RU2079941C1 - Device for determining the characteristics of single supershort pulses of laser radiation - Google Patents

Abstract

FIELD: measuring laser equipment connected with recording, analysis and determination of characteristics of laser radiation. SUBSTANCE: the device is a three-dimensional volumetric structure. It has two control signal channels with cells-gates; the cells-gates are installed in such a manner that their opening occurs in mutually perpendicular directions; and the channel of the signal under analysis, in which the direction of propagation of radiation is perpendicular to the planes of the cells-gates. Astigmatic telescopic beam spreading systems are installed in the control signal channels, and a stigmatic telescopic system is provided in the channel of the signal under analysis. A two-dimensional photographic or photoelectric recording system with a matrix receiver for the fifth-order correlation function is located at the output. EFFECT: determination of intensity- versus-time dependence for single supershot pulses of laser radiation. 3 dwg

Description

The invention relates to the field of measuring laser technology related to the registration, analysis and characterization of laser radiation, in particular, the dependence of the intensity on time for single signals of laser radiation of short duration, up to 10 ^-13 10 ^{-14 C.}

где τ разница во времени задержек сигналов в каналах интерферометра,
I₁(t), I₂(t) интенсивности сигналов в каналах интерферометра;
t_s полная длительность исследуемого сигнала.Known devices for determining the characteristics of single ultrashort pulses of laser radiation are based on measuring second-order correlation functions or similar functions and analyzing their structure to obtain information about the pulse duration. Various physical methods are used to measure these functions. One of the options is to use a two-beam interferometer circuit with the formation of the second optical harmonic in the nonlinear optical crystal at the output with the corresponding type of synchronism. The recorded response is described by a second-order correlation function

where τ is the time difference between the signal delays in the channels of the interferometer,
I ₁ (t), I ₂ (t) signal intensities in the channels of the interferometer;
t _{s is the} total duration of the signal under investigation.

([1] с. 36 37).Time interval τ $\genfrac{}{}{0ex}{}{\text{(2)}}{\text{I}}$ , in which the correlation function is nonzero, allows you to determine the duration of the analyzed radiation pulse

([1] p. 36 37).

Another option involves recording the luminescence fluorescence that occurs when the ultrashort optical signals are counterpropagated in a cell with a dye that provides luminescence excitation during two-quantum absorption. The logged response is described by the function
Ψ (τ) = I ⁽²⁾ (0) (1 + r ² ) + I ⁽²⁾ (τ) 4r,
where I ⁽²⁾ (τ) is the second-order correlation function,
r is the ratio of signal intensities corresponding to the forward and backward propagation of radiation.

Time interval τ $\genfrac{}{}{0ex}{}{\text{(2)}}{\text{Ψ}}$ , in which the function J (τ) is different from the background value I ² (O) (I + r ² ), allows one to determine the pulse duration
τ _pul = τ $\genfrac{}{}{0ex}{}{\text{(2)}}{\text{Ψ}}$ / 2
([1] p. 37 44).

Для затворов на квадратичном электрооптическом эффекте, отклик описывается вырожденной функцией корреляции третьего порядка

зависящей только от одного аргумента и потому не содержащей дополнительной информации по сравнению с функцией корреляции второго порядка. Интервал времен τ $\genfrac{}{}{0ex}{}{\text{(2)}}{\text{I}}$ или τ $\genfrac{}{}{0ex}{}{\text{(3)}}{\text{I}}$ , в котором соответствующая функция отлична от нуля, позволяет определить длительность анализируемого импульса
τ_pul= τ $\genfrac{}{}{0ex}{}{\text{(2)}}{\text{I}}$ /2 или τ_pul=τ $\genfrac{}{}{0ex}{}{\text{(3)}}{\text{I}}$ /2
([1] стр. 57 61).The third version of the scheme is based on the use of high-speed optical shutters. For shutters operating on a linear electro-optical effect, the response described by the second-order correlation function is recorded

For shutters with a quadratic electro-optical effect, the response is described by a degenerate third-order correlation function

depending on only one argument and therefore not containing additional information compared to the second-order correlation function. Time interval τ $\genfrac{}{}{0ex}{}{\text{(2)}}{\text{I}}$ or τ $\genfrac{}{}{0ex}{}{\text{(3)}}{\text{I}}$ , in which the corresponding function is nonzero, allows you to determine the duration of the analyzed pulse
τ _pul = τ $\genfrac{}{}{0ex}{}{\text{(2)}}{\text{I}}$ / 2 or τ _pul = τ $\genfrac{}{}{0ex}{}{\text{(3)}}{\text{I}}$ / 2
([1] p. 57 61).

