## Abstract

We present a compact iodine-stabilized laser system at 633 nm, based on a distributed-feedback laser diode. Within a footprint of $27 \times 15\,\,{\rm{cm}}^2$, the system provides 5 mW of frequency-stabilized light from a single-mode fiber. Its performance was evaluated in comparison to Cs clocks representing primary frequency standards, realizing the SI unit Hz via an optical frequency comb. With the best suited absorption line, the laser reaches a fractional frequency instability below ${10^{- 10}}$ for averaging times above 10 s. The performance was investigated at several iodine lines, and a model was developed to describe the observed stability on the different lines.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. INTRODUCTION

Due to their simplicity and reliability helium–neon (He–Ne) lasers at a wavelength of 633 nm are used widely for interferometric length measurements [1] and metrology applications [2]. Without any additional reference, Zeeman-stabilized and two-mode frequency-stabilized He–Ne lasers have shown instabilities of $2 \cdot {10^{- 11}}$ and $3 \cdot {10^{- 10}}$, respectively, at averaging times of 1000 s, and frequency drifts of about $2 \cdot {10^{- 8}}$ over several months [3,4] with typical output powers of less than a milliwatt. These properties well meet the requirements of commercial laser interferometers. He–Ne lasers with internal iodine cells stabilized to Doppler-free molecular hyperfine lines of iodine achieve an instability down to $1 \cdot {10^{- 13}}$ at 1000 s averaging time, and an absolute uncertainty of $2.1 \cdot {10^{- 11}}$ [5]. The stabilization of these systems is more demanding, and they are used mostly for calibration.

However, He–Ne lasers require relatively large volumes even at low output powers, have a low power efficiency, and do not offer the possibility for wide-bandwidth frequency tuning. Furthermore, the technical know-how for building and maintaining He–Ne lasers is vanishing, and hence alternative techniques in this wavelength range are needed.

Stabilizing a diode laser (DL) to a molecular or atomic reference is a promising substitute for He–Ne lasers, as this eliminates their drawbacks [6]. A narrow linewidth 633 nm DL stabilized to Doppler broadened iodine absorption lines has reached an instability of $1 \cdot {10^{- 9}}$ at 1000 s averaging time as evaluated with a wavelength meter. This laboratory setup employs an iodine cell with a length of 30 cm. Because of a low pressure (14°C saturation temperature), a relatively long effective interaction length of 90 cm has to be used for the spectroscopy [7].

Here we present a simple and compact shoe-box-sized DL system at 633 nm with fiber output, as direct one-to-one replacement of stabilized He–Ne lasers in industrial applications, such as interferometric length measuring systems or laser trackers [8]. As these systems employ specific optical components, the operational wavelength of 633 nm is a mandatory requirement. This rules out the use of diode-pumped solid state (DPSS) lasers or robust DLs stabilized to rubidium (Rb) at 780 nm. So far, available narrow-linewidth DLs at 633 nm have been complex extended cavity DLs (ECDLs) that are not robust enough for industrial application. In our system, a robust distributed-feedback (DFB) laser diode is stabilized to Doppler-broadened iodine $({^{127}{{\rm{I}}_2}})$ absorption lines, and the system includes a double-stage isolator and a fiber coupling (Fig. 1). To achieve a compact design, Doppler-free saturation spectroscopy is not used because a more complicated setup with a larger cell and higher optical power to saturate the weak molecular transition would be required [9]. The 633 nm DL system presented here with a relatively small iodine cell (3.3 cm length) reaches a fractional frequency instability of $1.9 \cdot {10^{- 11}}$ at 1000 s averaging time. The stability of the laser system stabilized to different iodine lines was evaluated using an optical frequency comb.

