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Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 1 — Jan. 13, 2003
  • pp: 27–38
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Fabrication and analysis of a three-layer stratified volume diffractive optical element high-efficiency grating

Diana M. Chambers, Gregory P. Nordin, and Seunghyun Kim  »View Author Affiliations

Optics Express, Vol. 11, Issue 1, pp. 27-38 (2003)

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We have demonstrated a high-efficiency grating (>80%) using a three-layer Stratified Volume Diffractive Optical Element (SVDOE). Its angular sensitivity was measured optically and shown to agree extremely well with simulations performed using rigorous coupled wave analysis (RCWA). Further simulations predict an increase in efficiency as the number of layers is increased. An SVDOE consists of binary grating layers interleaved with homogeneous layers. The binary grating layers are shifted laterally relative to each other to emulate a volume holographic grating with slanted fringes. Creating the slanted fringe structure permits the preferred incidence angle of the SVDOE to be rotated to any arbitrary position. Achieving the relative offset between grating layers is the most challenging fabrication step and required the development of a high-precision alignment technique that was implemented on a contact mask aligner. The approach is based on monitoring the diffraction signal of a beam that is transmitted through gratings on the substrate and those on the mask as they are translated with respect to one another during pre-exposure alignment. The homogeneous layers are fabricated using a polymer material, SU-8, that is spin-coated and then planarized during its curing process.

© 2002 Optical Society of America

1. Introduction

The SVDOE structure consists of binary grating layers interleaved with homogeneous layers as illustrated in Fig. 1. An incident wave impinges on the SVDOE from Region I then transmits through the element and exits at an angle in Region II. The incident wave in this figure is shown normal to the SVDOE rather than at an angle. Ridges in the grating layers are composed of a high refractive index material whereas the grooves and homogeneous layers utilize a material with a low refractive index. The thickness of each layer is denoted by d where l is the layer number within the structure, ranging from 1 to L. The binary grating layers diffract a wavefront as it passes through the structure and the homogeneous layers permit propagation through distances appropriate for constructive interference of the preferred diffraction order. While the individual binary grating layers are relatively thin, incorporation of preferential constructive interference via the homogeneous layers permits an SVDOE to attain diffraction efficiencies comparable to a volume holographic element.

Fig. 1. Schematic illustration of the stratified volume diffractive optic element (SVDOE) structure. Binary grating layers are interleaved with homogeneous layers to achieve high efficiency. The gratings are shifted relative to one another, much like standard fringes in a volume grating, as a means to control the preferred incidence angle.

Since the layers in this type of structure must be fabricated sequentially, the binary grating layers can be laterally shifted relative to one another (as illustrated in Fig. 1) to create a stratified diffractive optic structure analogous to a volume grating with slanted fringes. This allows an element to be designed with high diffraction efficiency into the first order for any arbitrary angle of incidence, including normal incidence, which opens possibilities for very compact grating component designs.

While there are a number of other techniques for fabricating gratings with high diffraction efficiency into the first order, they are often limited by available materials or by the size of the features that must be patterned and aligned. The SVDOE approach presented here allows a very flexible choice of material system and retains feature sizes that are, in general, much larger than comparable binary approximations to a blazed grating.

2. Fabrication considerations

The application for this work is a beam deflection/scanning element for a coherent lidar system. Specifications for the element are an operating wavelength of 2.05µm, deflection angle of 32°, normally incident illumination (for a compact instrument and mechanical stability), and diffraction efficiency as high as possible. These specifications imply a grating period of 4µm, which can be accomplished easily using contact lithography. Trade-off studies using rigorous coupled wave analysis (RCWA) [2

02. M.G. Moharam, D.A. Pommet, E.B. Grann, and T.K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance marix approach” J. Opt. Soc. Am. A 12, 1077–1086, (1995). [CrossRef]

] with modifications as discussed in Ref. [1

01. D.M. Chambers and G.P. Nordin, “Stratified volume diffractive optical elements as high-efficiency gratings,” J. Opt. Soc. Am. A 16, 1184–1193, (1999). [CrossRef]

] led to a prototype SVDOE design with three grating layers having material specifications and design parameters as shown in Fig. 2. This prototype design predicts relatively high diffraction efficiency, 81.8%, and demonstrates all the principles necessary for multi-layer fabrication while maintaining individual layer parameters that are readily achievable. Diffraction efficiencies reaching into the range of 92–96% were predicted with designs using five grating layers.

