- Email: [email protected]
Field matching Y-branch for low loss power splitter
Optics Communications 248 (2005) 423–429 www.elsevier.com/locate/optcom
Field matching Y-branch for low loss power splitter J. Gamet a, G. Pandraud
b,*
a Opsitech S.A., 15 rue des Martyres, 38000 Grenoble, France Department of Microelectronics, Electronic Instrumentation Laboratory, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Mekelweg 4, Room 16.120, 2628 CD Delft, The Netherlands b
Received 21 September 2004; received in revised form 8 November 2004; accepted 16 December 2004
Abstract A new approach for lowering the loss at the branching point of a Y-branch power splitter is proposed. By adding a succession of low refractive index regions with selective parameters in the straight waveguide before the branching region, the field matching is improved due to a power pre-splitting effect. The beam propagation method (BPM) is applied for the analysis of the new Y-branch power splitter. This is shown that the loss can be reduced by 50% from a recent work. We also fabricated and tested a 1 · 8 splitter formed by cascaded field matching Y-branches. An improvement of 1 dB from standard Y-branches is achieved while the polarisation dependent loss (PDL) remains lower than 0.25 dB. 2004 Elsevier B.V. All rights reserved. PACS: 42.79.F; 42.15.E; 42.82.E Keywords: Optical planar waveguide components; Power splitters; Y-branch
1. Introduction Passive optical networks (PON) use for distributive broadband communication services 1 · N power dividers for splitting (i.e. combining) optical signals. The basic unit for these 1 · N power dividers is often a Y-branch. However, the implementation of low cost broadband PON requires high *
Corresponding author. Tel.: +31 15 2781602; fax: +31 15 2785755. E-mail address: [email protected] (G. Pandraud).
quality components at a low price. Therefore, devices on silicon substrate have received increasing interest in the last few years. Silica-on-silicon waveguides have superior advantages such as low propagation loss (typically lower then 0.1 dB/cm). This is ideal for single components such as arrayed waveguide gratings [1] or group of functions on a same chip [2]. The major limitation when designing Y-branch with silica waveguides is the transmission loss due to the minimum width of the gap between the two branching waveguides limited by photolithography and
0030-4018/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.12.040
424
J. Gamet, G. Pandraud / Optics Communications 248 (2005) 423–429
etching process. The excess loss then generated is generally not suitable for practical applications. A number of Y-branches have been explored for minimizing the loss at the branch. Low loss can for example be achieved when the two output branches run parallel to each other along an optimized distance and are then tilted at a specific angle [3]. To overcome technological limitations Y-branch with a wide gap have shown a calculated loss as low as 0.15 dB [4]. Finally, a multimode interference (MMI) section before the branching region helps to lower the loss down to 0.08 dB [5]. In this paper, we propose a new way of designing Y-branches for high refractive index contrast silica waveguides. We will show that the proposed Y-branch, while used in a 1 · 8 splitter, can meet the stringent requirements of low loss and low PDL. We have developed computer aided simulation tools based on a 2D BPM [6] algorithm to design the proposed Y-branch. The second section of the paper describes the technique for the loss reduction and the simulation results. In Section 3, we present the results obtained when the new Y-branch is placed in a 1 · 8 splitter. Section 4 concludes the paper.