## 2. EXPERIMENTAL SETUP

#### A. Stabilized Laser System

Figure 1 shows the system in its $27\,\,{\rm{cm}} \times 15\,\,{\rm{cm}}$ housing. Light emitted from the DFB laser diode first passes an isolator to prevent perturbations by reflections back into the laser diode. Behind the isolator, the light is split by a beam splitter (BS), and the main beam is coupled to a single-mode fiber by a fiber coupler mounted to the housing. A small part of the light is used for spectroscopy, which is further split by a second BS. The reflected part is sent through the iodine cell onto a photo diode (PD), while the transmitted beam is monitored by a second PD to provide a reference signal for normalization of the absorption spectrum. To achieve strong absorption, the 3.3 cm long iodine cell (with purity according to the manufacturer ${\gt}{{98}}\%$) was heated to a temperature of 60°C. This temperature is a good trade-off between strong absorption (of approximately 50%) for the strongest lines and small heating power. Using published iodine vapor pressure data [10] interpolated by the Antoine equation [11], we estimate a saturated iodine vapor pressure of 616 Pa inside the cell.

By varying the diode temperature, the optical frequency can be tuned over a range of $\Delta \nu = 245\,\,{\rm{GHz}}$ without mode hops to scan the iodine spectrum (Fig. 2). The laser current has a much smaller impact on the laser frequency of about 1 GHz per 1 mA with significant power variation [12]. However, due to its high actuator bandwidth, the current is used in the lock to iodine to correct for fast laser frequency fluctuations.

Depending on the diode temperature, the power at the fiber output is between 4.5 and 6.5 mW. To stabilize the laser frequency to a peak of an absorption line via a 1f-lock-in technique, the laser current is modulated at a frequency ${f_{{\rm{mod}}}} = 21\,\,{\rm{kHz}}$. The corresponding peak-to-peak frequency modulation deviation of the emitted light was kept as small as $\Delta {\nu _{{\rm{mod}}}} = 5\,\,{\rm{MHz}}$, which is much smaller than the Doppler-broadened iodine linewidth.

When the laser is used for interferometry, this modulation leads to a phase modulation of the interference signal, depending on the path difference. Hence, the interference contrast is reduced if the data acquisition averages over the modulation. If we allow for a maximum peak-to-peak phase modulation of $\pi$ (contrast reduced to the zeroth-order Bessel function ${J_0}(\pi /2) \approx 0.5$), this limits the path difference to ${L_{{\rm{coh,}}\pi}} \approx \frac{c}{{2\Delta {\nu _{{\rm{mod}}}}}} = 30\,\,{\rm{m}}$. Instead, if the data acquisition is fast enough to follow the modulation of the interference fringes, it will not limit the coherence length. The coherence length is then determined by the linewidth $\delta \nu$ of the laser diode, which is less than 1.5 MHz. Assuming a Lorentzian line profile, the coherence length is then ${L_{{\rm{coh}}}} = \frac{c}{{\pi \delta \nu}} \gt 63\,\,{\rm{m}}$ [13].

The system automatically scans the iodine spectrum, identifies the correct absorption line, and locks to that line within less than 5 min. After initial power-on, the system needs 10–15 min until all the parameters (especially the temperature of the iodine cell) are settled and the laser frequency is stabilized.

#### B. Frequency Measurement

The long-term instability and the absolute frequency $\nu$ of the laser system are characterized in comparison to two Cs fountain clocks via a hydrogen maser and an optical frequency comb (Fig. 3). The comb spectrum of the comb-generating Er:fiber-based fs-laser oscillator is centered around 1560 nm. After amplification in an Er-doped fiber amplifier (EDFA), the second-harmonic comb spectrum around a wavelength of 780 nm is generated [second-harmonic generation (SHG)], which in a nonlinear fiber (NLF) generates a super-continuum spanning 600–750 nm [14]. The fields of the super-continuum and the DFB-laser system (DL) are overlapped using a BS. With a volume Bragg grating (VBG), most of the comb lines besides those near the line of the DFB laser at 633 nm are filtered out to improve the signal-to-noise ratio (SNR) of the beat note detected with a PD. For band-pass filtering of the radiofrequency beat signal, tracking oscillators (TOs) are phase-locked to the signal. Thus, clean signals are provided to the inputs of frequency counters (CNTs) in $\Lambda$-averaging mode [15] (K + K FXE) for dead-time-free synchronous measurement and recording of the RF frequencies. To make sure that the center frequency of the beat signal is tracked correctly despite the frequency modulation of the laser, different TOs with slightly different, asymmetrically chosen parameters and two CNTs are used. The frequency difference between these two channels is in the range of a few kilohertz ($\Delta \nu /\nu \approx {10^{- 11}}$); thus, significant measurement errors due to cycle slips of the tracking filters can be excluded. The optical absolute frequency $\nu$ is calculated from the beat frequency ${f_{{\rm{beat}}}}$:

