Diffractive optical elements (DOEs) are lightweightoptical components with a large range of applica-tions. These include laser beam shaping [1], intra-cavity diffractive mode selection [2], optical inter-connection [3], wavelength separation [4], anddisplays [5].It is advantageous for some applications of DOEs,
notably security, to be able to produce different out-put patterns in different circumstances, makingcounterfeiting more difficult and costly. There hasbeen a considerable amount of work on the designof pattern formation DOEs that produce differentimages at different wavelengths [6–9]. DOEs havealso been designed where the output from theDOE is changed by the polarization of the incidentlight [10–12], by the angle of incidence [13], or bythe output plane where the image is viewed [14].One parameter that has not, to our knowledge, been
exploited for such pattern formation DOEs is themode of operation of the element, i.e., whether itworks in reflection or transmission.
The early computer generated holograms werebinary transmission elements [15]. The introductionof the kinoform by Lesem et al. [16] allowed reflectiondevices to be developed [17]. It is clear, therefore,that for many years it has been understood thatDOEs can be made to operate as either reflectionor transmission devices. This has been exploited toallow applications where one or other approach isfavorable. Transmission devices generally alloweasier viewing and are more suited to some displayapplications, such as stereograms [18]. In appli-cations where the DOE is coated in a protectivematerial with a similar refractive index to the sub-strate, such as security devices, reflection devicesare used because the diffractive structure becomesinvisible to transmitted light. The objective of thiswork is to devise a method for designing singleelements that will produce different output patternsin reflection and transmission from the same diffrac-tive surface. These devices will be referred to asreflection–transmission DOEs.
We recently introduced the concept of using a DOEto replace the output coupler in a laser cavity tosimultaneously optimize the fundamental modeand shape the output beam [19]. Here we extend thisidea to pattern formation elements and demonstratetheir successful operation experimentally.Figure 1 illustrates how an RT DOE operates. A
portion of the incident light is reflected from the dif-fractive structure to form one far-field image and theremaining light is transmitted and forms a second,different, far-field image.As indicated in the diagram, the phase delay, ϕ, is
different for the two modes of operation. It is thisproperty that gives the required degree of freedom.When operating in transmission mode the phase de-lay for a pixel is given by
ϕT ¼ 2π½nðλÞ − 1�h=λ; ð1Þ
where nðλÞ is the wavelength dependent refractiveindex of the substrate, h is the etch depth, and λ isthe wavelength. Similarly, the phase delay givenby the same pixel in reflection mode is
ϕR ¼ 4πh=λ: ð2Þ
In both cases it is assumed that the surroundingmaterial is air.
2. Design Algorithm
The two color algorithm we have previously de-scribed [20] uses a different phase delay producedby separate wavelengths to generate different outputpatterns. In this paper we alter the algorithm to ex-ploit the dependence of the phase delay on the modeof operation.The first step is to generate the unquantized phase
profiles, ϕT and ϕR. These are optimized indepen-dently to generate each of the desired outputs. Weuse the Gerchberg–Saxton algorithm [21] followedby the modified iterative Fourier transform algo-rithm [22] to achieve this.
The two color algorithm used the term α, defined asthe ratio of the phase delays at the two wavelengths.Based on Eqs. (1) and (2), α is replaced by
αRT ¼ 2=ðn − 1Þ ð3Þfor single wavelength RT DOEs. This assumes thatthe first pattern is for transmission and the secondis for reflection. Strictly speaking there is a π-phaseshift in reflection if the refractive index is greater inthe transmitting medium than in the incidentmedium [23]; however, bulk phase shifts have noeffect on the output intensity pattern so this canbe ignored.
Having defined αRT the quantization process canbe carried out. To do this, values of h that causephase delays greater than 2π are considered. Themaximum value of h and the number of quantizationlevels are specified. These choices are limited by fab-rication issues. Taghizadeh et al. [24] give a generaldiscussion of these issues.
Figure 2 illustrates how the quantization is carriedout. Dividing the maximum depth into the number oflevels gives the available values of h, represented bythe numbers 1–8 in the figure. The quantization iscarried out on each pixel independently. The depthshT and hR required to give ΦT and ΦR, respectively,can be calculated by rearranging Eqs. (1) and (2). Ifwe define h0
T as the etch depth equivalent to a 2π-phase delay in transmission and h0
R as the etch depthequivalent to a 2π-phase delay in reflection, thenadding h0
T to hT and h0R to hR give alternative etch
depths, which produce the same effective phase de-lay. As shown in Fig. 2, multiples of h0
T and h0R can
be added until the total etch depth reaches the max-imum depth limit specified.
