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Laser longitudinal mode selection technology

1. Significance and principles of longitudinal mode selection

in order to obtain a good monochromatic and coherent laser beam, the laser is required to oscillate at a single frequency. In general, a multi transverse mode laser is a multi frequency laser, and the frequency interval of a multi longitudinal mode laser is larger. The number of vertical and horizontal oscillations of the laser is determined by the cavity length, the gain linewidth of the working material and the excitation level. Because only those longitudinal mode frequencies within the gain linewidth can really vibrate and form multi longitudinal mode oscillation. Some practical applications, such as optical communication, laser holography, precision measurement, require that the laser has high monochromaticity and high coherence, and must work at a single frequency, and the selection of longitudinal mode is a necessary condition for single frequency work

set the approximate frequency range of laser oscillation determined by gain linewidth and excitation level (threshold) as Δ v. The frequency interval between two adjacent oscillating longitudinal modes allowed by the cavity is δ v. Then the number of longitudinal modes that actually vibrate is Δ v/δ v。 It can be seen that reducing the longitudinal modulus of oscillation (i.e. selecting the longitudinal mode) can be achieved in two ways: one is to try to compress the gain bandwidth of the laser Δ v； The second is to try to increase the frequency interval between two adjacent oscillation longitudinal modes δ v。 The following selection methods of longitudinal formwork are based on this

2. Method of longitudinal mode selection

(1) dispersion cavity method. When the working substance has multiple fluorescent spectral lines or a wide spectral band, the placement of dispersion prisms or reflection gratings in the cavity has seriously restricted the implementation of new energy vehicles, and the optical elements can be used to roughly select the longitudinal modes. The linewidth of the selected frequency oscillation is compressed to 0 Nm or so

① prism dispersion cavity. A dispersion prism is built into the cavity, and the narrowest wavelength range of its frequency selective oscillation is determined by the role divergence of the prism and the beam divergence angle. Let the top angle of the prism be a, and the beam is at the minimum deflection angle δ M mode passes through the prism (i.e. the optical path is symmetrical), because

n=sin[（ δ M+a)/2]/sina/2 ()

the role dispersion of prism is defined as:

d λ= d δ m/d λ ()

after deriving equation (20-10), there is:

d λ= d δ m/dn·dn/d λ= 2sina/2/(1-n2sina/2)1/2·dn/d λ ()

in order to minimize the insertion loss of the prism, the light incidence angle I should be incident at Brewster angle IB

then there is: sina/2=sinib/n()

substituted into (20-12) formula, then:

d λ= 2siniB/(n2(1-sin2iB))1/2·dn/d λ ()

let the divergence angle of the intracavity oscillating beam be θ， Then the minimum wavelength interval of the laser oscillation spectral line in the cavity is:

Δλ min=1/D λ·θ ()

Δλ MI in automobile n= (N2 (1-sin2ib)) 1/2/2sinib · dn/d λ·θ ()

if taken θ= 1mrad (milliradian) Δλ min≈1nm。

The 488nm and 514.5nm spectral lines of the argon ion laser can be separated by this method② grating dispersion cavity. This dispersive cavity uses a reflection grating to replace a reflector of the resonator. From the grating equation:

s (sina1+sina2) =k λ ()

where D is the grating constant, A1 is the incident angle, A2 is the reflection angle, and K = 0, 1, 2, 3... Is the series of the principal maxima of interference

raster character scatter

d=da2/d λ= K/dcosa2=d(sina1+sina2)/λ dcosa2=sina1+sina2/λ Cosa2()

when a1=a2=a0 (grating flare angle):

d=2tga0/λ ()

the allowable beam divergence angle in the laser cavity is θ， The allowable oscillation spectral line width due to grating dispersion should be:

Δλ=θ/D= λ/2tga0· θ (20-20)

such as A0 = 30 ° θ＝ 1mrad, which can be calculated in the visible light band Δλ About a few tenths of a nanometer (nm). It can be seen that its dispersion selection ability is higher than that of prism, and there is no transmission loss of beam. It can be applied to a variety of laser mode selection in a wide spectral region

dispersive cavity method can select narrow oscillating spectral lines from a wide range of spectral lines, but there is still an interval of Δ A series of discrete oscillation frequencies of v=c/2nl - multiple longitudinal modes. Therefore, the dispersive cavity method is only a rough selection. In order to further select the single longitudinal mode, other methods need to be used

