[Laser Technology Sharing] Introduction to Typical Optical Resonator Locking Methods

[Laser Technology Sharing] Introduction to typical optical resonant cavity locking methods

In order to make the optical resonant cavity work in a stable resonance state, it is generally necessary to dynamically adjust the cavity length through a negative feedback control system to cope with interference from the external environment. This process is called "cavity locking".

The principle of cavity locking is shown in Figure 1 below. First, an error signal related to the resonance state of the laser in the cavity is obtained through the photodetector. The characteristics of the error signal are: if the cavity length exactly meets the resonance conditions as the benchmark (zero point position), the error signal is near the benchmark (zero crossing point).

Once the error is not zero, it means that the cavity length has shifted from the resonance position. After the error signal is processed by appropriate proportional integral derivative (PID), the feedback voltage is transferred to the cavity length control element (usually a piezoelectric driver) located on the resonant cavity, forming a closed loop. The cavity length control element adjusts based on this signal until the error approaches zero to maintain the resonance of the resonant cavity.

Figure 1 Schematic diagram of cavity locking

What needs to be explained here is that if the stability of the resonant cavity is higher than that of the laser, we can use the resonant cavity as a frequency reference to stabilize the frequency of the laser (referred to as "frequency stabilization"). The specific method is similar to the above-mentioned cavity locking process, except that the feedback voltage output by the PID is loaded onto the piezoelectric driver and acousto-optic modulator on the laser to control the frequency of the laser.

It can be seen that the error signal plays a very important role in the feedback system. How to generate a high-quality error signal is the key to realizing the lock cavity. This article will introduce three different error signal generation methods, namely: PDH locking, HC locking, and Tilt locking, and analyze and compare their characteristics and application scope.

1. PDH locking

PDH is a combination of the initials of the names of three scientists, R. V. Pound, R. Drever, and J. L. Hall. The earliest article describing this method was published in Applied Physics B in

1983. The central idea of ​​the article is to use an optical resonator to stabilize the laser frequency and phase [1].

This method draws on the idea of ​​using microwave cavity for microwave frequency stabilization. The principle is shown in Figure 2 below.

First, the laser entering the resonant cavity is phase modulated (PM). After the laser enters the resonant cavity, the cavity reflected light is detected by the photodetector (PD), mixed with the phase modulation frequency (Mixer), and then demodulated. After adjusting the relative phase of the two channels, the error signal for cavity locking can be obtained through low-pass filtering (LP).

Figure 2 PDH lock cavity schematic

PDH technology is currently the most widely used frequency stabilization solution in the fields of optical frequency standards, gravitational wave detection, and atomic physics. However, this method requires the phase adjustment of the laser itself, and the system structure is relatively complex, which puts certain requirements on the performance of electro-optical modulators, signal generators and other instruments and equipment.

2. HC locking

HC locking is a technology proposed by T. W. Hansch and B. Couillaud [2] (referred to as HC locking).

Different from PDH, this method does not require direct modulation of the laser itself, but is implemented by using a linear polarizing element (polarizer or wave plate) placed in the resonant cavity.

This polarizing element can change the polarization state of the light in the cavity into an elliptical polarization state related to the resonance frequency, and then separates the two orthogonal polarization states through a combination of a quarter-wave plate (λ⁄4) and a polarizing beam splitter (PBS). After receiving them with two detectors (PD1, PD2), the error signal can be obtained after the difference between the two. Its working principle is shown in Figure 3 below.

Figure 3 Schematic diagram of HC cavity locking

Since HC technology requires the placement of polarizing elements in the cavity, it is not suitable for laser frequency stabilization applications that have extremely stringent internal cavity loss control; however, it can be applied to situations where there is a crystal in the cavity, such as frequency doubling cavities and cavity length locking of optical parametric oscillators.

3. Tilt Locking

Another cavity locking method is Tilt Locking[3]. As the name suggests, this method requires introducing a certain tilt on the cavity mirror to generate a high-order spatial mode (such as TEM01), and then extract the error signal through inter-mode interference with the fundamental mode (TEM00).

Specifically, when TEM00 is close to resonance, TEM01 deviates from the resonance state and will be completely reflected by the cavity, similar to the sideband signal generated by phase modulation in PDH. At this time, the cavity reflected light includes two modes: TEM01 which is completely reflected and TEM00 which is partially reflected.

As shown in Figure 4 below, a quadrant detector (QD) detects the cavity reflected light. When the laser resonates in the cavity, the phase difference between TEM01 and TEM00 is π⁄2, and the output of the two adjacent quadrants of the QD is zero after subtraction; when the cavity length shifts from the resonance position, the QD will output a corresponding error signal.

Figure 4 Tilt Locking lock chamber schematic

Tilt Locking technology is characterized by using very few devices to generate error signals, but this method itself is sensitive to mechanical stability.

At the same time, it requires a certain cavity mirror tilt, which means that it cannot achieve ideal cavity light mode matching, which to some extent also limits its application in high-precision resonators.

In summary, the above three lock chamber solutions each have their own advantages and disadvantages. This article only briefly introduces the working principle and applicable occasions. The specific choice of lock chamber technology must be determined according to the specific experimental technical requirements and experimental conditions.

References

[1] Appl. Phys. B 31, 97 (1983)

[2] Opt. Commun. 35 (3), 441 (1980)

[3] Opt. Lett. 24 (21):1499-501 (1999)