2. Design and analysis Segmented waveguides have shown [7] that they can help to reduce the insertion loss of integrated optical circuits. They act as an equivalent waveguide with a lower effective index. They increase the propagating mode field size and allow a perfect matching with standard optical fibers. Fig. 1 shows the proposed field matching Y-branch and its equivalent waveguide. It is known that the
gap, S, between the two output waveguides should be no less than 2 lm when plasma enhanced chemical vapor deposition (PECVD) process is used to deposit the cladding layer (otherwise there may exist air voids at the tip of the Y-branch). This limitation is a bottleneck for silica waveguides as they require a thick cladding, unlike optical fibers, to provide good optical isolation and keep the transmission loss as low as possible. The gap S influences the coupling between the incoming guided mode and the output ‘‘supermode’’. By introducing a segmentation, a presplitting occurs improving the matching with the double-peaked intensity profile of the two output waveguides. Using a 2D BPM, we carefully adjust the parameters of the segmented section. The BPM is a forward algorithm that does not take into account the multiple reflections occurring in the segmented section. Prior to this work, we investigated the coupling efficiency of segmented sections with single mode fibers. The measured return loss was found to be the same as for standard waveguide. A 2D algorithm is then enough to simulate the proposed device as the reflections can be neglected. The refractive indexes of the segmented section are Nclad and Ncore alternatively and can be represented (Fig. 1) as a layer of uniform equivalent index Neq. When expressing Neq as a function of the parameters of the segmented section, we have
N eq N clad ¼ ðN core N clad Þ g with g = a/K, where a is the length of a core segment and K the total length of a period. At k = 1.55 lm, the cladding index (Nclad) is 1.444 and the core index (Ncore) 1.454 (DN = 0.69%), the effective slab index (Nslab-eff) used in 2D simulations is 1.451. We first measured the indexes in the visible using the m-lines excited through prism coupling [8]. We extrapolated the indexes in the telecommunication window applying the following equation for the cladding index: N clad ¼ 1:45 3:05556 103 k2 þ 3:288040 103 k2
Fig. 1. The proposed low loss Y-branch and its equivalent effective index.
with k the wavelength expressed in lm. DN has been taken constant and previous designs [9] in
J. Gamet, G. Pandraud / Optics Communications 248 (2005) 423–429
the telecommunication window have shown a good agreement with our extrapolated values. For the TE-polarized mode, with S = 2 lm, the optimum equivalent index Neq required for a low loss transition through the Y-branch was found to be 1.4475 ± 0.0005 with a transition length Lt of 80 ± 10 lm (Fig. 2). The minimum excess loss is found to be 0.04 dB. This is 50% less than the recently reported excess loss obtained with a MMI section. Residual loss still comes from the mismatch between the fields in the branching region but for comparison, theoretical excess loss of a Y-branch without segmented region is 0.4 dB. The filling with the appropriate index of the branching region would have been enough to improve the standard Y-branch. Unfortunately, our process has been optimized for a specific DN. Optimizing the process to find the required index would have been long and extra etching steps would have been needed. Based on the proposed process we managed to built successfully a broad range of devices [1,9]. With the optimized parameters, we can deduce g = 0.5 (i.e. a = K/2) and we have N*K = 80 lm with N the number of period. We assume for this rela-
425
tively short length that the propagation loss through the segmented waveguide region is very low and independent of K-parameter, so we have chosen K = 8 lm (i.e. a = 4 lm) leading to N = 10. When adjusting for TE and TM polarization, taken into account the birefringence due to the current fabrication process, the PDL is found low for 13 periods but the excess loss is 0.06 dB (Fig. 3). In the current fabrication process, the waveguide core layer height is 4.5 lm and the width is defined by lithography as 4.5 lm. Before the branching the incoming waveguide is tapered from 4.5 to 11 lm. This section has been designed long enough to avoid extra loss. Fig. 3 shows the minimum of PDL according to the number of chosen periods. To satisfy both a low PDL and a low loss we considered in the following 13 periods. In that case as stated in Fig. 3, the excess loss is 0.06 dB.
3. Experimental results To verify our numerical investigations, we fabricated 1 · 8 splitters using the proposed segmented Y-branch and Y-branch without the
Fig. 2. Transition loss of the proposed Y-branch versus segmentation characteristics.
426
J. Gamet, G. Pandraud / Optics Communications 248 (2005) 423–429 0,1
0,02
0,08
Loss [dB]
0,06 0,01 0,04
PDL [dB]
PDL
Loss TE
0,02
0
0 8
9
10
11 Periods
12
13
14
Fig. 3. Excess loss and PDL of the optimized proposed Y-branch.
