CN1226655C - Phase compensation method and device for improving super diffraction limit of laser beam energy density - Google Patents

Abstract

A phase compensation method and device for improving the energy density of laser beams beyond the diffraction limit, the method comprising: using a compensating phase plate at the end of the lowest-order transverse mode laser collimation and amplification system to perform phase compensation on the diffraction-limited beam; using Gaussian beam propagation in principle; when determining the structure of the phase plate, firstly adopting a reverse transfer algorithm to infer the continuous phase distribution of the phase plate from the required far-field compressed beam wavefront, then using diffraction theory to obtain its far-field distribution from the Gaussian beam with additional phase distribution, and optimizing the distribution of the phase plate; then quantizing the phase plate with the optimized continuous phase distribution, and optimizing it with diffraction theory at the same time, and finally obtaining the phase structure of the quantized distribution; the phase plate structure satisfies: the compression ratio of the main lobe of the beam reaches 0.8, the energy loss ratio of the main lobe is 0.93, and the energy density ratio is 1.16. The device is composed of a laser, a shaping collimation system, a beam amplification device, and a compensating phase plate in sequence.

Description

Phase Compensation Method and Device for Improving Superdiffraction Limit of Laser Beam Energy Density

Technical field:

The invention relates to wavefront phase compensation, in particular to a phase compensation method and device for improving the super-diffraction limit of laser beam energy density. In particular, it refers to compressing the beam divergence of the collimated and amplified single transverse mode laser with a beam divergence less than the optical diffraction limit by designing a suitable phase plate, but at the same time ensuring that the beam energy is concentrated in the compressed far-field diffraction main lobe, so that the compressed A phase compensation correction technology for increased energy density, the main application direction is laser communication and other laser applications that require small divergence.

Background technique:

In long-distance free space laser communication, especially in communication between satellites, it is required that the receiving end of optical communication has sufficient signal laser power to ensure the bit error rate of the required information transmission, which mainly involves the transmitting power of the laser (receiving power and Proportional to), the divergence of the collimated emitted laser (receiving power is inversely proportional to its square), the aperture of the receiving primary mirror (receiving power is proportional to its square), the sensitivity of the optical receiver, etc. However, due to the structure and weight of the laser itself and the limitation of the energy and weight that the satellite can provide, the maximum available single-mode laser emission power has a certain limit value. The size of the receiving optical aperture basically determines the size and weight of the optical terminal, because the satellite load weight and size constraints make the receiving optical aperture have a certain value range, generally less than 300 mm. In addition, the sensitivity of the optical receiver also has a limit value due to the limited bandwidth, that is, the quantum limit sensitivity. Therefore, for long-distance laser communication under the various constraints mentioned above, it should be required that the divergence of the laser collimated emission beam should be as narrow as possible, that is, close to the optical diffraction limit, and it generally needs to reach several to tens of microradians to ensure The communication receiving end has a sufficiently high receiving power. In addition, the laser beam control technology with smaller divergence also has practical significance in other military and civilian applications of lasers.

The beam output by the laser itself has a mode with the smallest divergence, that is, the lowest-order transverse mode, which is usually described by a Gaussian beam. The laser output in the single lowest transverse mode state has reached the optical diffraction limit. In order to further reduce the beam divergence, a telescope system is generally used for optical collimation and amplification of the beam, but an ideal telescope system has a minimum divergence limit under the aperture limit, that is, the optical diffraction limit, which is inversely proportional to the emission aperture. Therefore, the minimum divergence of the single transverse mode laser beam or the amplified beam is determined by the Gaussian wave waist of the transverse mode and the diffraction limit of the emission aperture. Ideally, the output beam will reach or be very close to the diffraction limit of the Gaussian beam. The present invention utilizes the compensating phase plate to compress the beam divergence exceeding the optical diffraction limit for the single transverse mode laser beam or the collimated and amplified expanded beam, and also makes the energy concentrated on the compressed far-field main lobe, thereby A far-field emission main lobe with no energy reduction and a divergence smaller than the diffraction limit is obtained. This can effectively ensure that the receiving end of optical communication has a sufficiently high receiving power for long-distance laser communication under the limitation of the maximum possible laser power and sensitivity.

