L A Ageev - Spontaneous s_ gratings and specific features of their formation and evolution in photosensitive agcl_ag films - страница 1
ISSN 0030-400X, Optics and Spectroscopy, 2006, Vol. 100, No. 2, pp. 291-299. © Pleiades Publishing, Inc., 2006.
Original Russian Text © L.A. Ageev, E.D. Makovetskii, V.K. Miloslavskii, 2006, published in Optika i Spektroskopiya, 2006, Vol. 100, No. 2, pp. 328-336.
Spontaneous S_ Gratings and Specific Features of Their Formation and Evolution in Photosensitive AgCl_Ag Films
L. A. Ageev, E. D. Makovetskii, and V. K. Miloslavskii
Kharkov National University, Kharkov, 61077 Ukraine e-mail: firstname.lastname@example.org Received February 22, 2005
Abstract—The formation and evolution of spontaneous S_ gratings in photosensitive waveguide AgCl-Ag films under the action of a laser beam are investigated experimentally and theoretically. It is found that in the cases of s and p polarizations of laser radiation these gratings differ significantly not only in the period but also in the structure and spatial and temporal stability. The different character of the gratings is explained in detail by the competition between the S_ gratings and other gratings evolving simultaneously in the film and the change in the scattering indicatrix in the case of p polarization as a result of intense evolution of degenerate C gratings. The regularity of S_ gratings on TM0 modes in the case of p polarization and large angles of incidence makes it possible to increase the accuracy of determining the refractive indices of substrates using AgCl films corresponding to the cutoff thicknesses of TM0 waveguide modes.
PACS numbers: 42.62
As is known [1, 2], spontaneous gratings are formed on surfaces of solids irradiated with a high-power laser beam. The reasons for this phenomenon are the interference of an incident wave (with a wavelength X) with the surface TM modes excited as a result of the light scattering and the mass transfer in the interference field. At oblique incidence of an inducing beam, the type of a spontaneous grating depends on the beam polarization. In the case of linear p polarization, in a wide range of angles of incidence (p, so-called  S_ and S+ gratings evolve with the following azimuthal angles a of the grating vectors: a = 0° and 180° (a is counted from the plane of incidence) and periods
ds-, s+ = X/(1 - sin(p). (1)
These spontaneous gratings are dominant because, in the case of p polarization, scattered TM modes have the largest amplitude at a = 0° and 180°. The dominance of spontaneous S_ and S+ gratings is confirmed by the calculation of the azimuthal dependence of the increment in their evolution due to positive feedback [4, 5]. However, the diffraction reflections in the given geometry are crescent-shaped rather than pointlike, which indicates the formation of S_ like gratings evolving on the modes with a Ф 0°. It was ascertained in  that, irrespective of the type of the irradiated material, at (p a 35°, spontaneous S_ and S+ gratings are attenuated and disappear due to the evolution of regular degenerate C gratings. Periodic oscillations of the amplitudes of spontaneous S_ and S+ gratings due to their competition in the nonlinear evolution stage were predicted theoretically in . However, as far as we know, such oscillations have not been revealed experimentally.
Spontaneous gratings have also been found in photosensitive films with waveguide properties: Ag-doped AgCl films (AgCl-Ag) ; AgBr-Ag, AgI, and As2S3 films ; and photopolymer films . Here, we will restrict our consideration to AgCl-Ag films since similar regularities in the evolution of spontaneous S_ and S+ gratings have been observed for the films of other materials.
A thin AgCl film deposited on a transparent substrate (glass) is an asymmetric waveguide, in which both TEm and TMm modes can propagate . However, these films are insensitive to visible light. To increase the film sensitivity, silver is incorporated into the film to precipitate as very small grains and form an absorption band peaked at 500 nm in the AgCl spectrum. Exposure of a film to a low-power gas laser beam leads to the excitation of waveguide modes in the film due to the light scattering by Ag grains. In the interference field formed by the incident wave and a scattered mode, silver mass transfer to the interference minima occurs, which finally leads to the formation of a quasi-periodic structure composed of microgratings (spontaneous grating domains). The mechanism of silver mass transfer was described in [7, 8]. In contrast to spontaneous gratings on surfaces of solids, evolution of spontaneous gratings on scattered TE and TM modes is possible in films. These gratings have different propagation constants depending on the photosensitive layer thick-
Fig. 1. Schematic diagram of the setup for generation and investigation of spontaneous gratings: (1) single-mode He-Ne laser (X = 632.8 nm, P = 8 mW), (2) X/2 plate on a vertical goniometer (for rotation of the plane of polarization), (3) collecting lens (F = 9.5 cm), (4) screen with an aperture for the laser beam, and (J) a sample on a horizontal goniometer.
ness; i.e., spontaneous gratings in photosensitive planar waveguides are characterized by a larger variety.
Spontaneous S_ and S+ gratings were first found in thin (h < hTM0, where hTM[ is the cutoff thickness of the
TM0 mode) AgCl-Ag films exposed to He-Ne  and He-Cd  laser radiation. Spontaneous gratings arose in the case of an s-polarized laser beam, exciting scattered TE0 modes with periods similar to (1) in the film:
where neff is the effective mode index (here, neff = nTEo).
