Fig. 1. Schematic of photon deceleration using two laser pulses at different frequencies. A plasma wake of wavelength λ_p is excited by an intense driver laser pulse (blue curve) with a relatively short initial wavelength λ_d0. The signal laser pulse (red curve) with a relatively long initial wavelength λ_s0 is trailing the driver pulse. An appropriate time delay is introduced between the two laser pulses such that the signal laser pulse sits at the front of the second wake bubble that excited by the driver pulse.

Fig. 2. Gradients of refractive indices for signal laser pulses with different carrier wavelengths λ_s0 = 1 μm (blue curve), 5 μm (red curve), and 10 μm (yellow curve). The plasma density profile (black curve) is taken around the density peak between the first and second wake bubbles excited by a driver laser pulse with a normalized vector potential a_d0 = 4, and the plasma has an initially uniform electron number density n₀ = 0.0005n_dc in the region x ≥ 0, where ndc=meωd02ϵ0/e2 is the critical plasma density corresponding to the wavelength λ_d0 of the driver pulse.

Fig. 3. PIC simulation results for photon deceleration using two laser pulses at different frequencies. The plasma electron density n_e and the transverse electric fields of the signal laser E_s are shown for cases with different initial carrier wavelengths: (a) λ_s0 = 1 μm at t = 3000T_d0; (b) λ_s0 = 5 μm at t = 1500T_d0; (c) λ_s0 = 10 μm at t = 230T_d0. Here, T_d0 = λ_d0/c is the wave period of the driver laser. The corresponding on-axis distributions of the gradients of the refractive indices and the transverse electric fields of the signal laser are compared in (d)–(f). The inset in (f) shows the temporal waveform of the output light pulse at the central wavelength λ_c ≈ 45 μm. The corresponding Wigner spectrograms of the on-axis transverse electric fields of the signal pulse and the on-axis electron density are shown in (g)–(i), respectively. It should be noted that the snapshots in (b) and (c) are taken at the moments when the photons of the signal lasers are decelerated sufficiently, whereas the snapshot in (a) is taken at the end of the simulation.

Fig. 4. (a)–(c) Spectra (red curves) of modulated signal pulses with different initial wavelengths λ_s0 = 1, 5, and 10 μm, respectively, in which the initial spectra (blue curves) are also shown for comparison. (d)–(f) Time evolutions of the central wavelengths (yellow curves) of the modulated signal lasers and the energy conversion efficiencies ζ (black curves). Here, the energy conversion efficiencies ζ are defined as the ratios of the modulated signal laser energies in the spectral regions (d) λ ≥ 1.03 μm, (e) λ ≥ 10 μm, and (f) λ ≥ 30 μm to the initial signal laser energy.

Fig. 5. (a) Central wavelength λ_c, normalized amplitude a_s, and energy conversion efficiency ζ of the modulated signal laser pulse as functions of the signal laser intensity. Here, the energy conversion efficiency ζ is defined as the ratio of the modulated signal laser energy in the spectral region λ ≥ 30 μm to the initial signal laser energy. (b) Plasma density profiles modified by signal laser pulses with different intensities a_s0 = 1 (black curve) and a_s0 = 8 (red curve) at t = 230T_d0. This display region includes the first and second wake bubbles that are excited by the driver laser pulse with a_d0 = 4, and the plasma has an initially uniform electron number density n₀ = 0.0005n_dc in the region x ≥ 0.

Fig. 6. PIC simulation result for photon deceleration or acceleration when the signal laser pulse is longer than the plasma wake bubble. (a) Plasma electron density n_e and transverse electric field of signal laser E_s at t = 800T_d0. (b) Corresponding Wigner spectrograms of the on-axis transverse electric fields of the signal pulse and the on-axis electron density. In this simulation, the driver laser has a normalized amplitude a_d0 = 3. The signal laser initially has a duration of 200 fs, a wavelength λ_s0 = 10 μm, and a normalized amplitude a_s0 = 1. The signal laser is launched after the driver laser with a time delay of 347 fs, so that the peak of the signal laser pulse is located at the front of the third wake bubble behind the driver pulse.