CC BY
19
UDC 535.41.111
V.M. Petrov ', A.V. Khomenko 2,Ya.A. Krinitsky ', A.M. Garcia 2
' St. Petersburg State Polytechnical University. 2 Ensenada Center for Scientific Research and Higher Education.
LIGHT PRESSURE DETECTION BY TWO-WAVE MIXING IN THE PHOTOREFRACTIVE BaTiO, : Co CRYSTAL
The paper studies the high-sensitive detection of light radiation pressure using an adaptive interferometer based on photorefractive 45°-cut BaTiO3 : Co crystal. For small phase modulation measurement the authors employed a polarization filtering, which ensured the linear regime of signal detection in the photorefractive crystal with nonlocal response. It was demonstrated that the proposed method of light pressure measurement could be used as a broadband photodetector. It was experimentally found that the sensitivity was 2 ^W in the wavelength range from 488 to 1600 nm.
ADAPTIVE HOLOGRAFIC INTERFEROMETER, LIGHT PRESSURE, TWO-WAVE MIXING, PHOTOREFRACTIVE CRYSTAL, HIGH-SENSITIVE DETECTION, BROADBAND PHOTODETECTOR.
Introduction
It is well known that light exerts pressure on an illuminated object that is a result of the momentum transfer from photons to the object, which reflects, absorbs, or refracts the light [1]. Even though light pressure is negligible in common practice, nowadays it has numerous applications ranging from manipulation on biological particles and nanotechnology up to cooling and trapping atoms [1—3].
In this paper we consider a highsensitive detection of light pressure using an adaptive holographic interferometer based on photorefractive 45°-cut BaTiO3 : Co crystal. In our experiment, the light pressure causes a displacement of a reflecting membrane, and this response is measured by the adaptive interferometer. We demonstrate that the device based on light pressure measurement can be used as a broadband achromatic photodetector with linear response.
Adaptive Interferometer with Linear Phase Demodulation
In our experiments we measured the increased vibrations of a reflecting membrane caused by the pressure of light being amplitude-modulated. An adaptive interferometer with photorefractive crystal is well known as a simple and efficient configuration for measuring small vibrations [4]. In most industrial applications
the fast response time of the photorefractive crystal is needed and many efforts were made to develop the setups with photorefractive semiconductors and sillenite crystals, which have the fastest response time. However, these crystals have low electro-optic coefficients, which results in weak two-beam coupling even with external field enhancement of the photorefractive effect. In our experiments with highly reflective membrane the major factor leading to the loss of light should be the weak coupling, or, in the other words, the low reflectivity of the photorefractive grating. Thus to achieve high light efficiency and as a result maximum sensitivity we have to choose a crystal with high reflectivity even at the expense of response time. For our experiments we selected 45°-cut BaTiO3, which provides one of the strongest grating reflectivity without resorting to an externally applied electric field [5, 6]. While the absence of the electric field is an appreciable advantage in itself, in this case the diffusion mechanism of the photorefrac-tive grating recording is dominant. As a consequence the photorefractive grating is n/2-phase shifted with respect to the interference pattern. The signal and the reference waves are in phase in the exit of the crystal, and it results in the weak quadratic detection of the signal wave phase modulation. To provide high-sensitive linear detection we employed a photorefractive interferometer with different polarizations of
Fig. 1. Experimental setup:
1 — Nd : YAG laser (X = 532 nm), 2 — beam splitter, 3 — BaTiO3 5 — X/4 retarder, 6 — vacuum chamber with reflective membrane.
8 — laser (X = 488, 632, 1600 nm), 9 — function generator, 10 — lock-in amplifier; R, S — the reference and the signal beams, respectively
Co crystal, 4 — polarizer, 7 — intensity modulator,
the interfering waves and polarization filtering [7, 8].
The scheme of the holographic interferometer, which provides counter-propagating two-wave mixing in the photorefractive crystal, is shown in Fig. 1. The photorefractive crystal, BaTiO3 : Co, has cobalt concentration of approximately 0.01 mol. % and the length of 4 mm along the grating wave vector. The angle between the interfering beams was 170°. A frequency-doubled Nd : YAG laser (X = 532 nm) was used as a light source for the interferometer. The reference beam R has horizontal polarization, while the signal beam S is elliptically polarized. The quarter-wave retarder, which controls the signal beam polarization, introduces a phase shift between vertical and horizontal polarization components. The photorefractive grating is recorded by the interference pattern of the horizontal component of the signal beam and the reference beam. Only light with extraordinary polarization is reflected by the grating due to the great difference between effective electro-optic coefficients for ordinary and extraordinary waves [6]. In our experimental setup the light with vertical polarization is reflected, and therefore the reference beam passes the crystal without reflection by the grating, and this feature increases the interferometer efficiency.
