rus
Issue #4/2019
V. A. Komotskii, Yu. M. Sokolov, N. V. Suetin
New Optoelectronic Schemes Constructed Based on Relief Reflective Diffractive Structures with Rectangular Profile
New Optoelectronic Schemes Constructed Based on Relief Reflective Diffractive Structures with Rectangular Profile
The article describes a number of new schemes designed to measure small angular displacements and oscillations, to modulate laser radiation, and also to filter the spectrum of optical radiation in the visible and infrared wavelengths. The operation of these schemes is based on the effects observed when a laser beam is reflected from deep diffractive relief structures with a rectangular profile, with a relief depth from a quarter of the wavelength to several wavelengths due to laser radiation. The applications of these devices are varied. For example, sensors of small angular displacements and vibrations can be used in the study of vibrations and in the design of seismometers and tiltmeters. A mechanically driven modulator operates in the low-frequency modulation region, but can provide analogue modulation of the radiation power with different modulation depths from zero to one hundred percent. Optical filters built on the basis of deep relief reflective structures have oscillating dependences of the transmission coefficient on the wavelength. It is possible to select parameters in such a way that the filter has a zero transmission coefficient at a given wavelength and a transmission coefficient close to unity in another given area. The advantages of a filter of this type can be attributed simply to its production and the possibility of realigning the spectral characteristics of the filter within wide limits.
DOI: 10.22184/1993-7296.FRos.2019.13.4.392.404
DOI: 10.22184/1993-7296.FRos.2019.13.4.392.404
Теги: laser radiation modulator measuring instrument of small angular oscillations optical spectrum filter relief diffraction structure измеритель малых угловых колебаний модулятор лазерного излучения рельефная дифракционная структура фильтр оптического спектра
The article describes a number of new schemes designed to measure small angular displacements and oscillations, to modulate laser radiation, and also to filter the spectrum of optical radiation in the visible and infrared wavelengths. The operation of these schemes is based on the effects observed when a laser beam is reflected from deep diffractive relief structures with a rectangular profile, with a relief depth from a quarter of the wavelength to several wavelengths due to laser radiation.
Article received for editing 13.02.2019
Article accepted for publication 27.02.2019
INTRODUCTION
The work of the presented schemes is based on diffraction effects observed when a laser beam is reflected from a deep relief structure (DRS), which has a rectangular relief profile, and the width of the protrusion is equal to the width of the depressions (shape of the type: «ideal meander»). The depth of the relief Hp is in the range from a quarter of the wavelength to several wavelengths of laser radiation. With a normal incidence of an optical beam with a wavelength λ on a DRS, after it is reflected from the relief structure, the phase front of the reflected wave gets spatial phase modulation with a phase difference depth equal to: . When analysing the spatial spectrum of the wave, after its reflection from the DRS, we will use, instead of the depth of the phase difference, the quantity that we will call: «the amplitude of the spatial phase modulation of the wave front». With a normal incidence and reflection of the optical beam from the DRS, the magnitude of the amplitude of the spatial phase modulation is: . However, if the angle of incidence θ is not zero, then the amplitude of the spatial phase modulation decreases with increasing angle of incidence according to the following law:
. (1)
We especially note that with an oblique incidence of the optical beam on the DRS, we will only consider a scheme in which the plane of incidence – the reflection of the optical beam is strictly parallel to the lines of the relief of the DRS. At the same time, there are no shadowing effects on the part of the grooves of the grooves of the DRS, which would be observed with an oblique incidence of the optical beam across the grooves. To build real devices, we use DRSs, the period of which is much longer than the radiation wavelength: . Under these conditions, the analysis of the spatial spectrum after the reflection of an optical wave from a DRS with the shape of an ideal meander gives the following formula for calculating the power of the zero diffraction order [1, 2, 6, 9]:
, (2)
Pэфф = Pin · R is the effective radiation power, at the input, Pin is the power of the radiation incident on the DRS, R is the reflection coefficient of the radiation from the surface of the DRS.
Expression (2) is important for the subsequent analysis of the operation of the circuits, since in all the circuits under consideration we use only the radiation of the zero diffraction order. The first and higher orders of diffraction are not used in these schemes, therefore we will not consider them here. The dependences of the power of zero order on the angle of incidence of the optical beam on the DRS for two values of the depth of the DRS are shown in Fig. 1 (a, b).
It should be noted that the experimental studies conducted in [1] at DRS with different depths showed that the experimental and calculated dependences P0 (θ) coincide with very high accuracy.
