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Recently, a simple common-path, two-color interferometer has been used for Doppler-free saturated dispersion spectroscopy of iodine. We have used such a set-up to stabilize a Nd:YAG laser for the first time, to our knowledge. This method requires only a small number of low-cost optical components compared to frequency modulation techniques. We have measured a root Allan variance of 5·10-12 for 0.2 s, and below 5·10-11 for integration times up to 300 s.
©2004 Optical Society of America
1. Introduction
Optical laser interferometers are used for a wide range of precision industrial and scientific applications, e.g. surface analysis, length calibration, spectroscopy and frequency standards. The measurement accuracy of these applications strongly depends on the frequency stability of the light source. Thus, monolithic, non-planar Nd:YAG ring lasers are widely used due to their intrinsic high frequency stability properties. If even higher stability requirements have to be fulfilled, the laser frequency can be actively stabilized to optical cavities or molecular resonances [1, 2, 3]. This is commonly achieved by modulation of the laser frequency. Modulation-free stabilization methods have come into use [4, 5], and have the advantage of simplicity and a low-cost optical set-up compared with traditional frequency modulation methods. An error signal is produced by two phase-shifted signals generated from the same reference source.
Matsumoto and Honda [4] have described a simple, modulation-free stabilization technique for a Nd:YAG laser using a common-path, two-color interferometer, which consists of two nonlinear crystals and an iodine cell. The interferometer output provides a Doppler broadened dispersion signal of the iodine absorption spectrum. The authors report relative frequency stability of a few 10-8 for integration times up to 4000 s. Hong et al. have used a modified version of the common-path, two-color interferometer to resolve hyperfine components of iodine with saturation spectroscopy [6]. The measured dispersion signals of the R(56)32-0 iodine line show high signal-to-noise (S/N) ratios, and they were suggested for a simple, Doppler-free Nd:YAG laser frequency stabilization.
In the present paper, we report on the first frequency stabilization of a Nd:YAG laser using the latter method. We describe the generation of error signals and our experimental set-up. Afterwards, we present our experimental stabilization results. We have measured the beat frequency between our laser system and a stable reference laser. From the beat frequency time series, we have calculated the frequency noise spectral density and the root Allan variance for the unstabilized and stabilized laser system. Finally, we discuss a number of noise sources that influence the error signal.
2. Experiments
The simple configuration of the common-path, two-color interferometer and the frequency stabilization set-up are shown schematically in Fig. 1. The interferometer consists of a wedged, periodically poled Potassium Titanyl Phosphate (PP:KTP) crystal for frequency doubling, an iodine cell, a highly reflective mirror and two inexpensive biconvex lenses (f 1=100mm, f 2=50mm) for mode matching. The light entering the interferometer is focussed into the PP:KTP crystal by the first lens, and second harmonic, green light is generated. Both infrared (IR) and green radiation are collimated sufficiently by lens two (an achromatic lens is not necessary), traverse the iodine cell and are reflected by the mirror M1. The second harmonic light leaving the crystal and the counter-propagating green light reflected from the mirror act as pump and probe beam for saturation spectroscopy. While the green light probes the hyperfine components of the iodine lines, the IR light is almost unaffected by the iodine. It serves as a phase reference and again generates green light on its second pass through the PP:KTP crystal. This second harmonic wave interferes with the green light containing the spectral iodine information. Scanning the laser frequency over iodine resonances yields a sub-Doppler dispersion spectrum at the interferometer output [6].
Fig. 1. Schematic of frequency stabilized Nd:YAG laser with a common-path, two-color interferometer. For further details see text.
Relative phase control between the two second harmonic waves was achieved by transversal translation of the PP:KTP crystal with a micrometer stage. The 5 cm long iodine cell (from the Physikalisch-Technische Bundesanstalt, Germany) had Brewster windows. Its cold finger temperature was set to 15°C. A dichroitic mirror (HR 532 nm, HT 1064 nm) was used to separate the fundamental and second harmonic light leaving the interferometer. A Schott BG39 band-pass filter absorbed residual IR laser light before the interferometer output signal was detected by a silicon photodiode.