 The disadvantages of these systems are that they do not allow an unambiguous interpretation of the results without involving additional information. Due to the symmetry of the second-order correlation function, information on the asymmetry of the signal cannot be obtained. In the spectral representation of the intensity distribution, information on the phases of the spectral components cannot be obtained.

Great opportunities are opened up by the application of third-order correlation functions depending on two arguments τ ₁ and τ ₂ .

для которых разработаны методы обработки, позволяющие определить структуру сверхкоротких оптических сигналов в виде зависимости интенсивности сигнала от времени и отмечены возможности снижения роли случайных аддитивных помех ([2] с. 162 163).

for which processing methods have been developed that make it possible to determine the structure of ultrashort optical signals in the form of a dependence of signal intensity on time and the possibilities of reducing the role of random additive noise are noted ([2] p. 162 163).

Known measuring devices for determining the characteristics of ultrashort pulses of laser radiation with a three-beam intensity correlator, in which the result is recorded at the output of the third-order correlation function. One of the variants of the three-beam intensity correlator contains a nonlinear crystal at the output for generating optical harmonic at a frequency of 3ω (ω is the frequency of the initial optical signal), at a frequency of the third optical harmonic ([2] p. 164 165). An example of such a system is a three-beam Michelson interferometer. Due to the displacement of the mirrors in two channels of the interferometer, three signals are generated at the output with time delays 0, τ ₁ and τ ₂ . The signals are sent to a nonlinear crystal, in which the third optical harmonic emitted by the filter is generated. As a result, at the output for a set of different combinations of delays τ ₁ and τ ₂ , using the same repetitive pulses, one can obtain a sequence of samples describing a third-order function, based on which analysis it is possible to restore the structure of the analyzed signal.

 Another variant of the circuit contains two nonlinear crystals. An optical signal is formed in the first crystal at a frequency of 2ω at a frequency of the second harmonic. A harmonic is formed in the second crystal at the total frequency (2ω + ω).

 The disadvantage of these schemes is that for registration it is required to use a sufficiently large set of repeating identical in structure signals and the inability to use them for the analysis of single optical signals.

The closest to the claimed invention in technical essence and the achieved effect of the prototype is a device for measuring the duration of ultrashort pulses of laser radiation, which is based on a two-beam correlator with an electro-optical shutter [3] (Fig. 1). In this and further figures, as well as in the text, the following notation is adopted:
1 beam splitter
2 mirror
3 astigmatic telescopic system,
4 stigmatic telescopic system,
5 shutter polarizer,
6 electro-optical shutter cell,
7 depicting an optical system,
8 output plane or registration plane.

The indices of the numbers indicate the serial number of the corresponding element when using several elements of the same type in the device. The considered circuit contains at the output an electro-optical cell 6 operating as a high-speed shutter [3] The dividing plate 1 and mirror 2 ₁ send a powerful control signal E ₁ (t) propagating along the electro-optical cell 6 acting as a shutter into one channel of the interferometer. Using another mirror 2, a weak signal E ₂ (t) is sent to another channel of the interferometer, which plays the role of the subject. This signal is expanded by a telescopic system 4 and also passes through an electro-optical cell. Cross polarizers 5 ₁ and 5 ₂ are part of the electro-optical shutter. When the control signal passes through the cell in certain places, shifting in time along with the signal shift, the effect of birefringence is created, which leads to the opening of the shutter. The studied signal at each moment of time intersects with the control signal at a certain point of the shutter with a certain time shift. Thus, a scan is recorded at the output by the coordinate of the time pattern determined by the second-order correlation function for the structure of the signal under study and the shutter transmission function, which in turn is determined by the intensity of the control signal. Registration is performed for a single optical signal. The resulting picture using the optical system 7 is recorded in the output plane 8 or photoelectric linear multi-element or matrix detector, or photographically. The disadvantage of the prototype, as well as other devices that form the second-order correlation function, is the inability to obtain an unambiguous result for changing the signal intensity over time: the symmetry of the second-order correlation function does not allow to determine the asymmetry of the signal, phase information cannot be obtained in the signal intensity spectrum.

 The aim of the invention is to provide a device for obtaining information about the structure of a single ultrashort laser signal, determined by the distribution of signal intensity over time, without involving any additional information.

 This is achieved by forming in the process of recording a two-dimensional correlation function of the third order or a degenerate two-dimensional correlation function of the fifth order for a single ultrashort radiation signal, regardless of its structure. The optical scheme of the device is based on a three-beam correlator with a three-dimensional three-dimensional structure.

