Frequency-stabilized Lasers

For some laser applications, e.g. in high-resolution laser spectroscopy, optical data transmission and in various scientific experiments, one requires laser light with a particularly stable optical frequency. Usually, at the same time one requires a narrow linewidth, making the optical frequency very well defined. Therefore, frequency-stabilized lasers can be seen as narrow-linewidth lasers with the additional feature of having a particularly stable emission frequency. For that purpose, some special technique for stabilizing the emission frequency is applied.

As the wavelength of laser light is closely related to its optical frequency, wavelength-stabilized lasers can be considered to be the same as frequency-stabilized lasers. Note, however, that stabilization techniques which are based on wavelength measurements (e.g. with wavemeters) are inherently different from those directly measuring optical frequencies, and are ultimately more limited in precision.

In many cases, the requirements on frequency stability are by far not as demanding as in extreme cases of optical frequency standards e.g. for optical clocks, where sub-Hertz linewidths and sub-Hertz stability may be needed. Simpler stabilization techniques are then sufficient, reaching frequency stability only e.g. in the kilohertz or megahertz range.

In some cases, one needs to stabilize not only the optical frequency, but also the optical phase. That means that deviations of the optical phase must be limited to a certain range (e.g. well below 1 rad). Note that even the slightest systematic frequency deviation would in the long run result in arbitrarily large phase deviations.

Frequency Stability of Unstabilized Lasers

We first consider the frequency stability of unstabilized lasers, i.e., without applying any special stabilization techniques.

The emission linewidth can easily be far smaller than the gain bandwidth or alternatively the bandwidth of an intracavity bandpass filter. This is basically because very tiny differences in laser gain (or net gain) may favor one or a few resonator modes, so that lasing occurs only on those. However, this does not necessarily result in high frequency stability; the emission frequency may easily drift in a range which is far larger than the emission linewidth. For example, the laser gain spectrum or the wavelength of peak transmission of a bandpass filter may drift due to thermal effects. This can not only lead to mode hopping to neighbored modes, but also to relatively large frequency changes.

Frequency Stabilization by Optical Feedback

A substantial improvement of frequency stability can often be achieved by optical feedback from some device which provides frequency selectivity with a higher degree of stability than the laser itself. An example is the passive stabilization of a laser diode with optical feedback from a volume Bragg grating, where the latter does not only have a reflection bandwidth which is much smaller than the width of the laser gain spectrum, and is also not affected by temperature changes and changes of carrier density in the laser diode. Although the obtained frequency stability is not particularly high, it is at least substantially better than that without stabilization.

Better stability can be achieved, for example, with high-finesse optical resonators having a stable mechanical setup and careful protection against environmental influences – typically, vibration isolation and temperature stabilization. The laser then must be reliably locked to one particular resonator mode, i.e., preventing any jumps to unwanted resonator modes. The latter becomes tentatively more demanding when using a relatively long reference cavity, as required for a particularly small linewidth. One may then require one or more additional optical filters.

Such methods with optical feedback are called passive stabilization in contrast to methods of active stabilization, which involve some kind of automatic feedback mechanism.

Active Frequency Stabilization

Active frequency stabilization techniques involve some kind of feedback system which automatically acts back on the laser such that the drift of its emission frequency is largely suppressed. For that, one requires the following:

• There must be a device for accurately detecting any deviations from the wanted laser frequency. This can again be some kind of carefully stabilized optical resonator (a reference cavity) with temperature control and vibration isolation, plus additional means for generating a strongly frequency-dependent electronic output signal (see below for examples). Particularly high stability can be achieved with cryogenic resonators [10]. High-Q microresonators are also an interesting option [21]. An alternative approach is to utilize a narrow optical transition of some atoms, ions or molecules; for example, see Ref. [11].
• The laser must be frequency-tunable in a sufficiently large range, at least as wide as the possible drift range without frequency stabilization.
• Some electronic controller needs to translate detected frequency deviations into a suitable correction signal which can be applied to the laser. A typical solution is a PID controller (PID = proportional–integral–derivative) or a PI controller, where the control parameters should be carefully optimized, taking into account the detailed tuning characteristics of the laser and possibly also those of the frequency measurement device. The performance can substantially depend on the quality of the electronic controller.

