RU2085984C1 - Parametric amplifier and electromagnetic wavelength converter - Google Patents

Abstract

FIELD: quantum electronics. SUBSTANCE: device use power of acoustic wave for modulation of refraction index of linear glass fiber so that coherent light beam is output, which carrier frequency belongs to arbitrary bandwidth in which fiber attenuation is significantly low. When conversion steps frequency up, power of beam to be converted is increased. If losses are not taken into account, received gain is equal to frequency factor of output beam. In order to convert optical beams, carrier of acoustic wave is in range of 50-500 MHz. Converter is designed as glass fiber which cross section is decreased along spreading of acoustic wave. EFFECT: acoustic wave is used for pumping. 2 dwg

Description

 The invention relates to quantum electronics and can be used to obtain a wide range of wavelengths of electromagnetic, including light coherent radiation.

 Various wavelength converters of light radiation are known, ranging from dye lasers with optical pumping to various types of parametric converters with increasing and decreasing output radiation carrier. All these types of converters have one significant drawback associated with the fact that they require energy in the form of expensive high-power optical radiation as a pump, for which various types of discharge lamps or high-power lasers are used. This leads to the fact that the overall dimensions of the converters are much larger than the dimensions of the optical medium in which the conversion is performed directly.

. Легко видеть, что для заметного сдвига несущей выходного излучения несущая накачки ω_p должна быть сравнима с ω_i, т. е. накачка должна находиться в оптическом диапазоне. Недостатком такого преобразователя является необходимость в дорогостоящем оптическом источнике накачки. Кроме того, при фиксированной ω_p выходное излучение может быть получено только с двумя несущими

. Для перестройки ω требуется перестройка w_p и изменение углов, под которыми накачка и преобразуемое излучение вводятся в оптическую среду.The prototype is a parametric optical converter with increasing frequency [1, p. 78-94] In such a converter, the conversion is carried out in a nonlinear optical medium, in which non-linear crystals of the LiNbO ₃ type are used. Converted radiation and pumping, which is optical radiation, are introduced into such a crystal at a certain angle to the crystallographic axes. As a result of the conversion, the output receives radiation either with the total carrier ω = ω _i + ω _p , where ω _{i is the} carrier of the input radiation, ω _{p is the} pump carrier, or with the difference frequency

. It is easy to see that for a noticeable shift in the carrier of the output radiation, the pump carrier ω _p should be comparable to ω _i , i.e., the pump should be in the optical range. The disadvantage of this converter is the need for an expensive optical pump source. In addition, for a fixed ω _{p, the} output radiation can be obtained with only two carriers

. For the tuning of ω, a tuning of w _p and a change in the angles at which the pump and the converted radiation are introduced into the optical medium are required.

 Finally, in the prototype under consideration, a nonlinear optical medium is required. Although there are a lot of such media, all of them have a thousand times greater attenuation than the best linear media, for example, glass-based media from which fiber optic fibers with attenuation of less than 1 dB / km are made. All of these disadvantages are eliminated in the present invention.

 The invention consists in the following.

 Electromagnetic radiation and a traveling acoustic wave are introduced into a fiber made of a linear medium, for which this fiber is also a sound pipe. Due to the photoelastic effect, a change in the refractive index of the fiber regions is proportional to the medium induced by the acoustic deformation wave. In this case, a system of regions parallel to each other with an increased refractive index is formed in the fiber, moving at the speed of the acoustic wave. The shape of the sound pipe is such that, as it moves, each such area decreases in volume. Depending on the ratio of the acoustic wavelength Λ and the electromagnetic wavelength l, either each of these regions is a movable dielectric resonator that can store and carry the radiation introduced into it, or the entire system of movable regions is a movable distributed Bragg reflector (DBR) created by an acoustic wave . In any case, the radiation introduced into the fiber is compressed either due to the fact that during the movement the transverse dimensions of the movable resonator containing it are reduced, or due to the fact that one of the reflective surfaces of the resonator formed from the entire fiber is a movable DBR, which, like The piston compresses the radiation located in the fiber. When the radiation is compressed, its carrier increases and, in proportion to it, the energy of the stored radiation. If a traveling acoustic wave is launched in the opposite direction, then the radiation stored in the resonators expands and the wavelength of the received radiation decreases in this case.