 The essence of the proposed technical solution lies in the fact that the circuit for determining the duration of single ultrashort laser radiation signals based on measuring the second-order correlation function, containing two channels: (channel of the signal under study with an astigmatic telescopic system and a channel of the control signal with a shutter cell), according to the invention It is arranged in the form of a three-dimensional three-dimensional structure and the second channel of the control signal with a gate cell is additionally introduced into it. Note that both channels with control signals contain astigmatic telescopic systems, and the channel of the signal under study contains a stigmatic telescopic system. A significant difference between the proposed system and all known ones is that as a result of using a three-channel scheme with a three-dimensional structure and high-speed optical shutters, the opening of which occurs in mutually perpendicular directions, and the signal under investigation propagates perpendicular to the planes of the gate cells, a two-dimensional is formed and recorded third-order correlation function or degenerate two-dimensional fifth-order correlation function for the analyzed signal when used the use of shutters operating on a linear or quadratic electro-optical effect, respectively, and the information is recorded for a single optical signal of arbitrary shape. When using shutters operating on a linear electro-optical effect and providing a two-dimensional third-order correlation function during registration, the well-known processing method is used ([2] p. 163 164, [4]). When using gates operating on a quadratic electro-optical effect and giving a fifth-order degenerate two-dimensional correlation function during registration, the processing method additionally considered in the application is used, which makes it possible to unambiguously obtain the signal structure in the form of a dependence of intensity on time.

The proposed solution is illustrated in FIG. 2, which shows an optical diagram of a correlator with a three-channel three-dimensional structure. Dotted lines emphasize the volumetric structure of the circuit. The proposed scheme for the formation of three channels in a three-dimensional structure contains dividers of light beams 1 ₁ 1 ₂ made in the form of translucent mirrors or dividing cubes and mirrors 2 ₁ 2 ₆ .

The light beam dividers are designed so that they provide a high intensity of the control signals E ₁ (t) and E ₂ (t) and a low intensity of the investigated signal E ₃ (t). Astigmatic telescopic systems 3 ₁ , 3 _{2 are} installed in two channels with control signals, which expand the light beams in one direction using cylindrical optics and form flat beams directed to the gate cells 6 ₁ , 6 ₂ in mutually perpendicular directions. Shutter cells can operate on a linear electro-optical effect (Pockels effect ([5] on a quadratic electro-optical effect (Kerr effect) [3, 6] or on the basis of the saturable absorption effect [7 9]. For the operation of shutters based on electro-optical effects, polarizers have been introduced into the system 5 ₁ 5 _{3 1 May} wherein polarizers ₃ and 5 are parallel and perpendicular to them on May _2. for valves operating on the basis of the saturable absorption polarizers are not required. In the channel with a test signal E ₃ (t) is set stigmatic telescopic system 4, wasps fected extension beam to illuminate the entire area-gate cells using spherical optics. The test signal is directed perpendicular to the plane-gate cells. The optical system 7 provides in output plane 8, which is a recording plane, the image structure-gate cells tonal values for all t _s registration time Registration can be performed either in the simplest case, photographically, or photoelectricly on a matrix receiver.

The scheme works as follows. The studied pulse of radiation
E (t) = ε (t) • cos [ωt]
two dividing plates 1 ₁ , 1 ₂ and mirrors 2 ₁ 2 ₆ sent to the three channels of the interferometer, and two signals
E ₁ (t + τ ₁ ) = ε ₁ (t + τ ₁ ) • cos [ω (t + τ ₁ )]
and
E ₂ (t + τ ₂ ) = ε ₂ (t + τ ₂ ) • cos [ω (t + τ ₂ )]
designed to control gate cells 6 ₁ , 6 ₂ and are characterized by high field intensities and time delays associated with their propagation in the cell planes
τ ₁ = x / ν _x , τ ₂ = y / ν _y ,
Where
ν _{x x} and ν _{y y the} speed of propagation of light signals in cells. Third signal
E ₃ (t) = ε ₃ (t) • cos [ωt] is analyzed. It is characterized by a low field strength and practically does not cause an electro-optical effect. Using the astigmatic telescopic systems 3 ₁ and 3 _{2, the} control signals E ₁ (t + τ ₁ ) and E ₂ (t + τ ₂ ) turn into wide flat beams propagating in mutually perpendicular directions in the planes of two electro-optical cells 6 ₁ and 6 ₂ . The third signal E ₃ (t) is expanded by a stigmatic telescopic system 4 and passes sequentially through the gate cells 6 ₁ and 6 ₂ perpendicular to the cell planes. At the output of the correlator, the intensity distribution in the analyzed light beam by the optical system 7 is focused into the registration plane 8 and is photoelectrically recorded on a matrix receiver or photographed. The scheme is designed in such a way that the optical paths of the light beams of the three channels of the correlator are aligned for the middle of the gate cells. This leads to the fact that the delays of the signals τ ₁ and τ ₂ change during registration, both in the positive and in the negative direction.

