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Abstract
Two 2nd order PQ:PMMA reflecting VBGs with Bragg wavelengths of 488.8 nm and 525.6 nm were recorded using 532 nm as the recording wavelength. The formation of 2nd order PQ:PMMA VBG is explained and simulated based on the diffusion model of the PQ molecules in the PMMA matrix. The 525.6 nm VBG successfully served as the ECDL cavity mirror of a 522 nm diode laser and achieved more than 10000-fold output spectrum narrowing,
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
1.1 PQ:PMMA
PQ:PMMA (Phenanthrenequinone: poly-methyl-methacrylate) is known as an inexpensive holographic recording photopolymer with small shrinkage and has been studied for more than two decades [1–3]. The absorption coefficient spectra of PQ:PMMA with PQ concentration of 1.0 wt% before and after exposure and pure PMMA samples are shown in Fig. 1. Before exposure, PQ:PMMA has high absorption in the spectral range of 400 – 500 nm. By absorbing a photon in this spectral range, a PQ molecule can react with MMA or PMMA. Such reaction slightly reduces local refractive index and the absorption drops dramatically after PQ is completely depleted in the same spectral range. Therefore, yellowish PQ:PMMA turns colorless after exposure. Consequently, PQ:PMMA has the potential to serve as visible optical material as long as PQ is depleted. The recording light with lower absorption coefficient can penetrate deeper into the photopolymer sample and record a thicker grating. Therefore, 532 nm is commonly chosen to be the recording wavelength due to the laser availability and the relatively low absorption coefficient of unexposed PQ:PMMA.
Fig. 1 The solid black curve and dashed red curve are the absorption coefficient spectra of PQ:PMMA before and after exposure, correspondingly. The dotted blue curve is the absorption spectrum of pure PMMA sample.
1.2 Volume Bragg grating for laser spectrum narrowing
Both reflecting and transmitting Volume Bragg gratings (VBG) are known to have narrow diffraction/reflection spectral width and can serve as optical elements which provide simple and effective ways to stabilize and control the laser output wavelength [4,5], reducing the laser output spectral width [6], and even achieve single longitudinal mode operation [7]. Reflecting VBG is usually preferred since it can provide even simpler and more compact laser configuration [8]. The most commonly used VBGs for laser applications are made of the photo-thermal refractive (PTR) glass [9]. However, all photopolymers have the potential to serve as the recording material of VBG. Hsieh et. al reported using a PQ:PMMA transmitting VBG to serve as an wavelength selection and spectrum narrowing optical element in an external cavity diode laser (ECDL) system [10].
The fabrication of VBG usually uses two-beam interference scheme. Therefore, the shortest reflecting wavelength or the Bragg wavelength (λB) of a reflecting VBG is the recording laser wavelength. Consequently, a reflecting PQ:PMMA VBG using 532 nm laser for recording will not have λB at some important visible laser wavelengths such as 520 nm, 488 nm, and 450 nm where PQ:PMMA has relatively low absorption after exposure as shown in Fig. 1.
1.3 2nd order component of recording grating in photopolymer
Zhao et. al provided a mathematical model on the development of the refractive index distribution as a function of time during recording based on the diffusion nature of the monomer of photopolymers [11]. A parameter R was introduced to describe the formation and development of higher harmonic components. The 2nd order Fourier component was addressed and experimentally demonstrated on thin holographic film [12]. Neipp et. al investigated the recording of 2nd order transmission grating in a thin sheet of PVA/acrylamide photopolymer [13]. With the knowledge of the refractive index distribution, the diffraction behaviors of the grating can be obtained using rigorous couple wave analysis (RCWA) [14]. The existence of higher order components in the recorded grating leads to diffraction at the wavelengths corresponding to these components. Such effect limits the recording speed and the diffraction efficiency corresponding to the desired 1st order component. Therefore, the existence of the 2nd order component is considered as a drawback for hologram and holographic optical storage applications. However, this effect reveals a new method for VBG recording. By carefully controlling the recording parameters, a practical reflecting VBG with λB shorter than the recording laser wavelength can be possible.
