1. Introduction

High finesse optical cavities are becoming more and more important in a wide range of applications. In fundamental physics research they can be used to enhance a very weak signal, like the magnetic birefringence of vacuum [1, 2], or the production rate of yet to be discovered particles like the axion [3]. In such experiments it is required that light be trapped as long as possible within a strong magnetic field perpendicular to the propagation direction of the light. Both very high finesse and long cavities are therefore necessary. In metrology cavities are used to precisely define a reference length, hence a frequency, locking to them a light source with large gain [4, 5].

The cavity decay time τ_d is defined as the time at which the stored energy is reduced by a factor e after turning off the input. It is related to the finesse ℱ and the mirror separation d by the formula:

In a recent paper [6] the role of losses in long storage time optical cavities has been studied. One critical application cited there is the possibility of developing a filter cavity [7] to be used in gravitational wave interferometers such as LIGO [8] or VIRGO [9]. An improvement of the sensitivity could be obtained by using squeezed light for which the squeezed quadrature must be rotated as a function of frequency. Such a rotation can be realized by reflecting the squeezed light from a cavity with linewidth comparable to the frequency interval in which the rotation has to be done, typically 50 Hz. Up to now the sharpest cavity ever made has a linewidth of about 125 Hz [10], i.e. still a factor of two and a half too large.

In this paper we report on a cavity, operating at the wavelength λ = 1064 nm, having a decay time of 2.7 ms, that corresponds to a linewidth of 59 Hz, thus demonstrating that the technology is now available. This measurement has been performed using the apparatus of the PVLAS experiment [1] (PVLAS: Polarization of Vacuum with LASer), whose aim is to detect the magnetic birefringence of vacuum by means of an ellipsometer coupled to a system of two rotating permanent magnets. The ellipsometer has a very high sensitivity thanks to the use of a high-finesse Fabry Perot cavity and of heterodyne detection.

From equation (1) it follows that a long storage time can be obtained by using a large mirror separation d and/or high finesse ℱ. Cavity mechanical stability, which is necessary for locking a laser, puts stringent requests on d: in practice one wants the cavity placed on a single stable structure decoupled from environmental noises like seismic or acoustic vibrations, or temperature changes. A typical size for d would then not exceed a few meters, the standard length of an optical table. Larger interferometers do exist, for instance, gravitational wave interferometers have mirror separations as large as few kilometers, but they need costly developments and complicated isolation systems for each mirror. Here we have demonstrated that very large storage times can be realized with commercially available products.

Assuming two identical mirrors with intensity transmissivity T_m, reflectivity R_m and losses P_m, such that R_m + T_m + P_m = 1, the cavity finesse is determined by:

For a stationary resonating Fabry-Perot cavity we define its transmissivity T_FP and its reflectivity R_FP as functions of the transmitted power P_t, the reflected power P_r and the input power P_in through the relations:

The formulas listed above completely characterize a lossy Fabry Perot cavity with identical mirrors.

2. Experimental apparatus

The new layout of the PVLAS experiment has been recently redesigned and built from scratch. The measurement principle has been described in several papers (see Ref. [1] for a recent review). We recall here only a few specific characteristics of the new set-up.

In Figure 1 a scheme of the new apparatus is shown. A 2 W continuos wave Nd:YAG (λ = 1064 nm) non planar ring oscillator laser [14] is coupled to a high finesse Fabry Perot cavity by a matching lens and two steering mirrors. The laser output is elliptically polarized, a quarter wave plate and a half wave plate are used to maximize the coupling into a two stage optical isolator which prevents back reflected light from re-entering into the laser source. The half wave plate also regulates the amount of laser power used in the experiment. The ellipsometer is kept in vacuum: the beam enters the chamber through an optical window with anti reflective coating. Before the window, another half wave plate aligns the polarization along the desired axis. The ellipsometer is formed by a pair of crossed polarizers with extinction ratio σ² better than 10⁻⁷: the first one, indicated as P, determines the polarization axis, while the second (A - analyzer), analyzes the beam. Between the two polarizers, a very high finesse Fabry Perot resonant cavity is used as an optical path amplifier; the laser is frequency locked to the cavity with a modified Pound-Drever technique [15]. The ordinary and the extra-ordinary beams exiting the analyzer are collected onto two separate InGaAs 1 mm² photodiodes, and the resulting photocurrents are then amplified using two low noise transimpedance current amplifiers. The outputs are then collected for off line analysis. A picture of the apparatus can be seen in Figure 2.