где r₁ и r₂ электрооптические постоянные, n₁ и n₂ начальные показатели преломления материалов ячеек.Consider the action of a circuit with electro-optical cells operating on the basis of a linear electro-optical effect (Pockels cells). The control signals E ₁ (t + τ ₁ ) and E ₂ (t + τ ₂ ) cause birefringence in cells 6. The differences in the refractive indices Δn ₁ and Δn _{2 that} exist between the indices for extraordinary n _e1 , n _e2 and ordinary n _o1 , n _o2 rays are equal, respectively

where r ₁ and r _{2 are} electro-optical constants, n ₁ and n _{2 are the} initial refractive indices of the cell materials.

где γ угол между направлением первого поляризатора 5₁ и ориентацией вектора напряженности электрического поля для обыкновенного луча. Это иллюстрируется на фиг. 3, на которой представлено формирование составляющих электрического поля анализируемого светового сигнала в электрооптической ячейке для двойного лучепреломления, вызываемого полем E₁(t+τ₁). Действие первой электрооптической ячейки 6₁ вносит фазовые сдвиги
ΔΦ_1o=(ω/c)l₁n_1o, ΔΦ_1e=(ω/c)l₁n_1e,
где l₁ толщина ячейки в направлении распространения анализируемого сигнала. Ячейка должна быть достаточно тонкая, чтобы за время распространения анализируемого светового сигнала через ячейку затвор не происходило заметного изменения показателя преломления за счет управляющего сигнала, то есть не происходило снижения временного разрешения. В частности, для временного разрешения δt толщина ячейки должна быть не более l = δt c/n, где n
показатель преломления материала ячейки, то есть для

с толщина l≈0,2 мм. После второго поляризатора 5₂, скрещенного с первым, с учетом малости изменений показателей преломления имеет место

где постоянные А₁ и α₁ равны

Полученное поле можно представить как результат воздействия на анализируемое излучения с амплитудой ε₃(t) затвора с изменяющимся во времени пропусканием T₁(t+τ₁), пропорциональным E₁(t+τ₁).Consider the action of the first shutter cell. The analyzed field is presented in the form of two components corresponding to ordinary and extraordinary rays.

where γ is the angle between the direction of the first polarizer 5 ₁ and the orientation of the electric field vector for an ordinary beam. This is illustrated in FIG. 3, which shows the formation of the electric field components of the analyzed light signal in an electro-optical cell for birefringence caused by the field E ₁ (t + τ ₁ ). The action of the first electro-optical cell 6 ₁ introduces phase shifts
ΔΦ _1o = (ω / c) l ₁ n _1o , ΔΦ _1e = (ω / c) l ₁ n _1e ,
where l _{1 is the} thickness of the cell in the direction of propagation of the analyzed signal. The cell must be thin enough so that during the propagation of the analyzed light signal through the gate cell, there is no noticeable change in the refractive index due to the control signal, that is, there is no decrease in time resolution. In particular, for the time resolution δt, the cell thickness should be no more than l = δt c / n, where n
the refractive index of the cell material, i.e., for

s thickness l≈0.2 mm. After the second polarizer 5 ₂ , crossed with the first, given the small changes in the refractive indices,

where the constants A ₁ and α ₁ are equal

The obtained field can be represented as the result of exposure to the analyzed radiation with a gate amplitude ε ₃ (t) with a time-varying transmission T ₁ (t + τ ₁ ) proportional to E ₁ (t + τ ₁ ).