Statistical evaluations of this design as a function of layer parameters were conducted to assess fabrication tolerances. The criterion for establishing tolerance was a 5% reduction in the diffraction efficiency of the element as predicted by RCWA. For both grating and homogeneous layer thickness, the tolerance for this prototype design was found to be 50nm. The offset between grating layers was required to be within 100nm.

The tolerance required for the thickness of both grating and homogeneous layers can be achieved using standard microfabrication techniques. Grating layers are be fabricated using sputter deposition, contact lithography, and reactive ion etching. Homogeneous layers are applied using a polymer material that is spin coated over the grating layers and cured on a hotplate. This approach is preferred over other methods because the material completely fills the grating grooves then forms a planar interface without the need for chemical mechanical polishing. The particular photopolymer used here, SU-8, is capable of forming very robust layers that resist damage during subsequent processing.

Fig. 2. Design parameters for a three layer prototype using measured refractive index values.

The alignment of grating layers within 100nm is the most difficult requirement to meet given that the structure will be fabricated using multiple photolithographic steps in a contact mask aligner. Typical layer-to-layer alignment tolerances that can be attained with visual photolithographic techniques are on the order of 1µm. Hence, SVDOE fabrication required development of an unconventional, high-precision alignment technique. Such a technique has been developed for this work based on diffraction through the various SVDOE layers. It is anchored with simulation and implemented through a computer-controlled, piezo-driven actuator which replaces a manual actuator in the mask-aligner.

3. High-precision layer alignment technique

Details of a high-precision alignment technique that was developed to meet the fabrication tolerance for SVDOE layer-to-layer alignment will be discussed in this section.

3.1. Description

It has been suggested that the diffraction pattern produced by the superposition of identical gratings could be used for precise alignment [3

03. Y. Torii and Y. Mizushima, “Theory of alignment monitoring by diffraction from superimposed dual gratings,” J. Opt. Soc. Am. 68, 1716–1731, (1978). [CrossRef]


05. D.C. Flanders, H.I. Smith, and S. Austin, “A new interferometric alignment technique,” Appl. Phys. Lett. 31, 426–428 (1977). [CrossRef]

]. This concept makes use of the fact that the intensity, particularly in the zero and first diffracted orders, is periodic as a function of relative displacement of the gratings along their grating vector [6

06. K. Kodate, T. Kamiya, and M Kamiyama, “Double diffraction in the Fresnel region,” Japl J. of App. Phy. 10, 1040–1045, (1971). [CrossRef]


08. S. Noda, N Yamamoto, M Imada, H Kobayashi, and Makoto Okano, “Alignment and stacking of semiconductor photonic bandgaps by wafer-fusion,” J. of Lightwave Tech. 17, 1948–1955, (1999). [CrossRef]

]. The work referenced above in this area of double diffraction has been concentrated in either obtaining maximum contrast in the diffraction pattern or in using it to enforce perfect alignment between two objects. However, double diffraction may readily be applied to the problem of interest here, namely achieving a specific alignment offset between gratings.

The diffraction pattern needed to align the grating layers in an SVDOE can be generated by using the phase grating on the substrate and the amplitude grating on the mask within the clear aperture of the grating region. A typical microfabrication alignment process uses a set of fixed alignment marks that should be “perfectly aligned” when placement is correct. For an SVDOE that implies that a separate set of alignment marks is required for each offset distance, i.e. for each design. The benefit of the approach described here is that a single photolithographic mask can be used for any SVDOE design with a specific deflection angle, e.g. any number of grating layers can be fabricated by changing the applied alignment offset.

The specific form of the pattern from double diffraction is a function of the separation distance between the gratings. A typical pattern in the zeroth diffracted order consists of major peaks and minor peaks, as illustrated in Fig. 3 for two gratings separated by 25µm as they are displaced relative to each other, or offset, from 0 to 12µm along their grating vectors. The magnitude of the peaks varies with the separation distance between the gratings; the relative position of major compared with minor peaks can even interchange. This is illustrated in Fig. 4, which is generated by the same two gratings as Fig. 3, but with a separation distance equal to 50µm rather than 25µm. Therefore, knowledge of this distance is critical for determining and applying appropriate alignment parameters.

