and Tricks for Experimentalists: Laser Stabilization

Tips and Tricks for Experimentalists: Laser Stabilization Principle T&T: Noise spectrum of the laser Frequency Stabilization to a Fabry Perot Interferometer (FPI) Principle of FPI T&T: Preparation, noise free mount; measurement of finesse Side of Fringe Lock T&T: Generation of error signal, locking range Hänsch Couillaud Method (Pound) Drever Hall Technique T&T: RAM, Servo Electronics Frequency stabilization to absorbers Stabilization to weak signals T&T: 1st, 2nd, 3rd harmonic generation, NICE Ohms Research Training Group 1729 Fritz Riehle; Lecture: June 5, 2014

Schematic of a laser frequency stablization Atomic absorbers or macroscopic frequency filter ν ν = ν 0! Fig. 11.278 from J. Helmcke & F. Riehle: Frequency Stabilization of Lasers in: Springer Handbook of Lasers and Optics 2nd ed.; Editor: F. Träger (2011)

Dye laser, Diode laser, Gas laser, Solid state laser, Widely tuneable laser sources All lasers have specific (different) noise power spectral densities (PSD) Tip: Know about the PSD of your laser PSD of dye laser ( ) and HeNe ( ) From F. Riehle: Frequency Standards Basics and Applications; Wiley VCH (2004)

Trick: Measurement of frequency fluctuations (Recall lecture by Uwe Sterr) From F. Riehle: Frequency Standards Basics and Applications; Wiley VCH (2004) Trick: How to discriminate between amplitude fluctuations and frequency fluctuations? (1. check contributions of AM (how?); 2. if too high -> apply intensity stabilization)

Trick: Method to reduce the PSD in a diode laser

The Fabry Perot interferometer

Fabry Perot interferometer is used for wavelength measurement for frequency stabilization of lasers The Fabry-Perot interferometer

Laser stabilization to FPI L Laser λ 2 mirrors with high reflectivity = optical resonator If L = m λ / 2 holds, then transmitted light can be used to stabilize the laser frequency to a suitable resonance of the FPI! But: Δν/ν = Δλ/λ = ΔL/L

Which effects can change the (optical) length? Optical length variation Trick: Vacuum housing (air pressure) Aging Trick: low drift material, crystal Thermal length variation Tricks: temperature stabilization to <1μK; temperature independent material Vibrations, acoustics, seismics Tricks: active vibration isolation to <1μg; ideal mounting Brownian motion Tricks: glas > crystal, cooling

Aging of an FPI

Properties of FPI materials ΔL = α L ΔT measure of the stiffness of a material Ε = stress/strain = F/A / ΔL/L

Measurement of seismic noise From thesis Ch. Hagemann, 2013 University of Hannover

Thermal expansion of Si K.G. Lyon and G.L. Salinger and C.A. Swenson and G.K. White, Linear thermal expansion measurements on silicon from 6 to 340 K, J. Appl. Phys., (1977), 48, 865 868. J. P. Richard and J. J. Hamilton, Cryogenic monocrystalline silicon Fabry Perot cavity for the stabilization of laser frequency, Rev. Sci. Instrum. 62, 2375 2378, (1991).

Optimizing the cavity mounting 4 point support from below finite element simulation: 0.2 1 2 3 4 5 6 0. 3 0. 2 0. 1 a y (m/s 2 ) Δν beat (khz) 0.0-0.2 8 4 0-4 120 khz/ms -2 0 5 10 15 0. 0-0.1-0.2-0.3 8 4 0-4 The spacer is held in its horizontal symmetry plane a = 10 m/s 2 deformations magnified by 10 7-8 0 5 10 15 t (s) 0.2 0 2 4 6 8 10 0.3 0.2 0.1-8 a y (m/s 2 ) 0.0-0.2 0.0-0.1-0.2 z Δν beat (khz) 80 1 2 3 4 5 4 0-4 1.5 khz/ms -2-0.3 8 4 0-4 T. Nazarova, F. Riehle, U. Sterr, Appl. Phys. B 83, 531 536 (2006) -0.1 nm uz 0.1 nm -8 improvement by factor 100 0 1 2 3 4 5 t (s) -8