Super-diffraction limit technology usually refers to the technology of compressing the spot size generated by the point spread function of the imaging system, that is, the Airy disk, in imaging optics. Under ideal conditions, the point spread function is determined by the aperture of the imaging lens. (See 1. Principles of Optics, M. Born and E. Wolf, 7th (extended), p464). The earliest people used the amplitude pupil function to realize the compression of the Airy disk (2.C.J.R.Sheppard, Optik 48, 339 (1977), 3.R.Boivin and A.Boivin, OPT.Acta 27, 587 (1980), 4. Z.S.Hegedus, Opt.Acta 32,815 (1985)), but this method makes the energy loss of transmission very big. Then the phase plate method was adopted (5.J.J.E.Wilkins, J.Opt.Soc.Am.40, 222(1950), 6.T.R.M.Sales and G.M.Morris, in Joint International Symposium on Optical Memory and Optical Data Storage, Vol.12 of 1996 OSA Technical DigestSeries (Optical Society of America, Washington, D.C., 1996), pp.290-292, 7.T.R.M.Sales and G.M.Morris, Opt.Lett., 22, 582(1997)), that is, using a phase pupil The filter changes or compensates the spatial phase distribution of the incident beam to achieve spot compression. The principle is basically the same as that of the amplitude pupil filter, but it effectively improves the problem of energy transfer loss when using the amplitude pupil filter. In addition, there is also a pupil filter using an amplitude and phase hybrid structure to achieve far-field spot compression (8. Z. S. Hegedus and V. Sarafis, J. Opt. Soc. Am. A 3, 1892 (1982)). The effective compression of the light spot has made this technology widely used in optical information storage (9.A.B.Marchant, Optical Recording: a Technical Overview (Addison-Wesley, Reading, Mass., 1990) Chp.5, p.101), confocal microscopy ( 10. T.Wilson, Confocal Microscopy (Academic, London, 1990), Chap.5, p.171) and imaging and laser printing, etc. have been applied. However, when the above-mentioned super-resolution technology is used to compress the width of the main lobe of light waves in the far field, it is inevitable that the energy of the main lobe is continuously transferred to the side lobes. Therefore, although the diffraction main lobe is reduced, the energy of the diffraction main lobe is also reduced. This does not pose a problem in imaging optics, where the main purpose is to increase resolution. However, when it is used to compress the divergence of the laser emission beam, although the width of the main lobe is compressed, this compression is meaningless when the energy contained in the main lobe is much lower than the energy in the original beam width. In addition, in the super-resolution theory of imaging optics, only the peak intensity ratio (Strehl ratio) of the main lobe before and after compression is defined, but the energy ratio and energy density ratio of the main lobe before and after compression are not defined, which shows that the above-mentioned super-resolution In the technology, the energy conversion of the main lobe is not considered, or the amount of energy of the main lobe is not the key to the problem. Moreover, the compensation phase plate is to perform phase compensation on the focused or converging beam of the lens, that is, to implement super-resolution transformation at the last stage of the optical system. If this kind of beam is used for laser collimation and emission, because the emission beam needs additional lens for collimation and amplification, this means that the phase plate is not placed at the end of the optical system, so the optical elements after the phase plate will destroy the phase compensation The wavefront of the beam makes the beam that reaches the super-diffraction limit be distorted again, and the finally obtained beam is equivalent to the situation without phase compensation of the super-diffraction limit. In addition, in the calculation of imaging optics, the super-diffraction limit technology uses a plane wave model, which is not suitable for laser beams, and Gaussian propagation optics is more accurate in laser applications.