 

Fig. 1 Scheme of the apparatus. The granite optical table, 4.8 m × 1.5 m, is shown together with the optical components and the five vacuum chambers. The two magnets, which play no role in the present work and are shown only for the sake of completeness, are used in the PVLAS experiment to generate a magnetic birefringence. HWP = Half wave plate; P = Polarizer; A = Analyzer; WPs = Wave plates; PRF = Reflection photodiode; PTR = Transmission photodiode; PEXT = Extinction photodiode.

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Fig. 2 A wide-angle picture of the PVLAS apparatus. The two blue cylinders are the permanent magnets: they are hanging from an aluminium structure mechanically decoupled from the rest of the optical table.

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The vacuum structure comprises five ultra high vacuum metal chambers plus a 13.5 mm internal bore pyrex pipe through each of the two magnets. Vacuum pumping systems, each composed of a scroll pump and a turbo molecular pump, are used to evacuate the chambers below 10⁻⁷ mbar. During optical measurements vacuum is guaranteed by Non Evaporable Getter pumps, which have no magnetic or moving parts. The optical and vacuum components of the apparatus are mounted on an air suspended monolithic granite optical table. A computer controlled feedback system, acting on the table legs, provides seismic isolation. The complete apparatus is mounted inside a class 10 000 clean room.

The Fabry Perot cavity mirrors have diameter 25.4 mm and thickness 6 mm. They are manufactured by ATFilms (Boulder, CO, USA) from super-polished fused silica substrates and the reflecting surfaces are obtained by ion beam sputtering technique. The mirrors are mounted inside two identical titanium vacuum chambers: each chamber contains a piezo-motor-operated mirror mount with three degrees of freedom (the angles θ_x, θ_y, θ_z). During maintenance operations on the optics, the chambers of the mirrors can be isolated from the rest of the vacuum structure by means of two pairs of gate valves. This preserves the surface of the mirrors from air contamination. The upper part of the mirror vacuum chambers is equipped with a large view-port that allows inspection of the mirror surface while the Fabry Perot is in operation with the laser locked to it. Particular attention is paid when placing the mirrors into operation. A clean mirror is taken out from the manufacturer’s packing and quickly mounted on its support to limit the exposure of its surface to dusty air. All operations are performed inside the clean room as close as possible to the vacuum chamber.

The mirrors can also be studied in a separate small scale facility. Although this facility is not housed in a clean environment, the design of the cavity allows for a safe mounting procedure: the two cavity mirrors face each other from the opposite ends of a rigid 17 mm cylindrical ceramic spacer, with pumping hole, that limits the dust-carrying air flows on the mirror surface during mounting. The cavity assembly is kept inside a rough vacuum chamber (pressure ≃ 1 mbar), and can be accessed through two viewports. After alignment of the incoming beam with the cavity axis, a 100 mW Nd:YAG non planar ring oscillator laser can be locked to the cavity and measurements of the cavity finesse and transmission can be performed. The cavity decay time is measured with a fast photodiode for which the measured response time is 0.7 μs. The measured laser shut-off time is shorter than 2 μs.

3. Results

We mounted two mirrors out of a batch of seven without any particular selection or cleaning. The mirrors were produced with the goal of reaching the best finesse possible. For these mirrors the manufacturer quoted a transmissivity of 2.9 ± 0.2 ppm. Scatter losses from these super-polished substrates are declared to be less than 1.5 ppm. The mirrors have radius of curvature 2 m which, for our cavity length d = 3.303 ± 0.005 m, means a beam radius at the mirror w_m = 1.2 · 10⁻³ m. To match this geometry, a lens with focal length f = 1.5 m has been properly placed between the laser and the cavity. By using the steering mirrors and the tilt controls of the cavity mirror mounts, the cavity axis was aligned along the center of the vacuum pipe. This is important to avoid possible losses coming from the diffraction of the beam tails on the vacuum components. With the laser locked to the cavity we have measured the two quantities:

 

Fig. 3 Decay of the light transmitted from the cavity after switching off the laser frequency locking system. The decay is fitted with the exponential function a + be^−t/τ_d, and gives for the decay time τ_d = 2.70 ± 0.02 ms.