On the dependences shown in Fig. 1 (a, b), the black dots mark the midpoints of the linear portions of the curves P0 (θ). One of the points on each of these curves corresponds to the angle of incidence θ = 45°, which is optimal if this DRS is used as part of a block new reflector.
Suppose we set the DRS to the initial position at which the angle of incidence corresponds to one of the points Т1, Т2, Т3... If at the same time the DRS will deviate by a small angle in the plane parallel to the lines of the DRS relief, then the increment of power of the zero diffraction order will be proportional to the increment of the deviation angle of the DRS, Δθ, from the initial position:
ΔP0 = SθP · Δθ. (3)
Here SθP is the steepness of the linear transformation of the angle deviations to changes in the power of the zero diffraction order. Note that the linearity of the transformation is violated near areas in which the power reaches maximum and minimum values. In practical devices, described below, linear dependency areas are used for linear analogue modulation of laser radiation, as well as in the construction of small oscillation sensors. Next, we consider a number of devices based on the DRS.
LASER RADIATION MODULATOR
The modulator [4,6], has a mechanical drive. It can be used for static power control at the output of the circuit and for modulating the radiation power of a laser with low frequencies. The device can be designed to work in both visible and infrared wavelengths. A feature of the scheme is the use of the DRS in the corner reflector unit (CRU), which ensures the constant direction of the output reflected radiation beam with the angular deviation of the DRS.
The modulator circuit is shown in Fig. 1. The device contains a block of a corner reflector (1), which is located on the path of the radiation beam emanating from the laser (2). On one of the BUO planes, a DRS (3) is installed, which has a rectangular profile in the form of a meander. The surface of the DRS has a high reflectivity. The DRS lines are located in the plane of incidence – the reflection of the laser beam. The depth of the relief of a DRS Hp, is usually several times greater than the wavelength λ of the modulated radiation. The characteristic of one of the DRS options is depicted in Figure 1 (b). On the second plane of the BCU, a mirror (4) with a high reflection coefficient is attached. The DRS planes and mirrors are located at a right angle and form an angular reflector, which returns a laser beam incident on it in the opposite direction. The CRU is connected with the axis of the electromechanical drive (5), which ensures its rotation at the given angles. The axis of rotation of the drive lies in the plane of the DRS and is perpendicular to the plane of incidence of the reflection of laser radiation. Provided that the axis of rotation passes through the centre of the region of incidence of the laser beam on the DRS, the optical beam from the laser will not move along the plane of the DRS when turning the CRU. The direction of the output radiation beam after reflection from the mirror (4) does not change when the CRU is rotated around the axis. After reflection from the CRU, the radiation decays into diffraction orders and then, after reflection from the auxiliary mirror (6), is directed to the diaphragm (7), which extracts only zero order from the diffraction pattern. Other orders, indicated by dotted lines in the figure, are cut off by an absorbing screen surrounding the aperture.
The mechanical drive with the CRU is installed on the coordinate table (8), which provides movement in two coordinates and rotation of the drive with the CRU and is intended to set the CRU at the optimum position relative to the input laser beam. The modulation of the power of the radiation beam in the zero diffraction order occurs as a result of the rotation of the BCF under the action of a drive. To control the output beam power during the control measurements, a photodiode (9) was installed at the output.
Consider some of the characteristic parameters of the modulator. On the one hand, the period of the DRS, Λp, must be substantially smaller than the diameter of the laser beam Dп, which is necessary for a good angular separation of the diffraction orders. Moreover, for a good separation of diffraction beams on the plane of the diaphragm it is necessary that the distance L from the CRU to the diaphragm satisfies the condition: L ≥ k Dп · Λр / λ, where k is a coefficient equal to about 2–3. From this relationship it is clear that the dimensions of the device decrease with a decrease in the period of the DRS. However, the period of the DRS should be significantly longer than the wavelength of the laser radiation: . Taking into account these conditions, we used a DRS with a period of 100 μm for an experimental model of a modulator of a helium-neon laser beam. It should be noted that the amplitude characteristics of the modulator are determined by the depth of the DRS relief and do not depend on its period. A more detailed analysis of the choice of DRS parameters can be found in [6].