segmented section. Straight and bent waveguides were added to the photolithographic die to provide references. The bent test waveguides follow the outside shape of the 1 · 8 splitters. The 1 · 8 splitters with the optimized Y-branch and without are 33 mm long and 2.25 mm wide. The fabrication process uses PECVD process to deposit the silica layers. The cladding is deposited in three steps of 6 lm (to ensure optical isolation) and then heated up at 1000 C during 3H. This process is required as the PECVD technique introduces hydrogen that causes loss at 1.5 lm [10]. To reduce loss due to the curved waveguides, the minimum bent radius is kept higher than 8 mm. The other parameters are the same as the one of the numerical example depicted in Fig. 3 when a = 4 lm and the number of periods 13. Fig. 4 shows a schematic 3D view of the fabricated device as well as the incoming and outgoing TE modes. Optical paths are designed using P-curves family combining loss optimization and widening at the interface between curved and straight waveguides to minimize PDL [11]. The wavelength window for optical communication goes from 1528 to 1620 nm (C-band and L-band). In this window both splitters have a flat response and can be considered as wavelength insensitive. However the 1 · 8 splitter using the
proposed Y-branch outperform the conventional one by about 1 dB. In Fig. 5 the total loss is presented and includes the coupling loss. For the measurements the 1 · 8 splitters have been pigtailed with standard SMF28 fibers (a eight fiber block is used at the output). From the straight waveguides also placed on the samples we are able to estimate the interfaces loss and then to go back to the loss of a single 1 · 2 Y-branch. The 1 · 8 splitter with segmentations provides a 0.4 dB excess loss from a straight waveguide. When the bent test waveguide loss is subtracted, the excess loss truly generated by the Y-branches falls down to 0.2 dB (worst case at 1530 nm). Experimentally each proposed Y-branch introduces then 0.06 dB. We have a perfect matching with our simulations as we took 13 periods to provide a low PDL. The PDL was measured for the eight outputs over the telecommunication wavelength range. The PDL is calculated based on four scans at orthogonal states of polarization, using Mueller Matrix algorithms in the optical communications wavelength window. In Fig. 6, one can see that the worst value over the scanned wavelength window is 0.25 dB. The experimental loss and PDL of the new Y-branch show an significant improvement compared to the recent Y-branch using a MMI section.
J. Gamet, G. Pandraud / Optics Communications 248 (2005) 423–429
427
Fig. 4. 3D view of the fabricated Y-branch with the input and output TE fields.
4. Conclusion A new technique for the reduction of the loss of a Y-branch optical power splitter is proposed. The effective refractive index at the branching is controlled by adjusting the parameters of a segmented section. The intensity in the branching region is lowered and the incident power tends to be pushed
into the two outputs waveguides. The loss is reduced and calculated to be 0.04 dB for silica waveguides. The optimum parameters of the Y-branch have been found using a 2D BPM and a simple uniform equivalent index method. To verify our numerical investigations we fabricated and tested a 1 · 8 splitter based on the designed low loss Y-branch. The measured loss of
428
J. Gamet, G. Pandraud / Optics Communications 248 (2005) 423–429
Fig. 5. Comparison between 1 · 8 splitter with segmented junction and without.
Fig. 6. Eight outputs PDL of a 1 · 8 splitter with the optimized Y-branch.
0.06 dB per branch is in agreement with the computation. The splitter designed to be low PDL shows a worst value over the eight scanned outputs of 0.25 dB.
Acknowledgement The authors thank J.M. Daley and the reviewers for their helpful comments.
References [1] G. Pandraud, A.P. Vonsovici, Electron. Lett. 39 (2003) 1119. [2] Y. Yamada, S. Suzuki, K. Moriwaki, Y. Hibino, Y. Tohmori, Y. Akatsu, Y. Nakasuga, T. Hashimoto, H. Terui, M. Yanagisawa, Y. Inoue, Y. Akahori, R. Nagase, Electron. Lett. 31 (1995) 1366. [3] Z. Weissman, E. Marom, A. Hardy, Opt. Lett. 14 (1989) 293. [4] M. Saito, H. Hono, H. Takahashi, Jpn. J. Appl. Phys. 38 (1) (1999) 115.
J. Gamet, G. Pandraud / Optics Communications 248 (2005) 423–429 [5] Q. Wang, S. He, L. Wang, IEEE Photon. Technol. Lett. 14 (2003) 1124. [6] R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, J. Select. Top. Quantum Electron. 6 (2000) 150. [7] Z. Weissman, I. Hendel, J. Lightwave Technol. 13 (1995) 2053. [8] T.N. Ding, E. Garmire, Opt. Commun. 48 (1983) 113.
429
[9] J. Gamet, G. Pandraud, A.P. Vonsovici, Opt. Eng. 43 (2004) 1474. [10] G. Grand, J.P. Jadot, H. Denis, S. Valette, A. Fournier, A.M. Grouillet, Electron. Lett. 26 (1990) 2135. [11] F. Ladouceur, P. Labeye, J. Lightwave Technol. 13 (1995) 481.
