الخصائص الفيزيائية لليزر

الوقت المقدر للقراءة: 19 الدقائق

Laser is a kind of optical radiation that uses the principle of stimulated radiation of atoms or molecules to excite the working substance. All photons in the same laser beam have the same frequency, the same phase, and the same polarization and propagation direction. Therefore, the laser is coherent light radiation with good monochromaticity, strong directionality, and extremely high brightness. The laser processing technology is a systematic engineering integrating light, mechanics, and electricity. It also intersects with many disciplines such as physics, materials, machinery, and automation. It is one of the frontier areas of scientific and technological development. Laser technology and equipment have developed rapidly in recent years, and have received increasing attention from countries all over the world.

Features of laser

As coherent light, the laser has many characteristics.

Good Monochromaticity

The essence of light is a kind of electromagnetic wave radiation. For electromagnetic wave radiation, the longer the coherence length, the narrower the spectral line width, and the purer the color, that is, the better the monochromaticity of light. Taking the HeNe laser as an example, the laser coherence length is about 4×10⁴m. Before the advent of lasers, the best monochromatic light source was a krypton lamp, which produced a coherent length of light radiation of about 0.78m. Visible excitation is the simplest light source in the world.

High Brightness

High brightness is another outstanding feature of the laser. Generally, the light radiation intensity emitted by the unit light-emitting area ΔS, the unit light radiation width Δν, and the divergence angle θ are defined as the monochromatic brightness B_λ of the light source.

B_λ =P/ΔSΔνθ² (2.1)

In the formula, P is the laser power.

Although the total power emitted by the sun is high, the light radiation width Δν is very wide, the divergence angle θ is large, and the monochromatic brightness is still very small.

Although the Δν and θ are small, the laser has high monochromatic brightness. It is reported that the laser monochromatic brightness B_λ produced by high-power lasers is even 100 trillion times higher than that of the sun.

Strong Directionality

It can be seen from the mechanism of laser generation that under the condition of the uniform propagation medium, the divergence angle θ of the laser is only limited by the engagement;

θ=1.22λ/D (2.2)

In the formula, λ is the wavelength and D is the diameter of the light source spot.
The distance between the earth and the surface of the moon is about 3.8×10⁵km. The laser beam reaches the moon with the best focus, and its spot diameter is only tens of meters.

Good Coherence

The longest time interval during which light produces coherence is called the coherence time τ. In the coherence time, the farthest distance the light travels is called the coherence length Lc.

L_c =cτ=λ²/Δλ (2.3)

In the formula, c is the speed of light.
Because the laser bandwidth Δλ is very small, the coherence length Lc is very long. In fact, if the monochromaticity is good, the coherence is good, and the coherence length is also longer.

Highly Concentrated Energy

Some military, aviation, medical, and industrial lasers can produce high laser energy. For example, the output power of الليزر for nuclear fusion can be as high as 10¹⁸W. It can overcome the repulsive force between nuclei and realize nuclear fusion reaction. With the development of laser ultrashort pulse technology, people can use pulse amplification technology to obtain lasers. With peak power up to 10¹⁵W from Ti-doped sapphire laser devices used to generate extremely short laser pulses.

The Basic Principle of Laser Generation

The Interaction of Light and Matter

Basic Assumptions of Atomic Theory

Assumption of atomic stationary state All matter is composed of atoms. The atomic system is in a series of discontinuous energy states. Around the nucleus, the orbit of electrons is discontinuous, and the atom is in a stable state with constant energy. It is called the stationary state of the atom, and the state corresponding to the lowest energy of the atom is called the ground state.

If the electron in the outer orbit of the atom obtains a certain amount of energy from the outside. The electron will jump to the outer orbital motion. The energy of the atom increases, and at this time the atom is called an atom in an excited state.

Frequency conditions The atom transitions from one stationary state E₁ to another stationary state E2. The frequency ν is determined by the following formula.

hν= E₂ – E₁ (2.4)

A kind of monochromatic light corresponds to a photon produced by the same transition of an atom. hν is the energy of a photon.