Here are some of the results of an experimental study of the modulator layout. The modulator layout was assembled. in accordance with the scheme shown in Fig.2. The relief structure was made using photolithography technology and chemical etching of the substrate from glass, followed by vacuum deposition of an opaque reflective aluminium film onto the surface of the relief. The depth of the relief of the DRS was determined by the method described in [2], it was Hp = 2,48 ± 0,025 мкм, and taking into account that the experiments were carried out with helium – by a neon laser, the ratio of depth to wavelength was: Hp / λ = (3,92 ± 0,04). This parameter value is close to the value that corresponds to the graph in fig. 1 (b). To observe the shape of the modulation of the optical beam power at the output, after the diaphragm (7), a photodiode FD‑24K with a load resistor was installed. The signal at the photodiode load is proportional to the radiation power at the modulator output in the zero diffraction order. A harmonic signal was applied to the input of a mechanical drive. The output waveforms corresponding to the various input levels of the drive are shown in Fig. 3. As can be seen from the graphs given, with moderate amplitudes of the input oscillations, the shape of the output signal almost repeats the shape of the input harmonic signal (curves 1, 2). With a modulation depth close to 100%, nonlinear distortions are observed (curves 3 and 4). Thus, in contrast to widely used slotted modulators with interrupted optical beam, this type of modulator makes it possible to obtain a harmonic modulation with a given modulation depth. In this case, the spatial structure of the output beam is not distorted by its interruption. A modulator can be designed for different wavelength ranges of laser radiation.
MEASUREMENT OF SMALL ANGULAR VIBRATIONS OF OBJECTS, APPLICATION OF THE ANGULAR SHIFT SENSOR TO BUILD A SEISMOMETER
As follows from the previous section, when the DRS oscillates, there is a transformation of the angular deviations of the DRS into changes in the radiation power of zero order diffraction. Essentially, the above scheme can serve as a sensor for small angular displacements. If you place the DRS on the oscillating object, then at the output of the photodetector installed in zero diffraction order, you can get a signal proportional to the angular deviation of the DRS. In this case, we make the DRS on a substrate – a thin plate or on a film, and glue this substrate to the surface of the object under study. Experiments on the measurement of angular oscillations of structures using DRS were described in [1], and the simplest scheme was used without an angular reflector. The minimum detected amplitude of oscillations was of the order of Δθ = 10–5 radians when detecting oscillations in the frequency band up to 1 kHz.
It is of interest to use an angular oscillation sensor with the use of a CRU with DRS as an angular oscillation sensor in a seismometer design. In many well-known seismometer designs, inductive type sensors are used that produce an output signal proportional to the earth surface displacement velocity. In the low frequency range, the sensitivity of such sensors decreases. Inductive sensors cannot detect static changes in surface inclination. The use of an optoelectronic sensor built with the use of a CRU with DRS allows you to extend the frequency range of measurements in the direction of low frequencies. In this case, it is possible to measure not only dynamic, but also static slopes.
A simplified diagram of an instrument for measuring earth oscillations is shown in Fig. 4. On the basis of the device (1), an axis of rotation is mounted in elastic suspensions, or in bearings, on which a physical pendulum (2) is fixed, which is disk-shaped in this drawing. The centre of gravity of the physical pendulum is located below the axis of rotation at some distance: RОС. In the area of the axis of rotation, with the help of a sleeve, the CRU (3) is attached to the disk, the two faces of which are at right angles to each other. On one side of the corner reflector is a reflecting DRS with a rectangular profile (4), and on the other side there is a mirror (5). The DRS is fixed on the edge of the CRU in such a way that the relief lines are perpendicular to the axis of rotation of the physical pendulum and are actually parallel to the disk plane. A semiconductor laser (6) is installed on a horizontal platform of the base (1) so that its radiation beam is directed to the DRS. A rotating mirror (7) was installed in the path of the laser beam returned after reflecting it from the DRS (4) and then from the mirror (5), by means of which the diffraction beam of radiation is directed to the aperture (8), which emits zero-order radiation diffraction. The isolated zero-order radiation beam is directed to the photodetector (9), with the output signal obtained from its output. Permanent magnets (10) are fixed on the vertical rack of the base (1), with its flat surfaces located parallel to the surface of the metal disk (2) near its surface. The magnets are designed for optimal damping of disk oscillations due to the effect of eddy currents in a metal disk when it moves.