2. Simulation of the 2nd order component in PQ:PMMA
Shih et. al provided a set of simplified rate equations with diffusion of PQ molecules and required parameters for simulating the refractive index distribution of PQ:PMMA [15]. Following the same approach and using the parameters in Table 1, the refractive index distribution as a function of time can then be estimated. The simulated refractive index as a function of time and position is shown in Fig. 2(a). At the recording time at 7000 sec, the refractive index distribution and the irradiance distribution are shown in Fig. 2(b). The Fourier components can then be obtained as shown in Fig. 3(a).
Table 1. Simulation parameters
Fig. 2 (a) The simulated refractive index distribution as a function of time and position. (b) The green curve with open triangle indicates the recording laser intensity distribution. The red curve with open circle indicates the refractive index variation after 7000 sec continuous exposure.
Fig. 3 (a) Fourier components of the refractive index distribution in Fig. 2(b). The 1st order and the 2nd order components are about the same amplitude yet in opposite phase. (b) The blue curve with solid triangle is the refractive index distribution under the recording light irradiance of 0.9 W/cm2. The black curve with solid circle is the refractive index distribution under the recording irradiance of 0.015 W/cm2. The red curve with open circle is identical with the one in Fig. 2. The total recording time in all three cases are 7000 sec.
The formation of the M-shaped refractive index distribution mainly depends on the PQ diffusion coefficient, the recording light intensity and the grating period. In practice, PQ diffusion coefficient is fixed once the sample is made. With given grating period, low recording light irradiance makes the refractive index distribution match better with the recording light irradiance distribution as the black curve with solid circle in Fig. 3(b) since the PQ molecules can diffuse further into the illuminated region then react with MMA or PMMA. Under high recording irradiance condition, PQ molecules at any position can react rapidly except those located at the destructive interference nodes of the two-beam interference pattern. As those PQ molecules diffuse away from the nodes, the recording light irradiance soon becomes strong enough for the reaction and result in the sharp deep trenches with high walls as shown as the blue curve with open triangle in Fig. 3(b). Clearly, stronger or weaker recording light irradiance does not necessarily lead to stronger 2nd order grating. This result agrees with the prediction given in [11] which shows that the maximum 2nd order component peaks at R value equal to 0.1 under the assumption of no decrease of diffusion coefficient. The R parameter is defined as the product of the diffusion coefficient of the monomer and the square of the grating wavenumber divided by the polymerization rate which is roughly proportional to the recording light irradiance. For a chosen photopolymer with fixed diffusion coefficient, smaller recording grating period requires stronger recording light irradiance to maintain the same R value, consequently.
3. Recording and characterizing the 2nd order reflecting PQ:PMMA VBGs
The basic recording experimental setup is shown in Fig. 4. A single longitudinal mode 2-W 532 nm laser (Coherent, Verdi) served as the recording light source. 2 mm thick PQ:PMMA samples were prepared following the procedure described in [16]. The PQ:PMMA samples were sandwiched between two BK7 prisms with index matching fluid filling the gaps between the PQ:PMMA sample and the prisms. The main laser beam was split by a beam splitter into two recording beams and form a symmetry recording scheme. Therefore, the recorded reflecting VBG should have its grating surface parallel to the sample surface. The prisms allowed smaller angle between the two recording beams inside the sample; therefore, the recorded λB of 1st order VBG can be longer. The recording beam size was about 1.5 mm. A shutter was placed on one of the recording beams to block the beam for monitoring the diffraction efficiency of the 1st order VBG using the other recording beam.
Fig. 4 Two-beam interference recording scheme for recording reflecting VBG. All mirrors are protected silver mirrors. A collimated 650 nm diode laser output is collinear to the 532 nm recording beam for aligning purpose.
Two experiments were performed. Both experiments tried to record 2nd order VBGs with λB shorter than the recording wavelength, 532 nm. The target λB of the first and second experiment were set to be around 522 nm and 488 nm, respectively.