(2) short chamber method. For a certain resonator, any standing wave oscillation that falls within the fluorescence linewidth and whose gain is above the threshold level can form laser oscillation, which is the multi longitudinal mode working state

the interval between two adjacent longitudinal modes is:

Δ Vq=c/2nl()

according to formula (20-21), longitudinal mode frequency interval Δ VQ is inversely proportional to the length of the spectral cavity. In order to obtain a single frequency oscillation in the laser gain curve, we can try to increase the longitudinal mode frequency interval so that there is only one longitudinal mode oscillation within the effective width of the fluorescence spectral line. Therefore, it can be achieved by reducing the cavity length L, which is the so-called principle of selecting longitudinal mode by short cavity method

this method is simple and practical, and can be widely used in various lasers, especially low-power gas lasers

such as the effective width of the fluorescence spectrum of He Ne laser Δ Vg=1500mhz (equivalent Δλ= 0.005n according to the reason why the jaw cannot be clamped, the engineers of Jinan assaying suggest the following preventive measures to customers and friends: about M), when l=1m,

Δλ q=c/2nL=3 × 108m/s/2 × one × 1m = 150mhz

that is, the laser may have 1500mhz/150MHz equal to 10 longitudinal modes oscillating at the same time

if the cavity length of the laser is shortened to 10cm, then Δ V=1500mhz, at this time, only one longitudinal mode can oscillate

the short cavity method is only applicable to lasers with narrow fluorescence linewidth, otherwise the cavity length will be too short to be used. In addition, it should be pointed out that due to the shortening of the cavity length, the laser output power is significantly reduced, so this method is not suitable for high-power lasers

(3) Fabry Perot etalon method. In order to overcome the shortcomings of short cavity method and obtain single longitudinal mode oscillation with large power output, a Fabry Perot etalon is usually inserted into the resonator to select the longitudinal mode

the Fabry Perot etalon is equivalent to a filter, which has different transmittance for light of different wavelengths (or frequencies) according to the following formula:

t（ λ)= 1/(1+Fsin φ/2) ()

where: F = 4 ρ/(1- ρ) 2； φ＝ π/2 λ·Δ；ρ Is reflectivity; φ Represents the phase difference of two adjacent outgoing rays participating in multi beam interference in the etalon; Δ Is the optical path difference

Δ= 2ndcosi

so the transmittance of the etalon can be expressed as

t（ λ)= (1- ρ) 2/(1- ρ) 2+4 ρ sin2 φ/2 ()

the condition for the maximum transmittance is:

Δ= 2ndcosi=K λ= K. C/V ()

from formula (20-24), the interval between adjacent frequency values with maximum transmittance can be calculated as:

Δ V=c/2ndcosi ≈ c2nd()

from the above-mentioned transmission light multi beam interference principle, the reflectance of the etalon ρ The larger the spectral width is, the narrower the selectivity is

it can be seen that for multi longitudinal mode lasers, after inserting a etalon into the resonator, we should appropriately select the thickness D and reflectivity of the etalon ρ， Make the peak frequency interval of the etalon Δ V is equivalent to the fluorescence linewidth of the laser, so that within the effective gain linewidth, only one longitudinal mode can pass through, and the remaining longitudinal modes are "filtered out" by the etalon because of their low transmittance, so as to achieve the purpose of selecting longitudinal modes

The advantage of selecting longitudinal mode of the Fabry Perot etalon is that the thickness d of the parallel plane plate of the etalon can be adjusted to be very thin. Therefore, single longitudinal mode oscillation can also be obtained for working substances with wide gain linewidth and argon ions, ruby, YAG, etc., which can be applied to high-power lasersin addition to the above-mentioned longitudinal mode selection methods, there are other methods, such as compound cavity method, adding metal film absorption method in the cavity and adding some saturable absorption dye medium

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