Measured clock laser instability 10-12 Combined instability of two clock lasers, stabilized to reference cavities. Laser linewidths 1 Hz σ y ( 2, τ ) 10-13 10-14 10-15 laser phase noise thermal noise in the cavity mirrors cavity drifts 0,01 0,1 1 10 100 1000 integration time, s

Thermal noise fundamental limit to length stability S x (f) due thermal fluctuations (Brownian motion) spacer mirror substrates coatings Σ 2k T S spacer = π f S substrate L 3π R B ( f ) ϕ 2 spacer 4k T π f B S coating ( f ) = d 2 cϕcoating E 2 2kBT 1 σ ( f ) = ϕ π f π Ew (1 + σ )(1 2σ ) πew ULE spacer (L=100 mm) and mirrors 0 0 substrate 2 10 4 10 2 10 m Hz m Hz m Hz 10 18 2 17 17 0.2 Hz Hz Hz Hz Hz 0.08 Hz 2 2 ν σ ν = 2ln(2) 2 L S x ( f ) f σ ν = 0.4Hz K. Numata, A. Kemery and J. Camp, Phys. Rev. Lett. 93, 250602 (2004) Possible improvements: long spacer reduces everything larger waist materials with lower loss ϕ = 1/Q

Mechanical line quality factor Q Si (111) crystalline quartz fused silica Measurement of the mechanical Q factor at cryogenic temperatures R. Nawrodt, A. Zimmer, S. Nietzsche, W. Vodel, P. Seidel

Single crystal Si (111) (111) for the cavity axis: the largest Young s modulus. Top of the cavity 3 fold rotational symmetry Three supporting points in the horizontal plane: Poisson ratio can be reduced from 0.4 to 0.048.

Measurement of the finesse by decay time of energy in FPI

Side-of-fringe stabilization Pros: Simple to implement Lock point is largely independent of laser intensity fluctuations Cons: Lock point does not coincide with the center of resonance (defined by the attenuator) Lock point is not very stable against coupling to frequency reference Capture range isveryasymmetric

Generation of an error signal by square wave modulation

Generation of an error signal by harmonic frequency modulation

Hänsch-Couillaud Stabilization Finesse is different for different polarizations. Ellipticity changes near resonance. T. W. Hänsch and B. Couillaud, Laser frequency stabilization by polarization spectroscopy of a reflecting reference cavity, Opt. Commun. 35 (3), 441 (1980) (Hänsch Couillaud technique)

Error signal of the Hänsch Couillaud Pros: Simple to implement inexpensive Cons: Lock point is sensitive to baseline drift of the error signal Lock point is affected by technical laser noise at low Fourier frequencies

Frequency stabilization of a laser to an FPI Pound Drever Hall stabilization Drever, Hall et. al. Appl. Phys. B 31 (1983) 97 1005

Electro-optic modulator as phase modulator For δ < 1 only carrier and the first order sidebands remain

Frequency stabilization of a laser to an FPI Pound Drever Hall stabilization Drever, Hall et. al. Appl. Phys. B 31 (1983) 97 1005

Double-balanced mixer D4 D1 LO D3 D2 RF

PDH: dispersive and absorptive signals

Maximizing the error signal

Electronic stabilization scheme

Servo design for an ultrastable laser multiple integrators high gain at low frequencies, where the perturbations are largest 40 db/decade db/decade leads to phase shift ~ 270 at lower frequencies no problem for stability, as long as phase margin at unity gain (~ 3 MHz) OK loop gain (db) db/decade db/decade poor transient behaviour to lock, first use fewer and gain limited integrators frequency (Hz) db/decade db/decade From Uwe Sterr s lecture ((does not exactly correpond to the stabilization scheme before)) H. Stoehr, PhD Thesis (2004)