CRU (3) has the ability to rotate relative to the disk, which is necessary for the initial setup, i. e. to ensure the installation of the initial optimal angle of incidence of the laser beam on the DRS (4). On the horizontal part of the base (1) there are three adjustment screws, which are designed to set the base to its original horizontal position. In this case, two screws are placed on one side of the base on a line perpendicular to the plane of the disk, and the third screw is placed on the opposite side of the base. With the help of the third adjustment screw it is possible to fine-tune the base inclination in the disk plane and set the optimum angle of incidence of the laser beam on the DRS
When the base of the device is horizontally moved, the physical pendulum rotates relative to the base in the direction opposite to the base movement due to inertia forces along with the surface on which it is installed. As a result, a change occurs in the angle of incidence of the laser beam on the DRS in a plane parallel to its lines, which causes a change in the power of the zero diffraction order, which is proportional to the deflection angle of the physical pendulum. The electrical signal from the photodiode output contains two components. One component of the signal is proportional to the slope of the surface on which the instrument is mounted. In this case, both the variable and the constant component of the surface slope are recorded at the output. The second component of the output signal is proportional to the horizontal displacement of the surface on which the device is installed. In this case, the device does not respond to static displacements in the horizontal direction, but responds only to oscillations in the horizontal direction parallel to the plane of the physical pendulum. The output level of this component will decrease in the region of oscillation frequencies lower than the resonant frequency of the physical pendulum; however, this decrease will not be as rapid as with instruments with an inductive oscillation sensor.
OPTICAL SIGNAL FILTERS BUILT USING DRS
As can be seen from the expression (2) the power transfer ratio from the input to the output of the device, in which diffraction is applied to the DRS, depends on the radiation wavelength. This relationship can be used to filter optical radiation. The simplest filter scheme using the DRS is shown in Fig. 5. Along with this scheme it is possible to apply a more complex scheme containing an angled reflector.
Calculated parameters of filters. First, we consider the simplest filter that suppresses radiation at certain wavelengths. The dependence of the transmission power of the radiation power kp = P0 / Pэфф on the radiation wavelength, λ, is determined by the relation (2). Fig. 6 shows a family of calculated dependencies kp (λ) for different values of the parameter θ the angle of incidence of the light beam on the relief structure with a depth equal to: Hp = 0.6 μm. On the graphs there are marked areas of low and areas of high transmit power of radiation from the input to the output of the filter. This graph demonstrates the possibility of restructuring the frequencies of the maxima and minima of the transmittance of filters by changing the angle of incidence of the input optical beam. At different angles of incidence, zero-out (minimum) values of the filter transmission coefficient correspond to different wavelengths, whose coordinates on the axis of the wavelengths can be calculated by the formula:
(4)
As the ratio Hp / λ increases, the frequency of the location of the minima and maxima of the dependence kp (λ) on the wavelength scale increases. Selecting in a certain way the depth of the DRS and the angle of incidence of the optical beam, we can select or suppress certain spectral lines.
Let's consider as an example the following problem: select the radiation of the spectral line of an argon laser, which has a wavelength: λ2 = 0.514 μm and at the same time suppress the radiation of another strong spectral line with a wavelength: λ1 = 0.488 μm. For this, the filter transfer coefficient must be maximum at the wavelength of 0.514 μm, and at the wavelength of 0.488 μm it must be minimum.
As a result of the calculations described in detail in [7], we chose the depth of the DRS Ηp = 3 μm. Graphs of the dependences of the transmission coefficients on the wavelength are shown in Fig. 7 (a, b). As can be seen from graph No. 1, shown in Fig. 7 (a), a filter with parameters: Ηp = 3 μm, θ = 31.35° suppresses radiation with a wavelength of λ1 = 0.488 μm and passes radiation with a wavelength equal to λ2 = 0.514 μm.
If you rebuild If the filter changes the angle of incidence and sets it equal to: θ = 35.53° then for the same depth of the DRS, Ηp = 3 μm, the filter will transmit radiation with a wavelength equal to λ1 = 0.488 μm and suppress radiation with a wavelength of λ2 = 0.514 μm, as can be seen in graph No. 3 in Fig. 7. (b).
Curve number 2 in Fig. 7 (a) shows how the filter characteristic changes if the DRS is manufactured with an error and its depth is Ηp = 3.2 μm instead of depth Ηp = 3 μm, provided that the angle of incidence of the beam remains 31.35°. The positions of the minima and maxima will change significantly as compared with curve 1.
However, the inaccuracy of manufacturing is easy to compensate by changing the angle of incidence. To do this, change the initial angle of incidence of the input optical beam from the angle θ = 31.35°to another angle of incidence θ = 36.81°. As a result, after changing the angle of incidence of the input beam, we obtain the calculated curve of the transfer coefficient as a function of wavelength, which in fact repeats curve No. 1 in Fig. 7 (a) with high accuracy. Thus, with a different depth of the DRS equal to Ηp = 3.2 μm, you can easily compensate for the change in the spectral characteristics of the filter. After restructuring the circuit and installing a new angle of incidence θ = 36.81°, the calculated dependence of the transmission coefficient on the wavelength is shifted along the wavelength axis, and it almost completely coincides with the dependence calculated by combining the parameters: θ = 31.35 and Ηp = 3 μm. In practice, it will be necessary to fine tune the angle of incidence to minimize the output radiation with a given wavelength.