The interaction between the radiation field and matter, especially the co-resonance interaction, laid the physical foundation for the advent and development of lasers. When the frequency of the incident electromagnetic wave is consistent with the resonance frequency of the medium, resonance absorption (or gain) will occur. The generation of and the interaction of light and matter will involve the cooperation of the field and the medium.

Stimulated Absorption

Assuming that the two energy levels of the atom are E₁ and E₂, and E₁< E₂ if there is a photon with energy satisfying formula (2.4) irradiated, the atom may absorb the energy of this photon and transition from the low-level E₁ state to the high-level The E₂ state. This kind of atomic absorption of photons and the transition from a low energy level to a high energy level is called the stimulated absorption process of the atom (Figure 2.2).

Spontaneous Radiation

The state of an atom at a high energy level after being excited is unstable. Generally, it can only stay on the order of 10^-8s. It will spontaneously return to a low energy state without external influence, and at the same time radiate energy to the outside world. For the photon with hν = E₂-E₁, this process is called the spontaneous emission process of the atom. Spontaneous radiation is random, the emission direction and initial phase of each photon of radiation are different, and the radiation of each atom is independent of each other, so the light of spontaneous radiation is incoherent Figure 2.1.

Stimulated Emission and Optical Amplification

An atom at an excited state energy level, if it is excited by a photon with external energy hν and satisfying formula (2.4) before it emits spontaneous emission, it may transition from a high-energy state to a low-energy state, and at the same time emit a Photons with the same frequency, same phase, same direction, and even the same polarization state with external photons. This process is called stimulated emission of atoms [Figure 2.2]

If an incident photon triggers stimulated emission and add one photon, these two photons continue to trigger stimulated emission and add two more photons, and then four photons multiply into eight photons… and so on, under the action of one incident photon, the atomic system may obtain a large number of photons with exactly the same state and characteristics. This phenomenon is called optical amplification. Therefore, the stimulated emission process causes the atomic system to radiate a large number of photons with the same frequency, the same phase, the same propagation direction, and the same polarization state as the incident light, that is, identical photons. Light amplification caused by stimulated radiation is an important basic concept in the mechanism of laser generation.

Population Reversal

From the definition of spontaneous emission and stimulated emission, it can be seen that the spontaneous emission of the light-emitting mechanism of ordinary light sources is dominant, but the emission of lasers is mainly stimulated emission of atoms. In order to make the stimulated radiation dominate the atomic system and make it continue to emit lasers. We should try to change the distribution of the atomic system when it is in thermal equilibrium so that the number of atoms at high energy levels continues to exceed the number of atoms at low energy levels, that is, the number of particles is achieved.

In order to achieve population inversion, energy must be input into the system from the outside. So that as many particles in the system as possible absorb energy. Then transition from a low energy level to a high energy level. This process is called the excitation or pumping process. The excitation methods generally include light excitation, gas discharge excitation, chemical excitation, and even nuclear energy excitation. For example, ruby lasers use optical excitation, helium-neon lasers use electrical excitation, and dye lasers use chemical excitation.

Laser Production Conditions

In a working substance that has achieved population inversion (such as light excitation or electrical excitation), stimulated radiation can be dominated, but the photon that first triggers stimulated radiation is generated by spontaneous radiation, and spontaneous radiation is Random. Therefore, the light amplification achieved by stimulated radiation is also random and disordered on the whole. It requires a series of devices to be added.

Optical Cavity

Two mirrors that are parallel to each other are installed at the two ends of the working material. An optical resonant cavity is formed between the two mirrors. One of which is a total reflection mirror and the other is a partial reflection mirror.

Among the photons emitted in all directions, except the photons propagating along the axial direction. They all leave the optical resonant cavity quickly, and only the light along the axial direction is continuously amplified, forming oscillations in the cavity back and forth. Therefore, in the laser tube, the step-adjusted light is continuously amplified to form light with greater amplitude. In this way, the light is reflected back and forth between the mirrors that are parallel to each other at both ends of the tube. Then the fully amplified light passes through a partial mirror to emit monochromatic light with the same phase.

