OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 25 — Dec. 6, 2010
  • pp: 25649–25656
« Show journal navigation

Holographic filter with cascaded volume Bragg gratings in photopolymer waveguide film

Kwon-Yeon Lee  »View Author Affiliations


Optics Express, Vol. 18, Issue 25, pp. 25649-25656 (2010)
http://dx.doi.org/10.1364/OE.18.025649


View Full Text Article

Acrobat PDF (1618 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A novel holographic filter using a photopolymer-based cascaded volume Bragg gratings (CVBGs) is proposed and experimentally demonstrated in this paper. The filter was designed to attain a narrow spectral bandwidth characteristic without increasing the thickness of photopolymer used, at 1550nm operating wavelength region. The proposed filter is consisted of a 45° slanted grating working as a surface-normal input/output coupler and a non-slanted reflection grating acting as a narrow-band wavelength selective filter, and it was embedded in the photopolymer film as a waveguide mode. The fabricated filter showed that the bandwidth at the center wavelength of 1547.85nm was about 0.45nm.

© 2010 OSA

1. Introduction

Holographic volume Bragg gratings (VBGs) have a great potential as useful devices for fiber optic communication systems such as tunable filters, notch filters, wavelength-division demultiplexers, and grating couplers, because of its use to make a narrow bandwidth of holographic filters. Numbers of studies introduced VBG structured holographic filters using various types of holographic recording materials such as photorefractive crystals, dichromated gelatin, photopolymers, and photosensitive glasses [1

1. K. Buse, F. Havermeyer, W. Liu, C. Moser, and D. Psaltis, “Holographic filters,” in Photorefractive materials and their applications 3, P. Gunter and J. P. Huignard, eds. (Springer-Verlag, 2007), pp. 295–317.

]. Among those materials, photopolymer is the one of attractive materials for making VBG that provide high diffraction efficiency, dry fabrication processing, and low price. However, because of the limitation in thickness of most available photopolymers, the feasible wavelength bandwidth of fabricated VBG is still broad. For example, the bandwidth of conventional VBG using commercially available DuPont photopolymer films with few tens of micrometers thick is at several tens of nanometers. The thickness limitation influence filter performance makes it difficult to meet the spectral bandwidth requirements for wavelength-division multiplexing (WDM) optical communication systems. In this paper, we introduce a design approach and fabrication procedures of a new type holographic filter with a CVBGs structure embedded in photopolymer waveguide film. For recording CVBGs, a 20μm-thick DuPont photopolymer HRF600x123-20 is adopted because they used for recording transmission and reflective hologram with high refractive index modulation over a broad range of grating periods [2

2. W. J. Gambogi, W. A. Gerstadt, S. R. Mackara, and A. M. Weber, “Holographic transmission elements using improved photopolymer films,” Proc. SPIE 1555, 256–267 (1991). [CrossRef]

].

2. Structure and operation characteristics

The schematic diagram of the proposed holographic filter is illustrated in Fig. 1
Fig. 1 Schematic diagram of a waveguide-CVBGs filter.
. The filter is composed of two VBGs; a slanted VBG with a grating inclination angle φ=45 (45-VBG), a non-slanted VBG with a grating inclination angle φ=0 (0-VBG), where the grating inclination angle is the angle between the grating vector K1 (or K2) and the z axis as shown in Fig. 1. Those VBGs are embedded in a photopolymer film with thickness tg wherein, two gratings are separated by a waveguide of length zL along the direction of beam propagation. Iinc, It, and Iout denote the intensities of the incident input beam, the transmitted beam, and the output reflected beam, respectively. zo is the position of the incident input beam on the surface of the 45-VBG, wg is the width of the gratings, and the dg1 and dg2 are the grating lengths for the 45-VBG and the 0-VBG, respectively. In this scheme, if the refractive index of the photopolymer film is higher than that of the surrounding medium, the photopolymer film acts as both of the grating medium and the waveguide layer to guide diffracted beam between the gratings. We name this type of filter “a waveguide-CVBGs filter” according to its structure. In the configuration of Fig. 1, the 45-VBG is operating both as an input and output coupler [3

3. M. L. Jones, R. P. Kenan, and C. M. Verber, “Rectangular characteristic gratings for waveguide input and output coupling,” Appl. Opt. 34(20), 4149–4158 (1995). [CrossRef] [PubMed]