CONCLUSION
As a result of the research, the possibility of constructing three types of new devices, based on the principle of diffraction of an optical beam on a deep relief structure, is shown. The use of sensors with DRS in seismometers may possibly expand the frequency range of recording in the direction of low frequencies. New filter schemes based on the DRS can be applied not only in the visible wavelength range, but also in different regions of the infrared range. For the IR range of the DRS can be made on the surfaces of metal plates with high reflection.
These studies were carried out in the Laboratory of Optoelectronics of the Institute of Physical Research and Technology of the Faculty of Physical, Mathematical and Natural Sciences of the RUDN University with the support of program 5–100.
Article received for editing 13.02.2019
Article accepted for publication 27.02.2019
INTRODUCTION
The work of the presented schemes is based on diffraction effects observed when a laser beam is reflected from a deep relief structure (DRS), which has a rectangular relief profile, and the width of the protrusion is equal to the width of the depressions (shape of the type: «ideal meander»). The depth of the relief Hp is in the range from a quarter of the wavelength to several wavelengths of laser radiation. With a normal incidence of an optical beam with a wavelength λ on a DRS, after it is reflected from the relief structure, the phase front of the reflected wave gets spatial phase modulation with a phase difference depth equal to: . When analysing the spatial spectrum of the wave, after its reflection from the DRS, we will use, instead of the depth of the phase difference, the quantity that we will call: «the amplitude of the spatial phase modulation of the wave front». With a normal incidence and reflection of the optical beam from the DRS, the magnitude of the amplitude of the spatial phase modulation is: . However, if the angle of incidence θ is not zero, then the amplitude of the spatial phase modulation decreases with increasing angle of incidence according to the following law:
. (1)
We especially note that with an oblique incidence of the optical beam on the DRS, we will only consider a scheme in which the plane of incidence – the reflection of the optical beam is strictly parallel to the lines of the relief of the DRS. At the same time, there are no shadowing effects on the part of the grooves of the grooves of the DRS, which would be observed with an oblique incidence of the optical beam across the grooves. To build real devices, we use DRSs, the period of which is much longer than the radiation wavelength: . Under these conditions, the analysis of the spatial spectrum after the reflection of an optical wave from a DRS with the shape of an ideal meander gives the following formula for calculating the power of the zero diffraction order [1, 2, 6, 9]:
, (2)
Pэфф = Pin · R is the effective radiation power, at the input, Pin is the power of the radiation incident on the DRS, R is the reflection coefficient of the radiation from the surface of the DRS.
Expression (2) is important for the subsequent analysis of the operation of the circuits, since in all the circuits under consideration we use only the radiation of the zero diffraction order. The first and higher orders of diffraction are not used in these schemes, therefore we will not consider them here. The dependences of the power of zero order on the angle of incidence of the optical beam on the DRS for two values of the depth of the DRS are shown in Fig. 1 (a, b).
It should be noted that the experimental studies conducted in [1] at DRS with different depths showed that the experimental and calculated dependences P0 (θ) coincide with very high accuracy.
On the dependences shown in Fig. 1 (a, b), the black dots mark the midpoints of the linear portions of the curves P0 (θ). One of the points on each of these curves corresponds to the angle of incidence θ = 45°, which is optimal if this DRS is used as part of a block new reflector.
Suppose we set the DRS to the initial position at which the angle of incidence corresponds to one of the points Т1, Т2, Т3... If at the same time the DRS will deviate by a small angle in the plane parallel to the lines of the DRS relief, then the increment of power of the zero diffraction order will be proportional to the increment of the deviation angle of the DRS, Δθ, from the initial position:
ΔP0 = SθP · Δθ. (3)
Here SθP is the steepness of the linear transformation of the angle deviations to changes in the power of the zero diffraction order. Note that the linearity of the transformation is violated near areas in which the power reaches maximum and minimum values. In practical devices, described below, linear dependency areas are used for linear analogue modulation of laser radiation, as well as in the construction of small oscillation sensors. Next, we consider a number of devices based on the DRS.