рассматривается действие второй электрооптической ячейки затвора 6₂. Составляющие

, соответствующие обыкновенному и необыкновенному лучам во второй ячейке 6₂, имеют вид

где γ угол между направлением второго поляризатора 5₂ и ориентацией вектора напряженности электрического поля обыкновенного луча и равный углу g, определенному выше. Действие второй ячейки затвора 6₂ вносит фазовые сдвиги
Dv_2o= (ω/c)l₂n_2e, ΔΦ_2e= (ω/c)l₂n_2o,
где l₂ размер ячейки в направлении распространения анализируемого сигнала. После третьего поляризатора 5₃, скрещенного со вторым, имеет место

где постоянные А₂ и α₂ имеют вид
A₂= 2r₂n $\genfrac{}{}{0ex}{}{\text{3}}{\text{2}}$ A₁•sinγ•cosγ•(ωl₂/2c),
α₂=α₁+(ω/c)l₂(n_2o-n_2e)/2.
Дополнительно к воздействию затвора, работающего на первой ячейке 6₁, в данном случае имеет место воздействие второго затвора, работающего на второй ячейке 6₂, с амплитудным пропусканием T₂(t+τ₂), пропорциональным E₂(t+τ₂).Similarly for the field

the action of the second electro-optical shutter cell 6 _{2 is considered} . Components

corresponding to the ordinary and extraordinary rays in the second cell 6 ₂ have the form

where γ is the angle between the direction of the second polarizer 5 ₂ and the orientation of the electric field vector of the ordinary beam and equal to the angle g defined above. The action of the second gate cell 6 ₂ introduces phase shifts
Dv _2o = (ω / c) l ₂ n _2e , ΔΦ _2e = (ω / c) l ₂ n _2o ,
where l _{2 is} the cell size in the direction of propagation of the analyzed signal. After the third polarizer 5 ₃ , crossed with the second, takes place

where the constants A ₂ and α ₂ have the form
A ₂ = 2r ₂ n $\genfrac{}{}{0ex}{}{\text{3}}{\text{2}}$ A ₁ • sinγ • cosγ • (ωl ₂ / 2c),
α ₂ = α ₁ + (ω / c) l ₂ (n _2o -n _2e ) / 2.
In addition to the effect of the shutter operating on the first cell 6 ₁ , in this case, there is the effect of the second shutter operating on the second cell 6 ₂ , with an amplitude transmission T ₂ (t + τ ₂ ) proportional to E ₂ (t + τ ₂ ).

Соотношения интенсивностей сигналов I₁(t), I₂(t) и I₃(t) в каналах схемы можно описать коэффициентами r₁, r₂ и r₃
I₁(t)=r₁I(t), I₂(t)=r₂I(T), I₃(t)=r₃I(t).At the output, the intensity distribution of the generated signal is recorded photoelectrically, followed by computer processing or photographically, followed by photometry and processing. The recorded intensity distribution has the form

The ratios of signal intensities I ₁ (t), I ₂ (t) and I ₃ (t) in the circuit channels can be described by the coefficients r ₁ , r ₂ and r ₃
I ₁ (t) = r ₁ I (t), I ₂ (t) = r ₂ I (T), I ₃ (t) = r ₃ I (t).

осуществляется переход к спектральному представлению

Анализ зависимости I $\genfrac{}{}{0ex}{}{\text{(3)}}{\text{ω}}$ (ω₁, ω₂) от ω₁ при условии ω₂=0 позволяет получить информацию о модуле спектра сигнала

Амплитуды спектральных компонент сигнала определяются с точностью до постоянной I_ω(0), которая в конечном итоге задается шкалой, в которой измеряется интенсивность.We get that at the output a third-order correlation function is recorded for the time distribution of the intensity of the signal under study. An analysis of the resulting picture, which is a third-order correlation function for gate cells with a linear electro-optical effect, is performed using known methods [2] p. 163-164. [4] In the registered picture for

transition to spectral representation

I dependency analysis $\genfrac{}{}{0ex}{}{\text{(3)}}{\text{ω}}$ (ω ₁ , ω ₂ ) from ω ₁ under the condition ω ₂ = 0 allows obtaining information about the modulus of the signal spectrum

The amplitudes of the spectral components of the signal are determined accurate to a constant I _ω (0), which is ultimately determined by the scale in which the intensity is measured.

Это позволяет определить ψ′(ω₁) и, следовательно ψ(ω). На основании величин модуля спектры

и фаз спектральных компонент j(ω) рассчитывается зависимость интенсивности сигнала от времени в виде обратного преобразования Фурье.Analysis of the behavior of the imaginary part of derivative I $\genfrac{}{}{0ex}{}{\text{(3)}}{\text{ω}}$ (ω ₁ , ω ₂ ) with respect to ω ₂ under a number of conditions ω ₂ = 0, the phase origin is determined by the expression ψ (0) = 0, the origin of the time t ₀ is described by the expression ψ ′ (0) = t _o = 0 gives

This allows us to determine ψ ′ (ω ₁ ) and, therefore, ψ (ω). Based on the values of the modulus, the spectra

and phases of the spectral components j (ω), the dependence of the signal intensity on time is calculated in the form of the inverse Fourier transform.

