Experimental apparatus: 

the tandem-multipass Fabry-Perot interferometer

            In a typical Brillouin scattering experiment one reveals acoustic or spin waves with frequencies in the range between about 1 and 150 GHz. In order to extract the weak inelastic component of light from the elastically scattered contribution, a high-resolution spectrometer is required. To this aim, the best combination of high resolution and good throughput is achieve using a Fabry-Perot interferometer (FPI)[i] as a scanning spectrometer. This system consists of two very flat mirrors mounted accurately parallel to each other with a variable spacing. For a fixed distance L₁ the interference condition is such that only light of wavelength L₁ will be transmitted, with L₁=m L₁/2 where m is an integer. Therefore, this instrument acts as a band-pass frequency filter whose peak transmission is close to unity over a narrow spectral interval, as shown in Fig.1. 

Fig. 1

However, one has different interference orders which are separated in frequency by c/2L₁ Hz. This interorder spacing is called the free spectral range (FSR). The width of the transmission peak determines the resolution of the instrument. The ratio of the FSR to the width is known as the finesse F, whose value depends on the mirror reflectivity R, although strumental aperture and mirror flatness are also important parameters. In practice, the finesse is limited to values less than about 100 and this places an upper limit on the possible contrast, where the contrast C is the ratio of maximum to minimum transmission given by:[ii]

                                                      C=1+4F²/p²                       (1)

In opaque materials, it is usual that the elastically scattered light exceeds the intensity of the Brillouin component by more than a factor of 10⁴-10⁵, so that the above contrast is not sufficient for measuring in such a situation. A way for increasing the spectral contrast is the introduction of the multi-pass operation: by sending back a few times the light through the same interferometer, the contrast can be increased up to values close to 10¹⁰ and this is sufficient for Brillouin scattering experiments in opaque materials.

In order to avoid the overlap of neighbouring interference order and extend the range of frequency investigated, it is possible to combine two interferometers of unequal mirror spacing (tandem operation), as shown in Fig. 2. 

Fig. 2

The first interferometer of spacing L₁ transmits wavelengths

L₁ = 2L₁/m₁                                                               (2a)

for integral m₁, while the second interferometer of spacing L₂ transmits wavelengths

  L₂ = 2L₂/m₂                                                                   (2b)

for integral m₂.

Only if L₁ = L₂ light will be transmitted through the combination. It is important to notice, however, that to scan the transmitted wavelength, it is necessary to increment the mirror spacings L₁ and L₂ by DL₁, and DL₂ such that:

   DL₁/ L₁ = DL₂/ L₂                                                                       (3)  

In the Sandercock interferometer this condition is achieved mounting the interferometers on the same scanning stage, one with the mirror axis parallel to the scan direction, the other off set by an angle a. It is clear that the spacings of the two interferometers satisfy the equation                      L₂=L₁cosa.  The synchronization condition given by Eq. 3 is thus satisfied. In this way, it is possible to increase the FSR by a factor 10-20 over that of the single interferometer, although, as shown in Fig. 3, small ghosts remain of the suppressed orders.

Fig. 3

 The real interferometer

Now we present a synthetic description of the real tandem-multipass interferometer introduced by J. R. Sandercock about twenty years ago, opening the way for direct observation of surface magnons in thin films. A detailed description of this instrument can be found in Ref. [iii] and [iv]. The principle of the construction of the interferometer is illustrated in Fig. 4. 

Fig. 4

A scanning stage consisting of a deformable parallelogram rides on top of a roller translation stage. The former, actuated by a piezoelectric transducer, provides completely tilt-free movement of the interferometer mirrors over scan lengths up to 10 mm or more. The latter enables the mirror spacing to be set to the desired value in the range 0-50 mm. A small parallel-plate capacitor is then used to measure the scan displacement and this information is used in a feedback loop in order to linearize the scan displacement with respect to the applied scan voltage.

The advantages of this construction system are summarized below:

(a) completely tilt-free scan;

(b) highly linear scan (less than 0.5 nm non-linearity over 5 mm scan);

(c) ability to change mirror spacing without losing alignment; and

(d) stable against temperature change despite simple construction of aluminum and cast iron.

In order to avoid the noise caused by building vibrations, which typically have their maximum amplitudes in the range 10-20 Hz, the complete optical system can be isolated by a soft passive springs in the form of damped air columns. An alternative and even better solution is to mount the optical table rigidly on the floor, but to isolate the interferometer from the optical table by means of a dynamic isolation systems, using feedback control[v]. Note that an enclosure is required around the interferometer to protect it from sound waves which can excite high-frequency resonances in the system and to reduce the influence of thermal fluctuations and dust.

            It is important to recall here that for useful and easy operation of the interferometer, a simple procedure for obtaining mirror alignment is needed. This is achieved in Sandercock-type interferometers, by a motorized variation of the position of a few optical components, which permits to operate in reflection from the two Fabry-Pèrot cavities, instead of in the transmission mode.

Given the low intensity of the Brillouin signals, single-photon counting is necessary for the detection system. Low-noise photomultiplier tubes (PMT) having dark counts not higher than 1-2 counts per second are generally used for this purpose. A disadvantage of this type of detector is the low quantum efficiency of the photocathode. Quite recently a new generation of low-background noise, single-photon avalanche photodiodes with a quantum efficiency higher than a typical PMT, have also been available. The electronics that follows is standard when single- photon signals are passed to an amplifier, a pulse shaper, and then counted and stored by an multichannel analyzer.  

Fig. 5

            Figure 5 shows a schematic diagram of the whole experimental apparatus used for a BLS experiment in the backscattering configuration, which is usually exploited in the case of experiments on thin films and layered structures. In addition to the box containing the tandem-multipass interferometer and the optical components necessary for the multipass operation (3+3 passes in our case), one can see the external optics which is needed to focus the incident laser beam onto the surface of the specimen. In usual experiments the specimen is placed between the poles of an electromagnet with the external magnetic field applied perpendicular to the scattering plane and parallel to the film surface. In backscattering geometry the same lens (usually a commercial camera objective) is used to focus light and to collect the back-scattered photons for analysis through the interferometers. In this geometry, due to the conservation of the wavevector component parallel to the film surface, the wavevector of magnons revealed in the spectra is linked to the optical wavevector k_I by the simple relation:

q_|| =2 k_I sin q_i                                                 (4)      

where  q_i  is the angle of incidence of light. In order to reduce the noise level and to suppress signals from acoustic phonons an analizer is put at the entrance of the interferometer in order to stop scattered photons whose polarization is parallel to that of incident photons.