LASER RADIATION MODULATOR
The modulator [4,6], has a mechanical drive. It can be used for static power control at the output of the circuit and for modulating the radiation power of a laser with low frequencies. The device can be designed to work in both visible and infrared wavelengths. A feature of the scheme is the use of the DRS in the corner reflector unit (CRU), which ensures the constant direction of the output reflected radiation beam with the angular deviation of the DRS.
The modulator circuit is shown in Fig. 1. The device contains a block of a corner reflector (1), which is located on the path of the radiation beam emanating from the laser (2). On one of the BUO planes, a DRS (3) is installed, which has a rectangular profile in the form of a meander. The surface of the DRS has a high reflectivity. The DRS lines are located in the plane of incidence – the reflection of the laser beam. The depth of the relief of a DRS Hp, is usually several times greater than the wavelength λ of the modulated radiation. The characteristic of one of the DRS options is depicted in Figure 1 (b). On the second plane of the BCU, a mirror (4) with a high reflection coefficient is attached. The DRS planes and mirrors are located at a right angle and form an angular reflector, which returns a laser beam incident on it in the opposite direction. The CRU is connected with the axis of the electromechanical drive (5), which ensures its rotation at the given angles. The axis of rotation of the drive lies in the plane of the DRS and is perpendicular to the plane of incidence of the reflection of laser radiation. Provided that the axis of rotation passes through the centre of the region of incidence of the laser beam on the DRS, the optical beam from the laser will not move along the plane of the DRS when turning the CRU. The direction of the output radiation beam after reflection from the mirror (4) does not change when the CRU is rotated around the axis. After reflection from the CRU, the radiation decays into diffraction orders and then, after reflection from the auxiliary mirror (6), is directed to the diaphragm (7), which extracts only zero order from the diffraction pattern. Other orders, indicated by dotted lines in the figure, are cut off by an absorbing screen surrounding the aperture.
The mechanical drive with the CRU is installed on the coordinate table (8), which provides movement in two coordinates and rotation of the drive with the CRU and is intended to set the CRU at the optimum position relative to the input laser beam. The modulation of the power of the radiation beam in the zero diffraction order occurs as a result of the rotation of the BCF under the action of a drive. To control the output beam power during the control measurements, a photodiode (9) was installed at the output.
Consider some of the characteristic parameters of the modulator. On the one hand, the period of the DRS, Λp, must be substantially smaller than the diameter of the laser beam Dп, which is necessary for a good angular separation of the diffraction orders. Moreover, for a good separation of diffraction beams on the plane of the diaphragm it is necessary that the distance L from the CRU to the diaphragm satisfies the condition: L ≥ k Dп · Λр / λ, where k is a coefficient equal to about 2–3. From this relationship it is clear that the dimensions of the device decrease with a decrease in the period of the DRS. However, the period of the DRS should be significantly longer than the wavelength of the laser radiation: . Taking into account these conditions, we used a DRS with a period of 100 μm for an experimental model of a modulator of a helium-neon laser beam. It should be noted that the amplitude characteristics of the modulator are determined by the depth of the DRS relief and do not depend on its period. A more detailed analysis of the choice of DRS parameters can be found in [6].
Here are some of the results of an experimental study of the modulator layout. The modulator layout was assembled. in accordance with the scheme shown in Fig.2. The relief structure was made using photolithography technology and chemical etching of the substrate from glass, followed by vacuum deposition of an opaque reflective aluminium film onto the surface of the relief. The depth of the relief of the DRS was determined by the method described in [2], it was Hp = 2,48 ± 0,025 мкм, and taking into account that the experiments were carried out with helium – by a neon laser, the ratio of depth to wavelength was: Hp / λ = (3,92 ± 0,04). This parameter value is close to the value that corresponds to the graph in fig. 1 (b). To observe the shape of the modulation of the optical beam power at the output, after the diaphragm (7), a photodiode FD‑24K with a load resistor was installed. The signal at the photodiode load is proportional to the radiation power at the modulator output in the zero diffraction order. A harmonic signal was applied to the input of a mechanical drive. The output waveforms corresponding to the various input levels of the drive are shown in Fig. 3. As can be seen from the graphs given, with moderate amplitudes of the input oscillations, the shape of the output signal almost repeats the shape of the input harmonic signal (curves 1, 2). With a modulation depth close to 100%, nonlinear distortions are observed (curves 3 and 4). Thus, in contrast to widely used slotted modulators with interrupted optical beam, this type of modulator makes it possible to obtain a harmonic modulation with a given modulation depth. In this case, the spatial structure of the output beam is not distorted by its interruption. A modulator can be designed for different wavelength ranges of laser radiation.