Invention content:

The technical problem to be solved by the present invention is to overcome the above-mentioned difficulties in the prior art, and to provide a phase compensation method and device for improving the super-diffraction limit of laser beam energy density. The caliber achieves the effect of diffraction-limited divergence of a larger caliber, which is very conducive to the lightweight and miniaturization of space laser communication terminals.

Basic scheme of the present invention is:

A phase compensation method for improving the super-diffraction limit of laser beam energy density, characterized in that:

① At the end of the lowest-order transverse mode laser collimation and amplification system, a compensating phase plate is used to perform phase compensation on the diffraction-limited beam;

② In principle, Gaussian beam propagation is adopted;

③ When determining the structure of the phase plate, the backpropagation algorithm is firstly adopted, that is, the iterative algorithm for inverting the continuous phase distribution of the phase plate from the wavefront of the required far-field compressed beam. After obtaining the phase structure of the compensated phase plate initially, the diffraction In theory, the far-field distribution of the Gaussian beam with additional phase distribution is obtained, and the distribution of the phase plate is optimized; then the phase plate with the optimized continuous phase distribution is quantized, and at the same time, it is optimized by diffraction theory, and finally the quantization is obtained. distributed phase structure;

④ The phase plate structure of the two rings with boundary is obtained by calculation, the phase plate structure satisfies: the compression ratio of the main lobe of the beam reaches 0.8, the energy loss ratio of the main lobe is 0.93, and the energy density ratio is 1.16.

The phase compensation device for improving the super-diffraction limit of the energy density of the laser beam established by using the phase compensation method for increasing the energy density of the laser beam above the super-diffraction limit has a structure that it sequentially includes: a laser, a shaping and collimation system along the forward direction of the laser beam. , a beam amplification device and a compensating phase plate.

Said laser is a lowest order single transverse mode laser.

This structure means that the actual effect of a 150mm caliber can be achieved by using a 120mm caliber emitting primary mirror, which meets the requirements of light weight and miniaturization of laser communication terminals.

Advantages of the present invention:

1. The super-diffraction limit technology of the present invention is to use an optical plate with phase distribution to compensate the collimated and amplified Gaussian laser beam, so that its divergence angle is compressed. The pure phase plate has the advantage of no absorption loss, and Gaussian optics is used to fit the laser The beam is practical, so the compensation accuracy is high.

2. In the design of the phase plate, the backward transfer algorithm combined with the optimization calculation of the forward diffraction has the advantage of being able to realize the global optimization calculation, and its characteristic is that the required results can be obtained relatively easily, especially the definition of The main lobe energy ratio and energy density ratio are used to judge the energy loss of the super-diffraction limit far-field spot obtained by phase compensation, which can not only achieve main lobe compression but also achieve main lobe energy concentration, making the application of this technology truly possible in principle. established. Considering the manufacturing process of the phase plate, the designed phase distribution is quantized and optimized, which makes the phase plate easy to manufacture.

In short, this method of phase compensation can achieve the effect of a larger diffraction-limited divergence with a smaller emission optical aperture, which is very conducive to the lightweight and miniaturization of space laser communication terminals.

Description of drawings:

FIG. 1 is a structural block diagram of a super-diffraction-limited phase compensation device for collimating laser beams according to the present invention.

Fig. 2 is a schematic diagram of the numerical calculation process of the super-diffraction limit compensation phase plate in the present invention

Fig. 3 is a schematic diagram of the phase distribution of the phase plate determined by the reverse algorithm in the present invention.

FIG. 4 is a schematic structural diagram of a quantized phase plate in the present invention.

Fig. 5 is a comparison diagram of the far-field light intensity distribution of the laser collimated emission beam before and after compression in the present invention.

