Photo induced gradient index lenses with W profile - OSA Publishing

Photo induced gradient index lenses with W profile Olivier Doyle and Tigran Galstian* Center for Optics, Photonics and Laser,Department of Physics, Engineering Physics and Optics Université Laval, Pavillon d’Optique-Photonique, 2375 Rue de la Terrasse, Quebec, Canada G1V 0A6 * Corresponding author: [email protected]

Abstract: Bicomponent composite material mixture and single beam photo polymerization method are used to create a micro lens with W -like distribution of refractive index; the flat analogy of the “Schmidt” lens. The choice of two key components of the mixture, which change their mutual miscibility after the photo polymerization of one of them, allows the creation of stable spatial modulation of the refractive index. References and links 1. 2. 3. 4.

5. 6. 7. 8.

1.

D. T. Moore, “Gradient-index optics: a review,” Appl. Opt. 19, 1035-1038 (1980). G. Lemaitre, “New Procedure for Making Schmidt Corrector Plates,” Appl. Opt. 11, 1630-1636 (1972). J. L. Coutaz, P. C. Jaussaud, and G. H. Chartier, “Realization of Schmidt plates by ion exchange in glass,” Appl. Opt. 21, 1066-1068 (1982). R. Bachelot, C. Ecoffet, D. Deloeil, P. Royer, and D. -J. Lougnot, "Integration of Micrometer-Sized Polymer Elements at the End of Optical Fibers by Free-Radical Photopolymerization," Appl. Opt. 40, 58605871 (2001). K. Saravanamuttu and M. P. Andrews, “Visible laser self-focusing in hybrid glass planar waveguides,” Opt. Lett. 27, 1342-1344 (2002). M. Kagami, T. Yamashita, and H. Ito, “Light-induced self-written three-dimensional optical waveguide,” Appl. Phys. Lett. 79, 1079-1081 (2001). A. Zohrabyan, A. Tork, R. Birabassov, and T. Galstian, “Self-written gradient double clad like optical guiding channels of high stability,” Appl. Phys. Lett. 91, 111912 (2007). R. Mehra, “Application of refractive index mixing rules in binary systems of hexadecane and heptadecane with n-alkanols at different temperatures,” Proc. Indian Acad. Sci. (Chem. Sci.), 115, 147–154 (2003).

Introduction

Traditional gradient index (GRIN) lenses have monotonically decreasing bell shaped refractive index profile [1]. Particular case is the so called Schmidt lens, which provides Wlike phase correction [2,3]. The fabrication of those lenses, e.g., in glass matrices, usually necessitates complex and costly processes or provides relatively limited modulation geometry and depth ∆n = nc - nper, where nc and nper are the values of the refractive index in the central and peripheral area of the lens, respectively. Those difficulties have generated significant interest in the development of cost-effective polymer lenses that would be thin and would provide high optical powers. Particularly interesting are the lenses made by photo polymerization [4]. For example, in the case of “single monomer” solutions, the creation of those elements is based on the spatially non uniform photo polymerization (using a corresponding spatially non uniform light intensity distribution) and on the dependence of the polymer chains’ density and length upon the local light intensity. However, the obtained gradient of the refractive index ∆n in such solutions cannot be very high neither very stable, particularly because of dark photo polymerization (local continuation and spatial propagation of the polymerization process once the light exposition is over). This is the reason why the partially polymerized (or non polymerized) part of the mixture is often chemically removed to maintain the high optical power of the lens [4]. Sometimes, to solidify the structure, the removed part is replaced by another polymer (with lower refractive index) at the “price” of reducing the refractive index gradient and respectively the optical power [5]. There are several other ways of obtaining stable refractive index gradient, for example, by the use of a #105215 - $15.00 USD

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Received 15 Dec 2008; revised 5 Feb 2009; accepted 6 Feb 2009; published 16 Mar 2009

30 March 2009 / Vol. 17, No. 7 / OPTICS EXPRESS 4970

mixture of two active (photo polymerizable) components, each being sensitive to a specific wavelength, and then using two consecutive expositions (with different wavelengths) in a way to polymerize those two compositions one after the other [6]. Recently a simple approach was introduced by using a mixture of one passive (P) and one active (A) components with strongly differing refractive indexes np ≠ na [7]. In fact, the materials A and P were chosen to be well miscible before the photo polymerization, but having low or no miscibility after the polymerization of the component A. The main hypothesis was based on the possible spatial counter diffusion (separation) of molecules of A and P that should bring to the creation of the refractive index gradient. The mechanism of such counter diffusion was supposed to be the local “depletion” of the molecules of the A in the high optical intensity areas (due to the photo polymerization) and thus the “attraction” of molecules of A from neighboring (low intensity) areas. In the same time, the reduced miscibility (with the polymerized A) of the P should move them in the opposed direction (out of high intensity areas). The use of this material composition allowed the creation of photo chemically and mechanically stable photo induced channels, which guide the light (e.g., exiting from an optical fiber) for extremely long distances (centimeters) [7]. Taking into account the limited distances of possible diffusion of the molecules of P, we have made the hypothesis that the spatial (transverse) distribution of obtained refractive index should have the form of the letter W. The good guiding and high stability of obtained waveguides were indirectly supporting that hypothesis; however we had no direct evidence neither for the W profile nor for the degree of modulation ∆n. In the present work, we use the same material composition to create W formed gradient index (W-GRIN) lenses and, following their studies, we provide direct proof of the spatial W form of the refractive index distribution as well as the corresponding modulation value. This value is then used to estimate the material separation degree. In addition, by using relatively thin samples, we show that the same approach may be used to create strong gradient index structures without the requirement of “self-guiding” condition (in contrast to the case described in Ref.[6] and in references therein). 2.