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The reported values have been obtained with a reduced cavity input power P_in = 0.55 W. The maximum available power from the laser at the cavity input can be as high as 1.2 W, but when using full power we observe amplitude instabilities in the cavity output, and also a smaller ratio $\frac{P_t}{P_{\text{in}}}=0.21$. By reducing the input power the output becomes stable and we obtain a higher coupling. This behavior can probably be explained with thermal lensing effects on the mirrors [16, 17]: when using 1.2 W as input, the power circulating in the cavity is P_c ≃ 100 kW, and the average intensity on each of the mirrors is $P_c/\pi w_m^2=2.7\hspace{0.17em}\text{MW}/{\text{cm}}^2$. This value is below the damage threshold for the mirrors, but it can cause lensing deformation of the reflecting surface. With a lower input, the power on each mirror surface is reduced to 1.85 MW/cm², and this is sufficient to avoid instabilities and obtain a better geometrical coupling.

Table 1 lists some of the most performing cavities ever realized. Our work represents an improvement of a factor larger than two with respect to previous results, and it is the biggest step since many years. Moreover, for the wavelength λ = 1064 nm, it features a value equal to the best finesse previously reported [21].

Table 1. Summary of a few Fabry Perot cavities with longest decay time ever realized, together with the highest finesse for λ = 1064 nm and the highest finesse in absolute. The coherence length is defined as ℓ_c = cτ_d.

View Table

The long decay time reported above stayed stable for several weeks in the long cavity set-up, however, the reflectivity of the second mirror degraded after air venting of the vacuum chamber. We replaced this mirror with a new one, which displayed a slightly worse performance, the new cavity having a decay time of 2.1 ms. An eye inspection with the aid of an IR viewer of the mirror surface with the laser locked to the cavity showed the presence of a couple of dust particles on the reflecting surface. Probably these particles prevent reaching a higher finesse.

We expected that an accurate cleaning of the mirror that gave the record result of Table 1 could restore its initial performance. For this reason we moved it to the 17 mm long test cavity and paired it with another mirror of the same batch. The mirrors were cleaned by using lens tissue with a few drops of acetone on it and then the cavity was assembled and inserted into the vacuum chamber. The decay time measured for the TEM00 mode of the cavity was 14.3 ± 0.1μs, which corresponds to a finesse of 789 000 ± 6 000. In the computation of the finesse a value of 0.08 mm has been added to the spacer length to take into account the curvature of the mirrors. For this cavity the beam radius on the mirrors is $w_m^{17\text{mm}}=0.21\hspace{0.17em}\text{mm}$. With such a small radius the probability of having many dust particles inside the light spot is very small, hence the slightly higher finesse.

We also measured the finesse of the cavity for higher order modes of the type TEM0n, with n up to 7, TEMm0, with m up to 2, and TEM11. The modes TEM0n have rectangular shape and their width W on the mirror is $W=2w_m^{17\text{mm}}$, while their length L is proportional to the mode order as [22]:

 

Fig. 4 Values of the finesse for different TEMmn modes of the 17 mm Fabry Perot cavity.

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4. Conclusion

The PVLAS experiment has realized a 2.7 ms decay time resonant Fabry Perot cavity at the optical wavelength λ = 1064 nm, with an increase of a factor larger than two with respect to previous interferometers. This decay time corresponds to a coherence length ℓ_c = 8.1 · 10⁵ m. The cavity fits on a standard optical table. Such a long decay time is obtained by employing mirrors with extremely high reflectivity matching the highest finesse ever realized at this wavelength. Such a high value of finesse is crucial for the experiments aiming at measuring the magnetic birefringence of the vacuum [1, 2]. This cavity shows that it is possible to realize the filter cavity foreseen in Ref [6], which is necessary for building a frequency dependent squeezing for the gravitational wave detectors.

The study also showed that cleaning procedures can be effective in restoring a high finesse value when mirrors’ performance degrades owing to dust contamination. Moreover, the loss distribution on the surface of the mirrors is not homogeneous and we believe this is due to the presence of dust particles.