Then, the unusual dynamics of S_ and S+ gratings was revealed : spontaneous S+ gratings, evolving in the initial stages of exposure, disappear with increasing exposure time and are replaced by S_ gratings. The competition of spontaneous S_ and S+ gratings becomes especially pronounced when the laser beam is focused . The pattern of anisotropic light scattering observed in the direction opposite to the incident beam direction exhibits a system of randomly arising, moving, and disappearing spots, which indicate the evolution of some microgratings and the disappearance of other microgratings (nonlinear optical turbulence). It was found that this turbulence is related to the evolution of spontaneous S_ gratings due to the suppression and elimination of S+ gratings. The competition observed is somewhat like that predicted in ; however, instead of periodic oscillations (according to ), random oscillations of spots related to leaky modes with an average frequency decreasing with increasing exposure time were observed in .
We observed S_ gratings when a p-polarized beam was introduced into AgCl-Ag films with h > hTMo
either through a prism [8, 14] or from air (at large angles of incidence) . Optical microscopy measurements  indicate a significant difference in the structure of S_ TE(0 and S_ TM0 gratings. In this study, we performed a more detailed investigation of the formation and evolution of spontaneous S_ gratings in films exposed to s- and p-polarized laser beams to explain the difference noted.
EXPERIMENTAL TECHNIQUE We studied spontaneous S_ TE0 and S_ TM0 gratings in AgCl-Ag films in the thickness range hTMo < h < hTE1, where hTM0, and hTE are the cutoff thicknesses of the corresponding modes:
2 n( n
(ns - 1 )
2 2 1/2
2n(n - ns)
2 1/2 --(--n---s---------1----)-------
(n - ns)
2 2 1/2 2(n - ns)
where X = 632.8 nm is the He-Ne laser wavelength. The cutoff thicknesses hTM0 = 94 nm and hTE1 =
273 nm were calculated using the tabular values of n = nAgCl = 2.06 and ns = 1.515 (glass). The photosensitive layer thickness was determined from the mass thickness calculated for the given geometry of material evaporation using a planar evaporator . In addition, the photosensitive layer thickness was measured from the lines of equal monochromatic order by the Tolansky method . AgCl-Ag films were deposited in vacuum on cold substrates by successive evaporation of AgCl and Ag. The mass thickness of Ag was about 10 nm, which determined the filling number for Ag films: q < 0.1.
A schematic diagram of sample exposure is shown in Fig. 1. A narrow He-Ne laser beam (P = 8 mW, the mode waist width at the output mirror w0 = 3 x 10-2 mm) passed through a quartz X/2 plate mounted on a vertical goniometer. Then the beam passed through a collecting lens (F = 9.5 cm) and an aperture in a screen oriented perpendicularly to the beam direction, after which it fell on a sample mounted on a horizontal goniometer. At a distance of 60 mm between the laser and the lens, the width of the focused beam waist on the sample was wF = 62 |im. The illuminated spot at (p Ф 0° has an elliptical form with an area SF(p) = SF(0)sec (p, where SF(0) = 3 x 103 | m2. The diffraction from spon-
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Fig. 2. Light scattering patterns on the screen (Fig. 1, 4) during the exposure of an AgCl-Ag film: (a) s polarization, angle of incidence ф = 35°; (b)p polarization, cp = 25°; (c)p polarization, cp = 35°; and (d)p polarization, cp = 50°. Designations: (1) laser beam, (2) arc of diffraction of the laser beam to the order -1 by S- te -like gratings, (3) anisotropic scattering flame related to the diffrac-
tion of S.f te modes by S± te gratings, (4) anisotropic scattering arcs related to the dominance of gratings, (5) arc of diffraction of the laser beam to the order -1 by S- tm -like gratings, and (6) flame related to the existence of -like gratings.
taneous S_ gratings to the order m = -1 at ф > ф*, where ф* = arcsin[(neff - 1)/2] (see ), was observed on the screen, which made it possible to investigate the spatial and temporal evolution of spontaneous S- gratings during the exposure. Since neff changes from ns to n, the least value ф* = 14°55' is obtained at h = hTMo
and neff = nTMo = ns. The periods of S- gratings at different h and ф were measured by autocollimation. The required (s or p) polarization of the inducing beam was obtained by rotating the X/2 plate. At ф > 50°, the periods of S- gratings dS > X, which makes it possible to
observe their spatial structure in an optical microscope (MII-4, observation in reflected light).