5

5. Q. Huang and P. R. Ashley, “Holographic Bragg grating input-output couplers for polymer waveguides at an 850-nm wavelength,” Appl. Opt. 36(6), 1198–1203 (1997). [CrossRef] [PubMed]

]. By this 45-VBG, a nearly surface-normal-incident input beam is 90 diffracted into the plane of the waveguide and guided toward the 0-VBG. The guided beam is then retro-diffracted by 0-VBG in the opposite direction, and again out-coupled by the 45-VBG. The second 0-VBG is working as a reflective grating which diffracts the guided beam back into the input/output coupler (45-VBG). Considering the functions of two gratings and the structure of device, we see that the spectral bandwidth of a waveguide-CVBGs filter is controlled not by adjusting film thickness but by the effective interaction length deff between the 0-VBG with a grating length dg2 and the guiding beam in photopolymer waveguide. Therefore the effective grating length from the guiding beam standpoint functionally substitutes for the thickness of the 0-VBG. In this structure, the two gratings are cascaded with different regions inside a single waveguide, the performance analysis of the waveguide-CVBGs filter becomes complicated. But still the angular and spectral characteristic of the filter may be dominated by the Bragg effect, since the filter is composed of a thick volume Bragg gratings with a wide and thick waveguide. In our proposed structure, the two VBGs are formed as transmission geometry and reconstructed in reflection mode of operation by surface-normal illumination on the 45-VBG. In Fig. 1, the grating vectors K1 (for 45-VBG) and K2 (for 0-VBG) have magnitudes of |K1|=2π/Λ1and |K2|=2π/Λ2 respectively, where Λ1 and Λ2are the grating periods. The grating periods of the two VBGs, each with a different periods, can be expressed separately from the Bragg condition [6

6. H. Kogelnik and T. P. Sosnowski, “Holographic thin film couplers,” Bell Syst. Tech. J. 49, 1602–1608 (1970).

] as Λ1=λc/2ngccos(45θc1) and Λ2=λc/2ngccos     θc2, where λc is the Bragg-matched coupling wavelength of the incident input beam, ngc is the average refractive index of the grating, θc1 and θc2 are the coupling angles of the incident beams for each 45-VBG and 0-VBG in the gratings, respectively. In case of ngc=1.49, θc1=0, θc2=0, we have a different grating periods Λ1=~0.735μm and Λ2=~0.520μm at 1550nm coupling wavelength.

3. Fabrication details

In this paper, two gratings are recorded by using a same Nd:YAG laser source with free-space wavelength λw=532nm. To write the different gratings with different optical setups, the laser beam is divided into two beams with a beamsplitter, and one beam is selected for constructing of the 0-VBG recording setup. The other beam used for constructing of the 45-VBG recording setup. Then the two laser beams are spatially filtered and then collimated by same optical components to obtain an identical collimating beam with a uniform phase–front for each setup. The each dimension of the collimated recording beams are7mm×7mm, and TE-polarized such that the electric field is perpendicular to the plane of incidence. The photopolymer is laminated onto a fused-silica glass substrate with dimensions of 85mm×25mm×1.5mm after one of the Mylar cover sheets is removed. Next, we recorded the 0-VBG inside the photopolymer, and then moved the sample to the 45-VBG recording setup position as shown in Fig. 2
Fig. 2 Experimental setup for fabricating 45-VBG.
. The 0-VBG is recorded by the conventional symmetrical recording geometry. In the experiment, the half angle of the recording beam in the air was30.987, and each recording beams had an equal intensity of 0.12mW/cm2 and exposure energy density was 49mJ/cm2. However, in the asymmetrical recording geometry as the 45-VBG, the material shrinkage is predominately in the normal direction to the surface of the grating, and it changes the grating slant angle and period. The measured shrinkage of the DuPont photopolymer HRF-600X123-20 with tg=20μm for a 45-VBG was ~4% after UV fixing processing. In this case, the recording angles of the 45-VBG in Fig. 2 with considering material shrinkage in air are calculated to be θwc1=27.215 and θwc2=16.426 respectively [5

5. Q. Huang and P. R. Ashley, “Holographic Bragg grating input-output couplers for polymer waveguides at an 850-nm wavelength,” Appl. Opt. 36(6), 1198–1203 (1997). [CrossRef] [PubMed]