Specific implementation plan:

Please refer to FIG. 1 first. FIG. 1 is a structural block diagram of a super-diffraction-limited phase compensation device for collimating laser beams according to the present invention. It can be seen from the figure that the device structure of the present invention includes: a laser 1 , a shaping and collimating system 2 , a beam amplification device 3 and a compensating phase plate 4 . The single lowest-order transverse-mode beam emitted by the laser 1 is collimated by the shaping and collimating system 2 to become a uniformly distributed Gaussian spot, or a light spot is output after being transmitted through an optical fiber, and the collimated beam is amplified by the beam amplifier 3 to obtain A Gaussian beam with a certain emission caliber (that is, a diffraction-limited beam) and a certain degree of divergence is compensated by the compensation phase plate 4 to obtain a spatially compressed far-field spot in the far field. The energy of the spot is basically constant. Assuming that the amplitude of the Gaussian beam after collimation and amplification is a(x, y), and the phase distribution of the compensation phase plate 4 is φ(x, y), then the complex amplitude of the beam after passing through the compensation phase plate 4 is b(x, y )for:

b(x,y)=α(x,y)exp(iφ(x,y)) (1)

The complex amplitude distribution B(f _x , f _y ) of the laser beam in the far field after phase compensation can be expressed as the following form,

B(f _x , f _y )=A(f _x , f _y )*Φ(f _x , f _y ) (2)

Where x, y are the coordinates of the phase plate, f _x , f _y are the coordinates of the output surface, A(f _x , f _y ) is the Fourier spectrum of α(x, y), Φ(f _x , f _y ) is the input The Fourier transform of the phase distribution exp(iφ(x, y)), therefore, proper control of the compensation phase function φ(x, y) may make the divergence of the compensated beam smaller than the original divergence of the beam.

The present invention still uses two parameters in imaging optics when evaluating the compression effect of the light spot, the first zero point ratio: G=x _s /x ₀ and Strehl ratio: S=I _sm /I _0m , where x _s and x ₀ denote the first zero value of the far-field diffraction main lobe with and without super-resolution phase plate, and I _sm and I _s0 denote the main lobe of far-field diffraction with and without super-resolution phase plate, respectively. The light intensity value at the center point of the petal. In addition, in order to measure the energy loss of the far-field diffraction main lobe after compression, the integral energy ratio of the far-field diffraction main lobe is defined: R _I =I _s /I ₀ , and the energy density ratio $T_I=\frac{I_{\mathrm{the\; s}}/x_{\mathrm{the\; s}}}{I_0/x_0}(=R_I/G),$ Among them, I _s and I ₀ are the integrated energy values of the far-field diffraction main lobe with and without super-resolution phase plate, respectively.

According to the literature (7, T.R.M.Sales and G.M.Merris Opt.Lett., 22, 582 (1997)), under the small signal approximation, the compression ratio of the far-field spot has the following relationship with the maximum value of the Starr ratio:

${\mathrm{<span\; class="notranslate">\; S</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \_</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}\underset{\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{<span\; class="notranslate">\; \&infin;</span>}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\frac{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; A</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="p"\; filenames="C0314210500103.png"\; state="\{\{state\}\}">p</figure-callout></span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; !</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; G</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

In the above formula, A represents the maximum value of the amplitude transmittance, ${\mathrm{\&eta;}}_1^A=3.8325$ is the position of the first zero point of the Airy disk.

When the far-field spot compression ratio (that is, the first zero ratio G) G<0.46, as the spot compression ratio decreases, the Starr ratio also decreases rapidly, that is, for relatively large compression, the Strehl ratio and the first zero There is a relationship S<G for the point ratio, which indicates that the rate of decrease of the peak light intensity is greater than the reduction of the far-field spot, that is, the energy loss is large. At this time, the energy density ratio T _I <1, this theoretical result is very important for laser communication. Adverse. However, when G>0.46, the above theoretical value has exceeded the small-signal approximation condition and loses its reference value, which shows that in the case of a small compression ratio, S≥G is entirely possible, that is, the decrease of the peak light intensity The speed can be smaller than the reduction of the far-field spot, and the energy density ratio T _I can be greater than 1. For this reason, the compensation phase plate 4 in the present invention is under a small compression ratio (i.e. G>0.46), the Strehl ratio does not decrease significantly, and the integral energy I _s of the entire far-field spot also decreases little and the energy density ratio T _I >1 obtained under four conditions.