The patterns observed on the screen (Fig. 2; h = 100 nm; the exposure time t = 5 min; ф = 25°, 35°, and 50°) demonstrate a significant difference in the S_ TEo and S_ TMo gratings. In the case of s polarization, the diffraction reflection 2 from the S_ TEo grating (the
order m = -1, Fig. 2a) is crescent-shaped and has a significant angular spread in the transverse (horizontal) direction. In addition, a small-angle anisotropic scattering reflection 3 (a so-called flame), intersecting the center of the laser beam 1, is observed along the y axis, which is perpendicular to the plane of incidence. The patterns obtained at ф = 25° and 50° are not shown here since they do not differ qualitatively. They also demonstrate a flame and a crescent-shaped reflection corresponding to the diffraction to the order m = -1. The position of the reflection 2 depends on ф: at ф < 33°, it is located on the left of the beam 1. With an increase in ф, the reflection 2 shifts to kx (here, kx = i(2n/X)sinф is the component of the wave vector of the laser beam that is parallel to the photosensitive layer); crosses the center of the beam 1; and, at ф > 33°, is located on the right
80 120 160 200
Fig. 3. Dependences of d0 on the thickness h of AgCl films (d0 = X/neff). Filled circles and the black curve show, respectively, the experimental values and the results of calculation by the dispersion equation for ТМ0 gratings (neff = 2.12). Open circles and the gray curve show the same for TE0 gratings (neff = 1.94).
of the beam (Fig. 2a). The intensity of the reflection 2 does not change.
In the case of p polarization, the patterns obtained at different ф are significantly different. At ф < 25°, the vertical diffraction reflection is absent; i.e., S_ TM0 gratings are not formed (Fi g. 2b). However, one c an see two anisotropic scattering arcs 4, passing through the centers of the initial and reflected beams. It will be shown below that the appearance of the arcs 4 is related to the formation of dominant CTEci gratings. At ф = 35°
(Fig. 2c), the reflection 5 corresponding to the diffraction to the order m = -1 can be clearly seen simultaneously with the attenuation of the arcs 4 from the C gratings. At the points of intersection of the arcs 4 and 5 (Figs. 2b, 2c), a significant increase in brightness is observed, which corresponds to the enhancement of certain S--like gratings. The reasons for this enhancement were discussed in . At ф = 50° (Fig. 2d), the arcs 4 disappear and a weak scattering reflection 6 extended along the kx axis becomes pronounced. This scattering reflection exists at all values of ф; however, it is weak against the background of the bright arcs 4. At the same time, the scattering reflection extended along the y axis is absent at all values of ф. Measurement of the periods of S- gratings in the two polarizations gives ds = 560 nm and dp = 660 nm at ф = 35°. These results, according to (2) and the calculation of neff by the dispersion equations , indicate the formation of gratings in the cases of s and p polarizations on the TE0 and ТМ0 modes, respectively.
The time evolution of different S- gratings is also different. With an increase in the exposure time, the diffraction reflection 2 from TE0 gratings shifts significantly in the kx direction, which indicates an increase in the period of the spontaneous ТЕ0 gratings with time. In this case, the angular width of the reflection narrows from several degrees to 30'. In the initial stage of exposure, the flame 3 demonstrates a strong optical turbulence. With increasing exposure time, the frequency of random oscillations of spots in the pattern decreases and the small-angle scattering reflection 3 in the coun-terpropagating beam decreases to complete disappearance. These results are similar to those obtained in , where this character of evolution was explained.
The character of the evolution of the reflection 5 from S_ TM0 gratings is different: long-term exposure
does not lead to a significant shift or change in the half-width of this reflection; only its length slightly decreases.
The dependences of the periods d on the film thickness h for the S_ TE(0 and S_ TM0 gratings were measured
at ф = 40° in the range of h from 70 to 180 nm, which corresponds to the existence of TE0 and TM0 modes.
Since the period of S_ TE0 gratings depends on the
exposure time, we measured the limiting values of d obtained at long exposure times. Figure 3 shows the values d0 = X/neff, where d0 = d[1 + (d/ X)sin ф]-1. A systematic decrease in d0 with increasing h is observed. Figure 3 also shows the dependences d0(h) calculated by the dispersion equations. The calculation method is co nsidered below.
The micrographs in Fig. 4 were obtained at ф = 70° since the periods of spontaneous S- gratings are much larger than X at this angle of incidence (the observation and photographing were performed in white light). The illuminated spot had the form of an ellipse extended in the kx direction, with axes of 60 and 170 |im (Fig. 4c). A portion of the spot with an area of 80 x 60 |im2 near the spot center was photographed. One can see a significant difference in the spontaneous S_ TE0 and S_ TM0 gratings not only in periods but also in shape.
On the whole, the quasi-periodic structure of spontaneous S_ TE0 gratings (Fig. 4a) consists of individual
small microgratings extended in the kx direction, with an average number of lines of about 10-15. Some microgratings are up to 10 | m in length and 3 | m in width. The vectors K of the microgratings have a spread with respect to the dominant direction, perpendicular to E0; they are separated by fairly wide bright areas, where their evolution is significantly reduced. The microgratings are poorly matched with each other in phase.
The quasi-periodicity of the structure of S_ TM0 gratings (Fig. 4b) is more pronounced. In the middle of the
Fig. 4. Micrographs of spontaneous gratings obtained in an MII-4 optical microscope in reflected white light. The gratings were formed at an angle of incidence cp = 70° in (a) s polarization (S- te -like gratings can be seen) and (b) p polarization ( S-tm -like