 Figure 1 shows several options for sound ducts in which radiation conversion can be carried out. For all options, it is assumed that a traveling acoustic wave propagates from top to bottom; figure 2 one of the possible designs of the transducer, consisting of a fiber 1, a known prism device 2 for inputting the converted radiation, several similar devices 3, 4 for outputting the converted radiation, a piezoelectric transducer 5 for excitation in the sound pipe of an acoustic wave absorbing insert 6 to suppress reflections of a traveling acoustic wave from the end of the sound duct.

 It is easier to explain the operation of the converter using a movable DBR using the example of a special case when the sound duct is a disk, since in this case there are analytical expressions for resonator modes, however, the properties of plane DBRs should be noted first. First, it makes sense to consider the interaction of waves in the well-known flat distributed Bragg reflector (DBR) created by a plane acoustic wave. Such a DBR is one of the main components of acousto-optics and is widely used in bulk acousto-optic modulators, difflectors, spectrum analyzers, etc. [2] It is known that a plane light wave with a wavelength l incident at an angle q = arcsin (λ / 2Λ) to planes of equal phases of a plane traveling acoustic wave, changes its propagation direction by an angle of 2θ. In this case, the carrier of the light wave changes to W, where Ω and L are the carrier and the length of the acoustic wave [3] It is shown below that in a similar situation qualitatively different effects take place for cylindrical waves.

где n показатель преломления среды;
m коэффициент модуляции показателя преломления акустической волной;
угол ψ равен фазе акустической волны.We will take as the basis of the analysis the results obtained when considering the interaction of plane infinite waves with a weak distributed bond arising between them in a plane periodic structure [3]. These results are reduced to the following. Full reflection from the infinite RBO takes place if

where n is the refractive index of the medium;
m modulation coefficient of the refractive index of the acoustic wave;
the angle ψ is equal to the phase of the acoustic wave.

Комплексные амплитуды a и b падающей и отраженной волн уменьшаются по модулю и изменяются в направлении z в соответствии с выражениями

(5),
где
φ = arg(κ/(-γ+jδ)) (6)
В результате эти волны образуют затухающую в направлении z стоячую волну, амплитуда которой изменяется в соответствии с выражением
E(z) = 2E_oexp(-γz-jφ/2)cos(πz/Λ-φ/2) (7).If we choose the direction of the z axis opposite to the direction of propagation of the acoustic wave, and the x axis in the plane of incidence of the light wave and assume that n changes in accordance with the expression

The complex amplitudes a and b of the incident and reflected waves decrease in absolute value and change in the z direction in accordance with the expressions

(5),
Where
φ = arg (κ / (- γ + jδ)) (6)
As a result, these waves form a standing wave damped in the z direction, the amplitude of which changes in accordance with the expression
E (z) = 2E _o exp (-γz-jφ / 2) cos (πz / Λ-φ / 2) (7).

At z = 0, the reflection coefficient
G = b / a = exp (-jφ / 2) (8).

 In accordance with (2), (6), (8) for z = 0 φ = -Ωt, i.e., the phase of the reflected wave φ relative to the phase of the incident wave uniformly changes in time due to the motion of the volume grating.