Threshold Condition of Light Oscillation

From the energy point of view, although the light oscillation increases the light intensity, the absorption, deflection, and projection of the light on the two end faces and the medium at the same time will weaken the light intensity. Only when the gain is greater than the loss, can the laser be output. It requires the working substance and the resonant cavity to meet the condition of “gain greater than the loss”, It also called the threshold condition.

Frequency Conditions

The role of the optical resonant cavity not only increases the effective length L of light propagation. But also forms a light standing wave between the two mirrors. In fact, the only light that satisfies the standing wave conditions can be amplified by stimulated radiation.

From L=kλ_n/2(k=1,2,3…), λ_n=c/nν, we have

ν=kc/2nL or Δν=c/2nL (2.5)

In the formula, n is an integer and c is the speed of light.
The frequency ν generated by stimulated radiation in the laser tube can be obtained from equation (2.4)

ν=( E₂ – E₁ )/h (2.6)

In the formula, h is Planck’s constant.

To make the frequency meet the formula (2.5) and formula (2.6). The cavity length of the resonant cavity needs to be adjusted. In summary, the basic conditions for forming a laser are as follows.

• The working substance can achieve population reversal under the excitation of the excitation source.
• The optical resonant cavity can continuously amplify the stimulated radiation. That is, meet the threshold condition that the gain is greater than the loss.
• Satisfy the frequency conditions of formula (2.5) and formula (2.6)

Characteristic parameters of laser beam quality

Lasers have been widely used in many fields, so the requirements for laser beam quality are getting higher and higher. Beam parameters (such as light intensity distribution, beamwidth, and divergence angle, etc.) are important factors that determine the effect of laser applications. How to use a simple, accurate, and practical method to measure and evaluate the beam quality of lasers emitted by lasers has become a key issue in laser technology research. Researchers have used laser beam focusing characteristic parameters K_F, diffraction limit multiple M² factor, far-field divergence angle θ₀, beam diffraction limit multiple factor β and Strehl ratio S_r to evaluate the laser beam quality, but these methods are suitable for different The laser quality evaluation of the application has failed to form a unified standard for evaluating the quality of the laser beam.

Beam focusing characteristic parameter K_F

The beam focusing characteristic parameter Kf, also known as the beam parameter product (BPP, beam parameters product), is defined as 1/4 of the product of the beam waist diameter d₀ and the beam far-field divergence angle θ₀

K_F=d₀θ₀/4 (2.7)

Equation (2.7) describes the principle that the product of the beam waist diameter and the far-field divergence angle is constant, and K_F is a constant in the entire beam transmission conversion system, which is suitable for evaluating the laser beam quality in the industrial field

The diffraction limit multiple M² factors

In 1988, A.E. Siegman defined the beam width product expressed by the second moment based on the spatial threshold of the actual beam and the spatial frequency threshold as the beam quality M² factor, which is equivalent to the infinite amount of information describing the complex amplitude of the light wave, through the second-order Rectangular form to extract the combination factor, a more reasonable description of the laser beam quality, was adopted by the International Organization for Standardization 1SO/TC172/SC9/WG1 draft standard in 1991. The M² factor is defined as

M2 =(actual beam waist diameter x actual beam field emission angle )/(ideal beam waist diameter x ideal beam field emission angle)= (πd0θ0 )/(4λ ) (2.8)

في الصيغة د₀ is the diameter of the laser beam waist: θ₀ Is the far-field divergence angle; λ is the wavelength.

The M² factor is a commonly used parameter to evaluate the quality of laser beams and is also called the beam quality factor. However, it should be pointed out that the definition of the M² factor is based on the second-order matrix definition of the beam width in the spatial threshold and the spatial frequency threshold. The beam waist width of the laser beam is determined by the light intensity distribution on the cross-section of the beam waist, and the far-field divergence angle is determined by the phase distribution. Therefore, the M² factor can reflect the intensity distribution and phase distribution characteristics of the light field, and it characterizes the extent to which an actual beam deviates from the limiting diffraction divergence speed. The larger the M² factor, the faster the beam marking a divergence.

