Laser-induced narrowband coherent synchrotron radiation: Efficiency versus frequency and laser power

We analyze the narrowband terahertz emission process occurring from electron bunches passing in a bending magnet, after a laser-induced sinusoidal modulation has been performed. In particular, we focus on experimental tunability curves, and power scalings with current and laser power. Theoretically, we simplify the problem formulation using the slowly varying envelope approximation. At low powers, the scaling with laser power appears to be quadratic, and analytical expressions for the tuning curves are obtained. Emission at first passage in the bending magnet, and after one full turn in the storage ring, are considered both experimentally and theoretically. The experiments are performed on the UVSOR-II storage ring.

Figure 1

Global view of the experiment at the UVSOR-II storage ring. Laser pulses with a sinusoidal modulation interact inside an undulator (FEL beam line), and the THz radiation analysis is performed at the terahertz BL6B beam line.

Figure 2

Detail of the pulse shaping system. A regenerative chirped pulse amplifier (Coherent Legend) is slightly modified. A high-reflectivity mirror is placed between the amplifier and the compressor, to extract the high-energy stretched pulses. These latter are sent to a Michelson interferometer, and the resulting modulated pulses are then focused on the electron beam, as in usual slicing experiments. CCR1 and CCR2 are high precision corner cube hollow retroreflectors from PLX Inc. (OW-25-0563), i.e., with 63 mm total aperture, $<0.5\mathrm{arc}\sec $ deviation, and $\lambda /4$ wavefront distortion (@ 633 nm).

Figure 3

Pulse shape, checked at very low modulation wave number, using a double sweep streak camera. (a) Raw streak camera image, where 100 successive pulses are recorded. (b) Pulse shape averaged over 3 ms, i.e., the rectangular area displayed in (a). Note that the phase fluctuations in (a) are due to mechanical vibrations of the Michelson’s mirrors (essentially at 60 Hz), with an amplitude of several hundreds of nanometer.

Figure 4

Typical autocorrelation trace (a) and spectrum (b) of the relatively short pulses (in the 10 ps range) obtained with the previous setup, which used an external pulse stretcher. (c) Autocorrelation of long pulses ($\approx 300\mathrm{ps}$ FWHM) using the actual pulse shaper.

Figure 5

Three typical emission spectra induced by the shaped laser pulses, for three different modulation frequencies. Each spectrum is rescaled to its maximum value.

Figure 6

Dependence of the peak terahertz emission frequency with the position of the Michelson mirror.

Figure 7

Response versus modulation wave number. (a) Signal detected by the bolometer versus modulation wave number (note that the shape is affected by the frequency responses of the bolometer, the beam line, etc.). (b) Reference spontaneous SR spectrum without laser. (c) Ratio between CSR and spontaneous SR [curve (a)/curve (b)]. In (c), the vertical scale is arbitrary. The typical values will be measured in Sec. 3c. At $15{\mathrm{cm}}^{-1}$, when the current is 10 mA, the typical pulse energy ratio is of the order of 20 000.

Figure 8

Terahertz energy per bandwidth unit versus beam current (a), and versus laser pulse energy (b). Squares: experimental data; full line: quadratic law fit. The insets represent the same curves in log-log units. In (a), the laser pulse energy is $800\mu \mathrm{J}$. In (b), the current is 4.8 mA. The modulation wave number is $15{\mathrm{cm}}^{-1}$.

Figure 9

Ratio between CSR and incoherent SR terahertz energy per pulse and unit bandwidth, at the modulation frequency ($15{\mathrm{cm}}^{-1}$). Squares: experimental data; full line: linear fit. Incident laser pulse energy: $800\mu \mathrm{J}$.

Figure 10

(a) Dependence of the form factor versus wave number, using Eqs. (11, b3). The vertical unit is arbitrary in the sense that we took $P=C=1$ in the calculation. “turn 0” corresponds to the parameters $R_{ij}$ associated with a straight transport from the undulator to the bending magnet. Labels “turn 0”, “turn 1”, “turn 2”, “turn 3”, correspond to $R_{ij}$ parameters associated to a straight transport, 1 full turn, 2 full turns, 3 full turns in the storage ring, respectively. Part (b) represents the sum of the first form factors: turn 0 only (red), sum of turns 0 and 1 (green), sum of turns 0, 1, and 2 (blue), sum of turns 0, 1, 2, and 3 (magenta).

Figure 11

Deformation of the form factor (and the emission spectrum) predicted at very high powers [numerical computation using Eq. (a13)]. (a) $w_0=0.1$, (b) $w_0=1$, (c) $w_0=10$, (d) $w_0=100$. Other parameters are $k_m=400$, ${\sigma }_L=0.3$, $r_{51}=-0.00053$, $r_{52}=0.0021$, and $r_{56}=-0.0029$.

Figure 12

Scaling of the terahertz emission power versus laser pulse power [numerical computation using Eq. (a13), and analytic results from Eq. (b16) valid when $w_0\ll 1/|k_m{r}_{56}|$]. Full and dashed lines are the maximum value of $|{\tilde{\rho }}_0^2(k)|$ computed numerically, and analytically, respectively (the two are indistinguishable in practice for $w_0<1$ here). Dotted line: the main peak area $\int |{\tilde{\rho }}_0^2(k)|dk$ computed numerically. Note that $w_0^2$ is proportional to the laser power, and that $\int |{\tilde{\rho }}_0^2(k)|dk$ is proportional to terahertz pulse energy. ${\sigma }_L=0.3$, $r_{51}=-0.00053$, $r_{52}=0.0021$, $r_{56}=-0.0029$, and $k_m=400$.

Figure 13

Form factor in the case of a Gaussian laser pulse with internal modulation: Numerical result from Eq. (a13) (dots) and approximation from Eq. (b16) (full line). $k_m=400$, ${\sigma }_L=0.3$, $w_0=0.1$, $r_{51}=-0.00053$, $r_{52}=0.0021$, and $r_{56}=-0.0029$.