where ${f_{{\rm{CEO}}}}$ is the carrier–envelope offset frequency and ${f_{{\rm{rep}}}}$ the repetition rate. Both frequencies are also recorded by K + K FXE CNTs. All CNTs use a reference signal at frequency ${f_{{\rm{ref}}}} = 10\,\,{\rm{MHz}}$ from an active hydrogen maser. The H-maser is referenced to a Cs fountain clock, which is a primary frequency standard realizing the unit hertz. The mode number $n$ of the comb line and the sign of ${f_{{\rm{beat}}}}$ are determined from a rough frequency measurement with a wavelength meter having a few tens of megahertz uncertainty. Figure 4 shows the measured absolute frequency of the laser stabilized to the line R(74) 8-4.#### C. Simulation of Doppler-Broadened Iodine Spectra

Each absorption line in Fig. 2 consists of several hyperfine transitions with Voigt line shapes. Their Gaussian widths are given by the Doppler broadening ($\delta {\nu _{{\rm{DB}}}} = 388\,\,{\rm{MHz}}$), and their Lorentzian widths contain natural and collision broadening. In the investigated frequency range, the upper state lifetime of iodine $^{127}{{\rm{I}}_2}$ is in the range of 300–400 ns [16], leading to a natural line width of about 400–500 kHz. At our vapor pressure and temperature, collision broadening amounts to ($\delta {\nu _{{\rm{co}}}} = 76.6\,\,{\rm{MHz}}$) [17]. Compared to these broadening contributions, additional transit time broadening can be neglected. For our simulations, the Voigt profile was calculated as the real part of the Faddeeva function [18].

The absorption lines around 633 nm are between rovibrational levels in the $X$ and $B$ potentials of iodine $^{127}{{\rm{I}}_2}$ and consist of several hyperfine structure (HFS) lines in a range of about 1 GHz. The number of hyperfine lines depends on the rotational quantum number $J^{\prime \prime} $ of the molecular ground state. Transitions with an even $J^{\prime \prime} $ have 15 hyperfine components and with an odd $J^{\prime \prime} $ have 21, due to the required symmetry of the homonuclear $^{127}{{\rm{I}}_2}$ molecular wavefunction [19].

The frequency and the relative intensity of the iodine hyperfine transitions were calculated using the program IodineSpec [20,21]. This software is based on molecular potentials for the two electronic states involved and an interpolation for hyperfine splittings and achieves a standard ($1\sigma$) frequency uncertainty of 1.5 MHz. The transmission spectrum $T(\nu)$ of iodine in the frequency region of the laser system was simulated by summing the Voigt profiles of the individual hyperfine transitions. The relative intensities given by the program were scaled to match the simulated transmission to the experimental data (Fig. 2).

A pressure shift of about ${-}{5.9}\;{\rm{MHz}}$ was included due to the high temperature of 333 K and corresponding vapor pressure of 616 Pa. The shift was obtained by scaling the pressure shift for a He–Ne laser stabilized to the R(127) 11-5 line of ${-}{9.5}\;{\rm{kHz/Pa}}$ at a temperature of 288 K (18 Pa) [22].

Figure 5 presents the simulated line shapes of the transmission spectra of line R(77) 8-4 (21 HFS components) and R(74) 8-4 (15 HFS components). The two lines illustrate the influence of the number of HFS components on the total profile. The profile with 15 HFS components is more sharply peaked and shows a smaller full width at half maximum (FWHM) compared to the one with 21 components. This behavior is typical for all lines in the tuning range of the DL.