The complex vectorial amplitudes of the
signal and reference waves, which enter the crystal through the opposite facets, are given by
S = Sn
(1 - i) sin 9 cos 9 sin2 9 + i cos2 9
M')
R = R
(1)
where S0 and R0 are the scalar amplitudes of the signal and reference, respectively; 0 is the angular position of the quarter-wave retarder;
is the phase modulation of the signal wave caused by the reflective membrane vibration.
The reference wave has vertical polarization; therefore the horizontal x component of the signal wave does not take part in the photorefractive grating build-up process. The grating recorded by the y component reflects the horizontal x component of the signal wave. The quarter wave plate changes the phase between the x and y components of the signal wave that allows the adjustment of the phase difference between the reflected signal wave and the reference one. Eq. (1) shows that the reference wave transmitted through the crystal is in phase with the reflected wave when the angular position of the retarder 0 = 45°. In this case the configuration shown in Fig. 1 provides high-sensitive linear detection of the fast phase modulation of the signal wave. The polarization
Fig. 2. An amplitude of the output signal versus the amplitude of signal wave phase modulation, A9, measured with (▲) and without (■) the quarter wave retarder. Solid curves are the best linear and parabolic fits of the experimental data
analyzer in front of the photodetector mixes the vertically polarized reference wave and the reflected signal one, which has horizontal polarization. The light intensity behind the polarization analyzer is
I(t) = PS2 sin2 a + TR0 cos2 a +
+14PTS0R sin 2a sin фО),
(2)
where P is intensity reflectance of the photorefractive grating, T is transmittance of the crystal, and a is an angle that transmission axis of the polarization analyzer makes with the x axis.
Obviously, the interferometer has the highest sensitivity when a = 45° and the amplitude of the intensity modulation is
M(t) = ^^/PтS0R sin q(t). (3)
Our experiments have confirmed that the proposed configuration of the interferometer allows linear detection of the phase modulation. We observed only the first harmonic of the signal when the quarter-wave plate was installed and aligned in the optimal position. Without the phase retarder, when the signal and reference wave had the same polarization, only the second harmonic was observed and the output signal dependence on the phase modulation
amplitude was quadratic. The results of those experiments (see Fig. 2) reveal a significant advantage in output signal of the «linearized» interferometer when a small phase modulation is detected. In that experiment the vacuum chamber with reflective membrane was replaced by a piezo-driven mirror. We used this result as an interferometer calibration to determine the membrane displacement in the measurements of light pressure.
We found experimentally the optimal positions of the quarter wave plate and the polarization analyzer, and that measure yielded the maximum sensitivity of the interferometer. The result obtained differs from the 45°-position predicted theoretically by approximately 20°. The measurements of the grating reflectance as a function of the polarization angle show that maximum value is also observed with our crystal sample when the polarization differs from the vertical one by 20°. Apparently, these discrepancies we can explain by the difference between the considered 45° crystal cut and the crystallographic orientation of our BaTiO3 : Co sample, which has been cut close to 30°.
An Achromatic Photodetector Based on Light Pressure Measurement
As a detector of light pressure we used a thin flexible highly reflective membrane placed in a vacuum chamber. The air pressure in the chamber was about 5 N/m2. The membrane
Fig. 3. An amplitude of the output signal as a function of the incident light power for three different wavelengths X: 1 - 488 nm, 2 - 633 nm, 3 - 1600 nm
was composed of a 5 ^m-thick nitrocellulose substrate coated with an 0.12 ^m-thick aluminum reflective layer. The measured reflectivity of the membrane was 85—95 % in the wavelength range of 0.4—1.6 ^m. The membrane was illuminated through the right-side windows of the vacuum chamber by the green CW light (see Fig. 1) that made possible to detect fast membrane displacement interferometrically. The laser beam causing this displacement entered the chamber from the left. It showed a periodical intensity modulation that resulted in increased vibrations of the membrane with amplitude depending linearly on the incident light intensity. As a source of the incident light we used lasers of three different wavelengths: 488, 633, and 1600 nm. The experimental results are presented in Fig. 3, where we show the photodetector amplitude as a function of the incident light intensity. The response of the photodetector is highly linear and achromatic. The measured signal-to-noise ratio at the incident light power of 20 ^W was about 10. Thus we estimated the sensitivity of the photodetector as 2 ^W taking it as a noise-equivalent power. It is of note that in the experiments with the vacuum chamber the noise level was nearly 30 times as high as that in the experiments with the calibration using piezo-driven mirror. Apparently, the increase in noise is associated with membrane
imperfections that scatter the signal wave. Therefore, the improvement of the membrane quality should allow reaching the sensitivities in excess of 1 ^W.
