This article introduces what frequency doubling is, the physical mechanism and device design of frequency doubling, etc.

An effect of using nonlinear materials to achieve laser frequency twice the frequency of the input light

Materials lacking inversion symmetry have a so-called X(2) nonlinear (see nonlinear crystal material) crystalline material. This nonlinearity can be used to achieve the frequency doubling effect, that is, the input light (pump light) generates another light with an intermediate frequency twice that of the input light (half the wavelength). This process is also known as second harmonic generation. In most cases, the frequency-doubled light propagates in a direction close to that of the pump light.

Figure 1. Typical schematic of frequency doubling: a near-infrared 1064nm input light produces 532nm green light when passing through a nonlinear crystal.

There are many non-linear crystal materials that are very suitable for frequency doubling, such as: lithium niobate (LiNbO3), potassium titanyl phosphate (KTP, KTiOPO4), and lithium triborate (LBO, LiB3O5).

The physical mechanism behind frequency doubling is as follows. Due to the existence of nonlinearity, the fundamental frequency light (pump light) generates a nonlinear polarized wave whose oscillation frequency is twice the fundamental frequency. According to Maxwell’s equations, this nonlinear polarized wave produces an electromagnetic field at this frequency. Due to the existence of phase matching, the generated second harmonic field mainly propagates in the direction of nonlinear polarized waves. The nonlinear polarized wave interacts with the pump light, so that the pump light is attenuated and the frequency-doubled light is enhanced, that is to say, the energy is transferred from the pump light to the frequency-doubled light.

When the pump light is weak, the frequency doubling efficiency is low and increases linearly with the increase of pump intensity. Thus the intensity of the frequency-doubled light is proportional to the square of the pump light intensity:

where the factor depends on many factors, such as: effective mode field area, crystal length and crystal properties.

When the loss of the pump light becomes significant, the further rise of the frequency-doubled light will become slower. Of course, the frequency-doubling optical power P2 cannot be greater than the fundamental frequency optical power P2.

The frequency doubling process is a phase-sensitive process. When the phase matching conditions are satisfied, the frequency doubling efficiency is higher. This means that the second harmonic fields generated at different locations of the nonlinear crystal will be superimposed at the exit surface of the crystal. With suitable phase matching and pump beams with high light intensity, high beam quality and suitable bandwidth, a frequency doubling process with a conversion efficiency greater than 50% can be achieved, and in some cases, it can even reach more than 80%. And by utilizing pump light with a flat-topped spatial and temporal shape, a frequency doubling efficiency of 90% is also possible. And if the phase matching conditions are not met, the conversion efficiency is usually very small. In this case, the energy transferred by the nonlinearity oscillates back and forth between the pump and the second harmonic instead of always traveling in one direction. The phase matching condition also makes it difficult to generate other nonlinear processes in the second harmonic generation process, such as the sum-frequency process of the second harmonic light and the pump light, and the generation of the second harmonic light of the second harmonic light. The phase matching conditions generated by subharmonics cannot satisfy the phase matching in other nonlinear processes.

When the pump light is in the form of pulsed light, such as mode-locked laser or Q-switched laser, high conversion efficiency can be obtained even if the average power is low. This is because, for these short pulses, lower average powers also result in higher peak powers, resulting in stronger nonlinear interactions. Note, however, that for nonlinear frequency transformation of ultrashort pulses, the effective interaction length and thus the conversion efficiency is limited by the group velocity mismatch, which results in a time-domain walk-off. This effect is not apparent in nanosecond pulses produced by Q-switched lasers, but in this case, it still causes some variation in the time-domain width of the pulses, usually the frequency-doubling pulses are slightly shorter than the pump pulses.

For the high-efficiency frequency doubling effect of medium power (such as in the case of continuous optical pumping), it is usually necessary to use intra-cavity frequency doubling, that is, by placing a frequency-doubling crystal inside the laser resonator to improve the laser intensity in the cavity. . Another technique is to use a resonant booster cavity outside the laser to achieve high-efficiency frequency doubling. This method works for both single-frequency light and mode-locked lasers, but usually requires a real-time stabilization of the resonators involved.

Effective frequency doubling can be achieved at lower power levels by means of nonlinear waves. The key to this approach is that waveguides can be used to propagate longer distances with small mode field areas (and thus high light intensities), whereas in ordinary bulk elements the interaction distance is limited to the Rayleigh length due to diffraction. magnitude.

High-quality waveguides can be fabricated using materials with high nonlinearity, such as lithium niobate (LiNbO3), lithium tantalate (LiTaO3), etc., using a variety of techniques. Such waveguides can be several centimeters long and can have low losses (<1dB/cm) and high second-harmonic conversion efficiencies (>100%/W at 1cm long waveguides).

But frequency doubling in waveguides also has a number of disadvantages that limit its effectiveness in many cases:

1. Waveguides require special fabrication techniques that do not work well for all materials. The existing materials with mature preparation conditions are lithium niobate (LiNbO3) and lithium tantalate (LiTaO3).
2. The pump light needs to be efficiently coupled into the waveguide. This results in coupling losses and requires tight alignment tolerances
3. Angle tuning is not possible within the waveguide.
4. Waveguides have higher propagation losses than common bulk materials.

For these reasons, the method of frequency doubling using waveguides is not very common.

Frequency doubling is a common technique used to generate short wavelength light:

1. Generate 532nm green light by frequency doubling a 1064nm laser using the output of a neodymium-doped or ytterbium-doped laser (see Green Lasers).
2. Many blue laser systems are produced by frequency doubling of a 0.9um laser (such as 914nm produced by Nd:YVO4).
3. By further frequency doubling (or by sum-frequency effect), it is possible to generate laser light in the UV region of shorter wavelengths (see UV lasers). The main challenges are the transparency, durability, and strong dispersion of nonlinear crystalline materials in this region (sometimes resulting in difficult phase matching or narrow phase matching bandwidths).

Lasers produced by frequency doubling of neodymium-doped lasers are similar in output power and beam quality to those produced by large-scale argon-ion lasers, but have much higher power conversion efficiency and longer lifetimes.

For ultrashort pulses, single-pass conversion efficiencies at short wavelengths are generally lower because significant group velocity mismatches limit interaction lengths, while optical damage limits applicable optical intensities.

When designing a frequency doubling device, many aspects need to be considered:

1. What kind of nonlinear crystal material is used? How to design a suitable AR coating? How does it need to be protected? Is it durable enough?
2. Use critical phase matching or non-critical phase matching?
3. What is the optimal crystal length and pump beam radius when considering beam divergence, spatial walk-off, group velocity mismatch and damage threshold?
4. For non-critical phase matching: To what extent should the temperature uniformity in the crystal heating furnace be controlled? What temperature can the coating withstand?
5. For critical phase matching: what is the spatial asymmetry of the beam at the second harmonic? How is the beam quality? Is walk-off compensation required?
6. When passing through the crystal in both directions: How do the relative phases of the fundamental and second harmonics change with propagation in different directions?
7. When using resonant frequency doubling: How to design an enhanced resonator to achieve the best frequency doubling performance and lowest sensitivity to external disturbances?

Therefore, careful research and design are required to find the best configuration before frequency doubling.