]. Unlike conventional recording setup for a 0-VBG, the interferometric recording architecture including a prism system as shown in Fig. 2 is applied in order to fabricate the input/output couplers with a 45 slanted volume phase grating. Before recording the 45-VBG, the sample was sandwiched by the two identical fused-silica 454590 prisms, and the refractive index matching oil which is inserted between the input prism and substrate, between the cover sheet and the output prism. After that, the sandwiched sample is placed on a rotation-translation stage, the rotation-translation stage is mounted on a 2-axis translation stage to arrange accurately the recording beams at the desired position inside photopolymer film. The dimensions of a fused-silica prism were of 60mm×60mm×25mm, and the prisms were antireflection coated to reduce reflections. The refractive-indices of the photopolymer film are ngw=~1.51 and ngc=~1.49 at λw=532nm and λc=1550nm. In addition, the glass substrate material is a fused-silica like that of prisms with refractive index npw=1.460 and npc=1.444 at λw=532nm and λc=1550nm. To attain a high contrast ratio of the recording interference pattern through the compensation of the incident powers for the different recording angles, the intensity of the two recording beams are adjusted to be Iwc1=0.15mW/cm2 and Iwc2=0.081mW/cm2 respectively. The dimensions and the separation length of the fabricated CVBGs are ~8.6mm(dg1)×7mm(wg) for a 45-VBG, ~8mm(dg2)×7mm(wg)for a 0-VBG, and 3mm (zL), respectively.

4. Experimental results and discussion

After recording the two gratings, the sample is fixed by UV light. The fixed sample is then mounted onto a rotation-translation-goniometer stage for performance testing as shown in Fig. 3
Fig. 3 Experimental setup for testing the fabricated waveguide-CVBGs filter.
. The spectral dependence of our device is measured using the Newport’s external cavity tunable laser with a center wavelength of 1550nm with tunable wavelength range of ± 30nm. The dimension of the incident laser beam at the surface of the sample is approximately2mm(z)×5mm(y). The polarization of the incident laser beam is controlled by a λ/2 plate and a linear polarizer. For the experiment the TE polarized incident beam was adopted, since waveguide-CVBGs filter is polarization-sensitive device with strong reflection efficiency for it [6

6. H. Kogelnik and T. P. Sosnowski, “Holographic thin film couplers,” Bell Syst. Tech. J. 49, 1602–1608 (1970).

]. The wavelength of the tunable laser is monitored using an optical spectrum analyzer and the intensity of the transmitted and the reflected output beams are measured through a detector. The intensity profile of reflected output beam is obtained by replacement of the detector with an infrared (IR) camera. It is noted that the proposed filter is very angularly-spectrally sensitive device to have combined properties of the planar waveguide and the volume Bragg grating. In Fig. 3, angular tuning is accomplished by rotating the sample about y-axis perpendicular to the sample’s facet. In this procedure, angular tuning at a given wavelength may lead to a wave-vector mismatch among the gratings and the incident and diffracted beams inside the sample. As the light of wavelength to satisfy the Bragg conditions of two gratings is diffracted, the precise angular and wavelength tuning are necessary. The adjusting procedure for an optimized coupling starts with the first step for tuning a tunable laser to the peak reflectance wavelength for the nearly normal incident input beam. The incident angle is then varied to the coupling angle having a peak reflectance, and then fine-tunes again the wavelength and the incident angle around the obtained values from the first step to confirm the optimizing coupling.

In this paper, we define the output reflectance of the filter as R=(Iout/Iinc)×100% and the transmittance of the 45-VBG as T=(It/Iinc)×100% in Fig. 3. Where the incident intensity of input beam Iinc denotes the intensity of the transmitted beam through the film region without grating at input coupling angle with considering the Fresnel and absorption losses, Iout is the intensity of the out-coupled output beam from the a 45-VBG in air, and Itis the intensity of the transmitted beam through the 45-VBG.