 Thus, as a result of processing the obtained information by known methods, the structure of the studied single ultrashort optical signal in the form of a dependence of intensity on time is uniquely obtained. In addition, under certain conditions (the average value of the interference signal is zero <N> = 0 and / or the symmetric structure of the probability density p (N) is the distribution of interference)), the role of random additive interference decreases, which was not the case with devices in which the functions were formed second-order correlations [2] p. 162-163).

 In the considered circuit, as noted, electro-optical cells operating on the basis of the quadratic electro-optical effect can be used as gates. In this case, a similar analysis gives the following.

где λ длина волны используемого излучения, B₁ и B₂ - электрооптические постоянные материалов ячеек.The differences in the refractive indices Δn ₁ and Δn ₂ between the indices for extraordinary n _el , n _e2 and ordinary n _o1 , n _o2 rays are equal, respectively

where λ is the wavelength of the radiation used, B ₁ and B ₂ are the electro-optical constants of the cell materials.

При введении коэффициентов r₁, r₂ и r₃, описывающих соотношения интенсивностей сигналов I₁(t), I₂(t) и I₃(t) в каналах схемы, распределение интенсивности имеет вид, близкий по структуре к функции корреляции пятого порядка

при выполнении условий

то есть описывается вырожденнной двумерной функцией корреляции пятого порядка.For the analyzed signal E ₃ (t), two cells act for the gates with time-varying transmittances T ₁ (t + τ ₁ ) and T ₂ (t + τ ₂ ) proportional to E $\genfrac{}{}{0ex}{}{\text{2}}{\text{one}}$ (t + τ ₁ ) and E $\genfrac{}{}{0ex}{}{\text{2}}{\text{2}}$ (t + τ ₂ ), respectively. A recorded intensity distribution that carries useful information about the signal structure, taking into account the smallness of changes in refractive indices up to non-existent constant factors, is described by the expression

When the coefficients r ₁ , r _2, and r ₃ are introduced, which describe the ratios of signal intensities I ₁ (t), I ₂ (t), and I ₃ (t) in the circuit channels, the intensity distribution has the form close to the structure of the fifth-order correlation function

subject to the conditions

that is, it is described by a degenerate two-dimensional correlation function of the fifth order.

С учетом вида интегралов, описывающих преобразование Фурье для интенсивности I(t+τ_k), и условий τ₁=τ₂, τ₃=τ₄, что приводит к соотношениям ω₁=ω₂, ω₃=ω₄, получаем

Анализ зависимости I $\genfrac{}{}{0ex}{}{\text{(5)}}{\text{ω}}$ (ω₁, ω₃) от ω₃ при выполнении условия ω₃=-ω₁ и с учетом эрмитовости выражения для спектра позволяет получить распределение амплитуд в спектре сигнала

где

определяется по измеренному распределению интенсивности для функции корреляции I⁽⁵⁾(τ₁, τ₃), a I_ω(0) определяется шкалой измерения интенсивности спектральных компонент.The processing of the results in comparison with the third-order correlation function in this case is somewhat more complicated. The transition to the spectral representation for I ⁽⁵⁾ (τ ₁ , τ ₂ , τ ₃ , τ ₄ ) gives

Taking into account the form of the integrals describing the Fourier transform for the intensity I (t + τ _k ) and the conditions τ ₁ = τ ₂ , τ ₃ = τ ₄ , which leads to the relations ω ₁ = ω ₂ , ω ₃ = ω ₄ , we obtain

I dependency analysis $\genfrac{}{}{0ex}{}{\text{(5)}}{\text{ω}}$ (ω ₁ , ω ₃ ) from ω ₃ under the condition ω ₃ = -ω ₁ and taking into account the hermitian expression for the spectrum, one can obtain the distribution of amplitudes in the signal spectrum

Where

is determined by the measured intensity distribution for the correlation function I ⁽⁵⁾ (τ ₁ , τ ₃ ), and I _ω (0) is determined by the scale for measuring the intensity of the spectral components.

