Wavefront: Some Issues Related to its Reconstruction and Shaping in Holography and Diffraction Optics
to its Reconstruction and Shaping in Holography and Diffraction Optics
A. V. Lukin
JSC «NPO «State Institute of Applied Optics», firstname.lastname@example.org, Kazan, Russia
In this paper we consider the problems of wavefronts shaping and transformation in holography and in diffraction optics. The simplest examples illustrate the similarity and difference in the physical nature of the processes of formation and intensity distribution of a single diffractive (holographic) lens and a classical lens for continuous and single-pulse laser radiation in a circle of diffusion. It was also proposed to generalize the theorems of Malus and Levi-Civita in cases of diffraction; the appropriate formula is given.
Keywords: light wave front, light velocity, lightwave length, Huygens-Fresnel principle, wavefront reconstruction, diffraction optics, holography, diffracted beam, coherence.
In the recent years, a need to replace imported optical fibres for special applications has been emerged, which has led to the development of a number of models of special fibres by PJSC PSPIMC, in particular, radiation-resistant fibre with preservation of the radiation polarization for fibre-optic Gyroscopes [1–3].
Further development of this technology led to the creation of mass production of a new type of fibre, a single-mode optical fibre with a core of undoped quartz glass OV-RSI125. The main parameters of the fibre are presented in the table. Two modifications have been developed with a protective coating of two types: a two-layer acrylate and a polyimide coating with a carbon sublayer. Modifications with silicone and urethane acrylate coatings are also available. Carbon coating is used to increase the long-term reliability of the fibre (Fig. 1), it contributes to maintaining strength when the fibre surface is exposed to moisture and prevents the diffusion of water and hydrogen molecules into the fibre core.
The results of testing an optical fibre OV-RSI125 with a polyimide coating with a carbon sublayer for exposure to elevated temperature, air tightness to a hydrogen-containing medium, and various types of ionizing radiation are presented in this article.
High temperature resistance tests
In the process of temperature exposure, the optical loss of the optical fibre changes. The tests for resistance to elevated temperatures were carried out as follows: an optical fibre in a 155 mm diameter free-winding was placed in a heat chamber with an accuracy of maintaining the temperature of ± 2 °C in an air atmosphere; the temperature changed stepwise up to +300 °C, the exposure time was 8 hours. During the exposure, the optical power at the fibre output was measured using a power meter with a measurement error of 10–5 mW. Optical losses before and after exposure were measured by the clipping method according to GOST R IEC60793–1–40–2012.
The test results are graphically presented in Fig. 2. At a temperature of 300 °C, the optical fibre loss increases by 0.15 dB / km and does not exceed 0.56 dB / km. After transition to normal conditions, the optical loss is practically restored to its original state.
Hydrogen gas resistance tests
The tests of the optical fibre for resistance to hydrogen gas were carried out in a test chamber and an oven according to the scheme (Fig. 3). Coils with a fibre of at least 200 m in length were placed in the test chamber, both ends of each sample being brought out through the chamber“s hermetic outlets. One end of the fibre was connected to a spectrum analyser to record the transmission spectrum of the fibre, the other end was connected to a white light source. The chamber is checked for air-tightness and placed in a drying cabinet, then a hydrogen atmosphere with a pressure of 10 bar is created in the chamber and heated to a temperature of 100 °С. The optical fibre samples were kept under these conditions for up to 40 h, sequentially measuring the transmission spectrum of the fibre (Fig. 4 a, b). A change in the transmission spectrum of OV-RSI125 fibre with a carbon-polyimide coating was not recorded (Fig. 4, a). At the same time, for the control fibre sample without a carbon coating, a characteristic change in the transmission spectrum at a wavelength of 1240 nm was recorded, which indicates the penetration of molecular hydrogen (Fig. 4b).
Ionizing radiation resistance tests
Fibre and with a core of undoped quartz glass as in OV-RSI125 they provide high resistance to ionizing radiation . Radiation-induced optical loss (RIL) in fibres with a quartz core is significantly less than that of germanium-silicate fibres.
To study the reaction of an optical fibre to the effects of various types of ionizing radiation, a technique was applied based on the recommendations of GOST RV 6015–002–2007. An optical fibre with a length of at least 100 m was tested in free winding to minimize the contribution of mechanical stresses to the RIL. During the exposure, the transmission spectrum of the fibre, the optical power at the working wavelengths (1.31 μm and 1.55 μm) at the fibre output were recorded. The effect of the introduced optical power (imitation of fibre operation) on the RIL was also investigated. Fibre samples were placed in an irradiation hall in a region of space with a given dose rate of ionizing radiation, and it was possible to change the temperature of the samples directly in this region. The ends of the samples of the optical fibre were connected by welding to an optical cable with the same fibre, which was laid through biological protection and connected to an optical radiation source, optical power meter, or spectrum analyser (Fig. 5).
Continuous gamma radiation resistance studies
The studies were carried out using a GUT‑200M simulator based on a 60Co gamma radiation source. A fibre sample was placed in a region with a uniform irradiation field of 1 Gy / s or 5 Gy / s.