Figure 4
Fig. 4 Normalized reflected intensity versus the (internal) incident angle for a fixed coupling wavelength.
shows the angular response of the normalized reflected intensity for a fixed coupling wavelength of 1547.85nm obtained by the above procedure. The input beam is positioned approximately at zo=5mm on the surface of the sample as shown in Fig. 1. As shown in Fig. 4, the measured input coupling angle was θc1=1.301 in the grating. It is also noted that the response curve decreased slightly asymmetrically at the central wavelength unlike the conventional uniform VBGs, with a full bandwidth of approximately 0.108 at the 98% decreased level of the peak response. The measured angular selectivity at the full width at half maximum (FWHM) inside the grating was about 0.026. Figure 5
Fig. 5 Spectral response of the transmittance of the 45-VBG for the fixed input coupling angle.
shows the transmittance spectrum of the 45-VBG for zo=2mm, 5mm at the fixed input coupling angle of θc1=1.301. As seen in Fig. 5, each dip in the transmittance spectrum corresponds to the Bragg diffraction of incident light into a waveguide mode supported by the 45-VBG, where each mode is associated with a specific coupling angle. It is noted that the measured Bragg coupling wavelength of the grating at the input coupling angle corresponds to the wavelength at which a maximum dip in the transmittance spectrum. The measured transmitted efficiencies at the coupling wavelength of 1547.85nm are 38% (i.e. the input coupling efficiency of 45-VBG is 62%) for the zo=2mm and 26.7% for the zo=5mm. To our knowledge, suitable theories are not available to model the spectral response of our waveguide-CVBGs configuration. Therefore, experimental results are analyzed and compared approximately by use of the Kogelnik’s coupled-wave theory [7

7. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

] without considering the effects of waveguide although it’s not accurate representation of the spectral responses of transmitted and reflected beams. Figure 5 also includes a simulation curve with the coupled-wave theory for a reflection grating at tg=20μm, φ=45, λc=1547.85nm, and refractive index modulation Δn = 0.0047. The refractive index modulation was obtained by using the measured reflection efficiency of the 45-VBG for the zo=5mm. If we consider only the curve around the wavelength of 1547.85nm by excluding the other guided modes in Fig. 5 as a conventional reflection grating, a measured wavelength bandwidths at the FWHM level for each curve at the coupling wavelength are ~1.7nm for the zo=2mm and ~1.3nm for the zo=5mm. It can be seen that the experimentally measured bandwidth is smaller than the theoretical value (~2nm), also the shape of experimental curves are more complicated because of the waveguide effect and the additional mode excitation resulting from the discontinuity between the waveguide and the VBGs.

Figure 6
Fig. 6 Normalized reflected intensity versus wavelength for the fixed input coupling angle.
shows the spectral response of the output reflected efficiency as a function of tuning wavelength in the range between 1538.60nm to 1549.35nm for the fixed input coupling angle of θc1=1.301 and the positions of the incident input beam of zo=2mm, 5mm. A measured wavelength bandwidth at the FWHM level is ~0.45nm for each curve of centered at 1547.4nm, and output reflectance R is ~9.7% for a zo=2mm and ~14.17% for a zo=5mm respectively. The Bragg coupling wavelength for the maximum dips in Fig. 5 are in agreement with those depicted in Fig. 6, indicating that other waveguide modes except the maximum dips does not nearly affect the reflectance spectrum because of the Bragg matching condition. Therefore, we can see that the spectral response in the case of our configuration is mainly due to the 0-VBG, the spectral bandwidth of the 0-VBG for the θc20 can be determined approximately from the coupled-wave theory as δλ0VBGλc2/2ngcdeff. Using the measured values with λc=1547.85nm and δλ0VBG0.45nm, we can calculated the effective interaction length deff of ~1.8mm. The calculated deff is shorter than the grating length of the 0-VBG, which is due to the fact that more of light is diffracted from the area closer to the input boundary of the 0-VBG and corresponds to the features of a uniform volume grating [3

3. M. L. Jones, R. P. Kenan, and C. M. Verber, “Rectangular characteristic gratings for waveguide input and output coupling,” Appl. Opt. 34(20), 4149–4158 (1995). [CrossRef] [PubMed]

]. Additionally, Fig. 6 shows a fit of the coupled-wave theory to the measured data for the zo=5mm with a fit parametersΔn=1.09×104, λc=1547.85nm, and deff=1.8mm. The output reflectance with respect to the positions of incident input beam zo on the surface of the 45-VBG were investigated. We observed from the measurement results, as zo gets closer toward the grating-waveguide boundary, the output reflectance is increased. This is because of that as the incident-beam position approaches to the grating-waveguide boundary, the leakage of the guided mode from the waveguide decreases, which is good agreement with the results of output-coupling effect in Ref. 4

4. S. D. Wu, E. N. Glytsis, and T. K. Gaylord, “Optimization of finite-length input volume holographic grating couplers illuminated by finite-width incident beams,” Appl. Opt. 44(21), 4435–4446 (2005). [CrossRef] [PubMed]

. On the other hand, strongly coupled few modes are appeared as seen in Fig. 6 with the incident beam approach to near zo=dg1, because of the waveguide effect similar to the input/output coupler formed inside the photopolymer waveguide [8

8. W. Driemeier, “Bragg-effect grating couplers integrated in multicomponent polymeric waveguides,” Opt. Lett. 15(13), 725–727 (1990). [CrossRef] [PubMed]

]. Therefore, it is seen that the position of incident input beam zo should be limited to a certain position within dg1 to avoid the unwanted waveguide effect and to optimize the performance in the device.