Laser frequency stabilization out of loop error spectrum Servo Bump noise increases around unit gain frequency noise will further increase and finally system oscillates there with increasing gain From Uwe Sterr s lecture H. Stoehr, F. Mensing, J. Helmcke and U. Sterr, Diode Laser with 1 Hz Linewidth, Opt. Lett. 31, 736 738 (2006)

Beat note between two independent diode lasers 1,0 relative optical power 0,8 0,6 0,4 0,2 1.5 Hz FW HM resolution BW: 1 Hz acquisiton time 4 s 0,0-20 -10 0 10 20 Δν(Hz) H. Stoehr, J. Helmcke, F. Mensing, U. Sterr, Opt. Lett. 31, 736 738 (2006)

Residual Amplitude Modulation (RAM) The delicate balance of a perfectly phase modulated laser field can easily be destroyed by the temperature dependent birefringence variation of the phase modulator crystal, scattering and etalon effects due to the crystal and other reflective surfaces, vibration of the optical table and mounts, spatial inhomogeneity of the rf electric field amplitude fluctuation of the rf power, frequency fluctuation of the laser. AM disappears if the crystal is rotated or by applying a dc voltage to the crystal, in addition to the rf modulation voltage

Residual amplitude modulation - Stabilization Fig. 1. Experimental scheme for active RAM stabilization. After passing through the phase modulator, a portion of the light is detected by PD1 for active RAM control, and PD2 is used for PDH signal and out of loop RAM measurement. EOM, waveguide based electro optic modulator; VRF, RF signal for phase modulation; VDC, direct current field applied to EOM for active RAM cancellation; IP, in line polarizer; P, freespace polarizer; BS, beam splitter; PBS, polarization beam splitter; HW, halfwave plate; QW, quarter wave plate; ISO, optical isolator; PD, photodetector; DBM, double balanced mixer; I(Q) mixer in phase (quadrature) port; φ, phase shifter; SA, spectrum analyzer; LO local oscillator (10.5 MHz); LF, loop filter; FFT, fast Fourier transform (FFT) analyzer. W. Zhang et al: Opt. Lett. 39, 1980 1983(2014) Collaboration JILA, PTB, Vienna

RAM suppression: Results Fig. 2. (a) RAM reduction realized with the active cancellation scheme. The power spectrum of the in-loop RAM signal received by PD1 is recorded on a spectrum analyzer with 100 Hz resolution bandwidth. The RAM signal with active servo on (red line) is 56 db lower than that without servo (black line). Blue line, shot noise floor. This remaining RAM is stable at the 3% level. (b) Left axis: power spectral density (PSD) of the out of-loop RAM fluctuations, i.e., off-resonant PDH signal obtained from PD2. The noise corresponding to RAM with active cancellation (red and green lines) is approximately 20 times lower than the result without servo (black line) at 1 Hz. At low Fourier frequencies, simultaneous in-phase and quadrature servos (red line) achieve better stability than that with only in-phase servo (green line). The noise floor (blue line) is set by the shot noise of PD2. Right axis: corresponding PSD of the frequency noise for the cavity-stabilized 1.064 μm laser. The voltage noise is converted to frequency noise by the slope of the cavity frequency discrimination.

Stabilization to a weak absorption signal Molecules have plenty of absorption lines (due to vibration,or rotation) Overtone (ν 1 + ν 3 mode) Overtones are weak and highly sensitive means of detection are necessary

Iodine stabilized He-Ne laser weak absorption Trick: Use build up resonator Small line on sloping Background Wavelength standard for the realization of the Meter Trick: Use 3rd harmonic detection

Trick: Third and higher harmonic techniques Output power is modulated Taylor expansion gives: sin 3 ω contains terms with sin (n ω) d 3 P L (ω)/dω 3 removes linear and quadratic background

Trick: NICEOHMS (Noise Immune Cavity Enhanced Optical Heterodyne Molecular Spectroscopy) J. Ye. L S Ma and J. Hall; Opt. Lett. 21 1000 1003 (1996) External build up resonator for absorption cell. High Finesse leads to low sideband power and any frequency fluctuation leads to high AM limiting the sensitivity Trick: Use modulation frequency to match the free spectral range