It is highly unlikely there is an exact solution thatfits for both ΦT and ΦR. Therefore we must compro-mise between the requirements for each wavelength;we have done this based on the quantization error.The error for a given level and mode of operation,M, is defined as
δL;M ¼ jϕeffL;M −ΦM j; ð4Þ
Fig. 1. (Color online) Illustration of the operation of a simulta-neous reflection and transmission device. Fig. 2. Illustration of the quantization process.
where ϕeffL;M is the effective phase for that level. The
phase is determined by using Eq. (1), for transmis-sion, and multiplication by αRT to give the phasein reflection. Removing multiples of 2π gives the ef-fective phase. The quantization error for a given levelis then considered to be the maximum of δL;Transmissionand δL;Reflection. For each pixel, the level that mini-mizes this value is selected. This level may not bethe optimum for either transmission or reflection in-dividually, but is the best fit when both transmissionand reflection are considered.Three quality measures can be used to assess the
operation of our element, mean square error (MSE),given by
MSE ¼ 1M
PP
�FðX;YÞ
�F−
GðX;YÞ�G
�2; ð5Þ
where M is the number of desired “on” orders, P isthe set of desired “on” diffraction orders, FðX ;YÞ isthe resulting intensity of the diffraction order in po-sition ðX ;YÞ, �F is the average intensity in the desired“on” orders, GðX ;YÞ is the desired intensity for thediffraction order at ðX;YÞ, and G is the average de-sired intensity in the “on” orders of the desired out-put pattern.Efficiency, η, is given by
η ¼P
P FðX ;YÞAP
E gðx; yÞ: ð6Þ
E is the set of all pixels in the element, and gðx; yÞ isthe input intensity at the pixel located at ðx; yÞ. A isthe proportion of light that is transmitted or re-flected, depending on the pattern being charac-terized.Cross-talk for a given mode of operation is a mea-
sure of the degree to which the pattern for the alter-native mode of operation appears. This parameter isdefined as
cross-talk ¼P
S FðX;YÞPE gðx; yÞ
; ð7Þ
where S is the set of desired diffraction orders for theother mode of operation minus any orders common toboth patterns.
3. Modeled Results
The design algorithm described in Section 2 has beenused to optimize a joint reflection transmission pro-file that generates the word “FRONT” when operat-ing in reflection mode and the word “BACK” intransmission mode. The input graphic images usedin the design process are shown in Fig. 3.
A design window of 128 × 128 pixels was chosenwith the images at the center of the design window.Upon completion of the first stage, the unquantizedprofile ΦT generates the BACK output with an effi-ciency of 80.7% and an MSE of 0.01%, while the pro-file ΦR generates the FRONT output with anefficiency of 80.4% and an MSE of 0.07%.
Finally the algorithm described above was used togenerate the quantized profiles. A maximum phasedepth of 2π in transmission mode was chosen alongwith 16 quantization levels. The chosen values forthe maximum phase are significantly smaller thanthose typically chosen for dual wavelength elements.The modeled outputs for operation in transmissionand reflection modes with illumination by a 633nmlight source and the use of a fused silica substrate areshown in Fig. 4.
For the RT DOE described here the efficiency,MSE, and cross-talk values are 65.9, 2.52, and 4.2%,respectively, for the BACK pattern and 66.6, 2.50,and 3.5%, respectively, for the FRONT pattern.
The modeled outputs show excellent agreementwith the desired images in Fig. 3. In particular thereis little sign of the problem of cross-talk often pre-valent in two color designs. The drop in efficiency be-tween the unquantized, independent profiles and thequantized RTDOE profile is also low compared to thevisible spectra of two color designs. Although there isa marked increase in nonuniformity, this is to be ex-pected when going from an unquantized to a quan-tized profile.
In our experience working with dual wavelengthelements, the performance of a particular elementcan be significantly influenced by the patterns cho-sen. In contrast, the RT DOEs seem to show very lit-tle pattern dependence. However it should be notedthat since this is a new type of device, we have onlylimited experience to base this comment on.
When comparing these results with previous ob-servations made for two color elements [25] it may,at first, seem unrealistic to have such a high qualityoutput when using only a 2 π maximum phase. The
Fig. 3. Input designs used for desired output intensity profiles. (a) has dimensions of 80 × 30 pixels, (b) 63 × 27 pixels.
explanation for this is simple, in the two color design,the shorter wavelength was defined as the primaryand, therefore, α < 1. In this case the transmissionmode is defined as primary; thus, for fused silica,Eq. (3) gives α ¼ 4:38. Had the reflection mode beenspecified as primary we would have a maximumphase of 8:76 π. Furthermore the large value of α isequivalent to a large wavelength separation; it haspreviously been shown [26] that this can lead to im-proved results. This is likely to be the reason for thelack of pattern dependence we see in RT DOEs, asmulticolor DOEs are often confined to the visualspectrum.
4. Experimental Results
A. Fabrication
In general, the fabrication is carried out using themultimask reactive ion etching technique describedby Taghizadeh et al. [24]. The only alteration made isthat a thin layer of aluminum is laid down as thefinal stage of fabrication. In standard reflection de-vices this is done to produce a fully reflective surface.However for the devices being consider an approxi-mately 50=50 ratio of transmittance to reflectanceis desirable. To achieve this, the layer of aluminumused is in the region of 20nm thick. Typically a100120nm thick layer is used for fully reflective de-
vices. The FRONT/BACK element has been fabri-cated with a 2 μm pixel size.