The material system and experimental procedure

The composition of the mixture used in the present work was described in details in the Ref.[7]. The active “host” matrix A is composed (all concentrations are done as wt% in the final solution) of 75% of the main monomer Dipentaerythritol pentaacrylate (DPEPA / SR399) that was purchased from Sartomer. That monomer is mixed with a photo initiation complex including 2% of IR140 dye (from Aldrich), 8% of CBr4 and 4% of Ethyl-dimethylamino-benzoate (EDMABzt). We also use 11% of Propylène Oxyde (PPO) as a passive low refractive index “guest” material P. Each of the above mentioned components is mixed with DPEPA separately, and then the final mixture is prepared by joining them all together and homogenized in an ultrasound bath for 30 minutes. The obtained solution is then mixed with the PPO at room temperature by using magnetic steering and then an ultrasound bath. The obtained final material mixture is then injected (by “drop fill” method) into the sandwich composed of two glass plates separated by spacers of 30 µm thickness. The spatially non uniform photo polymerization of the sample is obtained by means of a linearly polarized CW He-Ne laser beam (operating at 0.632 µm). The on-axis intensity of that “polymerizing” laser beam is 46.3±0.5 mW/cm2 and the typical duration of exposition is 15 minutes (followed by a uniform light exposition during 60 minutes, by a lamp, to solidify the rest of the volume of the sample). The spatial distribution of the laser intensity (at the position of the sample) is detected by means of a linear slit (of 10 µm of opening) and a photo detector, both being mount on a moving (in the traverse direction) stage. For this purpose, the sample is replaced by the couple of slit & detector (see Fig. 1).

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Fig. 1. Schematic

representation of the experimental set-up.

Once the complete photo polymerization of the sample is done, it is shifted in transverse direction (in the direction of the surface of the cell) using the same linear translation stage and the same He-Ne laser beam is used as a probe along with another focusing lens (to change its diameter, see later). The same couple of linear slit & detector are again used to scan the spatial distribution of the probe beam (at the position of the sample). Three types of experiments are then conducted to study the obtained material (and refractive index) distribution and corresponding optical power. First (see Fig. 1), the probe beam is focused to obtain an appropriate size of the beam (significantly smaller than the size of the recording beam, see Fig. 2) on the position of the 250

Diffracted power

Detected power (nW)

200

150

100

Probe laser profile 50

Polymerizing laser profile

0 2.5

3

3.5

4

4.5

Position (mm) Fig. 2. Cross symbols show the variation of the diffracted probe signal (transmitted through the sample and the diaphragm) and its measurement error versus the position of the sample (when the sample is moved in the transverse direction). The intensity profiles (measured at the position of the sample) of the polymerizing and probe laser beams are also presented by filled squares and filled triangles, respectively (the corresponding relative error is ≈5%).

sample by using a plano convex lens of focal distance F1 =10 cm. The sample is positioned at a distance d1 =17.5 cm from the lens F1. The transmitted, through the sample, light is analyzed by means of a photo detector, which is placed behind a 1mm diameter diaphragm on a distance d2 =39.5 cm from the sample (Fig. 1). In this configuration, the recorded sample is shifted in the transverse direction and the photo detector is providing information about the #105215 - $15.00 USD

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spatial distribution of the probe beam’s diffraction (divergence or convergence depending upon the position of the sample, see later). The corresponding results are shown in the Fig. 2 by using cross-like symbols (which are also serving as error bars). Two insets are added on the same Fig. 2 showing the spatial profiles of the polymerizing (filled squares) and probe (filled triangles) beams, measured at the position of the sample. Since the polymer matrix (A) and PPO (P) have slightly different optical absorption at the probe’s wavelength, a second experiment is conducted where the diaphragm is removed and the photo detector is placed immediately after the sample (d2 =1 cm, see Fig. 1). The probe beam’s incidence conditions are also changed by using d1 =3.5 cm and another lens F1 =3.5 cm. This is made to detect the spatial distribution of the concentration of materials using the difference of their absorption. Finally, a Shack-Hartman (SH) wave front sensor (model Haso, from Imagine Optic) is used to study the phase profile of a broadened probe beam that is covering the whole surface of the sample. The output surface of the sample is imaged onto the sensor plane of the SH to avoid possible errors because of additional diffraction (see Fig. 3). Thus, only the phase modulation is detected by the SH sensor. The corresponding results are presented in the figure 4 (note that this sample is different from the one presented in the Fig. 2).