(12)
где

Тогда в соответствии с (12) на расстоянии r от центра
β_Φ= l/r (13).Passing from plane waves and DBR to cylindrical, we consider in the cylindrical coordinate system (Φ, r) the interaction of a cylindrical light wave traveling along the azimuth and standing along r
J _l (βr) exp (-jωt-jmΦ) (9)
with a cylindrical azimuthally uniform acoustic wave running along the axis with longitudinal vibrations, which creates a corresponding traveling wave of changes in the refractive index
mH $\genfrac{}{}{0ex}{}{\text{(2)}}{\text{o}}$ (Br) exp (-jΩt) (10),
where the azimuthal index 1 is an integer equal to the number of field variations when the azimuth Φ changes by 2π;
J ₁ (x) Bessel function with index 1;
H $\genfrac{}{}{0ex}{}{\text{(2)}}{\text{o}}$ (x) Hankel function equal to H $\genfrac{}{}{0ex}{}{\text{(2)}}{\text{o}}$ (x) = J _o (x) -JN _o (x), here N ₀ (x) the Neumann function [3]
Since for any r the condition
β _Φ (r) ² + β _r (r) ² = β ² (11), where β _Φ and β _r
the azimuthal and radial components of the wave vector β, respectively, then for r = r ₀ we have

(12)
Where

Then, in accordance with (12), at a distance r from the center
β _Φ = l / r (13).

К оси цилиндра при r < ρ_o амплитуда волны быстро без осцилляций уменьшается как J₁(x) при x < 1. Таким образом, акустика r = ρ_o является одной отражающей стенкой для поперечного резонанса вдоль r. Второй отражающей стенкой является рассматриваемый ниже подвижной цилиндрический РБО, созданный бегущей акустической волной. Между этими стенками по кольцу распространяется бегущая световая волна, в которой в поперечном сечении (вдоль радиуса) поле описывается функцией J_l(βr) В результате имеем цилиндрический резонатор бегущей волны для азимутальных типов колебаний в виде волны типа "шепчущей галереи" [5] в котором возбуждена мода H_lro, где l, r, o количество вариаций соответственно по азимуту, радиусу и оси цилиндра.

To the cylinder axis, for r <ρ _o, the wave amplitude rapidly decreases without oscillations as J ₁ (x) for x <1. Thus, the acoustics r = ρ _o is one reflecting wall for the transverse resonance along r. The second reflecting wall is the movable cylindrical DBR considered below, created by a traveling acoustic wave. A traveling light wave propagates between these walls along the ring, in which the field is described by the function J _l (βr) in the cross section (along the radius). As a result, we have a cylindrical traveling wave resonator for azimuthal types of oscillations in the form of a “whispering gallery” wave [5] in which the H _lro mode is _excited , where l, r, o are the number of variations in azimuth, radius, and cylinder axis, respectively.

выполнена из поглощающего звуковую волну материала с волновым сопротивлением, равным волновому сопротивлению окружающей ее среды. На расстояниях много больших L, т. е. при x >> 1, корни функции J₀(x) расположены практически на одинаковом расстоянии друг от друга. Поэтому будем полагать, что на этих расстояниях, где и происходит взаимодействие, длина акустической волны постоянна и равна L.As for the acoustic wave, its amplitude is proportional to r ^-1/2 and there are no variations along the azimuth. So that there are no reflections from the center, propagating in the opposite direction, we assume that the middle of the cylinder with a radius

made of a sound wave absorbing material with a wave resistance equal to the wave resistance of its environment. At distances much larger than L, i.e., for x >> 1, the roots of the function J ₀ (x) are located at almost the same distance from each other. Therefore, we will assume that at these distances, where the interaction occurs, the acoustic wavelength is constant and equal to L.