Fig. 3. Example of double diffraction pattern in the 0th order by phase grating/amplitude grating with 4µm period. Separation is 25µm.
Fig. 4. Example of double diffraction pattern in the 0th order by phase grating/amplitude grating with 4µm period. Separation is 50µm

The key point that allows use of this double diffraction pattern for alignment is that it is periodic with relative position along the grating vector, or offset, of the gratings. In the case under discussion here, the period is always identical to that of the gratings. This characteristic permits formulation of an alignment scheme whereby that period is used to precisely position the gratings with respect to each other.

3.2. Contact mask aligner modifications

An alignment technique making use of double diffraction may be implemented by making four primary modifications to a contact mask aligner: 1) accommodation and direction of a light source to generate the diffraction pattern, 2) mounting a detector to record the pattern, 3) installing a high-precision actuator for control of relative position, and 4) establishing a computer interface to monitor and control the process.

The light source was introduced to the system via a custom substrate chuck. A channel machined within the chuck allowed the laser beam to enter parallel to the substrate and then a mirror inside the channel turned the beam by 90°. The beam exited the chuck through a window in its surface (0.25 inch diameter) and propagated upward through the substrate and mask to achieve the double diffraction effect. The turning mirror in the channel had fine adjustment capability to direct the beam through the system at an angle slightly away from normal to reduce backreflections that are known to cause laser instability [9

09. High Performance Diode Lasers, Models 56IMS001, 56IMS005 and 56IMS009 Operator’s Manual, Melles Griot.


10. Personal communication with Melles Griot.


The light source chosen was a power and temperature stabilized diode laser with a fiber optic pigtail and a collimating lens for beam delivery. A wavelength of 635nm was used for the diode laser since its proximity to the ubiquitous 632nm Helium Neon laser line implies that detector/filter components are readily available as is material property data. This wavelength is also benign to the photoresist on the substrate and can be transmitted through the components without adversely affecting the integrity of the layers. The only cause of instability in the source is backreflection into the laser system.

The detector for the diffraction pattern was placed above the mask in a mount such that its position was repeatable but that it is easily removed from the area to allow exposure of photoresist. The detector is a single element, amplified, switchable-gain, silicon device. It was positioned at a distance above the mask such that it would detect only the zeroth diffracted order. The zeroth order was used due to high contrast in its diffraction pattern.

A piezo-electric (PZT) driven actuator with 15mm of coarse, manual travel and 30µm of computer-controlled fine travel (1nm increments) replaced one of the manual actuators. Initial alignment of the gratings on the substrate and mask was performed manually, then the high-precision alignment was carried out under computer control. A PC-based system with a 16-bit analog-to-digital converter was installed to both control the PZT actuator and record the detector output.

3.3. Procedure

The procedure for creating an offset alignment has three basic steps: 1) Establishing a reference frame for the double diffraction signal; 2) Scaling the signal to one grating period within that reference frame; and 3) Controlling the PZT actuator to create the proper offset distance. Each of these will be discussed in detail below.

In order to make use of the double diffraction signal in offset alignment it is necessary to establish an accurate relative position for the peaks in the collected signal. This is accomplished by comparing signals that are generated by simulation to signals that are collected during an alignment process. Each type of signal is a function of relative offset between the gratings and is parameterized by separation distance between the substrate and the mask. Since there is a measure of uncertainty as to the absolute separation distance when using the mask aligner, the gross features in a signal and the distinctive peak position shifts with changing separation distance are compared between the two signal sets to determine and/or verify the distance. Once the separation distances associated with a set of collected signals are known, the relative position between the substrate and mask is also known based on simulation data. Thus a reference frame for the collected signals with respect to offset position is established.