## 3. EXPERIMENTAL RESULTS

To investigate the frequency-stabilized laser system, Doppler-broadened lines with 15 hyperfine components (P(54) 6-3, R(74) 8-4) and lines with 21 components (R(59) 6-3, R(77) 8-4) were used as reference. For both kinds of lines, we have chosen a strong line with a minimum transmission ${T_0} \approx 0.66$ and a weaker line with ${T_0} \approx 0.76$.

Stabilized on line R(74) 8-4, the optical frequency was measured over several days. For the other lines, the measurements lasted about 2 h. For each of these iodine lines, Table 1 shows the number of HFS components, the measured center frequency ${\nu _c}$ calculated from the beat measurements data, the frequency position of the simulated minimum ${\nu _{{\rm{sim}}}}$, and the difference $\Delta \nu = ({\nu _{\rm{c}}} - {\nu _{{\rm{sim}}}})$ between simulation and experimental results. Compared to the line width of around 850 MHz, the residual frequency differences smaller than 10 MHz represent a good agreement.

Figure 6 shows the modified Allan deviation mod ${\sigma _y}(\tau)$ of the measured DL frequency as a function of the averaging time $\tau$ for the four investigated lines. At short averaging times, the instability decreases proportionally to $1/\sqrt \tau$ as expected for white frequency noise. However, at longer averaging times $\tau \gt 100 \ldots 1000\,\,{\rm{s}}$, it starts to rise again.

The short-term instability can be explained by the SNR of the error signal. To generate the 1f-error signal, the laser frequency is modulated with rms amplitude $\Delta \nu _{{\rm{mod}}}^{{\rm{rms}}}$ near the tip of the peak. In the neighborhood of the transmission minimum ${T_0}$ at frequency ${\nu _0}$, the transmission can be approximated as $T(\nu) = {T_0} + {\kappa _{{\rm{sim}}}}/2\times(\nu - {\nu _0}{)^2}$. The error signal is given as the 1f-rms component of the corresponding photocurrent ${I_s}$:

Thus, the slope $D = {{\rm{d}}{I_s}/{{\rm{d}}\nu}}$ of the error signal is proportional to the curvature ${\kappa _{{\rm{sim}}}}$ at the peak:

Here ${P_0}$ denotes the power at the input of the iodine cell and $\eta$ the detector quantum efficiency. Using the slope $D$ and the noise spectral power density ${S_I}$ of the photocurrent, the short-term instability for a laser frequency ${\nu _{\rm{L}}}$ can be estimated [23] asThe stability is thus inversely proportional to the transmission curvature of the absorption peak. The width close to the peak is smaller for 15 HFS lines compared to the peak with 21 lines, and therefore their curvature is increased by approximately a factor of two. For all investigated lines, the curvature ${\kappa _{{\rm{sim}}}}$ is calculated from the simulated line shapes. Line R(59) has the smallest peak curvature with ${\kappa _{{\rm{sim}}}} = 1.09\,\,{\rm{GH}}{{\rm{z}}^{- {{2}}}}$ followed by lines R(77) (${\kappa _{{\rm{sim}}}} = 1.77\,\,{\rm{GH}}{{\rm{z}}^{- {{2}}}}$), P(54) (${\kappa _{{\rm{sim}}}} = 1.96\,\,{\rm{GH}}{{\rm{z}}^{- {{2}}}}$), and R(74) (${\kappa _{{\rm{sim}}}} = 2.83\,\,{\rm{GH}}{{\rm{z}}^{- {{2}}}}$). This order is also visible in the modified Allan deviation at intermediate averaging times (Fig. 6). The measured short term instability of the line R(74) (${\sigma _y}(1 {\rm{s}}) = 2 \cdot {10^{- 10}}$) can be compared with the fundamental limit due to photon shot noise of the detected light. With an incident power of ${P_0}{T_0} = 58\,\,\unicode{x00B5}{\rm{W}}$ at the photodetector, the photocurrent shot noise amounts to ${S_I} = \frac{{2{e^2}\eta {T_0}{P_0}}}{{h\nu}}$, resulting in the shot-noise-limited instability of ${\sigma _y}(\tau) = 2.6 \cdot {10^{- 11}} {(\tau /{\rm{s}})^{- 1/2}}$. This instability is a magnitude smaller than the measured Allan deviation at 1 s. Measuring the relative intensity noise spectrum of the laser diode, we discovered that in the frequency range near the modulation frequency, electronic noise of the detector is about a factor of 10 above the shot noise. With this noise, an instability of ${\sigma _y}(\tau) = 1.4 \cdot {10^{- 10}} {(\tau /{\rm{s}})^{- 1/2}}$ would be reached, which is in good agreement with the measured short-term instability.