We have used a commercial, monolithic non-planar Nd:YAG ring laser (Mephisto 2000NE, Innolight GmbH) which emitted up to 2W single frequency laser power in fundamental mode (TEM00). The laser frequency was varied by changing the crystal temperature, or by applying a voltage to a piezoelectric transducer (PZT) which was glued to the laser cavity. An internal intensity stabilization called noise eater reduced the laser relaxation oscillation. An optical isolator was placed between the laser and interferometer to suppress IR optical back reflections and ensure stable single frequency laser operation. Frequency doubling was achieved with an AR coated 5 mm long PP:KTP crystal (poling period 2Lc=9µm) that was mounted on a temperature stabilized copper mount (phase matching temperature 33.0°C). The PP:KTP crystal (manufactured by Raicol Crystals Ltd.) has the advantage of a higher doubling efficiency in comparison to a conventional KTP crystal, as it was used by Hong et al. [6]. We measured 1.8mW of second harmonic power in single-pass from 1.2W IR laser power. Only less than 1% of the IR laser power was used for frequency stabilization and the rest of the fundamental light can be separated behind the interferometer and used for other applications.
Figure 2 shows the modulation-free dispersion signal of the a 1 component of the R(56)32-0 iodine line. We measured this signal by scanning the laser frequency with the PZT and recording the bandpass-filtered (f=100-1000Hz) signal of photo detector 2. A sawtooth voltage ramp with 42Vpp amplitude was applied to the PZT with a frequency of 37.9 Hz, which resulted in a laser frequency shift of 134.4 MHz. For calibration of the PZT efficiency of 3,2 MHz/V, we used the published frequency seperation for the a1 and a5 component of the R(56)32-0 iodine line [2]. The linewidth of the a1 component of the R(56)32-0 line was dominated by pressure broadening and was measured to be 4.3 MHz. The signal to noise (S/N) ratio was 48 in a 900Hz measurement bandwidth. The other hyperfine components were also observed, whereas the closely spaced a 3/a 4 components were unresolved. These dispersion signals were comparable to reference [6]. Due to the high-pass filtering, they cannot be used as an error signal for frequency stabilization. The bandpass filter has to be replaced by a low-pass filter. Otherwise, low frequency drifts of the laser cannot be detected. Removing the high-pass filter and keeping all other values fixed decreases the S/N ratio. This can be seen in the dispersion signals in Fig. 3 that were only measured with a low-pass filter (cut-off frequency of 1 kHz). Fig. 3 shows 15 hyperfine components of the R(56)32-0 iodine line. The horizontal lines in (a), (d)-(f) are due to the limited input voltage range of the digital oscilloscope. The a 11/a 12 and a 13/a 14 are unresolved, due to the removed high-pass filter. The S/N ratio of the a 3/a 4 component was 13 instead of 61 for the bandpass-filtered signal. A voltage adder was used to shift the dispersion signal of the a 3/a 4 component to zero. Its absolute level was dependent on the laser power, which was not sufficiently stable (1% power stability) to use the error signal for frequency stabilization. Therefore, we used a low-frequency intensity stabilization for the IR laser light, and increased the cut-off frequency of the laser internal AC intensity stabilization to 1.5 kHz so that both control loops did not disturb each other. A small portion of laser light was detected by a temperature stabilized silicon photodiode as shown in Fig. 1. The detector signal was used to act on the pump laser diode current of the Nd:YAG laser. This improved the long-term stability of the laser (measured out of loop) by one order of magnitude, and the relative intensity noise (RIN) was 10-6 at 10Hz and 4·10-5 down to 0.1 Hz.
Fig. 2. Bandpass-filtered modulation-free dispersion signal of the a 1 component of the R(56)32-0 iodine line.
The low-pass filtered signals shown in Fig. 3 were used as error signals for the frequency servo. Two integrators with cut-off frequencies of 1 kHz and 100 Hz generated an actuator signal for the PZT. To increase the dynamic range of the frequency control loop, we used a second control loop that acted on the crystal temperature. This slow loop (compared to the PZT loop bandwidth) contained an integrator with a cut-off frequency of 0.2 Hz and kept the PZT voltage close to zero. We have measured a unity gain frequency of 1 kHz and a sufficiently large phase margin of 37°. We have also calibrated the error signal: When the laser frequency was locked to the a 3/a 4 component, the error signal slope was 0.23 V/MHz.
Fig. 4. Time series of the beat frequency of the stabilized and unstabilized Nd:YAG laser (a). Stabilized laser frequency measurement on a fine frequency scale (b).
3. Results
We have measured the beat frequency between our laser and the stable reference. The reference system consisted of a Prometheus 10 Nd:YAG laser by Innolight GmbH that emitted the fundamental mode at 1064nm and the second harmonic frequency. The reference laser was stabilized to molecular iodine with the third harmonic technique [7]. The system was built, and its stability was verified by the Physikalisch-Technische Bundesanstalt (Braunschweig, Germany). The root Allan variance is σ(2,τ)≤2·10-13 for integration times 1 s≤τ≤200 s.