Knowledge of offset position within data collected at multiple separation distances permits a specific separation distance to be determined for offset alignment. Among the considerations in determining a separation distance is the position of signal peaks with respect to the relative offset desired. A representative signal scan at the chosen distance is selected to determine the offset alignment parameters. The corresponding voltage ramp that was applied to the PZT to create the offset between gratings during collection of the signal scan is also selected. An example of a signal scan and its corresponding voltage ramp are shown in Fig. 5. One period of this signal and the corresponding segment of the voltage ramp are extracted, as illustrated in the figure. Recall that one period of the signal coincides with one period of the relative offset between the mask and substrate. The ordinate values of the extracted segments of the signal and the voltage ramp are scaled to one period of relative offset, using the known separation distance as a reference. This is shown in Fig. 6 where the signal period extracted from Fig. 5 is scaled to one period of relative offset. The corresponding simulated signal indicates that the peaks occur at an offset value of 2µm and at 4µm intervals thereafter, so the ordinate values of the selected period are scaled from 2µm to 6µm. Once the signal period and its associated voltage ramp are selected and scaled, the signal and voltage values corresponding to the desired alignment offset can be determined. For example, in Fig. 6, the desired offset value is shown as 2.5µm. The signal and voltage values, shown by the arrows, illustrate the signal that should be detected when that offset is achieved and the ending voltage ramp value that should be used to create the offset.

Fig. 5. Signal and ramp from an alignment scan. One period of the simulated signal is extracted from this curve to scale to one period of grating offset.
Fig. 6. Illustration of scaling one period of the measured alignment curve, and its corresponding ramp voltage segment, to the period of grating offset derived from simulation. Final alignment parameters are determined from this scaled curve.

The alignment parameters derived from the representative scan above, i.e., target signal and ending voltage, are then applied to create the alignment offset. First, a new voltage ramp is created which begins at the same initial value as that used in the alignment scans, but terminates at the ending value derived above. This new alignment voltage ramp is applied to the PZT while the double diffraction signal is monitored. When the terminating voltage is reached, the PZT motion ceases and the signal stabilizes as shown in Fig. 7. The detected signal is evaluated against two criteria. First, the beginning segment of the scan must match the set of alignment scans taken previously. Second, the final, stabilized signal value must agree with the target signal within a specified tolerance. The allowed tolerance is generally defined by the design parameters and the performance criteria. For the work described here the tolerance was maintained at ±0.1µm from the desired offset value. If the stabilized signal lies outside the tolerance, slight adjustments are made to the alignment ramp terminating voltage and the process is repeated until the desired tolerance is achieved. Once the stabilized signal lies within the tolerance, the substrate is brought into contact with the mask to prepare for exposure.

Fig. 7. Example signal and PZT ramp voltage measured during a scan for final alignment.

4. Fabrication of a three-layer SVDOE grating

4.1. Grating material deposition and process parameters

The grating material for this application is TiO2. It is deposited by RF sputtering at 5mTorr and 200W in a custom-built vacuum chamber, which results in a deposition rate of ~5.0nm per minute. The thickness of a film deposited with these parameters has been shown to be radially symmetric and also to decrease monotonically by approximately 5% from the center to the edge of a 3-inch glass substrate. An etch mask is created on the film by depositing 0.25µm of Chromium over Shipley 1811 photoresist that has been patterned using standard contact lithography and development techniques. The photoresist is lifted off to leave the Chrome etch mask. The TiO2 film is etched by RIE in a mixture of 20sccm CHF3 and 20sccm SF6 at a pressure of 15mTorr and a power of 175W using a Plasma-Therm 790. The etching rate is 252 Angstroms per minute.

For fabrication of gratings other than the first layer applied on the substrate there are two issues that must be addressed. The first issue is overexposure of the photoresist due to backreflections from underlying grating layers. Depositing an anti-reflective coating formulated specifically for photolithography (Brewer® XLX-20 ARC) immediately prior to the photoresist mitigates this problem. This ARC layer is removed at the same time as the photoresist. The second issue is damage to the homogeneous layer during RIE of the TiO2 grating. The etching rate of SU-8 in the CHF3/SF6 chemistry is 513 Angstroms per minute compared to the 252 Angstroms per minute etching rate for TiO2, implying that the SU-8 can be etched relatively deeply in a short period of time. Depositing a layer of silicon dioxide (SiO2) as an etch barrier between the SU-8 and the TiO2 adequately addresses this issue. Silicon dioxide is compatible with this configuration because its etching rate in CHF3/SF6 is 241 Angstroms per minute, which is approximately equal to that for TiO2, yet its refractive index is 1.526, which is very close to that of 1.576 for SU-8. Thus, SiO2 serves the purpose of slowing etching into the homogeneous layer while having minimal impact on performance of the SVDOE. Application of the subsequent SU-8 layer fills in any etching of the SiO2 layer.