Studies at different wavelengths
Fig. 6 shows the RIL at operating wavelengths. For an absorbed dose of up to 100 kGy, it is advantageous to operate this fibre at a wavelength of 1.55 μm due to significantly lower RIL; at the initial stage of irradiation, the difference in RIL for wavelengths of 1.55 μm and 1.31 μm is up to 5 dB / km. Moreover, for an absorbed dose of more than 100 kGy, the advantage over the operating wavelength of 1.31 μm, for which at a dose of 1 MGy an RNP of not more than 15 dB / km is achieved. In this experiment, the input optical power was less than 0.1 μW (to exclude the influence of the photobleaching effect). It should be noted that the RIL for the operating wavelength λ = 1550 nm are more sensitive to ambient temperature. During irradiation, the temperature at the source of gamma radiation rose by about 5 °C and then cooled by forced ventilation to the same 5 °C. You can notice in the areas in the area of radiation doses of 280Gy, 700Gy, 1.1 MGy sharp jumps of RIL by about 1 dB / km associated with the temperature in the irradiation room.
Low ambient temperature effect
The dependence of RIL on temperature is a known fact, elevated temperatures positively affect the resistance to ionizing radiation. This effect is called thermal annealing. At the same time, lower temperatures significantly impair the durability of the optical fibre [5, 6]. Glass grid defects that occur when exposed to ionizing radiation pass from an excited state to an intermediate state, are in this state for a long time, and then tend to the original state under the influence of thermal effects. At low temperatures, the transition of glass grid defects from an intermediate state to an initial state occurs much more slowly. . The aim of the study was to check the resistance of fibre OV-RSI125 to ionizing radiation at low ambient temperature minus 60 °C. Fig. 7 shows the dependence of the RIL at a wavelength of 1310 nm on the radiation dose up to 370 Gy at a temperature of minus 60 °C and the optical power introduced into the sample of 5 μW, as well as relaxation for 3 minutes after switching off the gamma radiation source. The maximum RIL at low temperatures with an absorbed dose of 370 Gy on the OB-RSI125 sample was 10 dB / km, which is consistent with the data of .
A vivid manifestation of the photobleaching effect can be seen in a fibre with an undoped quartz core . The effect of the input optical power into the fibre OV-RSI125 on radiation-induced losses is studied, which is extremely important to know when operating such optical fibres. Optical power from 6.5 μW to 4 mW at a wavelength of 1550 nm was introduced into four identical fibre samples of OV-RSI125 fibre using optical attenuators. The fibre was irradiated to a dose of 1Gy with a dose rate of 1.3 Gy / s at a temperature of +30 °C.
By increasing the input power by a thousand times, it was possible to reduce losses from 1.9 dB / km to 1.1 dB / km at an absorbed dose of 1Gy only due to the photobleaching effect (Fig. 8). Moreover, the dependence of the RIL on the optical power is nonlinear, and from the point of view of operation, it is advisable to introduce at least 1 mW of optical power at the indicated doses. As studies  show, the effect is manifested both with continuous input laser radiation and with pulsed.
Resistance to pulsed gamma radiation studies
Investigations of the resistance of optical fibre OV-RSI125 to pulse gamma radiation was transmitted on a pulsed linear induction electron accelerator with a pulse length of ~ 20 ns. Two identical samples of a single-mode isotropic fibre were tested at a wavelength of 1310 nm (30 μW power) at a room temperature (Fig. 9). The first sample received a dose of 6 Gy per pulse. It took about 4 ms to reach the RIL boundary of 10 dB / km. After a second, the sample recovered to a loss level of 0.45 dB / km. The second sample received a dose of 27 Gy and reached an RIL boundary of 10 dB / km in 7 ms. After a second of relaxation, the RIL of the second sample was 1 dB / km. Thus, with a difference in dose rate (and dose per pulse) of up to 4.5 times, the RIL differs by approximately 0.5 dB / km 1 s after exposure .
Resistance studies to pulsed neutron radiation showed (Fig. 10) that the RIL at a wavelength of 1550 nm was 1.8 dB / km 0.2 s after exposure for a duration of 60 μs with a dose of 4 krad and a fluence of 1.5 ∙ 1013 n / cm‑2.
In , it was revealed that the luminescence of an optical fibre occurs with pulsed ionizing radiation at a dose rate of more than 107 R / s as evidence by a series of experiments. The temporary form of luminescence arising in the fibre follows the shape of the gamma pulse. OV-RSI125 fibres were tested under similar conditions on a pulsed linear induction electron accelerator with a pulse length of ~20 ns. No optical power was introduced into the fibre sample; the signal was detected using a photodetector with a bandwidth of 80 MHz and a storage oscilloscope. The graph (Fig. 11) shows the signal associated with luminescence, where the voltage from the photodetector in volts is plotted on the vertical axis. The absorbed dose of 22 Gy per pulse with a duration of 20 ns corresponds to a dose rate of 109 Gy / s. The width of the luminescence curve at half maximum is about 20 ns, which corresponds to the pulse duration of the gamma source.
The results presented in the research confirm high resistance to increased operating temperature, hydrogen-containing medium, pulsed and continuous ionizing radiation of optical fibre OV-RSI125, developed and manufactured by PJSC PSPIMC. ▪