Figure 7
Fig. 7 Photograph of the intensity profile of the reflected output beam obtained by the IR camera.
shows the intensity profile of the output beam for the incident conditions θc1=1.301, λc=1547.85nmand zo=5mm, where the reflected output beam is captured by an infrared (IR) camera with a mounted zoom lens in Fig. 3. In Fig. 7, the angular separation of the two beams caused by the angle difference between the output beam and the back-reflected beam (left spot in Fig. 7) of the incident beam at the surface of the sample is observed. The shape of the output diffracted beam is a typical aspect for the 45-VBG with relatively long grating length as our rectangular-shaped grating configuration. The diffracted beam spreading can cause a significant loss as coupling the output beam inside a fiber however, it can be minimized by the reducing the grating length of the 45-VBG and also by altering the shape of the incident beam such as a collimated Gaussian beam.

In our experimental results, the measured input coupling angle and wavelength are shifted from the design values θc=0 and λc=1550nm, that are primarily due to the arrangement errors in optical setups. Moreover the output performance of the filter is sensitive to the throughout alignment from the fabrication to the measurement procedures. This can be corrected by more accurate alignment and recording, and testing processes. In addition, one of the most significant drawbacks associated with the DuPont photopolymer film have a nonplanar surface is its high attenuation when used it as a waveguide. The reported waveguide loss, measured by the prism coupling method at a wavelength of 850nm, was approximately 5.5dB/cm [5

5. Q. Huang and P. R. Ashley, “Holographic Bragg grating input-output couplers for polymer waveguides at an 850-nm wavelength,” Appl. Opt. 36(6), 1198–1203 (1997). [CrossRef] [PubMed]

], therefore holographic recording media with a low propagation loss and planar waveguide structure are critically needed to practical applications. Recent developments in holographic materials have made it possible to fabricate our special configuration in a planar waveguide type. One method to overcome this problem is using low-loss photopolymer material coated on the glass or photosensitive glass materials [9

9. I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, “Modeling of gaussian beam diffraction on diffraction on volume Bragg gratings in PTR glass,” Proc. SPIE 5742, 183–194 (2006). [CrossRef]

], VBGs can be fabricated directly as waveguide type in these media, leading to possibly better performance than the used type in this paper. Moreover, two VBGs in our experiments have constant amplitude over the grating regions, therefore the spectral profile in Fig. 6 is typical feature of the photopolymer(or photorefractive crystal)-based filters. However, the flat-top profile is highly desired for WDM system applications, which is expected through a hologram apodization method [10

10. J. M. Tsui, C. Thompson, V. Mehta, J. M. Roth, V. I. Smirnov, and L. B. Glebov, “Coupled-wave analysis of apodized volume gratings,” Opt. Express 12(26), 6642–6653 (2004). [CrossRef] [PubMed]

].

5. Conclusions

In this paper, a novel holographic filter operating at 1550nm wavelength region using a waveguide-CVBGs structure was proposed and experimentally demonstrated by using a 20 μm-thick DuPont photopolymer film HRF600x123-20. Detailed fabrication and testing procedures and a performance characteristic were also presented. The fabricated holographic filter had a peak reflectance of ~14.17% with a FWHM of ~0.45nm at center wavelength of 1547.85nm. It is shown that the CVBGs configuration embedded in a photopolymer waveguide film is potentially useful mean to overcome the limitation by the thickness of photopolymer used, to attain narrow spectral bandwidth characteristic without increasing the film thickness. We believe that our proposed the waveguide-CVBGs structure is widely applicable to integrated optics and WDM optical communications for narrower spectral bandwidth characteristics.

Acknowledgement

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0072569).

References and links

1.

K. Buse, F. Havermeyer, W. Liu, C. Moser, and D. Psaltis, “Holographic filters,” in Photorefractive materials and their applications 3, P. Gunter and J. P. Huignard, eds. (Springer-Verlag, 2007), pp. 295–317.

2.

W. J. Gambogi, W. A. Gerstadt, S. R. Mackara, and A. M. Weber, “Holographic transmission elements using improved photopolymer films,” Proc. SPIE 1555, 256–267 (1991). [CrossRef]

3.