4.2. Homogeneous layer deposition and process parameters

The homogeneous layers in the designs for this application must completely fill in the grooves of the binary grating layer and form a layer of specific thickness above the grating. Also, the final surface of the homogeneous layer must be planar to facilitate deposition and fabrication of subsequent grating layers. To achieve this planar surface without chemical mechanical polishing, a photopolymer material is applied over the grating and is then heat-cured to form a durable layer. The photopolymer chosen for this application is Nano XP SU-8, which is a robust polymer capable of withstanding subsequent wet chemical processes such as development and liftoff as described previously.

The SU-8 photopolymer is deposited over the grating by spin-coating and is cured through a number of bake steps on a hotplate. The formulation of SU-8 used in this project is susceptible to film stress induced during the curing process since its solvent is evaporated during these baking steps, not during spinning as is typical of most photoresist. Proper execution of the curing process should produce stress-free films. However, measurements of stress present in the films and the affect on optical performance were not conducted in this work. The thickness of an SU-8 film is affected by initial dispense volume and spin speed.

4.3. Offset alignment

Applying a known offset between successive grating layers is the most challenging fabrication step associated with SVDOE’s and was discussed in detail in Section 3.3. For the elements fabricated here, the double diffraction signal is measured while the substrate is translated approximately 15µm, which is greater than three grating periods, using the computer-controlled PZT actuator. A set of scans conducted at four to eight distinct separations has proven sufficient to calibrate separation distance.

After separation distance has been calibrated, a specific distance is chosen to use for the alignment process. A general rule for making this determination is to select the smallest separation distance that allows free movement between the substrate and the mask. Scans taken at a very small separation distance, e.g. 0–25µm, exhibit friction between the mask and substrate which is evident by a measured signal that is either constant or varying much more slowly than expected during the first 4–5µm of the scan. Once the static friction is overcome by the force on the PZT, the signal varies as expected for the remainder of the scan. A scan that is taken with friction between the components poses the possibility of alignment error being introduced during the scan, particularly rotation error. A scan at a very large separation distance, e.g. >100µm, poses a risk of alignment error being introduced during vertical translation to bring the mask and substrate into contact for exposure. Typical separation distances that are free from friction while being acceptably small are 37.5µm and 50µm.

A potential artifact resulting from offset alignment performed using a single sampling point as discussed here is relative rotation of the grating layers. The diffraction efficiency of the SVDOE is degraded when this occurs. An approach to mitigating rotation between grating layers is to use two or more sampling points strategically placed around the SVDOE region. Alignment could then be achieved by the same procedures discussed above with signals collected simultaneously from all sampling points.

4.4. Example SVDOE grating

The structure of a fabricated three-layer prototype is shown in the SEM micrograph in Fig. 8, where all grating and homogeneous layers are readily visible. The glass substrate is seen across the bottom of the micrograph with the first TiO2 grating on top of it. The grating is followed by a homogeneous layer that has filled in the grating grooves and by an SiO2 etch barrier layer. The second TiO2 grating, homogeneous layer, and etch barrier layer follows. Finally, the third TiO2 grating layer and its cover layer of SU-8 can be seen. A dicing saw was not available, so the sample shown in the micrograph was cleaved. Imperfections in the imaged surface are considered a result of the cleaving since micrographs of other samples show randomly oriented imperfections in all layers of the grating, including the substrate. Note the relative offsets of the grating layers. The structural parameters measured from the micrograph for this SVDOE and their corresponding design values are given in Table 1. The layers are numbered in increasing order beginning with the layers closest to the substrate.