Conclusion
In order to measure the light pressure we propose a new configuration of the adaptive photorefractive interferometer with highly efficient 45°-cut BaTiO3 : Co crystal. In this setup the two orthogonal linear polarization components of the signal wave play different roles. One of them builds up the photorefractive grating interfering with the reference wave inside the crystal but does not contribute to the output signal of the interferometer. The other component is reflected by the photorefractive grating and is mixed with the reference wave by the polarizer, which yields the output signal. The phase shift between two polarization components is controlled by the phase retarder that allows the linear phase demodulation using the crystal with nonlocal, local or mixed photorefractive response. We have applied this interferometer for measurements of light pressure. It was experimentally found that the sensitivity was 2 ^W over a wide spectral range. Our experimental results make possible to suggest a new type of the photodetectors based on the interferometric measurement of the light pressure.
REFERENCES
1. Ashkin A. History of optical trapping and manipulation of small-neutral particle, atoms, and molecules, IEEE J. Selected Topics in Quantum Electronics, 2000, Vol. 6, pp. 841-56.
2. Neuman K.C., Block S.M. Optical trapping, Rev. Sci. Ins'rum. 2004, Vol. 75, pp. 2787-809.
3. Petrov V.M., Hahn J., Petter J., Petrov M.P., Tschudi T. Precise subnanometer control of the position of a macro-object by light pressure, Op'. Let'., 2005, Vol. 30, pp. 3138-40.
4. Stepanov S.I. Application of photorefractive crystals, Rep. Prog. Phys, 1994, Vol. 57, pp. 39116.
5. Garrett M.H., Chang J.Y., Jenssen H.P., Warde C. Self-pumped phase conjugation and four-
wave mixing in 0°- and 45°-cut n-type BaTiO3:Co, Opt. Lett. 1993, Vol. 15, pp. 405-7.
6. Garrett M.H., Chang J.Y., Jenssen H.P., Warde C., High photorefractive sensitivity in an n-type 45°-cut BaTiO3 crystal, Opt. Lett. 1992, Vol. 17, pp. 103-5.
7. Ing R.K., Monchalin J.-P. Broadband optical detection of ultrasound by two-wave mixing in a photorefractive crystal, Appl. Phys. Lett., 1991, Vol. 59, pp. 3233-5.
8. Paivasaari K., Kamshilin A.A., Prokofiev V.V., Sturman B.I., Calvo G.F., Carrascosa M., Agullo-Lopez F. Linear phase demodulation in photorefractive crystals with nonlocal response, J. Appl. Phys., 2001, Vol. 90, pp. 3135-41.
THE AUTHORS
PETROV Victor M.
St. Petersburg State Polytechnical University, 29 Politekhnicheskaya St., St. Petersburg, 195251, Russia.
KHOMENKO Anatoliy V.
Ensenada Center for Scientific Research and Higher Education,
Carretera Ensensds-Tijuana 3918, Zona Playitas, 22860, Ensenada, Baja Clifornia, Mexico. KRINITSKY Yakov A.
St. Petersburg State Polytechnical University, 29 Politekhnicheskaya St., St. Petersburg, 195251, Russia.
GARCIA Alexandre M.
Ensenada Center for Scientific Research and Higher Education,
Carretera Ensensds-Tijuana 3918, Zona Playitas, 22860, Ensenada, Baja Clifornia, Mexico.