B. Experimental results
The experimental setup used for measuring the effi-ciency and capturing the output images from the dif-fractive optical elements is shown in Fig. 5. Figure 6shows the images captured for the fabricated ele-ment. The images have been captured using a CCDcamera in the setup shown in Fig. 5. As predicted bythe modeling, there is no evidence of cross-talk inthese images and they both exhibit satisfactoryvisual image quality. The only evident flaw in the im-age is some unwanted zeroth order energy in the re-flection case shown in 6(a), which does not appear inFig. 4(a). There are two possible explanations forthis, first the reflection images are viewed at anangle from the normal (∼10°). Turenen et al. [13]demonstrated how illuminating a DOE at an anglealtered the phase profile. An incident angle of 10° re-sults in a 2% change in the phase profile. As this non-normal incidence has not been accounted for in thedesign or fabrication, the etch depths will be thosefor the design wavelength at normal incidence.The impact of nonnormal incidence is thereforeequivalent to etch depth error on all the levels. Forthe element considered here a 2% error is equivalentto a 14nm misetch in the deepest etch. As shown byZeitner et al. [27], etch depth errors tend to result inunwanted zeroth order energy. Second, because thesurface is only partly reflective, secondary reflectionsfrom the back of the surface of the substrate may wellcontribute to this effect.
Typically, fabrication errors may also producezeroth order noise, but the lack of such an effect inthe transmission case suggests that this is not theprimary cause. As already stated the fabrication pro-cess is essentially the same as for standard singleoutput DOEs; we, therefore, expect the fabricationerrors to be similar to those quoted for such ele-ments, which is typically an etch depth accuracy of�5nm and an alignment accuracy of 0:51 μm.[28].This etch depth error is less than that attributedto nonnormal incidence.
Fig. 4. (Color online) Modeled outputs of the quantized profile op-erating in (a) reflection and (b) transmission modes.
He-Ne laser
Fig. 5. (Color online) Experimental setup for measuring efficiency and capturing output images.
Experimental measurements of efficiency havebeen made using the setup shown in Fig. 5, replacingthe CCD camera with a lightmeter and an aperture.The aperture is used to restrict the light incident onthe meter to the signal window. The efficiency is cal-culated by dividing the intensity measured whenproducing the pattern by the intensity of the spotproduced when passing the laser through an un-etched region of the substrate with the coating ap-plied. This gives a value of 58:3%� 2 in reflectionand 68:8%� 5 in transmission. This method of mea-suring the efficiency is limited because orders thatshould be “off” but are within the signal windoware included; any variability in the thickness ofthe aluminum layer is not accounted for, and to makemeasurements in reflection, a slight angle is re-quired, which will affect element performance. De-spite this we see good agreement with theory withthe transmission and the reflection results a few per-cent below and above the expected values, respec-tively.One of the potential applications of this new type of
diffractive element is in anticounterfeiting. The sur-face relief structure of DOEs make them more diffi-cult to copy than traditional amplitude holograms.Any added complexity, for example by adding multi-plexed patterns, makes counterfeiting even more dif-ficult. With this type of application in mind it is moredesirable to use eye safe sources, such as LEDs,rather than the He–Ne laser used to produce the out-puts shown in Fig. 6. The outputs generated by the
element when illuminated by the red LEDwithin theOsram multi-LED LRTB G6TG are shown in Fig. 7.The peak intensity of this LED source is ∼636nm.The visual quality of the images is again of a satis-factory standard; there is some blurring of the imageand a greater zeroth order energy than in the laserilluminated case, but this can be attributed to thenonpoint source nature of the LED source and theincreased bandwidth of the incident light. The latterpoint leads both to zeroth order energy because theetch depths are not optimized for the wavelengthsaway from 633nm and to reduced clarity of the imagecaused by dispersion. Despite these issues LED illu-mination clearly produces recognizable images, mak-ing this technology a suitable consideration for theapplication described.
5. Conclusion
We have introduced a DOE configuration that, to ourknowledge, has not been previously shown. This de-vice allows one output pattern to be formed when op-erating in transmission mode and a second, differentpattern to be formed when operating in reflectionmode. An algorithm, based on an existing dual wave-length DOE algorithm, for designing such elementshas been demonstrated and shown to give goodimage quality, especially in relation to cross-talk, awell known problem for dual wavelength elements.Modeled output from the designed elements showsefficiencies of over 60%. These results are well sup-ported by experimental readings from a fabricated
Fig. 6. (Color online) Output images from the fabricated element. The reflection case is shown in (a) and the transmission case in (b).
Fig. 7. (Color online) Output images from the fabricated element when illuminated by an LED source. The reflection case is shown in (a)and the transmission case in (b).
device. Furthermore experimental results usingLED illumination suggest such devices may be suita-ble in eye safe anticounterfeiting applications.
We acknowledge ESPRC studentship and BasicTechnology Grant no. GR/S85764. Partial supportof Network of Excellence on Micro-Optics is also ac-knowledged. The work described in this paper is cov-ered by patent application GB0700565.5.
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