Novel method for ultrashort laser pulse-width measurement based on the self-diffraction effect

Peng Xi; Changhe Zhou; Enwen Dai; Liren Liu

doi:10.1364/OE.10.001099

Optics Express
Vol. 10,
Issue 20,
pp. 1099-1104
(2002)
•https://doi.org/10.1364/OE.10.001099

Novel method for ultrashort laser pulse-width measurement based on the self-diffraction effect

Peng Xi, Changhe Zhou, Enwen Dai, and Liren Liu

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Peng Xi, Changhe Zhou, Enwen Dai, and Liren Liu, "Novel method for ultrashort laser pulse-width measurement based on the self-diffraction effect," Opt. Express 10, 1099-1104 (2002)

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Abstract

Previous pulse-width measurement methods for ultrashort laser pulses have broadly employed nonlinear effects; thus any of these previous methods may experience problems relating to nonlinear effects. Here we present a new pulse-width measuring method based on the linear self-diffraction effect. Because the Talbot effect of a grating with ultrashort laser pulse illumination is different from that with continuous laser illumination, we are able to use this difference to obtain information about the pulse width. Three new techniques—the intensity integral technique, the intensity comparing ratio technique, and the two-dimensional structure technique— are introduced to make this method applicable. The method benefits from the simple structure of the Talbot effect and offers the possibility to extend the measurement of infrared and x-ray waves, for which currently used nonlinear methods do not work.

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Fig. 1. Optical setup of pulse-width measurement based on the Talbot effect.

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Fig. 2. (98.4KB) The intensity distribution detected at one Talbot distance with different pulse width (central wavelength 800 nm).

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Fig. 3. Talbot effect of pulses with different wavelengths at a pulse width of 100 fs. The detected distance is z = 2nd ²/λ ₀.

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Fig. 4. Relationship between the intensity ratio S(Δτ) and pulse-width Δτ is shown in S(Δτ) ~ Δτ curves. 1/M is the opening ratio of the corresponding grating.

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Fig. 5. Illustration of the two-dimensional grating (black area denotes transparent; white area denotes opaque). The opening ratio is as follows: vertical 1/2, horizontal 1/3.

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Equations (11)

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r (t, Δ τ) = \exp [i ω_{0} t - 4 \ln 2 {(\frac{t}{Δ τ})}^{2}],

R (ω, Δ τ) = \frac{Δ τ}{4 \sqrt{π \ln 2}} \exp [\frac{- Δ τ^{2} {(ω - ω_{0})}^{2}}{8 \ln 2}] .

U (x, z, ω) = \frac{\exp (i \frac{2 π}{λ} z)}{\sqrt{i λ z}} \int_{- \infty}^{+ \infty} U_{0} (x_{0}, ω) \exp [- \frac{i π {(x - x_{0})}^{2}}{λ z}] d x_{0},

U_{0} (x) = \sum_{l} A_{l} \exp (i \frac{2 πlx}{d}) .

U (x, z, ω) = \exp (i \frac{2 π}{λ} z) \times \sum_{l} A_{l} \exp (i \frac{2 πlx}{d}) \times \exp (\frac{i 2 π l^{2} z}{\frac{2 d^{2}}{λ}}),

G (x, z, ω, Δ τ) = R (ω, Δ τ) U (x, z, ω) .

I (x, z, Δτ) = 2 π \int_{- \infty}^{+ \infty} {∣ G (x, z, ω, Δτ) ∣}^{2} dω .

I (x, z, Δτ) = \frac{Δ τ^{2}}{8 \ln 2} \int_{- \infty}^{+ \infty} \exp [- \frac{Δ τ^{2} {(ω - ω_{0})}^{2}}{8 \ln 2}]

\times \sum_{l,}^{+ \infty} \sum_{m = - \infty}^{+ \infty} A_{l} A_{m} \exp [i \frac{2 π (l - m) x}{d}] \times \exp [\frac{i 2 π (l^{2} - m^{2}) n ω_{0}}{ω}] dω .

P (h_{1}, h_{2}, Δτ) = \int_{h_{1} d}^{h_{2} d} I (x, z, Δτ) d x .

S (Δ τ) = \frac{P (\frac{1}{4}, \frac{3}{4}, Δ τ)}{P (- \frac{1}{4}, \frac{1}{4}, Δ τ)} .

Abstract

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Equations (11)

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