Петров В.М., Хоменко А.В., Криницкий Я.А., Гарсиа A.M. ДЕТЕКТИРОВАНИЕ ДАВЛЕНИЯ СВЕТА ПОСРЕДСТВОМ ДВУХВОЛНОВОГО СМЕШЕНИЯ В ФОТОРЕФ-РАКТИВНОМ КРИСТАЛЛЕ BaTiO3 : Co.
Сообщается о высокочувствительном детектировании давления светового излучения с использованием адаптивного интерферометра на основе фоторефрактивного кристалла BaTiO3:Co со срезом 45°. Для измерений с небольшой фазовой модуляцией была использована поляризационная фильтрация, которая обеспечивает линейный режим детектирования сигнала в фоторефрактивном кристалле с нелокальным откликом. Показано, что разработанный инструмент для измерения давления света можно использовать в качестве широкополосного фотодетектора. Экспериментально установлено, что чувствительность составляет 2 мкВт в диапазоне длин волн 488 — 1600 нм.
АДАПТИВНЫЙ ГОЛОГРАФИЧЕСКИЙ ИНТЕРФЕРОМЕТР, ДАВЛЕНИЕ СВЕТА, ДВУХВОЛНОВОЕ СМЕШЕНИЕ, ФОТОРЕФРАКТИВНЫЙ КРИСТАЛЛ, ВЫСОКОЧУВСТВИТЕЛЬНОЕ ДЕТЕКТИРОВАНИЕ, ШИРОКОПОЛОСНЫЙ ФОТОДЕТЕКТОР.
СПИСОК ЛИТЕРАТУРЫ
1. Ashkin A. History of optical trapping and wave mixing in 0°- and 45°-cut n-type BaTiO3:Co// manipulation of small-neutral particle, atoms, and Opt. Lett. 1993. Vol. 15. P. 405-407. molecules// IEEE J. Selected Topics in Quantum 6. Garrett M.H., Chang J.Y., Jenssen H.P., Electronics. 2000. Vol. 6. P. 841-856. Warde C. High photorefractive sensitivity in an
2. Neuman K.C., Block S.M. Optical trapping// n-type 45°-cut BaTiO3 crystal // Opt. Lett. 1992. Rev. Sci.. Instrum. 2004. Vol. 75. P. 2787-2809. Vol. 17. P. 103-105.
3. Petrov V.M., Hahn J., Petter J., Petrov 7. Ing R.K., Monchalin J.-P. Broadband optical M.P., Tschudi T. Precise subnanometer control of detection of ultrasound by two-wave mixing in a the position of a macro-object by light pressure// photorefractive crysta // Appl. Phys. Lett. 1991. Opt. Lett. 2005. Vol. 30. P. 3138-3140. Vol. 59. P. 3233-3235.
4. Stepanov S.I. Application of photorefractive 8. Paivasaari K., Kamshilin A.A., Prokofiev crystals// Rep. Prog. Phys. 1994. Vol. 57. V.V., Sturman B.I., Calvo G.F., Carrascosa M., P. 39-116. Agullo-Lopez F. Linear phase demodulation in
5. Garrett M.H., Chang J.Y., Jenssen H.P., photorefractive crystals with nonlocal response // Warde C. Self-pumped phase conjugation and four- J. Appl. Phys. 2001. Vol. 90. P. 3135-3141.
СВЕДЕНИЯ ОБ АВТОРАХ
ПЕТРОВ Виктор Михайлович — доктор физико-математических наук, профессор кафедры квантовой электроники Санкт-Петербургского государственного политехнического университета.
195251, Россия, г. Санкт-Петербург, Политехническая ул., 29
vikpetroff@mail.ru
ХОМЕНКО Анатолий Васильевич — научный сотрудник департамента прикладной оптики университета г. Энсенада, Мексика.
Carretera Ensenada-Tijuana 3918, Zona Playitas, 22860, Ensenada, Baja California, Mexico
КРИНИЦКИЙ Яков Андреевич — аспирант кафедры квантовой электроники Санкт-Петербургского государственного политехнического университета.
195251, Россия, г. Санкт-Петербург, Политехническая ул., 29 jackobian@inbox.ru
ГАРСИЯ Алехандро Мария — аспирант департамента прикладной оптики университета г. Энсе-нада, Мексика.
Carretera Ensenada-Tijuana 3918, Zona Playitas, 22860, Ensenada, Baja California, Mexic
© St. Petersburg State Polytechnical University, 2014