The beat frequency between the two stabilized laser systems was measured with an InGaAs photodiode and a frequency counter connected to a computer. The maximum sample frequency was 5 Hz, limited by the data rate to the computer. Fig. 4 shows the time series of the beat frequency for the stabilized and unstabilized laser system. The unstabilized laser frequency drifted 120MHz in 3000 s, the stabilized laser frequency drifted less than 300 kHz.
We have calculated the linear spectral density (LSD) and the root Allan variance (RAV) σ (2,τ) from the time series [8]. In order to estimate the LSD, we have used a variation of Welch’s overlapped segmented average method [9]: With increasing Fourier frequency, we increased the frequency resolution, which decreases the statistical error of the estimate due to the increased number of averages. For good selectivity and high frequency resolution, we used a Kaiser window with a peak side lobe level of -70 dB and a segment overlap of 62 %.
The results for LSD and RAV are shown in Fig. 5 and were plotted with a solid line for the unstabilized laser and with a dashed line for the stabilized laser. The frequency noise at 2Hz was suppressed by almost one order of magnitude. The noise reduction was higher for lower frequencies. At 1 mHz, the control loop suppressed the laser frequency noise by two orders of magnitude. Both the frequency noise of the unstabilized and stabilized laser increased for lower frequencies, probably due to thermal effects. For the stabilized laser, the laser frequency RAV was 5·10-12 for 0.2 s integration time and below 5·10-11 for integration times up to 300 s. This was an improvement up to two orders of magnitude compared to the free-running laser.
4. Limitations
The frequency stability of the common-path, two-color set-up was dominated by slow drifts and single spikes visible in the error signal which might be caused by the laser or interferometer. Thus, we investigated the influence of the second harmonic laser intensity noise and the interferometer stability on the frequency stability. Furthermore, we measured the stability of our voltage reference added to the error signal.
The intensity noise of the laser influenced the absolute DC level of the error signal, and hence the frequency noise. Thus, we stabilized the intensity with two servo control loops (internal noise eater and external intensity stabilization). The common method to verify the influence of laser intensity noise on the frequency stability by measuring the corresponding transfer function could not be used. This was due to the necessity of the intensity stabilization for the frequency lock, which would reduce a deliberate intensity modulation. Thus we used an equivalent method: We have measured the RIN at the interferometer output without the iodine cell with a temperature stabilized photodiode. The measured intensity noise consisted of laser intensity noise, noise from the frequency doubling process and additional noise from the interferometer set-up resulting from acoustics and mechanical vibrations. The laser RIN and the single pass second harmonic noise were one order of magnitude below the relative intensity noise at the interferometer output for frequencies below 0.1 Hz. Thus, the laser intensity noise at 1064nm and 532nm did not dominate the intensity noise at the interferometer output. External disturbances, such as touching the interferometer mirror mount, yielded phase shifts between the interfering waves and increased the intensity noise. Therefore, we expect that a stiff and compact set-up combined with a short interferometer armlength will accomplish an improvement of the interferometer stability.
Fig. 5. Linear spectral density (a) and root Allan variance (b) of the stabilized and unstabilized laser frequency.
A voltage reference was used to shift the error signal slope to zero. We measured the RIN from 10-4 Hz to 10 Hz. In analogy to the interferometer noise, we again used the error signal slope to calculate a corresponding frequency noise which was more than two orders of magnitude below the measured frequency noise (Fig. 5, (a) stabilized). More efforts are necessary to analyze further noise sources.
5. Conclusion
We have stabilized a Nd:YAG laser with Doppler-free error signals generated with a common-path, two-color interferometer for the first time, to our knowledge. Modulation-free, sub-Doppler dispersion signals were observed for the R(56)32-0 iodine line. The signal-to-noise ratio of the dispersion signals is critically dependent on electronic filtering. We improved the frequency stability compared to the free-running laser up to two orders of magnitude. The relative Allan variance was 5·10-12 for 0.2 s, and below 5·10-11 for integration times up to 300 s for the stabilized laser. Finally, we showed that the frequency stability was not limited by the laser intensity noise, the frequency doubling process and the interferometer stability. An increased stability of the error signal combined with longer frequency locking times would open interesting applications in the industrial field of length calibration and surface analysis, where low-cost stabilized reference lasers are needed.
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