Summary of work performed in Cates' lab at UVa: 3/10/2009-3/13/2009 Dave G. During the week of 3/10/2009 Mark Dalton and I performed several tests, building FP cavities of low to moderate finesse locked to a Coherent Verdi laser to demonstrate the "proof-of-principle" required to pursue this technology for the Hall C Compton polarimeter. In brief, we found that it was straightforward to build and lock cavities with gains > 100 with a relatively simple setup. It is not clear from our tests what the ultimate gain limit might be, but we were able to achieve cavity gains on the order of 300, albeit with a less stable lock. Some definitions of cavities: 1. CVI-Virgo mark 1: Input coupler = CVI 1 inch mirror with Rnom=98%, Radius of curvature= 1m Output coupler = Virgo 7 mm mirror Rnom=99.9%, flat Cavity length=98 cm 2. CVI-Virgo mark 2: Same as mark 1 with both mirrors more thoroughly cleaned. 3. Virgo-27: Input coupler = Virgo mirror with Rnom=99.9%, Radius of curvature=50 cm Output coupler = Virgo 7 mm mirror Rnom=99.9%, flat Cavity length=27 cm 4. Virgo-45 Same as Virgo-27, but cavity length=44.5 cm 5. Virgo-44 Same as Virgo-45, but cavity length=44 cm. 6. Virgo-REO-44 Input coupler = Virgo mirror with Rnom=99.9%, Radius of curvature=50 cm Output coupler = Research Electro-Optic (REO) mirror with Rnom=99.99%, flat length= 44 cm 7. Virgo-REO-43 Same as Virgo-REO-44, length=43 cm 8. Virgo-REO-27 Same as Virgo-REO-43, but length=27 cm The measured transmission of each mirror was as follows: 1. CVI, R=98%: Tmeas=0.0103 2. Virgo, flat: Tmeas=4E-4 (Tmeas=4.7E-4 after cleaning) 3. Virgo, rad.=50 cm: Tmeas=5.4E-4 4. REO flat mirror: Tmeas=1.5E-5 Power scaling tests: Initial measurements were performed Tuedsay, 3/10/2009 using cavity 1 (CVI-Virgo mark 1). P_verdi = nominal power out of Verdi laser P_inc = power incident on cavity input coupler P_trans = power transmitted out of cavity (locked) Gain = (P_trans/T)/P_inc P_Verdi P_inc P_trans Gain 0.1 W 27.3 mW 1.0 mW 91.6 0.2 W 56.6 mW 1.5 mW 66.3 2.0 mW (better lock) 88.4 0.5 W 145.0 mW 4.5 mW 77.6 5.0 mW (better lock 86.2 The maximum power was limited by poor transmission through the EOM (80%). This could be easily fixed with better mount. At the largest input power, the power stored in the cavity was about 12.5 W. Cavity variation tests: Next, we built a series of cavities with goal of varying the cavity linewidth, finesse, and gain. As described in Chapter 5 of R. Loewen's thesis (SLAC-R-632), from knowledge of the input and output mirror transmissions (T1 and T2), the incident power (Pinc), the power reflected from and transmitted through the cavity when on resonance (Pref and Ptran) one can extract: b = 1/(T1+T2+L1+L2) = Ptran/(Pinc*T2 + Ptran*T1-Prefl*T2) From b, the cavity finesse immediately follows: Finesse = 2*pi*b as well as the Gain: Gain = 4*T1*b**2 The total cavity loss is then 1/b and the combined mirror losses L1+L2 = 1/b-T1-T2 Finally, the laser power matched to the TEM00 mode of the cavity is: c0 = (Pinc*T2 + Ptran*T1-Prefl*T2)**2/(4*Ptran*T1*T2*Pinc) Note that c0 already accounts for the "impedence" mismatch that comes from non-optimal reflectance matching of the cavity mirrors. In principle, c0 should be 1.0 for a laser that is perfectly mode-matched to the cavity (and assuming no linewidth issues - to be discusssed later). The extracted cavity properties are listed below: Some comments: In the measurements below, some cavities were dis-assembled to check transmissions etc. and then re-assembled. That is the reason for some small changes in gemotery. In addition, the last cavity was never able to be locked "celanly", so the last entry is my estimate of the gain and coupling correcting for the noisiness of the lock. Cavity Length T1 T2 Pinc Pref Ptran b Finesse c0 L1+L2 FSR d_nu Gain Comment (cm) (mW) (mW) (mW) (%) (MHz) (kHz) CVI-Virgo mark-1 98 1.0E-2 4.0E-4 27.3 5.93 1.0 53.1 333.3 0.79 0.81 153.1 459.2 91.6 CVI-Virgo mark 2 98 1.0E-2 4.7E-4 26.8 5.93 1.6 60.9 382.4 0.83 0.57 153.1 400.29 127.0 Virgo-27 27 5.4E-4 4.7E-4 26.8 15.63 1.5 247.5 1555.3 0.90 0.30 555.6 357.2 119.1 Virgo-45 44.5 5.4E-4 4.7E-4 26.8 18.36 1.0 227.7 1430.8 0.73 0.34 337.1 235.6 81.8 Virgo-44 44 5.4E-4 4.7E-4 26.5 18.39 0.8 190.7 1197.9 0.83 0.42 340.9 284.6 65.0 Virgo-44 (clean) 44 5.4E-4 4.7E-4 26.6 17.63 1.1 228.7 1436.9 0.78 0.34 340.9 237.3 88.0 after cleaning Virgo-REO-44 44 5.4E-4 1.4E-5 26.6 15.00 0.10 462.1 2903.5 0.58 0.16 340.9 117.4 268.5 noisy lock Virgo-REO-43 43 5.4E-4 1.4E-5 26.6 12.40 0.13 483.3 3036.5 0.69 0.15 348.8 114.9 349.1 clean lock, after cleaning REO Virgo-REO-27 26.7 5.4E-4 1.4E-5 26.6 14.24 0.12 507.6 3189.3 0.58 0.14 561.8 176.15 324.9 noisy lock Virgo-REO-27* 26.7 5.4E-4 1.4E-5 26.6 12.40 0.14 507.1 3186.0 0.67 0.14 561.8 176.33 372.68 estimated Finally - from the above c0 values I attempted to extract the intrinsic linewidth of the Verdi laser. At various points, Mark and I estimated the amount of power unable to couple into the cavity due to improper mode matching. For the 1 m cavity, this was on the order of 20%, while for the shorter cavities, it seemed to be more like 10%. Correcting the c0 values above for the mode-match mis-coupling, one can assume that the residual is due to the intrinsic linewidth of the laser being to broad to couple to the cavity. Without going into the details, I estimate the laser linewidth to be on the order of 130 kHz.