Typical Methods of Laser Frequency Stabilization

Some particularly popular methods are described in the following:

Iodine-stabilized Lasers

A popular spectroscopic medium for laser stabilization is molecular iodine (I₂) [2, 3]. It can easily be held in a closed glass cell and has a wide range of absorption transitions in the visible spectral region, which can be accurately probed with Doppler-free saturation spectroscopy. For example, the technique can be applied to helium–neon lasers emitting at 633 nm, but also to frequency-doubled Nd:YAG lasers at 532 nm and to various laser diodes.

For other spectral regions, other media may have to be used. For example, there are methane-stabilized helium–neon lasers emitting at 3.39 μm.

Transmission Fringe Locking on a Resonator

A particularly simple method is called transmission fringe locking. Here, one uses an automated feedback system to keep the laser frequency on one side of a resonance of the resonator, e.g. such that the transmitted intensity is half that achieved on resonance. In contrast to operation on resonance, fringe locking most easily delivers an error signal: depending on the sign of the frequency deviation, the resonator transmission increases or decreases.

The accuracy achieved without method is not particularly high, even if a resonator with relatively high Q factor is used. For example, the accuracy can be affected by changes of laser power, and reaching a precision far better than the width of the resonances is difficult. A further disadvantage can be the narrow locking range: the error signals is informative only in a small range of frequencies.

Hänsch–Couillaud Stabilization

The method of Hänsch and Couillaud [4] employs polarization spectroscopy on an optical resonator. The linearly polarized laser radiation is reflected e.g. at a confocal reference cavity (used with off-axis incidence as a ring resonator for easy separation of reflected light). The cavity contains a polarizer, oriented at some angle against the input polarization. The reflected light is elliptically polarized, with the polarization state having a strong frequency dependence. The light is then sent through a <$\lambda /4$> waveplate and to a polarizing beamsplitter, followed by two photodetectors. The difference between the two photocurrents delivers the required error signal. The achieved frequency stability can be far higher than with transmission fringe locking, for example, and the method is still relatively simple, e.g. not requiring high-frequency modulation and photodetection as for Pound–Drever–Hall Stabilization.

Pound–Drever–Hall Stabilization

The Pound–Drever–Hall laser frequency stabilization technique [5, 14] is based on optical heterodyne detection with optical sidebands produced by RF phase modulation, e.g. in an electro-optic modulator. Essentially, one sends the laser light through a phase modulator (driven with an RF signal), then reflects it at the reference resonator and sends it to a fast photodiode. (The reflected light can be separated from the incident light with a polarizer and a <$\lambda /4$> waveplate.) Deviations of the a frequency from the resonance frequency lead to relative phase shifts of the generated sidebands against the fundamental frequency, which imply an intensity modulation of the reflected light. That modulation signal is sent to an RF mixer which is also fed with the drive signal of the phase modulator. Through an electronic low-pass filter, one can use the unconverted signal as the input e.g. of a PID controller.

The slope of the error signal with respect to small frequency deviations can be very high, enabling one to stabilize the frequency to a tiny fraction of the resonator bandwidth. At the same time, the locking range is rather large: in a wide frequency range, the error signals gives information on the sign of the frequency deviation. That also contributes to robust frequency locking.

Spatial Mode Interference (Tilt) Locking

Tilt locking [12] utilizes interference effects upon reflection of light at an optical resonator. The laser light has a frequency close to the frequency of a fundamental resonator mode (TEM₀₀), while it is not resonant with some higher-order resonator mode (e.g. TEM₁₀). As a result, the phase of the reflected fundamental mode light is strongly frequency-dependent, while the phase of the light corresponding to the higher-order mode is only weakly frequency-dependent. That results in a strongly frequency-dependent spatial intensity profile of the reflected light, which can be detected e.g. with a two-segment photodiode. Although being rather simple to implement, this method can provide a quite high frequency stability [15, 22] if the resonator is sufficiently stable.

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Encyclopedia articles:

• optical frequency
• optical frequency standards
• narrow-linewidth lasers
• stabilization of lasers