Far-field divergence angle θ

Assuming that the laser beam is transmitted along the z-axis, the far-field divergence angle is θ0, Expressed by the asymptote formula as

θ₀=lim=(w(z))/z (2.9)

In the formula, w(z) is the beam waist radius when the laser propagates to the z-axis. The far-field divergence angle characterizes the divergence characteristic of the beam propagation process, obviously, θ₀ The larger the beam divergence, the faster. In the actual measurement, after focusing or expanding the measured laser beam using a focusing optical system or a beam expanding focusing system, the ratio of the beamwidth measured on the focal plane to the focal length of the focusing optical system is used to obtain the far-field divergence angle. Because of θ₀, the size can be changed by beam expansion or focusing (such as using a telescope to expand the beam), so it is not accurate to use the far-field divergence angle as the beam quality criterion.

Laser beam brightness B

Brightness is an important parameter describing the characteristics of lasers. According to traditional optical concepts, the brightness of a laser beam refers to the energy emitted by a unit area of the light source surface perpendicular to a unit solid angle, expressed as

B =P/ΔSΔΩ (2.10)

In the formula, P is the total power (or energy) emitted by the light source; ΔS is the light-emitting area of the unit light source; ΔΩ is the emission solid angle. The laser beam is transmitted in a lossless medium or in a lossless optical system, and the brightness of the light source remains unchanged.

Equivalent beam quality factor M²_e

Since within the equivalent spot size defined by the second-order moment, the percentage of the power of the beam to the total power depends on the light field distribution, a method of describing the beam quality stipulates: the beam waist spot size and the far-field divergence angle defined in the area, the ratio of the laser power to the total power is 86.5%, and its equivalent beam quality factor is

م²_e =πω86.5θ86.5/λ (2.11)

In the formula, ω is the beam waist radius; θ is the far-field divergence angle.

Beam diffraction limit multiple factor β

From the far-field divergence angle θ. The β value can be defined as

β=(far-field divergence angle of actual beam)/(far-field divergence angle of ideal beam)=θ₀/θ_th (2.12)

The β value characterizes the degree to which the beam quality of the measured laser beam deviates from the ideal beam quality under the same conditions. The β value of the measured laser is generally greater than 1. The closer the β value is to 1, the better the beam quality. β=1 is the diffraction limit. The β value is mainly used to evaluate the laser beam just emitted from the laser resonator. It can reasonably evaluate the quality of the near-field beam. It is a static performance index and does not consider the effect of the atmosphere on the laser scattering turbulence. The measurement of the β value depends on For the accurate measurement of the beam far-field divergence angle, it is not suitable for evaluating long-distance beams.

Strehl ratio S_r

Strehl ratio S_r is defined as

س_r=(peak light intensity on the actual optical axis)/(peak light intensity on the optical axis) / =exp-(2π/λ)2(ΔΦ)2 (2.13)

In the formula, ΔΦ refers to the wavefront distortion that causes the degradation of the beam quality. S_r reflects the peak light intensity on the far-field axis. It depends on the wavefront distortion and can better reflect the influence of the beam wavefront distortion on the beam quality. Strehl ratio is often used in atmospheric optics, mainly used to evaluate the performance of adaptive optics systems to improve the beam quality. But S_r only reflects the peak light intensity on the far-field optical axis, and cannot give the light intensity distribution that energy applications are concerned about. In addition, it can only roughly reflect the beam quality, and cannot provide very useful guidance in the design of optical systems.

Surrounding energy ratio BQ value

The surrounding energy ratio, also known as the power ratio on the target surface (or in the barrel), is defined as the surrounding energy (or power) of the actual spot within the specified size and the surrounding energy (or power) of the ideal spot within the same size and the ideal within the same size The square root of the ratio of the energy (or power) surrounding the spot. Its expression is

BQ=√(E/E₀) or BQ=√(P/P₀) (2.14)

In the formula, E₀ (Or P₀) and E (or P) are respectively the ideal beam spot surrounding energy (or power) and the measured actual beam spot surrounding energy (or power) within the specified size on the target. The BQ value is for energy transmission and coupling This type of application combines the energy concentration of the beam on the target to evaluate the far-field beam quality. The BQ value includes atmospheric factors. It is a comprehensive index that describes the beam quality from the perspective of engineering applications and damage effects and is a dynamic index of the laser system affected by the atmosphere. The BQ value directly connects the beam quality and power density and is a reflection of the energy concentration. It has practical significance for the study of the energy coupling and destructive effects of the strong laser and the target.