Field matching Y-branch for low loss power splitter J. Gamet a, G. Pandraud
b,*
a Opsitech S.A., 15 rue des Martyres, 38000 Grenoble, France Department of Microelectronics, Electronic Instrumentation Laboratory, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Mekelweg 4, Room 16.120, 2628 CD Delft, The Netherlands b
Received 21 September 2004; received in revised form 8 November 2004; accepted 16 December 2004
Abstract A new approach for lowering the loss at the branching point of a Y-branch power splitter is proposed. By adding a succession of low refractive index regions with selective parameters in the straight waveguide before the branching region, the field matching is improved due to a power pre-splitting effect. The beam propagation method (BPM) is applied for the analysis of the new Y-branch power splitter. This is shown that the loss can be reduced by 50% from a recent work. We also fabricated and tested a 1 · 8 splitter formed by cascaded field matching Y-branches. An improvement of 1 dB from standard Y-branches is achieved while the polarisation dependent loss (PDL) remains lower than 0.25 dB. 2004 Elsevier B.V. All rights reserved. PACS: 42.79.F; 42.15.E; 42.82.E Keywords: Optical planar waveguide components; Power splitters; Y-branch
1. Introduction Passive optical networks (PON) use for distributive broadband communication services 1 · N power dividers for splitting (i.e. combining) optical signals. The basic unit for these 1 · N power dividers is often a Y-branch. However, the implementation of low cost broadband PON requires high *
Corresponding author. Tel.: +31 15 2781602; fax: +31 15 2785755. E-mail address: [email protected] (G. Pandraud).
quality components at a low price. Therefore, devices on silicon substrate have received increasing interest in the last few years. Silica-on-silicon waveguides have superior advantages such as low propagation loss (typically lower then 0.1 dB/cm). This is ideal for single components such as arrayed waveguide gratings [1] or group of functions on a same chip [2]. The major limitation when designing Y-branch with silica waveguides is the transmission loss due to the minimum width of the gap between the two branching waveguides limited by photolithography and
0030-4018/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.12.040
424
J. Gamet, G. Pandraud / Optics Communications 248 (2005) 423–429
etching process. The excess loss then generated is generally not suitable for practical applications. A number of Y-branches have been explored for minimizing the loss at the branch. Low loss can for example be achieved when the two output branches run parallel to each other along an optimized distance and are then tilted at a specific angle [3]. To overcome technological limitations Y-branch with a wide gap have shown a calculated loss as low as 0.15 dB [4]. Finally, a multimode interference (MMI) section before the branching region helps to lower the loss down to 0.08 dB [5]. In this paper, we propose a new way of designing Y-branches for high refractive index contrast silica waveguides. We will show that the proposed Y-branch, while used in a 1 · 8 splitter, can meet the stringent requirements of low loss and low PDL. We have developed computer aided simulation tools based on a 2D BPM [6] algorithm to design the proposed Y-branch. The second section of the paper describes the technique for the loss reduction and the simulation results. In Section 3, we present the results obtained when the new Y-branch is placed in a 1 · 8 splitter. Section 4 concludes the paper.
2. Design and analysis Segmented waveguides have shown [7] that they can help to reduce the insertion loss of integrated optical circuits. They act as an equivalent waveguide with a lower effective index. They increase the propagating mode field size and allow a perfect matching with standard optical fibers. Fig. 1 shows the proposed field matching Y-branch and its equivalent waveguide. It is known that the
gap, S, between the two output waveguides should be no less than 2 lm when plasma enhanced chemical vapor deposition (PECVD) process is used to deposit the cladding layer (otherwise there may exist air voids at the tip of the Y-branch). This limitation is a bottleneck for silica waveguides as they require a thick cladding, unlike optical fibers, to provide good optical isolation and keep the transmission loss as low as possible. The gap S influences the coupling between the incoming guided mode and the output ‘‘supermode’’. By introducing a segmentation, a presplitting occurs improving the matching with the double-peaked intensity profile of the two output waveguides. Using a 2D BPM, we carefully adjust the parameters of the segmented section. The BPM is a forward algorithm that does not take into account the multiple reflections occurring in the segmented section. Prior to this work, we investigated the coupling efficiency of segmented sections with single mode fibers. The measured return loss was found to be the same as for standard waveguide. A 2D algorithm is then enough to simulate the proposed device as the reflections can be neglected. The refractive indexes of the segmented section are Nclad and Ncore alternatively and can be represented (Fig. 1) as a layer of uniform equivalent index Neq. When expressing Neq as a function of the parameters of the segmented section, we have
N eq N clad ¼ ðN core N clad Þ g with g = a/K, where a is the length of a core segment and K the total length of a period. At k = 1.55 lm, the cladding index (Nclad) is 1.444 and the core index (Ncore) 1.454 (DN = 0.69%), the effective slab index (Nslab-eff) used in 2D simulations is 1.451. We first measured the indexes in the visible using the m-lines excited through prism coupling [8]. We extrapolated the indexes in the telecommunication window applying the following equation for the cladding index: N clad ¼ 1:45 3:05556 103 k2 þ 3:288040 103 k2
Fig. 1. The proposed low loss Y-branch and its equivalent effective index.