Passing from the description of the structure of the waves to the analysis of their interaction, we will bear in mind that for r ≫ Λ and ρ ≫ r _{o the} waves in each individual segment can be considered as plane. Therefore, to obtain RBO, it is necessary that β _r (r) = B / 2 or θ = arcsin [B / (2β)]. The wave incident on the BFR at such an angle will be reflected from it with an increase in the carrier by Ω, then it will be reflected from the internal acoustics r = ρ _o , it will again be reflected from the BFB, and at each reflection its carrier will increase by Ω. Since the period of a cylindrical RBD L is almost constant, and b _r (r) for θ <= 1 depends on r, the condition sinθ = B / (2β) is fulfilled only in a certain range of radii r, the size of which can be taken as the effective thickness of the DBR d . Let us estimate d for the case most interesting for practice when λ ≪ Λ or θ ≪ 1 In this case, for light in the visible range, the modulation frequency can be chosen in the range F = 50-500 MHz. Let sinθ = B / (2β) for r = r ₀ . Then at a distance of r _o + Δr, where Δr ≪ r in accordance with (13) we have β _Φ (r _o + Δr) = β _Φ (r _o ) (1-Δr / r _o ) and in accordance with (11) β _r (r _o + Δr) = β (r _o ) (1 + Δr / r _o ). In this case, in accordance with (7), (1), the attenuation dependence can be represented as
γ = (β / r _o ) (mr _o / (2sinθ)) ² -Δr ² ) ^1/2 (14)
The thickness of the DBR layer d is determined by the interval where γ> 0 Then from (14)
d = mr _o / sinθ (15)
and, integrating (14) in this interval, we obtain a complete attenuation in the DBR layer
σ = exp (∫γ (x) dx) = (π / 2) βr _o (m / (2sinθ)) ² (16)
As expected, at sufficiently large r _{0, the} attenuation of the wave as it passes through the DBR can be made arbitrarily large. Note that the wave transmitted through the RBO is already in the transparency zone of the periodic structure and therefore cannot in any way reduce the attenuation defined above.

характеризует степень более быстрого сокращения внешней акустики. Откуда ε = 2(β_r(r_o)/β_Φ(r_o))²/(1-1/q²) Поскольку

, то ε является величиной второго порядка малости относительно q Тем не менее при преобразовании внешняя акустика сокращается несколько быстрее внутренней, особенно при tgθ > 1.The transformation of the carrier network wave is due to the fact that the resonator mode in the resonator must be preserved with a decrease in the radius of its outer wall, which can be only with a corresponding decrease in the wavelength. If the wavelength decreases by a factor of q, then β _q = βq and the radius of the internal acoustics, determined from the condition β _q ρ _q = l, decreases by a factor of q. With a decrease in the radius of external acoustics by a factor of q, β _r (r ₀ / q) increases by a factor of q. Thus, for r = r ₀ / q, the bulk lattice will no longer be a DBR. However, since β _r decreases with decreasing r and is equal to 0 for r = r _q , then there always exists such r in the interval ρ _o / q <r <r _o / q, where β _q = π / Λ and where the bulk phase grating stands for a wave with λ _q = λ / q as a DBR. Equating the radial propagation constants at r = r ₀ and r = (1-ε) r _o / q, bearing in mind that β _Φ (r) = β _Φ (r _o ) r _o / r, we obtain the following equation for determining

characterizes the degree of faster reduction of external acoustics. Whence ε = 2 (β _r (r _o ) / β _Φ (r _o )) ² / (1-1 / q ² ) Since

, then ε is a second-order quantity of smallness with respect to q. However, during the conversion, the external acoustics contract somewhat faster than the internal one, especially for tgθ> 1.

From the above consideration it follows that in the case when the DBR provides almost complete reflection, i.e., when β _r = π / Λ, the wavelength λ of the converted light does not depend on the modulation coefficient, but only r is determined. As the modulation coefficient m increases, only the thickness of the DBR increases, but the conversion rate does not increase. Thus, the transformation of the carrier is carried out in the volume of the RBO, where the correspondence between the increase in the carrier and the speed of movement of the RBO is automatically established. In the cavity itself, i.e., in the region between the external and internal acoustics, there is no correspondence between b _r and π / Λ. Therefore, although the resonator is filled with a moving volumetric phase grating, the resulting energy exchange between the light and acoustic waves is zero. In fact, energy conversion occurs in the volume of the RBO.