Fig. 8. SEM micrograph of example fabricated three-layer SVDOE

The data in Table 1 indicate very promising results for fabrication of SVDOE gratings, although there is some room for improvement in layer thicknesses. For this work primary emphasis was placed on attaining grating offset alignment, at some expense to achieving exact layer thicknesses. The difference between design and measured values for the homogeneous layer thicknesses in particular were significantly greater than the desired tolerance of 50nm. In each case the achieved thickness was greater than the design value, implying that steps could be taken in the deposition of the layers, e.g., reducing dispensed volume or increasing spin speed, to bring the thickness closer to the tolerance. The grating layer thicknesses were much closer to tolerance than the homogeneous layers, remaining within 100nm of design values. In this case the achieved thicknesses were consistently less than desired, meaning that corrections could be made in the deposition process. For the most challenging fabrication step, offsets between grating layers, the achieved values were easily within the 100nm tolerance. This is the critical component of SVDOE’s and the measured data given here indicates that it can be successfully implemented.

Table 1. Structural parameters for fabricated three-layer SVDOE

View This Table

5. Performance of the three-layer SVDOE grating

The SVDOE shown in Fig. 8 was optically tested at the operational wavelength 2.05µm to determine its angular sensitivity. The measured structural parameters given in Table 1 were input to RCWA to generate simulated performance for comparison. Fig. 9 shows both the simulated and measured angular sensitivity for this SVDOE using TM polarization. The measured values compare very well with the simulated values both in magnitude and in form. The measured peak diffraction efficiency is also greater than 80%, which is almost identical to the design value of 81.8%. This is a positive confirmation that the performance of an SVDOE structure can be adequately simulated and that fabrication of such a device is possible.

These initial graphs assume a collimated input beam and vertical sidewalls for all gratings. Studies of removing these assumptions were performed which showed insignificant change in the overall behavior of the angular sensitivity.

The rapid fluctuations present in the simulated curves of Fig. 9 are a valid representation of the SVDOE behavior rather than a computational artifact. In the discussion of SVDOE diffraction properties in Ref. [1

01. D.M. Chambers and G.P. Nordin, “Stratified volume diffractive optical elements as high-efficiency gratings,” J. Opt. Soc. Am. A 16, 1184–1193, (1999). [CrossRef]

] there is an illustration of the sensitivity of diffraction efficiency as a function of both grating strength and homogeneous layer thickness. For both cases the diffraction efficiency began to exhibit fluctuations that became more severe as the refractive index difference between grating ridges and grooves was increased from 0.1 to 0.5. This is caused by Fresnel reflections between the grating layers that increased in magnitude with the increase in refractive index difference. For the three-layer SVDOE examined here the actual refractive index difference is ~0.71 indicating that the fluctuations in the simulated curves are to be expected.

Fig. 9. Diffraction efficiency (+1 Order) as a function of incidence angle for a fabricated three-layer SVDOE

The fluctuations are minimized in the measured data because it is taken with a laser beam, which has an inherent divergence angle, rather than the collimated beam assumed in the simulations. The divergence angle in the beam implies that the measured data is averaged over the angular region, which effectively averages over the Fresnel reflections as well. The measured data indicates, as has been discussed previously, that the diffraction efficiency is highly sensitive to Fresnel reflections between grating layers and that averaging over the beam divergence with different angles and, hence, reflections smoothes the system response.

6. Summary

We have designed and successfully fabricated a high efficiency grating using a three-layer SVDOE. This type of element is well suited to applications where more traditional grating methods cannot be employed due to limitations of either material choice or feature size. An SVDOE presents unique fabrication challenges, most notably aligning the offset of adjacent grating layers to achieve the desired incidence angle. We have developed an approach to create the grating layer offsets and have demonstrated that it can be successfully implemented. The offset alignment technique has been combined with a method for creating and planarizing homogeneous layers to fabricate an SVDOE designed for a specific application. Optical testing of the diffraction efficiency of this SVDOE confirmed that it performs very closely to its designed performance and, consequently, illustrates the viability of using SVDOE’s as high efficiency gratings.


This work was supported by NASA/Marshall Space Flight Center and National Science Foundation CAREER award ECS-9625040.