with k the wavelength expressed in lm. DN has been taken constant and previous designs [9] in
J. Gamet, G. Pandraud / Optics Communications 248 (2005) 423–429
the telecommunication window have shown a good agreement with our extrapolated values. For the TE-polarized mode, with S = 2 lm, the optimum equivalent index Neq required for a low loss transition through the Y-branch was found to be 1.4475 ± 0.0005 with a transition length Lt of 80 ± 10 lm (Fig. 2). The minimum excess loss is found to be 0.04 dB. This is 50% less than the recently reported excess loss obtained with a MMI section. Residual loss still comes from the mismatch between the fields in the branching region but for comparison, theoretical excess loss of a Y-branch without segmented region is 0.4 dB. The filling with the appropriate index of the branching region would have been enough to improve the standard Y-branch. Unfortunately, our process has been optimized for a specific DN. Optimizing the process to find the required index would have been long and extra etching steps would have been needed. Based on the proposed process we managed to built successfully a broad range of devices [1,9]. With the optimized parameters, we can deduce g = 0.5 (i.e. a = K/2) and we have N*K = 80 lm with N the number of period. We assume for this rela-
425
tively short length that the propagation loss through the segmented waveguide region is very low and independent of K-parameter, so we have chosen K = 8 lm (i.e. a = 4 lm) leading to N = 10. When adjusting for TE and TM polarization, taken into account the birefringence due to the current fabrication process, the PDL is found low for 13 periods but the excess loss is 0.06 dB (Fig. 3). In the current fabrication process, the waveguide core layer height is 4.5 lm and the width is defined by lithography as 4.5 lm. Before the branching the incoming waveguide is tapered from 4.5 to 11 lm. This section has been designed long enough to avoid extra loss. Fig. 3 shows the minimum of PDL according to the number of chosen periods. To satisfy both a low PDL and a low loss we considered in the following 13 periods. In that case as stated in Fig. 3, the excess loss is 0.06 dB.
3. Experimental results To verify our numerical investigations, we fabricated 1 · 8 splitters using the proposed segmented Y-branch and Y-branch without the
Fig. 2. Transition loss of the proposed Y-branch versus segmentation characteristics.
426
J. Gamet, G. Pandraud / Optics Communications 248 (2005) 423–429 0,1
0,02
0,08
Loss [dB]
0,06 0,01 0,04
PDL [dB]
PDL
Loss TE
0,02
0
0 8
9
10
11 Periods
12
13
14
Fig. 3. Excess loss and PDL of the optimized proposed Y-branch.
