Laser mode complexity analysis in infrared waveguide free-electron lasers

We analyze an optical phenomenon taking place in waveguide free-electron lasers, which disturbs, or forbids, operation in far infrared range. Waveguides in the optical cavity are used in far-infrared and THz ranges in order to avoid diffraction optical losses, and a hole coupling on output mirror is used for laser extraction. We show that, when the length of the waveguide exceeds a given limit, a phenomenon of “mode disorder” appears in the cavity, which makes the laser difficult, or impossible, to work properly. This phenomenon is even more important when the waveguide covers the whole length of the cavity. A numerical simulation describes this effect, which creates discontinuities of the laser power in the spectral domain. We show an example with an existing infrared Free-Electron Laser, which exhibits such discontinuities of the power, and where no convincing explanation was proposed until now.

Figure 1

Output laser power vs. wavelength, measured on FLARE at 16 MeV.

Figure 2

Typical convergence of cavity losses vs cavity round trip $N_c$.

Figure 3

Layout of FLARE Free-Electron Laser.

Figure 4

Numerical simulation of the output laser power of FLARE.

Figure 5

Total losses $L_{\mathrm{os}}$ of the cavity versus the extraction rate $T_x$.

Figure 6

Laser profile amplitude in the waveguide ($200\times 1\mathrm{cm}$), at various wavelengths: large power at $54.3{\mathrm{cm}}^{-1}$ (a) (c), and zero power at $53.5{\mathrm{cm}}^{-1}$ (b) (d); on the plane of gain (a) (b) and on the output mirror (c) (d).

Figure 7

Extraction rate $T_x$ (left side), and gain (right side) versus wavelength—required gain coefficient $g_o$ and FEL gain coefficient $G^{*}$.

Figure 8

Energy distribution of the eigenmodes ${\mathrm{TEM}}_{pq}$ of FLARE, at $\sigma =50{\mathrm{cm}}^{-1}$, versus $(p,q)$ indexes, and bottom curve in dB for $q=1$.

Figure 9

Layout of CLIO Free-Electron Laser.

Figure 10

Numerical simulation of the laser power vs wavelength for CLIO, for various electron beam energies.

Figure 11

Measurements of the CLIO laser power vs wavelength, for various electron beam energies.

Figure 12

Laser power $P_L$, cavity losses $L_{\mathrm{os}}$ and extraction rate $T_x$ versus waveguide length $d_w$, at $\lambda =10\mu \mathrm{m}$.

Figure 13

Diffraction losses $L_{\mathrm{dif}}$ versus waveguide length $d_w$ at various wavelength of the laser.

Figure 14

Laser power versus wavelength at various waveguide length $d_w$.

Figure 15

Diffraction losses $L_{\mathrm{dif}}$ versus wavelength at various waveleguide length $d_w$.

Figure 16

Amplitude profile of the laser, at the waveguide output (point A in Fig. 9), for various wavelength $\lambda$ and waveguide length $d_w$.

Figure 17

Amplitude profile of the laser, for $\lambda =20\mu \mathrm{m}$ and $d_w=3\mathrm{m}$, (a) on upstream mirror (point B in Fig. 9), and (b) on waveguide entrance (point C in Fig. 9).

Figure 18

Energy of the eigenmodes ${\mathrm{TEM}}_{pq}$ for CLIO at $\lambda =10\mu \mathrm{m}$ and $d_w=2\mathrm{m}$.

Figure 19

Layout of the FEL with a full waveguide configuration.

Figure 20

Amplitude profile of the laser on output mirror, for (a) $\lambda =19.9\mu \mathrm{m}$, (b) $\lambda =20\mu \mathrm{m}$, (c) $\lambda =20.1\mu \mathrm{m}$.

Figure 21

Laser power versus wavelength.

Figure 22

Amplitude profile of the laser on output mirror without extraction hole, for (a) $\lambda =19.9\mu \mathrm{m}$, (b) $\lambda =20\mu \mathrm{m}$, (c) $\lambda =20.1\mu \mathrm{m}$.

Figure 23

Laser power versus wavelength, without extraction hole (transmission mirror).

Figure 24

Laser profiles on output mirror without hole, and with broad gain profile, at $\lambda =20\mu \mathrm{m}$, for consecutive round trips $N_c$ in the cavity: $N_c=17$ (a), 18 (b) and 19 (c).

Figure 25

Profile convergence vs cavity round trip $N_c$, at $\lambda =20\mu \mathrm{m}$, (a) using a small cross section of gain, (b) and a large one.

Figure 26

Profile at $\lambda =20\mu \mathrm{m}$, using a uniform gain and a 2 mm hole coupling, and curve of losses and extraction rate vs wavelength.

Figure 27

Profile at $\lambda =20\mu \mathrm{m}$, with a uniform gain and a slit of 2.5 mm width, and curve of losses and extraction rate vs wavelength.

Figure 28

Laser profile amplitude in the waveguide ($200\times 1\mathrm{cm}$): (a) on the plane of gain and (b) on the output mirror, at various wavelength.

Figure 29

Required gain coefficient $g_o$ vs wavelength, (1) with extraction slit, and (2) with a transmission mirror (without slit).

Figure 30

Simulation of the output laser power of FLARE, without extraction slit (extraction by mirror transmission).