MEASUREMENT OF SMALL ANGULAR VIBRATIONS OF OBJECTS, APPLICATION OF THE ANGULAR SHIFT SENSOR TO BUILD A SEISMOMETER
As follows from the previous section, when the DRS oscillates, there is a transformation of the angular deviations of the DRS into changes in the radiation power of zero order diffraction. Essentially, the above scheme can serve as a sensor for small angular displacements. If you place the DRS on the oscillating object, then at the output of the photodetector installed in zero diffraction order, you can get a signal proportional to the angular deviation of the DRS. In this case, we make the DRS on a substrate – a thin plate or on a film, and glue this substrate to the surface of the object under study. Experiments on the measurement of angular oscillations of structures using DRS were described in [1], and the simplest scheme was used without an angular reflector. The minimum detected amplitude of oscillations was of the order of Δθ = 10–5 radians when detecting oscillations in the frequency band up to 1 kHz.
It is of interest to use an angular oscillation sensor with the use of a CRU with DRS as an angular oscillation sensor in a seismometer design. In many well-known seismometer designs, inductive type sensors are used that produce an output signal proportional to the earth surface displacement velocity. In the low frequency range, the sensitivity of such sensors decreases. Inductive sensors cannot detect static changes in surface inclination. The use of an optoelectronic sensor built with the use of a CRU with DRS allows you to extend the frequency range of measurements in the direction of low frequencies. In this case, it is possible to measure not only dynamic, but also static slopes.
A simplified diagram of an instrument for measuring earth oscillations is shown in Fig. 4. On the basis of the device (1), an axis of rotation is mounted in elastic suspensions, or in bearings, on which a physical pendulum (2) is fixed, which is disk-shaped in this drawing. The centre of gravity of the physical pendulum is located below the axis of rotation at some distance: RОС. In the area of the axis of rotation, with the help of a sleeve, the CRU (3) is attached to the disk, the two faces of which are at right angles to each other. On one side of the corner reflector is a reflecting DRS with a rectangular profile (4), and on the other side there is a mirror (5). The DRS is fixed on the edge of the CRU in such a way that the relief lines are perpendicular to the axis of rotation of the physical pendulum and are actually parallel to the disk plane. A semiconductor laser (6) is installed on a horizontal platform of the base (1) so that its radiation beam is directed to the DRS. A rotating mirror (7) was installed in the path of the laser beam returned after reflecting it from the DRS (4) and then from the mirror (5), by means of which the diffraction beam of radiation is directed to the aperture (8), which emits zero-order radiation diffraction. The isolated zero-order radiation beam is directed to the photodetector (9), with the output signal obtained from its output. Permanent magnets (10) are fixed on the vertical rack of the base (1), with its flat surfaces located parallel to the surface of the metal disk (2) near its surface. The magnets are designed for optimal damping of disk oscillations due to the effect of eddy currents in a metal disk when it moves.
CRU (3) has the ability to rotate relative to the disk, which is necessary for the initial setup, i. e. to ensure the installation of the initial optimal angle of incidence of the laser beam on the DRS (4). On the horizontal part of the base (1) there are three adjustment screws, which are designed to set the base to its original horizontal position. In this case, two screws are placed on one side of the base on a line perpendicular to the plane of the disk, and the third screw is placed on the opposite side of the base. With the help of the third adjustment screw it is possible to fine-tune the base inclination in the disk plane and set the optimum angle of incidence of the laser beam on the DRS
When the base of the device is horizontally moved, the physical pendulum rotates relative to the base in the direction opposite to the base movement due to inertia forces along with the surface on which it is installed. As a result, a change occurs in the angle of incidence of the laser beam on the DRS in a plane parallel to its lines, which causes a change in the power of the zero diffraction order, which is proportional to the deflection angle of the physical pendulum. The electrical signal from the photodiode output contains two components. One component of the signal is proportional to the slope of the surface on which the instrument is mounted. In this case, both the variable and the constant component of the surface slope are recorded at the output. The second component of the output signal is proportional to the horizontal displacement of the surface on which the device is installed. In this case, the device does not respond to static displacements in the horizontal direction, but responds only to oscillations in the horizontal direction parallel to the plane of the physical pendulum. The output level of this component will decrease in the region of oscillation frequencies lower than the resonant frequency of the physical pendulum; however, this decrease will not be as rapid as with instruments with an inductive oscillation sensor.