segmented section. Straight and bent waveguides were added to the photolithographic die to provide references. The bent test waveguides follow the outside shape of the 1 · 8 splitters. The 1 · 8 splitters with the optimized Y-branch and without are 33 mm long and 2.25 mm wide. The fabrication process uses PECVD process to deposit the silica layers. The cladding is deposited in three steps of 6 lm (to ensure optical isolation) and then heated up at 1000 C during 3H. This process is required as the PECVD technique introduces hydrogen that causes loss at 1.5 lm [10]. To reduce loss due to the curved waveguides, the minimum bent radius is kept higher than 8 mm. The other parameters are the same as the one of the numerical example depicted in Fig. 3 when a = 4 lm and the number of periods 13. Fig. 4 shows a schematic 3D view of the fabricated device as well as the incoming and outgoing TE modes. Optical paths are designed using P-curves family combining loss optimization and widening at the interface between curved and straight waveguides to minimize PDL [11]. The wavelength window for optical communication goes from 1528 to 1620 nm (C-band and L-band). In this window both splitters have a flat response and can be considered as wavelength insensitive. However the 1 · 8 splitter using the
proposed Y-branch outperform the conventional one by about 1 dB. In Fig. 5 the total loss is presented and includes the coupling loss. For the measurements the 1 · 8 splitters have been pigtailed with standard SMF28 fibers (a eight fiber block is used at the output). From the straight waveguides also placed on the samples we are able to estimate the interfaces loss and then to go back to the loss of a single 1 · 2 Y-branch. The 1 · 8 splitter with segmentations provides a 0.4 dB excess loss from a straight waveguide. When the bent test waveguide loss is subtracted, the excess loss truly generated by the Y-branches falls down to 0.2 dB (worst case at 1530 nm). Experimentally each proposed Y-branch introduces then 0.06 dB. We have a perfect matching with our simulations as we took 13 periods to provide a low PDL. The PDL was measured for the eight outputs over the telecommunication wavelength range. The PDL is calculated based on four scans at orthogonal states of polarization, using Mueller Matrix algorithms in the optical communications wavelength window. In Fig. 6, one can see that the worst value over the scanned wavelength window is 0.25 dB. The experimental loss and PDL of the new Y-branch show an significant improvement compared to the recent Y-branch using a MMI section.
J. Gamet, G. Pandraud / Optics Communications 248 (2005) 423–429
427
Fig. 4. 3D view of the fabricated Y-branch with the input and output TE fields.
4. Conclusion A new technique for the reduction of the loss of a Y-branch optical power splitter is proposed. The effective refractive index at the branching is controlled by adjusting the parameters of a segmented section. The intensity in the branching region is lowered and the incident power tends to be pushed
into the two outputs waveguides. The loss is reduced and calculated to be 0.04 dB for silica waveguides. The optimum parameters of the Y-branch have been found using a 2D BPM and a simple uniform equivalent index method. To verify our numerical investigations we fabricated and tested a 1 · 8 splitter based on the designed low loss Y-branch. The measured loss of
428
J. Gamet, G. Pandraud / Optics Communications 248 (2005) 423–429
Fig. 5. Comparison between 1 · 8 splitter with segmented junction and without.
Fig. 6. Eight outputs PDL of a 1 · 8 splitter with the optimized Y-branch.
0.06 dB per branch is in agreement with the computation. The splitter designed to be low PDL shows a worst value over the eight scanned outputs of 0.25 dB.
Acknowledgement The authors thank J.M. Daley and the reviewers for their helpful comments.
References [1] G. Pandraud, A.P. Vonsovici, Electron. Lett. 39 (2003) 1119. [2] Y. Yamada, S. Suzuki, K. Moriwaki, Y. Hibino, Y. Tohmori, Y. Akatsu, Y. Nakasuga, T. Hashimoto, H. Terui, M. Yanagisawa, Y. Inoue, Y. Akahori, R. Nagase, Electron. Lett. 31 (1995) 1366. [3] Z. Weissman, E. Marom, A. Hardy, Opt. Lett. 14 (1989) 293. [4] M. Saito, H. Hono, H. Takahashi, Jpn. J. Appl. Phys. 38 (1) (1999) 115.
J. Gamet, G. Pandraud / Optics Communications 248 (2005) 423–429 [5] Q. Wang, S. He, L. Wang, IEEE Photon. Technol. Lett. 14 (2003) 1124. [6] R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, J. Select. Top. Quantum Electron. 6 (2000) 150. [7] Z. Weissman, I. Hendel, J. Lightwave Technol. 13 (1995) 2053. [8] T.N. Ding, E. Garmire, Opt. Commun. 48 (1983) 113.
429
[9] J. Gamet, G. Pandraud, A.P. Vonsovici, Opt. Eng. 43 (2004) 1474. [10] G. Grand, J.P. Jadot, H. Denis, S. Valette, A. Fournier, A.M. Grouillet, Electron. Lett. 26 (1990) 2135. [11] F. Ladouceur, P. Labeye, J. Lightwave Technol. 13 (1995) 481.