Transcript G060319-00
Some Ideas on Coatingless all-reflective ITF Adalberto Giazotto (*) INFN- Pisa (*) Work done in collaboration with G. Cella Why Total Reflecting Mirrors? Experimental data from Yamamoto and Numata show a very high coating loss angle even at low temperature. d w0 MIRROR EC/EB=d/w0~10-4 16k BT ( Bulk ~ xTotal ( ) EC Coating ) EB 1 / 2 E 1 / 2 w01 / 2 Total Bulk Q 1 Total EC E Coating ~ C Coating ~ 410 8 EB EB ~ 2.510 7 The Virgo design Thermal noise curve is evaluated with a Q~106, and the maximum expected Q, due to coating losses, is Q~2.5 107. Standard Quantum Limit is about a factor 100 below Virgo TN i.e. equivalent to a Q=1010 ; consequently, for reaching SQL sensitivity Q should improve by 1010/ 2.5 107~ 400- For this reason it is interesting to explore Coating-less Mirrors This argument will become even more important if we want to go below SQL. h(f) [1/sqrt(Hz)] -12 10 -13 10 -14 10 -15 10 -16 10 -17 10 -18 10 -19 10 -20 10 -21 10 -22 10 -23 10 -24 10 -25 10 -26 10 -27 10 Total Seismic Noise Newtonian (Cella-Cuoco) Thermal Noise (total) Thermal Noise (Pendulum) Thermal Noise (Mirror) Mirror thermoelastic noise Shot Noise Radiation Pressure Quantum Limit Wire Creep Absorption Asymmetry Acoustic Noise Magnetic Noise Distorsion by laser heating Coating phase reflectivity 1 ~ hSQL LΩ M Virgo 28-3-2001 http://www.virgo.infn.it/ [email protected] 1 10 100 Frequency [Hz] 1000 10000 Rotation Parabolas as exact reflectors for closed geometrical optical trajectories y y 1 L x2 z2 2L 2 y x L/2 L x z y 1 L x2 z2 2L 2 No Beam Losses The spherical mirror surface is matched to the constant phase beam surface curvature Rotation Parabolas as reflectors for closed geometrical optics trajectories y x2 z2 y x 2L y L b 2b a x a L L L/2 L b y L x b a ax L x2 z2 y x 2L A Parabolic Reflector at distance L is equivalent to a spherical mirror with curvature radius L/2 Reflective cavity with Asymmetric Arms y L1 L2 x Cavity Beam Injection One of the main problems we faced was to find the way to inject a beam in the All Reflective Cavity. Tunnel Effect injection and extraction Parabolic Roof Prism Transverse cavity injection and extraction Corner Cube (V.Braginsky et al.) Example of Power Injection in a Parabolic Coatingless all-Reflective Cavity Lost Light Beam Splitter LASER Conventional BS: Light Losses Closed trajectories inside BS : No Light Losses Beam Splitter Total Reflection A REALISTIC CAVITY L1 -R3,T3 R3,T3 e d L4 f R4,T4 b L3 C g L2 U e i -R1,T1 R1,T1 α Some Peculiar Properties-1 If channel L3-L4 is antiresonating 1)Then U U 0 i.e. Thermal L3 L1 M3 W -R3,T3 R3,T3 f R4,T4 noise of mirror M3 does not affect U. Hence for stopping input of vacuum we can use a normally coated mirror 2)Consequently the amplitude C=0. i.e. there is no power on M3 3)Since U e i the Finesse F, i U defined as F , L1 2 e becomes F d L4 L4 b L3 C 2 . 2 R1 g L2 U e i -R1,T1 R1,T1 α U L1 2 Some Peculiar Properties-2 If channel L3-L4 is out of antiresonance with a small phase offset then 2 2 1 R1 2 4 )... 0 L 1 O ( c 1 R12 1 R12 2 1 R 2 1 2 4 O( )... 0 L c 2 4 1 R12 while C becomes i 1 R12 C O( 3 )... 1 R12 L1 M3 W -R3,T3 R3,T3 e L4 f R4,T4 L3 d b C These two equations seem to have important consequences. g L2 U e i -R1,T1 R1,T1 α Silica Reflectivity R1 Brewster angle θin L1 M3 W -R3,T3 R3,T3 e L4 f R4,T4 L3 d b C g L2 θin U e i -R1,T1 R1,T1 α DISCUSSION By considering that R12<<1, by stopping expansion to χ2 terms and by putting in evidence F 2 , we obtain: R12 2 R12 2 1 R1 1 R 2 0 2 2 2 0 1 1 L1 R1 L4 2 2 c c 1 R 1 R 2 1 1 This equation shows that we may change the finesse by the factor ΔF=1+ χ2 and still the phase shift due to thermal noises of M3 in L4 is 2 2 R1 depressed by the factor 1 because R12<<1. 2 1 Then it seems that in this cavity system we may change finesse, and consequently storage time, without affecting : 1)Thermal noise from channel L3-L4, which for χ2=0 is zero. 2)Cavity geometry. The independence of geometry from finesse seems to be a very important feathure of this system. 3 km Variable Finesse M. Recycling M. BS Thermal Noise With this optical configuration it is evident that every photon traverses a large amount of material; here the problem is transferred from normal mirror reflective coating bad loss angle to thermorefractive noise (TRN) of coatingless cavity. TRN spectral density is: 16Lbulk k BT 2 2 S 2 2 2 4 C w 0 Where: Lbulk is the thickness of traversed material,w0 the beam waist, ρ the bulk density, κ the bulk thermal conductivity coefficient, λ the wavelength, C the bulk thermal capacity and β is: 2 n 1 n 2 1 1 n T 6n p p T 3 1 p p Where αp is the bulk polarizability, n the bulk refractive index and α is the bulk linear thermal expansion coefficient. We tried to find data on β at different temperature and we only found 300K data for Silica, which has large C and small κ. Silica 300K Data for Sapphire give bad results since C is small and κ is very large compared with Silica Cristaline Quartz could be a good candidate for going to low temperature but we could not find any data. Conclusions This coatingless optical configuration has some interesting feathures: 1) Since all the surfaces are optically matched, antireflective coatings are not needed. 2) Power can be injected in the cavity in a straightforward way; use of tunnel effect injection or transversal cavity are unecessary. 3) The optical scheme can be made with variable finesse. This property can alsobe applied also to “normal” mirror configuration. It is evident that the draw back is the Thermo Refractive noise; an investigation for selecting cristaline bulks with low thermal conductivity and large thermal capacity is instrumental.