In the first experiment, the angle between the two recording beams was 60.9° inside the sample. The exposure parameters chosen were different from the simulation given above since longer exposure time seemed to introduce higher scattering and reduce the grating efficiency which agrees with the observation reported in [3]. After several tests, the exposure irradiance was set to be 0.104 W/m2 and the exposure time was 1500 sec. The measured λB of the 1st order VBG reflection spectrum is centered at 1044.3 nm as shown in Fig. 5(a) measured by an OSA (optical spectral analyzer, HP700950B) using a tapered amplifier (M2K laser, TAL-1060-2000-DHP) output as the light source. The OSA has the resolution of 0.6 nm. The 2nd order VBG reflection spectrum centered at 525.6 nm measured by a spectrometer (Ocean optic USB4000) is shown in Fig. 5(b) using a 522 nm laser diode (Thorlabs, L520) with slightly higher operation temperature as the light source. The spectrometer has the resolution of 0.4 nm. The measured spectral widths in both Fig. 5(a) and 5(b) have reached the resolution limits of the corresponding instruments. The λB of the 2nd order VBG is about 3.5 nm longer than half of the λB of the 1st order VBG because of the normal dispersion of PMMA. Several PQ:PMMA VBGs were made using the same exposure condition, the λB variation is about 2 nm which might be caused by the small wedge angle variation of the samples.
Fig. 5 (a) The 1st order spectrum with λB of 1044.3 nm and FWHM is about 610 pm which is about the resolution limit of the OSA. (b) The 2nd order spectrum with λB of 525.6 nm and the FWHM is about 420 pm which is about the resolution limit of the spectrometer.
A homemade Fabry-Perot interferometer using two high reflective mirrors was built to provide a higher resolution measurement of the 2nd order VBG reflection spectral width which is about 23 nm as shown in Fig. 6(a). Because of the extremely narrow diffraction spectrum, the diffraction efficiency of VBG is difficult to measure directly unless a wavelength tunable single mode or narrow linewidth laser is available. An alternative method is to use a single mode or narrow linewidth laser with wavelength slightly shorter than the VBG λB as the light source. By diffracting the incident laser light in an angle, the maximum diffraction efficiency of the VBG can be calculated [17]. As will be described in the following section, the required narrow linewidth laser can be made using another PQ:PMMA VBG with λB slightly shorter than 525.6 nm. With the required light source, the 2nd order VBG maximum diffraction efficiency was measured and calculated to be 0.21; therefore, the corresponding 2nd order VBG effective refractive index Fourier coefficient (Δn2) can then be estimated as 8.5 × 10−5. The 1st order VBG effective refractive index Fourier coefficient (Δn1) is estimated to be 7.1 × 10−5 using the 532 nm diffraction efficiency obtained during recording. These coefficients agree with the theoretical prediction as in [11] and the simulation result shown in Fig. 3 that the Fourier coefficients of the 1st and 2nd order VBGs can be close. By sandwiching the sample between two wedge prisms (Thorlabs BSF2550) with index matching fluid, the green diffracted light can be clearly observed by illuminating white LED light to the sample as shown in Fig. 6(b). The white and yellow spots are the front and back surface reflection of the front and back wedge prism, respectively.
Fig. 6 (a) A homemade Fabry-Perot interferometer measures the reflected 525.6 nm VBG spectrum which has spectral width about 23 pm. The maximum diffraction efficiency is about 0.21. (b) The grating was sandwiched between two wedge prisms with index matching fluid and was illuminated by a white LED. The white and yellow spots are the front and back surface reflection of the wedge prisms. The green spot is the diffraction of the 2nd order grating.
Several other samples were written with the same experimental configuration yet different in recording light irradiance and exposure time. As the exposure time increases, scattering appears to be stronger. The final and larger Δn2 with different recording irradiances are shown in Fig. 7(a). When using lower recording irradiance, longer exposure time is required to reach higher diffraction efficiency. In the meantime, the scattering becomes stronger and harder to achieve practical 2nd order VBG. Δn1, Δn2 and Δn2/Δn1 under different exposure irradiances are shown in Fig. 7(b). Clearly, the maximum Δn2 is achieved when the exposure irradiance is within the range of 0.026-0.104 W/cm2. By comparing the result with Fig. 4 in [11], the R parameters in the recoding condition should be about 0.10-0.11. The Δn2 of two different recording irradiances with different exposure time are shown in Fig. 7(c) with simulation result. The absorption cross section and diffusion coefficient of PQ are fitted to be about 2.32 × 10−20 cm2 and 5.5 × 10−19 m2/sec, respectively. These values are different from Table 1 and other references; therefore, further investigation should be applied. However, it is beyond the scope of this work. The Δn2 are only about one-third of the maximum possible value that the simulation predicted. The reason may be that the exposure time in the experiment is much shorter. When the exposure time increases, the scattering becomes stronger and reduces the diffraction efficiency. Also, the scattering effect varies in different samples. Therefore, the control of the exposure parameters and sample preparation may require further investigation.
