance to the crystal surface). The transient optical damage induces the initial sharp decrease of transmittance that reaches the minimum value, Tmin , at an exposure time, t = τ m , i.e., the transient optical damage is maximal at τm . The steady-state optical damage is developed when the transmittance reaches the steady-state value, Ts .
Dependences of the light-induced ordinary refractive index change, Δn, on the input power of a 514.5-nm laser beam focused on the +Z-face of the reduced crystal (sample #6; Table I) for: (1) the transient optical damage (Δntr ), i.e., at an exposure time, t = τ m (see Eq. (3)), and (2) the steady-state optical damage (Δns ), i.e., at t → ∝.
Kinetics of NT in the chemically reduced sample #6, when the laser beam is focused on the −Z-face, with the input power of 76 mW. The illumination was paused during four different periods: from 110.7 to 115.8 s ( = 5.1 s), from 125 to 146 s ( = 21 s), from 186.6 to 190.1 s ( = 3.5 s), and from 201.5 to 249.8 s ( = 48.3 s).
The NT kinetics caused by the dependence of the transient optical damage on the duration of a short-term pause in the illumination of the +Z-face at an input power, Pin =20 mW (sample #6). The illumination was paused for the three different tp periods: from 121.7 to 125.2 s ( = 3.5 s), from 145 to 146.4 s ( = 1.4 s), and from 159.7 to 160.5 s ( = 0.8 s). The transmittance decrease, δT, after such a pause depends on tp and, thus, it is caused by the developing of the transient pyroelectric optical damage due to the crystal cooling down. The steady-state transmittance, following after the fast transient changes (see Fig. 2), is established for 120 s of initial continuous illumination.
Kinetics of NT during the optical damage, developing dark relaxations of the steady-state optical damage after the four short-term pauses in illumination (input laser power is 175 mW, corresponding to light intensity, I ≈ 2.35 × 103 W/cm2, at the crystal surface), and fast damage recoveries for illumination periods consequent to each pause in sample #5 at ambient conditions. The illumination was paused during four different periods: from 200.4 to 203.6 s ( = 3.2 s), from 230.5 to 232.6 s ( = 2.1 s), from 247.4 to 248.2 s ( = 0.8 s), and from 265.7 to 276.4 s ( = 10.7 s). Transient optical damage rises, reaching a maximum value at τm , and relaxes during 58 s of the initial continuous illumination. Steady-state optical damage is developed after illumination for 200 s, since the steady-state value of the normalized transmittance is reached before a first pause in illumination. The partial transmittance recovery after each short-term pause is related to the compensation of the steady-state space-charge field by a transient pyroelectric field appearing, due to crystal cooling down.
Schematic diagram of the superposition of the different contributions in the light-induced space-charge field. As a first approximation, we have assumed that laser heats the crystal only in the region directly in line with a laser beam. Here, iPVE, ip , are the photovoltaic, primary pyroelectric, and the sum of gradient-induced (secondary and tertiary) pyroelectric currents, respectively; ∇T is the longitudinal temperature gradient arising at the beginning of the illumination, due to the significant attenuation of light intensity along the beam trace; (heat) and (cool) show the directions of the transient pyroelectric currents during the initial stages, after the laser switching on and switching off, respectively; the “clamping” arrows illustrate the partial elastic constraints (partially clamped conditions) created at the local heating of a small illuminated fraction of the crystal bulk.
Samples notation, optical absorption coefficient α values (at λ = 514.5 nm) for the reduced LiNbO3 samples, specific times, τ 1 and τm , for the transient optical damage, specific time, τ 2, of the steady-state optical damage developing, maximum magnitudes of light-induced ordinary index change for the transient, Δntr , and steady-state, Δns , optical damage. All of the optical damage parameters were measured at an input power, Pin = 50 mW, of a focused 514.5-nm laser beam, i.e., I = 670 W/cm2 at an entrance to the + Z-face of a crystal.
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