It should be noted that the width of the resonator is much smaller than the width of the DBR. For example, for m = 10 ^-4 sinθ = 0.01, we have ρ _o = (1-10 ^-4 / 2) r ₀ , and in accordance with (15), d = 10 ^-2 r ₀ . Thus, the converted radiation is concentrated in a narrow ring compared to the radius of the cylinder, which gradually transforms with the speed of the acoustic wave toward the center as it transforms. In the event that, at a distance r _0, radiation with a carrier ω _o is continuously introduced into a cylindrical resonator, then along r there will be radiation with different carriers ω = ω _o r _o / r, which are in different stages of conversion. As r decreases in accordance with (15), (16), the effective thickness d and the effective attenuation σ decrease. For example, with the indicated parameters and r _o = 10 cm, Λ _o = 0.6 μm, we have d = 100 μm, and the wave passing through the DBR is attenuated by an exp (-40) time.

If necessary, the attenuation of σ can be increased if, instead of an azimuthally homogeneous acoustic wave, we take an acoustic wave with an azimuthal index l, which changes the refractive index in accordance with n = n _o (1 + mH $\genfrac{}{}{0ex}{}{\text{(2)}}{\text{L}}$ (Br) exp (jΩt)), where l is chosen such that B _r (r) / B = sinθ. In this case, with increasing r, B _r (r) increases, as does β _r (r). Therefore, the mismatch between B _r (r) and β _r (r) increases more slowly.

 Thus, if light is introduced through the prism 2 (FIG. 1), which excites an azimuthal wave of the “whispering gallery” type in the fiber, then the traveling acoustic wave excited by the piezoelectric transducer 6 will entrain this wave. Due to the fact that the cross section of the fiber is reduced, the radiation introduced into the fiber will be compressed and its wavelength will be proportionally reduced. Placing prisms 3, 4 along the length of the optical fiber and adjusting the connection between the prisms with the optical fiber, it is possible to derive the required part of the radiation with the required wavelength.

для световода с диаметром D= 125 мкм требуется акустическая мощность 0,35 Вт. Уменьшение длины волны с 1,0 до 0,5 мкм может быть осуществлено в световоде длиной около 10 см при частоте модуляции 150 МГц. Площадь поперечного сечения световода может выбираться в диапазоне от 10^-8 до 10^-4 м², т.е. в 10⁴ раз. Во столько же раз может изменяться предельно допустимая мощность преобразуемого излучения.As estimates show, with a modulation coefficient

for a fiber with a diameter of D = 125 μm, an acoustic power of 0.35 W is required. A decrease in the wavelength from 1.0 to 0.5 μm can be carried out in a fiber with a length of about 10 cm at a modulation frequency of 150 MHz. The cross-sectional area of the fiber can be selected in the range from 10 ^-8 to 10 ^-4 m ² , i.e. 10 ⁴ times. The maximum permissible power of the converted radiation can be changed as many times.

Literature
1. Shen I.R. Principles of nonlinear optics. M. World, 1989.

 2. Balakshiy V.I. Parygin V.N. Chirkov L.E. Physical foundations of acoustooptics. M. Radio and Communications, 1985, 280 pp.

 3. House H. Waves and fields in optoelectronics. M. Mir, 1988, 432 p.

 4. Weinstein L.A. Electromagnetic waves. M. Radio and Communications, 1988, 440 pp.

 5. Dielectric resonators. / Ed. M.E. Ilchenko. M. Radio and Communications, 1989, 328 pp.

Claims (1)

 A parametric amplifier and a wavelength converter of electromagnetic radiation, consisting of a dielectric, in which amplification and conversion of electromagnetic radiation introduced at certain angles takes place, and pumping, characterized in that a linear dielectric waveguide is used as a dielectric, and a traveling acoustic wave as a pump, for of which this waveguide is a sound guide, the shape of the sound guide is such that as the acoustic wave propagates, its cross section gradually is getting lost.

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