Fig. 3. Schematic representation of the experimental setup with Shack-Hartmann sensor.

3.

Discussions

As it can be seen from the Fig. 2, the appropriate choice of the probe beam allows the demonstration of the complex W form of the obtained refractive index modulation. In fact, when the probe beam is passing (with the sample being moved in the transverse direction through the uniform area that was post-exposed by a uniform light), there is no noticeable modification of its transmission through the diaphragm. When we approach (from left to right) the laser polymerized area, we observe a significant drop of power, which is related to the fact that the probe beam “sees” a negative lens, which diverges the beam and thus reduces its transmission through the diaphragm. Obviously, the aberrations (which are certainly rather high since a circularly shaped beam is probing a “stretched” segment of a negative lens) in this particular geometry are not interesting us. With further movement to the center of the laser polymerized area, we see an increase of transmitted power, which is related to the fact that the probe beam now “sees” a positive lens. The further behavior is similar to the left side of the curve. W form of the transmission was also confirmed in the second experiment (not shown here because of the low modulation obtained and also for the sake of shortness) when the photo detector was positioned very close to the sample (without the diaphragm). In fact, in this case a slight modulation of inversed W form (as M) was observed since the PPO has lower absorption at the probe wavelength compared to the host matrix. Finally, the SH sensor is providing a good 2D picture (Fig. 4) of the phase modulation when the expanded probe beam is passing through the laser polymerized area. The color coding shows clearly that the phase modulation has circularly symmetric W form.

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Fig. 4. The 2D profile (bottom right photo) and horizontal & vertical histograms (top and left curves) of the phase of the probe beam passed through the laser polymerized zone, measured by a Shack-Hartman sensor.

In the case of traditional GRIN lenses, the optical power may be approximated as

OP ≈ 2 ∆nL / r 2 where L is the thickness of the lens and the r is the radius of the lens. In our case, the situation is more complicated (because of the W form), but we can make some estimations (of material movement) if we limit the digital pupil of the SH sensor to 0.35 mm. Then the probe beam is passing through the central part and is seeing only a positive lens. The experimentally obtained (by SH sensor) optical power is then ≈ 3.78 Diopters (with very small RMS aberrations ≈ 0.033 µm). We can further use the well known Lorentz-Lorenz formula [8] for the evaluation of the refractive index n of the mixture of two components with refractive indexes nj : 2

2

2

2

( n 2 − 1) /( n 2 + 2 ) = φ1 ( n1 − 1) /( n1 + 2 ) + φ 2 ( n 2 − 1) /( n 2 + 2 )

φ

j are the volume fractions of two components. Considering the following where approximate values of refractive indexes of two key components, n(PPO)D ≈ 1.367 for the PPO and n(Acril)D ≈ 1.49 for acrylates, we obtain approximately 55% of variation (reduction in the center of the exposed area) of the volume fraction of PPO to generate enough refractive index variation (∆n ≈ 0.0077) to obtain the observed 3.78 D of optical power.

4.

Summary

The obtained modulation is not so big, but further optimization (by changing material composition, geometry or exposition conditions, etc.) may be done to obtain higher optical powers. In fact, the choice of the materials is not optimized at all. First of all, this is because #105215 - $15.00 USD

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of the low adhesion of the main matrix to the glass. Thus, after three months of storage, the polymer films show some crack-delamination signs from the thick glass substrates of the sandwich, while the created W-GRIN structure is very stable (still well visible). The second reason is that, in spite of the fact that all materials (except the dye), used in the present mixture, are optically very transparent (no absorption band in the visible and near infrared); the use of the dye IR140 is creating scattering problems because of its low miscibility and aggregation already in the initial mixture. Note that its absorption is centered at 823 nm, but it is well bleached after the final polymerization process. We are presently evaluating the use of other photoinitiation complexes with better miscibility with the main mixture. What is important is that the W-GRIN structure is stable since the PPO is a chemically passive guest and the proposed method, to obtain the lens, is relatively simple and does not require wet processing or other costly manipulations. We must note however that the PPO may, in principle, be polymerized too (yielding Polypropylène Oxyde) in very special conditions, which are not satisfied in the very dilute mixture of PPO that we are using (also, the PPO may be easily replaced by another molecule). As we have mentioned already, the same approach may be used to create other types of strong gradient index structures (single, arrayed or patterned) without the requirement of “selfguiding” condition. Thus, even negative optical powers can be achieved by using compositions with np > na ( ∆n 0. The Ref. [7] is describing an example of few cm length guiding micro lens of