In the design of the phase plate, the present invention adopts the technical route shown in FIG. 2 to perform global optimization calculation on the structure of the compensation phase plate. It includes several parts such as backward transfer algorithm, optimized phase plate, phase plate quantization, error correction and phase plate output. Firstly, the backward transfer algorithm is used to give the structure of the qualified phase plate, and then the far-field distribution of the collimated and amplified Gaussian beam passing through the phase plate is calculated by using the diffraction theory, and the parameters in the reverse algorithm are adjusted, and they are kept far away. The results of the field distribution are compared, and the optimal phase plate structure conforming to the conditions is obtained. Usually, the phase of the phase plate given by the backpropagation algorithm is continuously distributed between [-π, π]. It is technically difficult or even impossible to make such a phase plate precisely, so the continuous The structure of the distributed phase plate performs phase plate quantization, that is, the continuous phase distribution is quantized into a stepped phase distribution. The far-field spot obtained by phase compensation using the quantized phase plate may have a certain deviation from the far-field spot obtained by using the continuous phase distribution compensation phase plate, so the quantized phase plate needs further error fix. Use the diffraction theory again to calculate the far-field distribution of the laser beam after passing through the quantized compensation phase plate, and compare the super-diffraction-limited far-field spot under the quantized compensation phase plate with the situation before the quantization phase plate, and change the corresponding parameters to optimize the quantized compensation phase plate. Finally, the optimized quantized phase plate is output.

Concrete technical solution of the present invention is as follows:

1. Since the present invention uses super-diffraction limit technology in laser emission, it is required that the laser output of the laser 1 in the structure diagram 1 must reach the optical diffraction limit, that is, the lowest-order transverse mode mode, which is usually described by a Gaussian beam . And the subsequent integer collimation system 2 and the beam amplification device 3 must ensure that the Gaussian beam is collimated and amplified without changing the beam quality of the Gaussian beam. The resulting output beam will be at or very close to the diffraction limit of a Gaussian beam. The compensating phase plate 4 placed behind the transmitting system performs phase compensation on the wavefront of the diffraction-limited or near-diffraction-limited Gaussian beam, thereby realizing the compression of the laser beam divergence, but the width of the beam divergence or the far-field diffraction main lobe of the beam While being compressed, the energy of the diffraction main lobe is reduced lower than the compression ratio of the main lobe, that is, the energy density ratio is greater than 1, which makes the present invention have practical significance. Therefore, in principle, the present invention needs to adopt the propagation of Gaussian beams.

2. The structure of the compensating phase plate in the present invention adopts the backward transfer algorithm to be solved. Given the amplitude distribution of the input light wave and the light intensity distribution of the far-field diffraction spot (of course, the diffraction spot satisfies a certain spot compression ratio and is guaranteed to produce an effective divergence), the undetermined solution for the phase plate on the input surface phase structure. The specific steps are as follows: assuming the target light intensity distribution on the output surface, and randomly or specially selecting the initial phase of the far-field light wave, performing an inverse Fourier transform on the constructed far-field complex amplitude, and transforming the amplitude of the transformed light wave complex amplitude The value is replaced by the known amplitude of the light wave on the input surface, and then the positive Fourier transform is performed, and the amplitude of the complex amplitude of the light wave transformed into the far field is expressed by the square root of the set far field diffraction light intensity to construct a new output light wave Repeat the amplitude and enter the next cycle. The integral energy of the input and output remains unchanged throughout the iterative process, and the output waveform is continuously compared with the far field of the Gaussian beam during the cycle. When the compression ratio meets certain conditions, the phase distribution on the input surface at this time is output. , thus determining the structure of the compensating phase plate.