и

где

определяются по измеренному распределению интенсивности в функции корреляции пятого порядка I⁽⁵⁾(τ₁, τ₃). Структура сигнала I(t) при вычисленных амплитудах

и фазах ψ(ω)) спектральных компонент определяется обратным преобразованием Фурье.Analysis of the behavior of the imaginary part of derivative I $\genfrac{}{}{0ex}{}{\text{(5)}}{\text{ω}}$ (ω ₁ , ω ₃ ) with respect to ω ₃ under the condition ω ₃ = -ω ₁ , taking into account the phase reference ψ (0) = (0), the time t _o (ψ ′ (0) = t _o = 0) and Hermitian conjugacy in the description of the spectrum, gives

and

Where

are determined by the measured intensity distribution in the fifth-order correlation function I ⁽⁵⁾ (τ ₁ , τ ₃ ). Signal structure I (t) at calculated amplitudes

and phases ψ (ω)) of the spectral components is determined by the inverse Fourier transform.

 An analysis of the role of additive random stationary interference can be performed in the same way as discussed above for the third-order correlation function.

где α_o/ коэффициент поглощения материала затвора без действия излучения, I_s интенсивность излучения, обеспечивающая насыщение поглощения, и, следовательно, предельное открывание затвора. Следует подчеркнуть, что в данном случае рассматривается пропускание фильтров - затворов для интенсивности излучения, а не для поля, как это делалось ранее. Регистрируемое распределение интенсивности, рассчитанное подобно тому, как это рассмотрено выше, имеет вид

Результат описывается более сложной функцией, чем в предыдущих вариантах схемы, но общий характер соответствует корреляционной функции третьего порядка для I₃(t), T_II(t+τ₁) и T₁₂(t+τ₂).
Выражение для I(τ₁, τ₂) может быть упрощено с учетом того, что управляющие сигналы I₁(t) и I₂(t) имеют интенсивность значительно меньшую, чем интенсивность I_s насыщения поглощения. В этом случае можно воспользоваться разложением в ряд по малому параметру I₁(t)/I_s или I₂(t)/I_s. С учетом коэффициентов r₁, r₂ и r₃, описывающих соотношения интенсивностей сигналов в каналах интерферометра, и ограничиваясь членами второго порядка малости, пропускания фильтров затворов будут описываться формулами

Регистрируемое распределение интенсивности с точностью до членов второго порядка малости и несуществующих постоянных коэффициентов будет описываться формулой

Переход к спектральному представлению в выражении для интенсивности I(τ₁, τ₂) с учетом спектрального представления корреляционных функций второго и третьего порядков дает

Исключим из рассмотрения области с ω₁, ω₂=0, тогда с точностью до несущественных постоянных множителей видим, что спектральное распределение интенсивности I_ω(ω₁, ω₂) совпадает со спектральным распределением для функции корреляции третьего порядка и описывается выражением

Анализ зависимости функции I_ω(ω₁, ω₂) от ω₁ при выполнении условия ω₂= -ω₁ позволяет определить амплитуды спектральных компонент сигнала подобно тому, как это описано выше

где

определяется из зарегистрированного распределения интенсивности

Анализ зависимости мнимой части производной I_ω(ω₁, ω₂) по ω₂ при выполнении условия ω₂=-ω₁, как и выше, позволяет определить фазы спектральных компонент сигнала. С учетом условия ψ(0)=0, характеризующего начало отсчета фазы, и принимая за начало отсчета времени t₀, определяемое условием ψ′(0)=0, получаем

где

Величины

определяются из зарегистрированного распределения интенсивности I(τ₁, τ₂). Структура I(t) при вычисленных амплитудах

и фазах j(ω))( спектральных компонент определяется обратным преобразованием Фурье.In the embodiment of a circuit with saturable absorption gates, the use of polarizers is not required. The gate transmission is determined by the current radiation intensities and is described by the formulas

where α _{o / is} the absorption coefficient of the shutter material without the action of radiation, I _s is the radiation intensity, which ensures saturation of the absorption, and, therefore, the maximum opening of the shutter. It should be emphasized that in this case the transmission of filter - gates is considered for the radiation intensity, and not for the field, as was done earlier. The recorded intensity distribution, calculated similarly as described above, has the form

The result is described by a more complex function than in the previous versions of the scheme, but the general nature corresponds to a third-order correlation function for I ₃ (t), T _II (t + τ ₁ ) and T ₁₂ (t + τ ₂ ).
The expression for I (τ ₁ , τ ₂ ) can be simplified taking into account the fact that the control signals I ₁ (t) and I ₂ (t) have an intensity much lower than the absorption saturation intensity I _s . In this case, one can use the series expansion in the small parameter I ₁ (t) / I _s or I ₂ (t) / I _s . Given the coefficients r ₁ , r ₂ and r ₃ describing the ratio of signal intensities in the channels of the interferometer, and limiting ourselves to the terms of the second order of smallness, the transmission of the gate filters will be described by the formulas