Fig. 7 (a) Selected Δn2 with different irradiance and exposure time. (b) Δn1, Δn2 and Δn2/Δn1 under different exposure irradiances. (c) The experimental and simulated Δn2 of different exposure time with two exposure irradiances show great agreement.
In the second experiment, the angle between the two recording beams was 65.6° inside the sample. The measured 2nd order grating was centered at 488.8 nm as shown in Fig. 8(a) which was measured by the same spectrometer and the same white LED as the light source abovementioned. The recording exposure irradiance was about 0.055 W/m2 and the exposure time was about 900 sec. By sandwiching the sample in between two wedge prisms and illuminated by a while LED as mentioned above, a blue 488.8 nm diffraction spot can be clearly observed in Fig. 8(b). This image is a clear proof of the existence of the 2nd order grating that can be justified by naked eyes.
Fig. 8 (a) The measured 2nd order grating spectrum with λB centered at 488.8 nm. The FWHM is about 0.6 nm. (b) The grating was sandwiched between two wedge prisms with index matching fluid and was illuminated by a white LED. The blue spot is the diffraction of the 488.8 nm 2nd order grating.
4. Using 2nd order PQ:PMMA VBG for diode laser output spectrum narrowing
The 2nd order PQ:PMMA VBG with λB of 525.6 nm abovementioned was used to serve as an external mirror to feedback a single transverse mode diode laser (Thorlabs PL520) which had total spectral width about 1.5 nm and was peaked at 522 nm. The ECDL configuration is shown in Fig. 9. The collimating lens L is an aspherical lens (Thorlabs C330TME-B) with focal length of 3.1 mm. The laser output were measured by a powermeter (Ophir Laserstar) and a scanning Fabry-Perot interferometer (Throlabs SA200-5B). The scanning Fabry-Perot trace in Fig. 10(a) shows the ECDL output spectral width was about 0.13 pm which is more than 10000-fold smaller than the original spectral width. With such ECDL as a narrow linewidth light source, the maximum diffraction efficiency of other VBG with λB slightly longer can be measured as mentioned in the previous section. The ECDL output power was about 13% lower than the diode laser at the same input current as shown in Fig. 10(b).
Fig. 9 Experimental setup of using 2nd order PQ:PMMA VBG as the external cavity mirror for 520 nm ECDL.
Fig. 10 (a) Scanning Fabry-Perot trace of the ECDL using 525.6 nm 2nd order PQ:PMMA VBG as the cavity mirror. 1.5 GHz is the free spectral range (FSR) of the scanning Fabry-Perot interferometer. (b) Diode laser and ECDL output power versus input current.
5. Conclusions
PQ:PMMA photopolymer has high absorption in the spectral range of 400 – 500 nm before exposure. However, after PQ molecules is depleted, the absorption in the same spectral range becomes much smaller and can be used as visible optics material. The diffusion of PQ molecule in PQ:PMMA allows the formation of 2nd order grating by carefully controlling the exposure. Using 532 nm as the recording wavelength, 2nd order reflecting VBGs with Bragg wavelength within 400 – 532 nm range with low absorption can be achieved. 2nd order reflecting PQ:PMMA VBGs with Bragg wavelength of 525.6 nm and 488.8 nm were successfully recorded and characterized. The 525.6 nm VBG was used in an ECDL scheme to feedback a 522 nm diode laser and achieved laser output spectrum narrowing for more than 10000-fold with only 13% reduction of the output power. This work provides a new, practical and powerful application for the undesired 2nd order component in photopolymer.
Funding
The work is funded by the Ministry of Science and Technology of Taiwan, R.O.C., with contract number 105-2221-E-008-075-MY3.
Acknowledgments
The authors would like to thank Prof. Shiuan-Huei Lin of National Chiao Tung University for offering the technical support on fabricating the samples and providing valuable ideas and helpful discussions.
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