OPTICAL SIGNAL FILTERS BUILT USING DRS
As can be seen from the expression (2) the power transfer ratio from the input to the output of the device, in which diffraction is applied to the DRS, depends on the radiation wavelength. This relationship can be used to filter optical radiation. The simplest filter scheme using the DRS is shown in Fig. 5. Along with this scheme it is possible to apply a more complex scheme containing an angled reflector.
Calculated parameters of filters. First, we consider the simplest filter that suppresses radiation at certain wavelengths. The dependence of the transmission power of the radiation power kp = P0 / Pэфф on the radiation wavelength, λ, is determined by the relation (2). Fig. 6 shows a family of calculated dependencies kp (λ) for different values of the parameter θ the angle of incidence of the light beam on the relief structure with a depth equal to: Hp = 0.6 μm. On the graphs there are marked areas of low and areas of high transmit power of radiation from the input to the output of the filter. This graph demonstrates the possibility of restructuring the frequencies of the maxima and minima of the transmittance of filters by changing the angle of incidence of the input optical beam. At different angles of incidence, zero-out (minimum) values of the filter transmission coefficient correspond to different wavelengths, whose coordinates on the axis of the wavelengths can be calculated by the formula:
(4)
As the ratio Hp / λ increases, the frequency of the location of the minima and maxima of the dependence kp (λ) on the wavelength scale increases. Selecting in a certain way the depth of the DRS and the angle of incidence of the optical beam, we can select or suppress certain spectral lines.
Let's consider as an example the following problem: select the radiation of the spectral line of an argon laser, which has a wavelength: λ2 = 0.514 μm and at the same time suppress the radiation of another strong spectral line with a wavelength: λ1 = 0.488 μm. For this, the filter transfer coefficient must be maximum at the wavelength of 0.514 μm, and at the wavelength of 0.488 μm it must be minimum.
As a result of the calculations described in detail in [7], we chose the depth of the DRS Ηp = 3 μm. Graphs of the dependences of the transmission coefficients on the wavelength are shown in Fig. 7 (a, b). As can be seen from graph No. 1, shown in Fig. 7 (a), a filter with parameters: Ηp = 3 μm, θ = 31.35° suppresses radiation with a wavelength of λ1 = 0.488 μm and passes radiation with a wavelength equal to λ2 = 0.514 μm.
If you rebuild If the filter changes the angle of incidence and sets it equal to: θ = 35.53° then for the same depth of the DRS, Ηp = 3 μm, the filter will transmit radiation with a wavelength equal to λ1 = 0.488 μm and suppress radiation with a wavelength of λ2 = 0.514 μm, as can be seen in graph No. 3 in Fig. 7. (b).
Curve number 2 in Fig. 7 (a) shows how the filter characteristic changes if the DRS is manufactured with an error and its depth is Ηp = 3.2 μm instead of depth Ηp = 3 μm, provided that the angle of incidence of the beam remains 31.35°. The positions of the minima and maxima will change significantly as compared with curve 1.
However, the inaccuracy of manufacturing is easy to compensate by changing the angle of incidence. To do this, change the initial angle of incidence of the input optical beam from the angle θ = 31.35°to another angle of incidence θ = 36.81°. As a result, after changing the angle of incidence of the input beam, we obtain the calculated curve of the transfer coefficient as a function of wavelength, which in fact repeats curve No. 1 in Fig. 7 (a) with high accuracy. Thus, with a different depth of the DRS equal to Ηp = 3.2 μm, you can easily compensate for the change in the spectral characteristics of the filter. After restructuring the circuit and installing a new angle of incidence θ = 36.81°, the calculated dependence of the transmission coefficient on the wavelength is shifted along the wavelength axis, and it almost completely coincides with the dependence calculated by combining the parameters: θ = 31.35 and Ηp = 3 μm. In practice, it will be necessary to fine tune the angle of incidence to minimize the output radiation with a given wavelength.
CONCLUSION
As a result of the research, the possibility of constructing three types of new devices, based on the principle of diffraction of an optical beam on a deep relief structure, is shown. The use of sensors with DRS in seismometers may possibly expand the frequency range of recording in the direction of low frequencies. New filter schemes based on the DRS can be applied not only in the visible wavelength range, but also in different regions of the infrared range. For the IR range of the DRS can be made on the surfaces of metal plates with high reflection.
These studies were carried out in the Laboratory of Optoelectronics of the Institute of Physical Research and Technology of the Faculty of Physical, Mathematical and Natural Sciences of the RUDN University with the support of program 5–100.
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