The recorded intensity distribution up to second-order terms of smallness and non-existent constant coefficients will be described by the formula

The transition to the spectral representation in the expression for the intensity I (τ ₁ , τ ₂ ) taking into account the spectral representation of the correlation functions of the second and third orders gives

We exclude from consideration the regions with ω ₁ , ω ₂ = 0, then, up to insignificant constant factors, we see that the spectral distribution of intensity I _ω (ω ₁ , ω ₂ ) coincides with the spectral distribution for the third-order correlation function and is described by the expression

An analysis of the dependence of the function I _ω (ω ₁ , ω ₂ ) on ω ₁ when the condition ω ₂ = -ω _{1 is} fulfilled, it is possible to determine the amplitudes of the spectral components of the signal, similar to that described above

Where

determined from recorded intensity distribution

An analysis of the dependence of the imaginary part of the derivative I _ω (ω ₁ , ω ₂ ) with respect to ω ₂ under the condition ω ₂ = -ω ₁ , as above, allows us to determine the phases of the spectral components of the signal. Taking into account the condition ψ (0) = 0, which characterizes the origin of the phase reference, and taking as the reference time t ₀ defined by the condition ψ ′ (0) = 0, we obtain

Where

Quantities

are determined from the recorded intensity distribution I (τ ₁ , τ ₂ ). Structure I (t) at calculated amplitudes

and phases j (ω)) (spectral components is determined by the inverse Fourier transform.

, связанную с указанным выше исключением из рассмотрения области w₁, ω₂=0 для функции I_ω(ω₁, ω₂). Дело в том, что условие ω₂ = -ω₁ с необходимостью включает значение функции I_ω(ω₁, ω₂) в точке ω₁=ω₂=0. Это обстоятельство оказывается не слишком существенным, если величина

пренебрежимо мала или равна нулю. Следует отметить, что это не относится к функции I_ω(ω), описывающей спектр сигнала, то есть деление на I_ω(0) не приводит к обращению в бесконечность величины

.It is necessary to note some inconsistency in the calculations

associated with the above exclusion from consideration of the region w ₁ , ω ₂ = 0 for the function I _ω (ω ₁ , ω ₂ ). The fact is that the condition ω ₂ = −ω ₁ necessarily includes the value of the function I _ω (ω ₁ , ω ₂ ) at the point ω ₁ = ω ₂ = 0. This circumstance is not too significant if the quantity

negligible or equal to zero. It should be noted that this does not apply to the function I _ω (ω), which describes the spectrum of the signal, i.e., division by I _ω (0) does not lead to the infinity

.

 Evaluation of the role of interference naturally coincides with that made above for the third-order correlation function.

 The temporary resolution of the device is determined by the speed of the shutter operating on the electro-optical cell ([10] p. 87-89).

We give some numerical estimates for the considered circuit with gates operating on the basis of the quadratic electro-optical effect. The temporal resolution dt determined by the shutter response time t _cel has a value of the order of 10 ^-12 s for a liquid shutter based on CS ₂ with a power of the control optical signal of the order of 100 MW ([10] p. 86-92). and for gates based on glasses, it is estimated to be less than 10 ^-14 s at a power estimated based on the magnitude of the nonlinear refractive index, two orders of magnitude larger [11]). Similar estimates hold for electro-optical crystals with a quadratic effect [12] For the total duration of the signal under investigation t _s = 10 ^-10 s and time resolution dt = 10 ^-12 s, the dimensions of the working area 2x ₀ , 2y ₀ in the cells should be larger (c / n) t _s = 2 cm and the working thickness of the region, l _z less than (c / n) dt = 0.2 mm. Registration should be performed with a resolution of at least 0.2 mm. For a temporary resolution dt of the order of 10 ^-14 with a cell working area thickness l _z must be less than 0.002 mm and the resolution is also better than 0.002 mm

 For shutters operating on the basis of a linear electro-optical effect and saturable absorption, the estimates are close to that given above for glasses and crystals [5]

Claims (1)

 A device for determining the characteristics of single ultrashort pulses of laser radiation, including a channel of the signal under study with a telescopic system, a control signal channel with a shutter cell and a registration system for the correlation function, characterized in that the device is made in the form of a three-dimensional volume structure, further comprises a second control signal channel with a shutter cell, the shutter cells in the control channels are installed so that they open in mutually perpendicular directions ia, the direction of propagation of the investigated signal perpendicular to the planes of the gate cells, astigmatic telescopic beam expansion systems are installed in front of the gate cells in the control signal channels, and the registration system for the correlation function is two-dimensional.

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