The fact that the observed frequency instability is determined by the lock to iodine is further supported by analyzing the free running laser fractional frequency noise. We observe that the power spectral density of the free running laser frequency fluctuations ${S_y}$ for small frequencies ($f \lt 10\,\,{\rm{kHz}}$) shows flicker noise behavior (${S_y}\!(f) = 4.5 \cdot {10^{- 19}}{f^{- 1}}$). This leads to a constant modified Allan deviation for the unstabilized laser ${\sigma _y}\!(\tau) = 6.5 \cdot {10^{- 10}}$ [24] at averaging times $\tau$ below 1 s. The measured short-term instability of the DL stabilized to line R(74) is below this value, which indicates that the short-term stability is limited by the stabilization to the iodine vapor cell.

Much stronger variations between the lines are seen in the long-term stability. Stabilized to line R(74) 8-4 (red) that shows the highest SNR, the laser system achieves the best frequency stability of all compared lines with a modified Allan deviation of ${\sigma _y} = 2.0 \cdot {10^{- 10}}$ at an averaging time $\tau = 1\,\,{\rm{s}}$ and ${\sigma _y} = 1.9 \cdot {10^{- 11}}$ at $\tau = 1000\,\,{\rm{s}}$. When stabilized to the second line with 15 HFS components, the Allan deviation rises at $\tau = (600\,\,{\rm{s}}$ –$1500\,\,{\rm{s}})$, while on the lines with 21 HFS, it rises already at $\tau = (100\,\,{\rm{s}}$ –$\;200\,\,{\rm{s}})$. We attribute this behavior to the different susceptibilities of these lines to environmental perturbations. Datasets shown in the figures in this paper are available (see Ref. [25]).

## 4. CONCLUSION

We have presented a compact, iodine stabilized DL system at 633 nm with relative frequency instability below ${10^{- 10}}$ ($2 \cdot {10^{- 11}}$ at $\tau = 1000\,\,{\rm{s}}$), which is competitive to Zeeman- and two-mode-stabilized He–Ne lasers. In addition, we have shown that the laser can be tuned over a wide frequency range so that a large number of possible Doppler-broadened iodine lines can be used. The absolute frequency and the observed behavior of the stability was in good agreement with simulations based on molecular potentials of iodine.

We found a significant dependence of the stability on the hyperfine structure of the Doppler-broadened absorption lines that were used for stabilization. Because of its small size, lower electrical power consumption, and high optical output power, such stabilized DL systems using an external iodine cell can become a valuable alternative to Zeeman- or two-mode-stabilized He–Ne lasers at 633 nm.

## Funding

Bundesministerium für Bildung und Forschung (FKZ 13N13954 (FinDLiNG)); European Metrology Programme for Innovation and Research (17FUN03 (USOQS)).

## Acknowledgment

Part of this work has received funding in the 17FUN03 USOQS project from the EMPIR programme co-financed by the Participating States and from the European Union’s Horizon 2020 research and innovation programme.

## Disclosures

CN, PL: TOPTICA Photonics (E).

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