June 15, 2014 / Vol. 39, No. 12 / OPTICS LETTERS
3445
Design and fabrication of constant-pitch circular surface-relief diffraction gratings on disperse red 1 glass James Leibold,1 Peter Snell,1 Olivier Lebel,2 and Ribal Georges Sabat1,* 1
Department of Physics, Royal Military College of Canada, P.O. Box 17000, STN Forces, Kingston, ON, K7K7B4, Canada 2
Department of Chemistry and Chemical Engineering, Royal Military College of Canada, P.O. Box 17000, STN Forces, Kingston, ON, K7K7B4, Canada *Corresponding author: [email protected] Received March 12, 2014; revised May 2, 2014; accepted May 2, 2014; posted May 5, 2014 (Doc. ID 208089); published June 5, 2014
Circular surface-relief diffraction gratings with a constant pitch were photo-inscribed on thin films of a disperse red 1 functionalized glass-forming compound using a novel holographic technique. Various light-interfering metallic fixtures, which consisted of annular rings with a sloped and polished inner surface, were designed and fabricated. Each of them allowed the inscription of stable and high-quality circular diffraction gratings with pitches ranging from approximately 600–1400 nm and depths up to 250 nm. This was accomplished by exposure to a collimated laser beam with an irradiance of 604 mW∕cm2 for 350 s. The resulting gratings had a diameter of 11.4 mm and had the advantage of being produced in a simple single-step procedure with no postprocessing or specialized equipment. The pitch and diameter of these circular gratings were dependent on the fixture geometry, while the depth was related to the exposure time. © 2014 Optical Society of America OCIS codes: (050.1950) Diffraction gratings; (050.1970) Diffractive optics; (050.2770) Gratings; (050.6875) Threedimensional fabrication; (090.1970) Diffractive optics; (310.6860) Thin films, optical properties. http://dx.doi.org/10.1364/OL.39.003445
Surface relief diffraction gratings (SRGs) can be produced by a variety of methods. Patterns can be directly imprinted onto a resist through electron beam lithography [1] or directly engraved into materials with focused ion beams [2] or laser milling [3]. These methods can be time consuming for large grating areas since each line is drawn individually. Photolithography is widely used in industry and involves using a photomask to expose an entire pattern onto a photoresist. It is convenient for creating large, complex patterns and can be combined with other microfabrication techniques [4], but it requires multiple processing steps. Nanoimprinting involves production of a mold, sometimes from a method listed above, which is then pressed into a polymer surface [5]. Although it is appropriate for mass production of a pattern, it is also a multiple step process that is ill suited for rapid development of new grating patterns. Direct laser interference patterning utilizes interference of coherent light to directly engrave surface patterns on commercially available polymers [6]. This method is a single step process, but the ablation of material requires a high-powered pulsed laser. The production of SRGs using materials containing azobenzene chromophores has proven to be an interesting area of study [7]. A thin film of an azo–polymer material, such as disperse red 1 (DR1) Poly(methyl methacrylate) (PMMA), has the ability to record holographic information in surface relief because of its photosensitive mass transport properties. These SRGs also have the ability of being thermally erased and optically rewritten [8]. Although the mechanism is not fully understood, there are successful models which explain the material transport as the result of changes to the elastic properties of the material when it is exposed to light [9]. Other papers have reported on the properties of DR1-functionalized glass-forming compounds [10]. Our group has recently 0146-9592/14/123445-04$15.00/0