M. L. Jones, R. P. Kenan, and C. M. Verber, “Rectangular characteristic gratings for waveguide input and output coupling,” Appl. Opt. 34(20), 4149–4158 (1995). [CrossRef] [PubMed]

4.

S. D. Wu, E. N. Glytsis, and T. K. Gaylord, “Optimization of finite-length input volume holographic grating couplers illuminated by finite-width incident beams,” Appl. Opt. 44(21), 4435–4446 (2005). [CrossRef] [PubMed]

5.

Q. Huang and P. R. Ashley, “Holographic Bragg grating input-output couplers for polymer waveguides at an 850-nm wavelength,” Appl. Opt. 36(6), 1198–1203 (1997). [CrossRef] [PubMed]

6.

H. Kogelnik and T. P. Sosnowski, “Holographic thin film couplers,” Bell Syst. Tech. J. 49, 1602–1608 (1970).

7.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

8.

W. Driemeier, “Bragg-effect grating couplers integrated in multicomponent polymeric waveguides,” Opt. Lett. 15(13), 725–727 (1990). [CrossRef] [PubMed]

9.

I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, “Modeling of gaussian beam diffraction on diffraction on volume Bragg gratings in PTR glass,” Proc. SPIE 5742, 183–194 (2006). [CrossRef]

10.

J. M. Tsui, C. Thompson, V. Mehta, J. M. Roth, V. I. Smirnov, and L. B. Glebov, “Coupled-wave analysis of apodized volume gratings,” Opt. Express 12(26), 6642–6653 (2004). [CrossRef] [PubMed]

OCIS Codes
(050.7330) Diffraction and gratings : Volume gratings
(060.2340) Fiber optics and optical communications : Fiber optics components
(090.0090) Holography : Holography
(090.2890) Holography : Holographic optical elements
(130.0130) Integrated optics : Integrated optics
(230.7408) Optical devices : Wavelength filtering devices

ToC Category:
Holography

History
Original Manuscript: September 8, 2010
Revised Manuscript: November 19, 2010
Manuscript Accepted: November 22, 2010
Published: November 23, 2010

Citation
Kwon-Yeon Lee, "Holographic filter with cascaded volume Bragg gratings in photopolymer waveguide film," Opt. Express 18, 25649-25656 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-25-25649


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. K. Buse, F. Havermeyer, W. Liu, C. Moser, and D. Psaltis, “Holographic filters,” in Photorefractive materials and their applications 3, P. Gunter and J. P. Huignard, eds. (Springer-Verlag, 2007), pp. 295–317.
  2. W. J. Gambogi, W. A. Gerstadt, S. R. Mackara, and A. M. Weber, “Holographic transmission elements using improved photopolymer films,” Proc. SPIE 1555, 256–267 (1991). [CrossRef]
  3. M. L. Jones, R. P. Kenan, and C. M. Verber, “Rectangular characteristic gratings for waveguide input and output coupling,” Appl. Opt. 34(20), 4149–4158 (1995). [CrossRef] [PubMed]
  4. S. D. Wu, E. N. Glytsis, and T. K. Gaylord, “Optimization of finite-length input volume holographic grating couplers illuminated by finite-width incident beams,” Appl. Opt. 44(21), 4435–4446 (2005). [CrossRef] [PubMed]
  5. Q. Huang and P. R. Ashley, “Holographic Bragg grating input-output couplers for polymer waveguides at an 850-nm wavelength,” Appl. Opt. 36(6), 1198–1203 (1997). [CrossRef] [PubMed]
  6. H. Kogelnik and T. P. Sosnowski, “Holographic thin film couplers,” Bell Syst. Tech. J. 49, 1602–1608 (1970).
  7. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  8. W. Driemeier, “Bragg-effect grating couplers integrated in multicomponent polymeric waveguides,” Opt. Lett. 15(13), 725–727 (1990). [CrossRef] [PubMed]
  9. I. V. Ciapurin, L. B. Glebov, and V. I. Smirnov, “Modeling of gaussian beam diffraction on diffraction on volume Bragg gratings in PTR glass,” Proc. SPIE 5742, 183–194 (2006). [CrossRef]
  10. J. M. Tsui, C. Thompson, V. Mehta, J. M. Roth, V. I. Smirnov, and L. B. Glebov, “Coupled-wave analysis of apodized volume gratings,” Opt. Express 12(26), 6642–6653 (2004). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited