LIGO SURF Report: Three Input Matching/Driving System for Electro-Optic Modulators

Transcription

1 LIGO SURF Report: Three Input Matching/Driving System for Electro-Optic Modulators Lucas Koerner, Northwestern University Mentors: Dr. Dick Gustafson and Dr. Paul Schwinberg, LIGO Hanford Abstract LIGO Interferometers use three consecutive Electro-Optic Modulators (EOMs) to introduce radio frequency sidebands onto the 1064nm wavelength laser. EOMs are optically intrusive and result in decreased laser power and increased optical distortion. To modulate at all three frequencies using one EOM we have developed a tunable LC circuit with voltage step-ups of 11.5, 8, and 1.5 at 26.7 MHz, 29.5 Mhz, and 68.8 MHz, respectively. The circuit has been shown to be effective by driving a broadband EOM, modulating a laser beam, and quantifying the sidebands with an Optical Spectrum Analyzer. 1. Information and Introduction This paper has been divided into two sections. The first, Information and Introduction, explains the aspects of LIGO that are relevant to this project. The second, Completed Work, discusses the work accomplished and the methods used. LIGO and Exploration with Sidebands Gravitational wave interferometers search for gravity waves from astrophysical sources, such as inspiraling binary systems, by detecting the strain upon the detector arms. This strain is measured by a phase shift in the laser light. The LIGO interferometers in Livingston, LA and in Hanford, WA maximize the sensitivity of the instrument to waves by extending the length of the arms to 4 kilometers. This length is not enough; by estimating the properties of the known astrophysical sources it is found that a simple Michelson interferometer requires a length of 10 5 m to 10 7 m, infeasible for an earth-based detector (1). Consequently, arm folding schemes have been developed to essentially multiply the effective length of the detector arms. The first folding scheme, a delay line, aligns many mirrors to expand the transverse dimension of the arms allowing the light to zig-zag back and forth many times. This folding technique is modified in the Harriot delay line by using two large curved mirrors rather than many smaller mirrors. Unfortunately, gravitational wave strength estimates require impractically large mirrors (2). A second folding technique, the Fabry-Perot cavity, traps laser light within two small mirrors, but, unlike the Harriot delay line, does not spatially seperate the light upon subsequent round trips of the cavity. The power within the cavity grows when the length of the cavity matches an integer number of the light wavelengths. Maintaining the length of the cavity to match the frequency of the laser presents a problem as the power of the light is symmetric about cavity resonance making it impossible to distinguish between too long and too short. The functionality of the Electro- Optic Modulators ensues here as the RF sidebands created by the modulation are used by the Pound-Drever-Hall locking technique. The combination of the RF sidebands with the carrier leaking from the cavity creates a measurable beat pattern from which the phase relation be-

2 2 tween the incident and reflected carrier beams can be determined (3). The RF sidebands are also used by the Length Sensing Control, which measures a gravity wave signal by an RF extraction technique (4). Electro-Optic Modulators The refractive index of the MgO : LiNbO 3 crystal of an EOM changes, in response to a drive voltage, V. An index of refraction change modifies the optical path length and results in a phase change, φ, given by: φ = πn3 0 rv λ l d, (1) with n 0 as the index of refraction at zero applied voltage, λ the laser wavelength, d the electrode seperation, and r the appropriate element of the Electro-Optic tensor (5). Applying a sinusoidal voltage leads to a phase modulation of φ(t) = Γ sin(ωt), where Ω is the frequency of modulation and Γ is the modulation index found from the parameters in Eq. 1. A phase modulation of a carrier, E 0 e iωt, may be expanded into discrete frequency components of ω ± kω using ordinary Bessel Functions: [ ] E 0 e iωt J k (Γ)e ikωt + ( 1) k J k (Γ)e ikωt k=0 k=0 (2) If Γ << 1, Bessel Functions above first order are assumed zero; hence, we have an approximation involving only the carrier and first order sidebands of frequency ω ± Ω (sums up to and including k = 1 in Eq. 2). EOMs exist in two forms: resonant and broadband. The resonant modulators are set to operate at a specific modulation frequency by the installation of an inductor to cancel the capacitance of the crystal and a transformer to match the impedence to 50 Ω (5). Broadband modulators lack a matching network and are a load of 20 pf with losses measured to be.36 Ω. Broadband modulators, because of the lack of impendence matching, require a higher drive voltage than resonant EOMs for equivalent modulation depths. Our goal is to develop an RF matching network to allow driving of a broadband EOM at reasonable levels of input voltage at all three sideband frequencies. Passing the laser through one EOM as opposed to three will reduce laser losses and distortions. 2. Completed Work With the rationale now explained the methods and results of the project are developed. RF Drive Circuit We created a general backbone upon which to design our three-frequency matching network. The concept, after unsuccessfully working with transformers, was to create a pi-network for each frequency isolated from the other frequencies to match the impedence of the EOM with 50 Ω. Knowing that the 29.5 M Hz modulation requires the most modulation depth while the 68.8 MHz the least we have willingly sacrificed the voltage step-up of the 68.8 M Hz path. The design involves series resonating inductor-capacitor (LC) combinations for both the 29.5 MHz path and the 26.7 MHz path. The series resonance of the 29.5 MHz path is tuned to 29.5 MHz while the series resonance of the 26.7 MHz path is detuned down to approximately 23MHz. Both the 29.5 MHz and 26.7 M Hz paths pass through a parallel res-