3. The phase plate structure obtained by backpropagation algorithm to achieve super-diffraction limit spot compression is not a first-order or second-order phase structure but a continuous phase distribution. For continuously distributed phase plates, the manufacturing process and precision can be controlled. To this end, we quantize the continuous distribution of the phase structure to obtain a step-like phase distribution. The quantized phase plate can be accurately realized by using the manufacturing process of the large-scale integrated circuit of binary optics.

4. In the quantization process of the phase plate, due to the influence of factors such as the selection of the phase turning position, the value of the phase difference between the inner and outer rings of the phase plate, and the size of the outer ring of the phase plate, the results of the actual far-field diffraction pattern may be affected. lead to varying degrees of deviation. Therefore, we have carried out corresponding numerical calculations on the influence of the changes of these related factors on the far-field diffraction pattern. During the calculation process, the turning position of the phase when the phase plate is quantized, the phase difference between the inner and outer rings of the phase plate, and the size of the outer ring of the phase plate are constantly changed, and then the structure of the phase plate is optimized to obtain the best super-diffraction-limited light Strong distribution, so as to obtain the parameters of phase plate quantization optimization.

Assume that the collimated and amplified laser beam is a Gaussian beam with a waist of ω ₀ =10 mm. Fig. 3 shows the schematic diagram of the phase distribution of the compensation phase plate obtained by using the reverse algorithm under the condition that the integral energy ratio R _I =I _s /I ₀ of the main lobe of the far-field diffraction before and after compression does not decrease substantially. It can be seen that the phase plate structure obtained by the reverse algorithm to achieve super-diffraction spot compression is not a second-order phase structure but has a continuous phase distribution. For the phase plate structure with a compression ratio of 0.8, its large profile has two steps, and the phase difference between the two steps is approximately π, so two phase rings plus a diaphragm can be used for phase quantization. form. When quantizing, assume that the radii of the inner and outer rings are r ₁ and r ₂ respectively, and the corresponding phases are  ₁ and  ₂ respectively. The result of quantization is shown by the dotted line in Fig. 4, where each parameter is set as follows: r ₁ =18.75mm, r ₂ =25mm, Δ= ₂ - ₁ =3.14rad.

Figure 5 shows the distribution of diffracted light intensity of Gaussian beams in the far field before and after phase plate compensation, where the compression ratio G=0.8, while the integral energy ratio R _I of the main lobe of far-field diffraction =0.93, and the energy density ratio T _I =1.16 .

Claims (2)

1, a kind of phase compensation method that improves the super-diffraction limit of laser beam energy density, it is characterized in that: ① At the end of the lowest-order transverse mode laser collimation and amplification system, a compensating phase plate is used to perform phase compensation on the diffraction-limited beam; ② In principle, Gaussian beam propagation is adopted; ③ When determining the structure of the phase plate, first adopt the reverse transfer algorithm, that is, the iterative algorithm that reverses the continuous phase distribution of the phase plate from the required far-field compressed beam wavefront, and after initially obtaining the phase structure of the compensated phase plate, then use the diffraction theory Calculate the far-field distribution from the Gaussian beam with additional phase distribution, and optimize the distribution of the phase plate; then quantize the phase plate with the optimized continuous phase distribution, and optimize it with diffraction theory at the same time, and finally obtain the quantized distribution phase structure of ④ The phase plate structure of the two rings with boundary is obtained by calculation, the phase plate structure satisfies: the compression ratio of the main lobe of the beam reaches 0.8, the energy loss ratio of the main lobe is 0.93, and the energy density ratio is 1.16. 2. The phase compensation device for improving the super-diffraction limit of the laser beam energy density according to the phase compensation method for improving the laser beam energy density of the super-diffraction limit according to claim 1 is characterized in that it is sequentially along the laser beam advancing direction : laser (1), shaping collimation system (2), beam amplification device (3) and compensating phase plate (4).

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