In addition to the above parameters, mode purity, spatial coherence, and global coherence are often used to describe the beam quality of lasers. Various parameters for evaluating beam quality have their own advantages and limitations. Table 2.1 summarizes the advantages and disadvantages of various parameters and applicable fields.

Parameters	Advantages	Limitations	Applications
KF	Only includes the two factors of beam diameter and far-field divergence angle of the beam	It cannot reflect the spatial distribution of light intensity	It is suitable for industrial fields
م2 عامل	They can objectively reflect the far-field divergence angle and high-order mode content of the beam and can analyze and characterize the beam transmission transformation relationship	The introduction of wavelength parameters is not suitable for comparison between the quality of laser beams of different wavelengths	The beam width and divergence defined based on the second-order moment Angle, suitable for the field of linear beam transmission
θ0	It characterizes the degree of beam divergence	Cannot reflect the spatial distribution of light intensity	Simple understanding of beam characteristics
B	Characterizes the coherence of the beam	Cannot reflect the spatial distribution of light intensity	Display and illumination
م2e	Defines the beam width in accordance with 86.5% of the light intensity	The introduction of wavelength parameters is not suitable for comparison between the quality of laser beams of different wavelengths
β	Only one parameter of θ needs to be measured	θ can be changed, the standard beam selection is not uniform	The quality evaluation of the unstable cavity laser beam
سr	Can objectively reflect the peak light intensity on the axis	Cannot reflect the spatial distribution of light intensity	Atmospheric optics and optical radar
BQ valve	Reflects the energy concentration on the focal spot in the far-field of the beam	The power in the barrel can be obtained from different beam energy distributions	The quality of the unstable cavity laser beam is evaluated
Mode purity	A measure of the deviation of the actual beam intensity distribution from the ideal beam intensity distribution	Not universal
Spatial coherence	Reflects the beam spatial coherence	Not universal
The global degree of coherence	Reflects the spatial coherence of the beam	Not universal

The output shape of the laser beam

The spatial shape of the laser beam is determined by the resonant cavity of the laser. Under given boundary conditions, the electromagnetic field distribution in the resonant cavity is determined by solving the wave equation. In a circular symmetric cavity, there is a simple spatial shape of the transverse electromagnetic field.

The transverse electromagnetic field distribution in the cavity is called the transverse mode in the cavity, which is expressed by TEM_mn. TEM₀₀ represents the fundamental mode, TEM₀₁، تيم₀₂ and TEM₁₀، تيم₁₁، تيم₂₀ represent low-order modes, and TEM₀₃، تيم_04, and TEM₃₀، تيم₃₃، تيم₂₁, etc. represent high-order modes. The output of most lasers is the high-order mode. In order to get the output of fundamental mode or low-order mode, it is necessary to adopt mode selection technology.

At present, the commonly used model selection techniques are based on increasing the loss of diffraction in the cavity. One method is to increase the cavity length by using a multi-refractive cavity to increase the diffraction loss in the cavity. The other method is to reduce the diameter of the laser’s discharge tube or increase the cavity length. A small aperture diaphragm is added to the cavity. The diffraction loss of the fundamental mode beam is very large and can reach the diffraction limit, so the divergence angle of the fundamental mode beam is small. From the perspective of increasing the laser pumping efficiency, the cavity mode volume should fill the entire active medium as much as possible, that is, in the long tube laser, the TEM₀₀ mode output dominates, while in the high-order mode laser oscillation, the fundamental mode only accounts for a small amount of the laser power. Part, so the high-order mode output power is large.