References and links


D.M. Chambers and G.P. Nordin, “Stratified volume diffractive optical elements as high-efficiency gratings,” J. Opt. Soc. Am. A 16, 1184–1193, (1999). [CrossRef]


M.G. Moharam, D.A. Pommet, E.B. Grann, and T.K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance marix approach” J. Opt. Soc. Am. A 12, 1077–1086, (1995). [CrossRef]


Y. Torii and Y. Mizushima, “Theory of alignment monitoring by diffraction from superimposed dual gratings,” J. Opt. Soc. Am. 68, 1716–1731, (1978). [CrossRef]


Y. Torii and Y Mizushima, “Optical ultramicrometer technique utilizing a composite diffraction grating,” Opt. Commun. 23, 135–138 (1977). [CrossRef]


D.C. Flanders, H.I. Smith, and S. Austin, “A new interferometric alignment technique,” Appl. Phys. Lett. 31, 426–428 (1977). [CrossRef]


K. Kodate, T. Kamiya, and M Kamiyama, “Double diffraction in the Fresnel region,” Japl J. of App. Phy. 10, 1040–1045, (1971). [CrossRef]


K. Kodate, T. Kamiya, H. Takenaka, and H. Yanai, “Double diffraction of phase gratings in the Fresnel region,” Jap. J. of App. Phy. 14, 1323–1334, (1975). [CrossRef]


S. Noda, N Yamamoto, M Imada, H Kobayashi, and Makoto Okano, “Alignment and stacking of semiconductor photonic bandgaps by wafer-fusion,” J. of Lightwave Tech. 17, 1948–1955, (1999). [CrossRef]


High Performance Diode Lasers, Models 56IMS001, 56IMS005 and 56IMS009 Operator’s Manual, Melles Griot.


Personal communication with Melles Griot.

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(050.7330) Diffraction and gratings : Volume gratings
(220.3740) Optical design and fabrication : Lithography
(220.4000) Optical design and fabrication : Microstructure fabrication

ToC Category:
Research Papers

Original Manuscript: November 14, 2002
Revised Manuscript: January 6, 2003
Published: January 13, 2003

Diana Chambers, Gregory Nordin, and Seunghyun Kim, "Fabrication and analysis of a three-layer stratified volume diffractive optical element high-efficiency grating," Opt. Express 11, 27-38 (2003)

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  1. D.M. Chambers and G.P. Nordin, �??Stratified volume diffractive optical elements as high-efficiency gratings,�?? J. Opt. Soc. Am. A 16, 1184-1193, (1999). [CrossRef]
  2. M.G. Moharam, D.A. Pommet, E.B. Grann, and T.K. Gaylord, �??Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance marix approach,�?? J. Opt. Soc. Am. A 12, 1077-1086, (1995). [CrossRef]
  3. Y. Torii and Y. Mizushima, �??Theory of alignment monitoring by diffraction from superimposed dual gratings,�?? J. Opt. Soc. Am. 68, 1716-1731, (1978). [CrossRef]
  4. Y. Torii and Y Mizushima, �??Optical ultramicrometer technique utilizing a composite diffraction grating,�?? Opt. Commun. 23, 135-138 (1977). [CrossRef]
  5. D.C. Flanders, H.I. Smith, and S. Austin, �??A new interferometric alignment technique,�?? Appl. Phys. Lett. 31, 426-428 (1977). [CrossRef]
  6. K. Kodate, T. Kamiya, and M Kamiyama, �??Double diffraction in the Fresnel region,�?? Japl J. of App. Phy. 10, 1040-1045, (1971). [CrossRef]
  7. K. Kodate, T. Kamiya, H. Takenaka, and H., Yanai, �??Double diffraction of phase gratings in the Fresnel region,�?? Jap. J. of App. Phy. 14, 1323-1334, (1975). [CrossRef]
  8. S. Noda, N Yamamoto, M Imada, H Kobayashi, and Makoto Okano, �??Alignment and stacking of semiconductor photonic bandgaps by wafer-fusion,�?? J. Lightwave Tech. 17, 1948-1955, (1999). [CrossRef]
  9. High Performance Diode Lasers, Models 56IMS001, 56IMS005 and 56IMS009 Operator�??s Manual, Melles Griot.
  10. Personal communication with Melles Griot.

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