synthesized a new azo–glass compound, which possesses the added benefits of easier purification, higher yield, and the production of high-quality thin films and SRGs [11]. The goal of this Letter is to introduce a novel method of inscribing circular SRGs onto azo–glass films using a three-dimensional (3D) beam splitting technique with a fixture called a circular diffraction grating generator (CDG). There have been other publications on the formation of circular diffraction gratings using interference patterns from standing spiral waves [12], Bessel beams [13], and fiber optic modes [14]; however, our technique is novel in its production method, and our circular gratings are created on a much larger scale than previously reported. Possible applications for this new technique may include: optical sensors [15], enhancement of LEDs [16], improvements in solar cell efficiency [17], plasmonic lenses [18], circular grating distributed feedback dye laser [19], and optical measuring techniques [20]. Assume a mirror in the shape of a hollow truncated cone. The inner surface of this shape is reflective and is the basis for a theoretical CDG. When a collimated laser beam, with a diameter sufficiently large to illuminate the entire reflective surface, is incident normally, the CDG will reflect the light toward the smaller aperture end, creating interference at the center with the directly incident light. This interference yields a pattern of circular constant-pitch concentric rings with sinusoidal intensity variation that can be photoinscribed on an azo–glass film placed at the back of the CDG along the smaller aperture end. If the angle of the mirrored surfaces of the CDG could be changed, it would modify the circular grating pitch. Figure 1 shows a schematic of a planar wave front incident onto a CDG where θ is the angle of the mirrored surface from the normal. At points A and B, the collimated wave front will be in phase. Using the law of sines © 2014 Optical Society of America
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OPTICS LETTERS / Vol. 39, No. 12 / June 15, 2014
Fig. 1. Schematic demonstrating the optical geometry of a cross section of a CDG.
with triangle ACD, it can be shown that AC DC cot θ. Using triangle ABC, it can be shown that BC AC cos 2θ. Substituting these two equations to find the difference in path length AC − BC, along with the use of trigonometric identities, gives AC − BC DC sin 2θ:
(1)
The phase difference δ is related to the optical path length difference as δ kAC − BC π, where k is the wavenumber for the light source k 2π∕λ, and the additional term of π is the phase change from the reflection on the CDG mirror. In order to find the pitch between each maxima or minima, we can state that 2π kAC − BC. By substituting Eq. (1) and isolating the length DC, it can be found that for a given CDG angle θ, the grating pitch Λ is given by Λ λ csc 2θ:
(2)
This equation demonstrates a practical limit to the smallest grating pitch that can be generated, which is dependent on the wavelength of the light source and is limited to Λ ≈ λ as θ approaches 45 deg. At CDG angles greater than or equal to 45 deg, the reflected light will never reach the sample surface, and no interference pattern will be generated. A similar geometric analysis of Fig. 1 shows that a maximum height y of the CDG is constrained by the radius of the smaller CDG aperture x and is dependent on the angle of the CDG θ. This is given by the following equation: y
x : tan 2θ − tan θ
perpendicular to the flat face. The material used was high-quality annealed carbon steel. After machining, the CDG fixtures were washed with solvent and dried with air. Approximately 500 nm of silver was then sputter coated onto each CDG in order to create a mirror-like finish. A total of five CDGs were machined with angles θ of 12.5, 20.8, 23.5, 31.2, and 40.4 deg. Azo–glass was synthesized according to [11]. Solutions of azo–glass were then prepared from powder by mixing with dichloromethane at 3 wt. % concentration. The solution was subsequently mechanically shaken and filtered with a 50-μm filter. Solid films were fabricated by spin casting the solution onto cleaned and dried microscope slides. At a rate of 1500 rpm, the solid films had a thickness of approximately 400 nm, as measured with a profilometer. An azo–glass sample was placed directly on the CDG facing the small aperture. The beam from a Verdi diodepumped laser with a wavelength of 532 nm was passed through a spatial filter, collimated, and circularly polarized by a quarter-wave plate. The resulting collimated beam had an irradiance of 604 mW∕cm2 . The beam diameter was controlled by a variable iris and was projected onto the CDG and sample. Real-time data of the diffraction efficiency at a localized point of the circular SRG is shown in Fig. 2 as a function of exposure time. This was accomplished by shining a low-powered He–Ne laser onto the sample where the grating was forming. This laser was mechanically chopped, and the first-order diffraction beam was incident onto a silicon photodiode. The signal from the photodiode was amplified by a lock-in amplifier and plotted as a function of time on a computer. The diffraction efficiency was calculated by dividing the first-order diffracted signal by that of the incident beam, which was measured in a similar manner. The steady increase and eventual plateau of the diffraction efficiency for exposures up to about 300 s is likely due to the physical migration of the molecules of the azo–glass as they are being displaced to form peaks and troughs of greater depths. Based on the results of this plot, efficient circular SRGs can be generated with exposure times greater than
(3)
If the actual height of a CDG is larger than the maximum height y predicted by Eq. (3), then the reflected beams will pass the center point of the sample. This will cause cross interference with the reflected beam from the opposite side of the CDG and will decrease the quality of the SRG being generated. If the actual height of the CDG is smaller than y from Eq. (3), then the resulting interference pattern will not reach the center of the sample resulting in a ring grating with a smooth circular center. Several CDG fixtures were machined and polished using manual equipment found in common machine shops. Care was taken to ensure that the reflecting conical surface was a true truncated cone, finishing at a knife edge on the minor aperture, with its central axis
Fig. 2. Typical localized diffraction efficiency of circular SRG in real time as it is inscribed by a CDG. The sudden drop just after 600 s is attributed to when the inscribing laser is turned off. Inset (a): Circular SRG produced in azo–glass and coated with gold. Inset (b): Circular diffraction pattern from SRG.
June 15, 2014 / Vol. 39, No. 12 / OPTICS LETTERS
300 s. Nonetheless, for the remainder of this experiment, an exposure time of 350 s was arbitrarily chosen. Circular SRGs, with a diameter of approximately 11.4 mm, were inscribed using the method described above, as seen in Fig. 2, inset (a). To verify that circular gratings were actually created, a collimated beam from a He–Ne laser was used to illuminate the SRG resulting in the circular diffraction pattern photographed in transmission 1 cm away from the sample, as seen in Fig. 2, inset (b). Atomic Force Microscopy (AFM) imagery of the surface profile of a circular SRG was taken, and an example is presented in Fig. 3. The AFM scans show a regular sine wave pattern aligned radially from the center of the circular SRG. The generated SRGs had depths of up to 250 nm, depending on laser exposure time. The total distances between multiple peaks were obtained from the AFM imagery and divided by the number of complete waves to get an average grating pitch for each scan. To further improve the accuracy of the results, scans were taken at the 0°, 90°, 180°, and 270° positions of each circular grating, and these results were averaged again. The black circle points in Fig. 4 represent AFM measurements of grating pitches taken by this method. AFM scans of the smooth center area of circular SRGs created with a CDG having a height less than the theoretical y
Fig. 3. CDG.
AFM scan of circular SRG generated by a 20.8 deg
Fig. 4. Theoretical and measured results of the SRG pitch versus CDG mirror angle θ. Measured results include data points taken from AFM, SEM, and diffraction angle measurements. The theoretical curve is plotted using Eq. (2).
3447
Fig. 5. SEM image of circular SRG generated from a 20.8 deg CDG. (a) At 2000 times magnification, the grating peaks can be visually resolved showing a highly regular grating pattern. (b) At 15000 times magnification gratings are clearly resolved.
from Eq. (3) do show evidence of random self-structuring formations; however, these are on the order of 20 times shallower then the gratings formed in the interference region. In order to verify that there were no unpredicted largescale effects, a scanning electron microscope (SEM) was used to image larger SRG areas (on the order of 150 μm), as seen in Fig. 5. Circular SRGs, generated from the 12.5, 20.8, 31.2, and 40.4 deg CDGs, were sputter coated with approximately 60 nm of gold and observed in the SEM. Individual gratings could still be visually resolved at magnifications of up to 2000 times. The grating pitches were measured at a magnification level of 15000 times, and these data points are included on Fig. 4 as crossed triangles. The third and last method for obtaining the grating pitch of these circular SRGs was done by measuring the diffraction angle from a low-powered He–Ne laser incident on a small portion of the grating. The resulting first-order diffracted beam was an arc of a circle. However, since the laser beam illuminated only a small area near the edge of the circular grating, it can be approximated as a linear diffraction grating since the radius of curvature of the grating is relatively large compared to the small area being illuminated. Therefore, the wellknown grating equation for normal incidence was used to calculate the grating pitch Λ. Accurate measurements of the first order diffraction angle were obtained using a Velmex rotary stage connected to a computer. Hollow square points in Fig. 4 represent grating pitches calculated by this method. The results in Fig. 4 demonstrate that the three independent methods of measuring the circular grating pitches written on azo–glass samples by CDGs are consistent and correlate very well with the predicted theory given by Eq. (2). Five circular SRGs, with pitches from 600 to 1400 nm and depths of up to 250 nm, were photoinscribed onto azo–glass films using a novel holographic technique made possible with a fixture called a CDG. The fact that the SRGs formed are circular is supported by the
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OPTICS LETTERS / Vol. 39, No. 12 / June 15, 2014
orientation of the gratings measured in the AFM scans as well as the circular diffraction pattern produced by illuminating the SRGs. The SRG depth and, to a certain extent, the diffraction efficiency can be varied depending on the inscribing laser irradiance and the amount of exposure time. The SRG pitches were measured using a variety of techniques and agreed very well with the theoretical predictions, which are dependent on the CDG geometry and wavelength of the inscribing light. The inside and outside diameters of the circular SRGs generated by this method can also be controlled by varying the size of a CDG’s smaller aperture x and height y. The main advantages of this method are that it is a single step, direct inscription process that produces SRGs that can be thermally erased and optically rewritten. It has relatively fast SRG production times on the order of 300 s with grating sizes only limited by the diameter of the collimated laser beam used to inscribe them. References 1. C. Vieu, F. Carcenac, A. Pepin, Y. Chen, M. Mejias, A. Lebib, L. Manin-Ferlazzo, L. Couraud, and H. Launois, Appl. Surf. Sci. 164, 111 (2000). 2. D. Moss, V. Ta’eed, B. Eggleton, D. Freeman, S. Madden, M. Samoc, B. Luther-Davies, S. Janz, and D. Xu, Appl. Phys. Lett. 85, 4860 (2004). 3. L. Shah, M. E. Fermann, J. W. Dawson, and C. P. Barty, Opt. Express 14, 12546 (2006). 4. K. Rastani, A. Marrakchi, S. F. Habiby, W. M. Hubbard, H. Gilchrist, and R. E. Nahory, Appl. Opt. 30, 1347 (1991).
5. Y. Chen, Z. Li, Z. Zhang, D. Psaltis, and A. Scherer, Appl. Phys. Lett. 91, 051109 (2007). 6. A. Lasagni, D. Acevedo, C. Barbero, and F. Mücklich, Adv. Eng. Mater. 9, 99 (2007). 7. A. Priimagi and A. Shevchenko, J. Polym. Sci. B 52, 163 (2014). 8. P. Rochon, E. Batalla, and A. Natansohn, Appl. Phys. Lett. 66, 136 (1995). 9. M. Saphiannikova, V. Toshchevikov, and J. Ilnytskyi, Nonlinear Opt. Quantum Opt. 41, 27 (2010). 10. H. Audorff, R. Walker, L. Kador, and H. Schmidt, Proc. SPIE 7233, 72330O (2009). 11. R. Kirby, R. G. Sabat, J. Nunzi, and O. Lebel, J. Mater. Chem.C 2, 841 (2014). 12. J. P. Vernon, S. V. Serak, R. S. Hakobyan, A. K. Aleksanyan, V. P. Tondiglia, T. J. White, T. J. Bunning, and N. V. Tabiryan, Appl. Phys. Lett. 103, 201101 (2013). 13. T. Grosjean and D. Courjon, Opt. Express 14, 2203 (2006). 14. J. K. Kim, Y. Jung, B. H. Lee, K. Oh, C. Chun, and D. Kim, Opt. Fiber Technol. 13, 240 (2007). 15. R. D. Bhat, N. C. Panoiu, S. R. Brueck, and R. M. Osgood, Opt. Express 16, 4588 (2008). 16. J. Zhu, H. Zhang, Z. Zhu, Q. Li, and G. Jin, Opt. Commun. 322, 66 (2014). 17. B. Janjua and G. Jabbour, in 2013 IEEE Photonics Conference (IPC) (IEEE, 2013), pp. 578–579. 18. J. M. Steele, Z. Liu, Y. Wang, and X. Zhang, Opt. Express 14, 5664 (2006). 19. Y. Chen, Z. Li, M. D. Henry, and A. Scherer, Appl. Phys. Lett. 95, 031109 (2009). 20. H. M. Shang, S. L. Toh, Y. Fu, C. Quan, and C. J. Tay, Opt. Lasers Eng. 36, 487 (2001).
3445
Design and fabrication of constant-pitch circular surface-relief diffraction gratings on disperse red 1 glass James Leibold,1 Peter Snell,1 Olivier Lebel,2 and Ribal Georges Sabat1,* 1
Department of Physics, Royal Military College of Canada, P.O. Box 17000, STN Forces, Kingston, ON, K7K7B4, Canada 2
Department of Chemistry and Chemical Engineering, Royal Military College of Canada, P.O. Box 17000, STN Forces, Kingston, ON, K7K7B4, Canada *Corresponding author: [email protected] Received March 12, 2014; revised May 2, 2014; accepted May 2, 2014; posted May 5, 2014 (Doc. ID 208089); published June 5, 2014
Circular surface-relief diffraction gratings with a constant pitch were photo-inscribed on thin films of a disperse red 1 functionalized glass-forming compound using a novel holographic technique. Various light-interfering metallic fixtures, which consisted of annular rings with a sloped and polished inner surface, were designed and fabricated. Each of them allowed the inscription of stable and high-quality circular diffraction gratings with pitches ranging from approximately 600–1400 nm and depths up to 250 nm. This was accomplished by exposure to a collimated laser beam with an irradiance of 604 mW∕cm2 for 350 s. The resulting gratings had a diameter of 11.4 mm and had the advantage of being produced in a simple single-step procedure with no postprocessing or specialized equipment. The pitch and diameter of these circular gratings were dependent on the fixture geometry, while the depth was related to the exposure time. © 2014 Optical Society of America OCIS codes: (050.1950) Diffraction gratings; (050.1970) Diffractive optics; (050.2770) Gratings; (050.6875) Threedimensional fabrication; (090.1970) Diffractive optics; (310.6860) Thin films, optical properties. http://dx.doi.org/10.1364/OL.39.003445
Surface relief diffraction gratings (SRGs) can be produced by a variety of methods. Patterns can be directly imprinted onto a resist through electron beam lithography [1] or directly engraved into materials with focused ion beams [2] or laser milling [3]. These methods can be time consuming for large grating areas since each line is drawn individually. Photolithography is widely used in industry and involves using a photomask to expose an entire pattern onto a photoresist. It is convenient for creating large, complex patterns and can be combined with other microfabrication techniques [4], but it requires multiple processing steps. Nanoimprinting involves production of a mold, sometimes from a method listed above, which is then pressed into a polymer surface [5]. Although it is appropriate for mass production of a pattern, it is also a multiple step process that is ill suited for rapid development of new grating patterns. Direct laser interference patterning utilizes interference of coherent light to directly engrave surface patterns on commercially available polymers [6]. This method is a single step process, but the ablation of material requires a high-powered pulsed laser. The production of SRGs using materials containing azobenzene chromophores has proven to be an interesting area of study [7]. A thin film of an azo–polymer material, such as disperse red 1 (DR1) Poly(methyl methacrylate) (PMMA), has the ability to record holographic information in surface relief because of its photosensitive mass transport properties. These SRGs also have the ability of being thermally erased and optically rewritten [8]. Although the mechanism is not fully understood, there are successful models which explain the material transport as the result of changes to the elastic properties of the material when it is exposed to light [9]. Other papers have reported on the properties of DR1-functionalized glass-forming compounds [10]. Our group has recently 0146-9592/14/123445-04$15.00/0
synthesized a new azo–glass compound, which possesses the added benefits of easier purification, higher yield, and the production of high-quality thin films and SRGs [11]. The goal of this Letter is to introduce a novel method of inscribing circular SRGs onto azo–glass films using a three-dimensional (3D) beam splitting technique with a fixture called a circular diffraction grating generator (CDG). There have been other publications on the formation of circular diffraction gratings using interference patterns from standing spiral waves [12], Bessel beams [13], and fiber optic modes [14]; however, our technique is novel in its production method, and our circular gratings are created on a much larger scale than previously reported. Possible applications for this new technique may include: optical sensors [15], enhancement of LEDs [16], improvements in solar cell efficiency [17], plasmonic lenses [18], circular grating distributed feedback dye laser [19], and optical measuring techniques [20]. Assume a mirror in the shape of a hollow truncated cone. The inner surface of this shape is reflective and is the basis for a theoretical CDG. When a collimated laser beam, with a diameter sufficiently large to illuminate the entire reflective surface, is incident normally, the CDG will reflect the light toward the smaller aperture end, creating interference at the center with the directly incident light. This interference yields a pattern of circular constant-pitch concentric rings with sinusoidal intensity variation that can be photoinscribed on an azo–glass film placed at the back of the CDG along the smaller aperture end. If the angle of the mirrored surfaces of the CDG could be changed, it would modify the circular grating pitch. Figure 1 shows a schematic of a planar wave front incident onto a CDG where θ is the angle of the mirrored surface from the normal. At points A and B, the collimated wave front will be in phase. Using the law of sines © 2014 Optical Society of America
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OPTICS LETTERS / Vol. 39, No. 12 / June 15, 2014
Fig. 1. Schematic demonstrating the optical geometry of a cross section of a CDG.
with triangle ACD, it can be shown that AC DC cot θ. Using triangle ABC, it can be shown that BC AC cos 2θ. Substituting these two equations to find the difference in path length AC − BC, along with the use of trigonometric identities, gives AC − BC DC sin 2θ:
(1)
The phase difference δ is related to the optical path length difference as δ kAC − BC π, where k is the wavenumber for the light source k 2π∕λ, and the additional term of π is the phase change from the reflection on the CDG mirror. In order to find the pitch between each maxima or minima, we can state that 2π kAC − BC. By substituting Eq. (1) and isolating the length DC, it can be found that for a given CDG angle θ, the grating pitch Λ is given by Λ λ csc 2θ:
(2)
This equation demonstrates a practical limit to the smallest grating pitch that can be generated, which is dependent on the wavelength of the light source and is limited to Λ ≈ λ as θ approaches 45 deg. At CDG angles greater than or equal to 45 deg, the reflected light will never reach the sample surface, and no interference pattern will be generated. A similar geometric analysis of Fig. 1 shows that a maximum height y of the CDG is constrained by the radius of the smaller CDG aperture x and is dependent on the angle of the CDG θ. This is given by the following equation: y
x : tan 2θ − tan θ
perpendicular to the flat face. The material used was high-quality annealed carbon steel. After machining, the CDG fixtures were washed with solvent and dried with air. Approximately 500 nm of silver was then sputter coated onto each CDG in order to create a mirror-like finish. A total of five CDGs were machined with angles θ of 12.5, 20.8, 23.5, 31.2, and 40.4 deg. Azo–glass was synthesized according to [11]. Solutions of azo–glass were then prepared from powder by mixing with dichloromethane at 3 wt. % concentration. The solution was subsequently mechanically shaken and filtered with a 50-μm filter. Solid films were fabricated by spin casting the solution onto cleaned and dried microscope slides. At a rate of 1500 rpm, the solid films had a thickness of approximately 400 nm, as measured with a profilometer. An azo–glass sample was placed directly on the CDG facing the small aperture. The beam from a Verdi diodepumped laser with a wavelength of 532 nm was passed through a spatial filter, collimated, and circularly polarized by a quarter-wave plate. The resulting collimated beam had an irradiance of 604 mW∕cm2 . The beam diameter was controlled by a variable iris and was projected onto the CDG and sample. Real-time data of the diffraction efficiency at a localized point of the circular SRG is shown in Fig. 2 as a function of exposure time. This was accomplished by shining a low-powered He–Ne laser onto the sample where the grating was forming. This laser was mechanically chopped, and the first-order diffraction beam was incident onto a silicon photodiode. The signal from the photodiode was amplified by a lock-in amplifier and plotted as a function of time on a computer. The diffraction efficiency was calculated by dividing the first-order diffracted signal by that of the incident beam, which was measured in a similar manner. The steady increase and eventual plateau of the diffraction efficiency for exposures up to about 300 s is likely due to the physical migration of the molecules of the azo–glass as they are being displaced to form peaks and troughs of greater depths. Based on the results of this plot, efficient circular SRGs can be generated with exposure times greater than
(3)
If the actual height of a CDG is larger than the maximum height y predicted by Eq. (3), then the reflected beams will pass the center point of the sample. This will cause cross interference with the reflected beam from the opposite side of the CDG and will decrease the quality of the SRG being generated. If the actual height of the CDG is smaller than y from Eq. (3), then the resulting interference pattern will not reach the center of the sample resulting in a ring grating with a smooth circular center. Several CDG fixtures were machined and polished using manual equipment found in common machine shops. Care was taken to ensure that the reflecting conical surface was a true truncated cone, finishing at a knife edge on the minor aperture, with its central axis
Fig. 2. Typical localized diffraction efficiency of circular SRG in real time as it is inscribed by a CDG. The sudden drop just after 600 s is attributed to when the inscribing laser is turned off. Inset (a): Circular SRG produced in azo–glass and coated with gold. Inset (b): Circular diffraction pattern from SRG.
June 15, 2014 / Vol. 39, No. 12 / OPTICS LETTERS
300 s. Nonetheless, for the remainder of this experiment, an exposure time of 350 s was arbitrarily chosen. Circular SRGs, with a diameter of approximately 11.4 mm, were inscribed using the method described above, as seen in Fig. 2, inset (a). To verify that circular gratings were actually created, a collimated beam from a He–Ne laser was used to illuminate the SRG resulting in the circular diffraction pattern photographed in transmission 1 cm away from the sample, as seen in Fig. 2, inset (b). Atomic Force Microscopy (AFM) imagery of the surface profile of a circular SRG was taken, and an example is presented in Fig. 3. The AFM scans show a regular sine wave pattern aligned radially from the center of the circular SRG. The generated SRGs had depths of up to 250 nm, depending on laser exposure time. The total distances between multiple peaks were obtained from the AFM imagery and divided by the number of complete waves to get an average grating pitch for each scan. To further improve the accuracy of the results, scans were taken at the 0°, 90°, 180°, and 270° positions of each circular grating, and these results were averaged again. The black circle points in Fig. 4 represent AFM measurements of grating pitches taken by this method. AFM scans of the smooth center area of circular SRGs created with a CDG having a height less than the theoretical y
Fig. 3. CDG.
AFM scan of circular SRG generated by a 20.8 deg
Fig. 4. Theoretical and measured results of the SRG pitch versus CDG mirror angle θ. Measured results include data points taken from AFM, SEM, and diffraction angle measurements. The theoretical curve is plotted using Eq. (2).
3447
Fig. 5. SEM image of circular SRG generated from a 20.8 deg CDG. (a) At 2000 times magnification, the grating peaks can be visually resolved showing a highly regular grating pattern. (b) At 15000 times magnification gratings are clearly resolved.
from Eq. (3) do show evidence of random self-structuring formations; however, these are on the order of 20 times shallower then the gratings formed in the interference region. In order to verify that there were no unpredicted largescale effects, a scanning electron microscope (SEM) was used to image larger SRG areas (on the order of 150 μm), as seen in Fig. 5. Circular SRGs, generated from the 12.5, 20.8, 31.2, and 40.4 deg CDGs, were sputter coated with approximately 60 nm of gold and observed in the SEM. Individual gratings could still be visually resolved at magnifications of up to 2000 times. The grating pitches were measured at a magnification level of 15000 times, and these data points are included on Fig. 4 as crossed triangles. The third and last method for obtaining the grating pitch of these circular SRGs was done by measuring the diffraction angle from a low-powered He–Ne laser incident on a small portion of the grating. The resulting first-order diffracted beam was an arc of a circle. However, since the laser beam illuminated only a small area near the edge of the circular grating, it can be approximated as a linear diffraction grating since the radius of curvature of the grating is relatively large compared to the small area being illuminated. Therefore, the wellknown grating equation for normal incidence was used to calculate the grating pitch Λ. Accurate measurements of the first order diffraction angle were obtained using a Velmex rotary stage connected to a computer. Hollow square points in Fig. 4 represent grating pitches calculated by this method. The results in Fig. 4 demonstrate that the three independent methods of measuring the circular grating pitches written on azo–glass samples by CDGs are consistent and correlate very well with the predicted theory given by Eq. (2). Five circular SRGs, with pitches from 600 to 1400 nm and depths of up to 250 nm, were photoinscribed onto azo–glass films using a novel holographic technique made possible with a fixture called a CDG. The fact that the SRGs formed are circular is supported by the
3448
OPTICS LETTERS / Vol. 39, No. 12 / June 15, 2014
orientation of the gratings measured in the AFM scans as well as the circular diffraction pattern produced by illuminating the SRGs. The SRG depth and, to a certain extent, the diffraction efficiency can be varied depending on the inscribing laser irradiance and the amount of exposure time. The SRG pitches were measured using a variety of techniques and agreed very well with the theoretical predictions, which are dependent on the CDG geometry and wavelength of the inscribing light. The inside and outside diameters of the circular SRGs generated by this method can also be controlled by varying the size of a CDG’s smaller aperture x and height y. The main advantages of this method are that it is a single step, direct inscription process that produces SRGs that can be thermally erased and optically rewritten. It has relatively fast SRG production times on the order of 300 s with grating sizes only limited by the diameter of the collimated laser beam used to inscribe them. References 1. C. Vieu, F. Carcenac, A. Pepin, Y. Chen, M. Mejias, A. Lebib, L. Manin-Ferlazzo, L. Couraud, and H. Launois, Appl. Surf. Sci. 164, 111 (2000). 2. D. Moss, V. Ta’eed, B. Eggleton, D. Freeman, S. Madden, M. Samoc, B. Luther-Davies, S. Janz, and D. Xu, Appl. Phys. Lett. 85, 4860 (2004). 3. L. Shah, M. E. Fermann, J. W. Dawson, and C. P. Barty, Opt. Express 14, 12546 (2006). 4. K. Rastani, A. Marrakchi, S. F. Habiby, W. M. Hubbard, H. Gilchrist, and R. E. Nahory, Appl. Opt. 30, 1347 (1991).
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