3 3 onator at 68.8 MHz which is in place to isolate the 68.8 MHz drive from the series resonances. An inductor set to resonate both the 29.5 MHz path and the 26.7 MHz path (this path transfers some inductance because it is detuned) is placed adjacent to the EOM. In order for the 68.8 M Hz path to resonate, extra capacitance is inserted before the inductor. This additional capacitance limits the step-up for the 68.8 M Hz path. The circuit design was optimized by modeling with the computer program Spice. This software tool proved invaluable as it accounted for interaction between paths as well as power dissipation in drives. During the optimization process we calculated and accounted for the losses of the inductors, Q = X r, where X is the reactance in ohms and r is the series resistance of the inductor (iron-powder torrodial core Q-values taken from ref 6). See Appendix for circuit design. The frequency triplexer was made tunable by applying tunable capacitors to all values of capacitance associated with a resonance. This is necessary because the winding of cores is inexact. By measuring the frequency response of the voltage across the EOM unobtrusively we tuned the capacitors to position the resonance peaks on frequency (see fig 1). Unobtrusive measurements that add very little stray capacitance are necessary to accurately measure the frequency response (wire-wrap around output to EOM, active probes on wire-wrap, active probes to network analyzer). The magnitudes of the voltage step-ups were measured at 11.5 for 26.7 MHz; 8 for 29.5MHz; and 1.5 for 68.8MHz (see fig 2) Voltage Across EOM Arbitrary Voltage (V) x 10 7 Fig. 2. Measurements of Voltage across the EOM with an input of 1 V. Solid line, dashed line, and dashed and dotted line are frequency sweeps of the 29.5 MHz, 26.7 MHz, and 68.8 MHz drives respectively. Because of the obtrusiveness of the active probes resonance peaks are slightly detuned in frequency x 10 7 Fig. 1. Measurements determining frequency of resonance peaks taken by probing with wire-wrap to active probes to Network Analyzer. The neccessity for unobtrusive measurements (very low applied capacitance) relegates the magnitudes meaningless. Solid line, dashed line, and dashed and dotted line are frequency sweeps of the 29.5 MHz, 26.7 MHz, and 68.8 MHz drives respectively. From left to right X corresponds to frequency of: MHz, MHz, and MHz. We have encountered problems with the 26.7 M Hz drive dissipating power into the 29.5 M Hz drive because of the proximity of 29.5 M Hz and 26.7 M Hz. To force the 29.5 MHz path to be high impendence at frequencies other than 29.5 MHz we have designed the series resonance with a high L to C ratio. A series resonator has a maximum impendence away from resonance when the L to C ratio is high. This has cut the power dissipation from the 26.7 MHz drive into the 29.5 MHz drive to.075 of the total input power (see fig 3).

4 New Focus Inc. specifications list V π = V for resonant EOMs Voltage across 29.5MHz drive Voltage from Photodiode(V) x 10 7 Fig. 3. Measurement of Voltage across the 29.5 MHz drive with an input of 1V from the 26.7 MHz drive. Power, αv 2, dissipated is.075 of the input power. Quantification using a scanning Fabry-Perot cavity Passing a 500mW laser through a broadband EOM driven by the frequency tri-plexer allows quantification of the optical sidebands created. The modulated beam, directed by two steering mirrors, enters a Fabry-Perot cavity with one mirror driven by a piezo-electric transducer, which scans the values of frequency resonate in the cavity. The output of the cavity seen by an amplified photodiode is measured by an oscilloscope triggered to the motion of the PZT. The fractional power and modulation index are calculated by measuring the voltage of the 3 pairs of sidebands and carrier. The relation between fractional power and modulation index is given by, P frac = 1 4 Γ2. The voltages are measured by importing traces from the oscilloscope to Matlab. Relevant calculations, fractional power, modulation index (Γ), and V π are displayed in Appendix Table 1. V π, the drive voltage required for a π phase shift, allows a comparison between our matching network and that in resonant EOMs. Our matching network compares well at 26.7 MHz and 29.5 MHz as the Arbitrary Fig. 4. An Oscilloscope trace showing the optical spectrum of the laser beam after being modulated by a broadband EOM driven by the triplexer. From left to right the blips correspond to: 68.8 MHz sideband, 29.5 MHz sideband, 26.7 MHz sideband, 1064 nm carrier, 26.7 MHz sideband, 29.5 MHz sideband, 68.8 MHz sideband. The broadness of the blips is an artifact of the resolution of the scanning Fabry-Perot Cavity. Acknowledgements I would like to thank mentors Dr. Richard Gustafson and Dr Paul Schwinberg for their guidance and wonderful attitudes. In addition, I am indebted to Josh Meyer and Richard Mc- Carthy for invaluable help in the Electronics Lab, as well as Doug Cook and Richard Oram who were integral to the setup of the scanning Fabry-Perot cavity. This summer work was supported by the California Insitute of Technology, the National Science Foundation, and LIGO. REFERENCES [1]Sigg, D. Gravitational Waves. LIGO-P D [2]Saulson, P. Fundamentals of Interferometric

5 5 Gravitational Wave Detectors. World Scientific [3]Black, E. An Introduction to Pound-Drever- Hall laser frequency stablization. Am. J. Phys [4]Schnupp, L. Talk at a European Collaboration Meeting on Interferometric Detection of Gravitational Waves [5]New Focus Inc. Practical Uses and Applications of Electro-Optic Modulators [6]Amidon Associates Inc. Product Guidebook. January This preprint was prepared with the AAS L A TEX macros v5.0.

6 6 3. Appendix Table 1: Frequency (MHz) Drive (V pp ) Amp (V ) Frac. Power Mod. Index (Γ) V π Carrier N/A 2.46 N/A N/A N/A

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