Stabilization system for holographic recording ofvolume Bragg gratings using a corner

cube retroreflector

Daniel B. Ott,* Ivan B. Divliansky, Marc A. SeGall, and Leonid B. GlebovCREOL, College of Optics and Photonics, 4000 Central Florida Blvd., Orlando, Florida 32816, USA

*Corresponding author: dott@creol.ucf.edu

Received 29 October 2013; revised 14 January 2014; accepted 15 January 2014;posted 16 January 2014 (Doc. ID 200320); published 12 February 2014

Volume Bragg gratings serve an important role in laser development as devices that are able tomanipulate both the wavelength and angular spectrum of light. A commonmethod for producing gratingsis holographic recording of a two collimated beam interference pattern in a photosensitive material. Thisprocess requires stability of the recording system at a level of a fraction of the recording wavelength. Anew method for measuring and stabilizing the phase of the recording beams is presented that isextremely flexible and simple to integrate into an existing holographic recording setup and independentof the type of recording media. It is shown that the presented method increases visibility of an interfer-ence pattern and for photo-thermo-refractive glass enables enhancement of the spatial refractive indexmodulation. The use of this technique allows for longer recording times that can lead to the use of ex-panded recording beams for large aperture gratings. © 2014 Optical Society of AmericaOCIS codes: (120.5050) Phase measurement; (120.7280) Vibration analysis; (090.7330) Volume

gratings; (050.1950) Diffraction gratings; (120.3180) Interferometry; (090.0090) Holography.http://dx.doi.org/10.1364/AO.53.001039

1. Introduction

Volume Bragg gratings (VBGs) are a widely usedoptical component for applications such as spectraland angular shaping, communications, and sensingdue to their ability to diffract into a single order withhigh efficiency when the Bragg condition is met.VBGs are created by producing a spatially varyingsinusoidal pattern of the refractive index inside aphotosensitive medium and are typically producedusing holographic exposure, lithography, phasemasks, or point by point inscription [1–3]. Thesemethods apply most readily to VBGs written into op-tical fibers. For VBGs in a bulk medium with aper-tures exceeding several millimeters, holographicrecording of a two-beam interference pattern (Fig. 1)is the most suitable approach. This method can be

used to create both reflecting and transmitting VBGsof different spatial frequencies by adjusting the re-cording angle of interference. To achieve high-qualityvolume gratings with high efficiency and periods aslow as 200 nm, it is necessary to be able to generatean interference pattern with high-fringe visibilityand a uniform period throughout the volume of themedium together. These conditions provide a con-stant resonance condition combined with high-contrast refractive index modulation (RIM). As anexample, for gratings being designed as output cou-plers for laser systems, it is usually necessary toachieve very specific spectral widths and angular se-lectivity in addition to precise diffraction efficiency,making it critical to have exact control over theRIM [4]. The primary detriment to obtaining consis-tent fringe visibility, and therefore high-qualityVBGs, is shifting of the interference fringes duringthe recording process. Such fringe movement couldbe due to vibrations of beam delivery optics or the

1559-128X/14/061039-08$15.00/0© 2014 Optical Society of America

20 February 2014 / Vol. 53, No. 6 / APPLIED OPTICS 1039

sample, as well as localized changes in therelative density of air along the paths of the record-ing beams.

By measuring and controlling the relative phasesin the recording beams, high-visibility fringes can bemaintained throughout the recording. The resultingVBG will have a consistent index modulation withefficient use of the material’s dynamic range. To con-trol the phase of the interference pattern, a numberof different methods have been proposed [5–10]. Oneof the most elegant and direct solutions is the use ofthe dynamically formed grating to diffract a portionof each recording beam into the other recording beamgenerating an interference pattern [7]. This processof dynamic wave-mixing allows for direct monitoringof the relative shift of the interference pattern andthe current grating structure. The drawbacks of thismethod relate to the restrictions that it places on therecording media. Using the dynamic grating forma-tion requires that the recording medium has low ab-sorption at the recording wavelength and that it doesnot introduce significant distortions into the beams.Most importantly, the material must also form aweak grating during the recording process. Thismay not always be the case when a latent image isformed and further development is necessary, orwhen the parameters of the recording substrate aresuch that a useful diffraction efficiency cannot beachieved. So, while the use of dynamic wave-mixingis applicable to some holographic recording setups, itlacks the flexibility necessary for recording gratingsin a variety of materials. The use of an auxiliaryreference grating to wave-mix the recording beamscan also generate an appropriate feedback signal.This can be achieved by placing a reflection or trans-mission grating next to or behind the recordingmedium [6,7,10]. A portion of the recording beamsis diffracted by the reference grating and is usedfor phase stabilization. The rest of the recordingbeam is used to expose the photosensitive materialto create the desired grating. Such systems removeany restrictions caused by the properties of the re-cording media. However, they also present a majorlimitation in that a reference diffractive elementcan only be used for a particular angle of incidenceat the recording wavelength. This limits the utilityof such stabilization systems to a particular record-ing angle corresponding to the resonance condition ofthe diffractive element thus being useful for creatingonly a specific grating period. To record a grating of adifferent spatial period requires a new reference gra-ting to be fabricated or purchased. Therefore, requir-ing a reference grating would nearly double the timerequirement for producing a particular grating whenreference gratings cannot be reused. The ability touse the same phase control system for any gratingperiod is a critical requirement for any universalrecording system for fabrication of gratings with dif-ferent parameters. To address the need for a versa-tile phase stabilization system, we propose a new,flexible phase measurement technique that can be

applied to most common holographic recording set-ups. In our approach, the reference grating is substi-tuted with a corner cube retroreflector and thefeedback signal is monitored at a different location.These improvements yield a new interferometer thatis both independent of the recording medium andable to be used to control the relative phase of a two-beam interference pattern with any spatial period.The system that we propose results in an effective,versatile, and simple to align system for measuringand controlling the relative phase in a holographicrecording.

2. Tolerances for Phase Stabilization

Before describing the method for stabilizing interfer-ence fringes, it is important to determine the effect ofan uncontrolled fringe pattern. When using two-beam interference to record a grating (Fig. 1), theresulting spatial RIM of the grating is directly pro-portional to the two-beam interference intensity pat-tern when operating within the linear region of thematerial photosensitivity curve [11]. This interfer-ence pattern is given by Eq. (1)

I�x� � I1 � I2 � 2���������I1I2

pcos�2kx sin θ� φ�; (1)

where I1 and I2 represent the irradiance of each re-cording beam, and the resulting index modulationprofile is proportional to the cosine with a period de-termined by the wave vector (k) of the recordingbeam and the angle of interference θ. The term φis the relative shift in phase between the two record-ing beams. Modification of any of the arguments inthe cosine of Eq. (1) will result in a shifting fringepattern. For the current analysis, the wave vectorof the recording laser is held constant and the angleof interference is assumed stable at the arc secondlevel such that no significant change in period occurs.In our setup, this stability has been confirmedexperimentally by measuring the angle stability of

Fig. 1. General recording and readout for a VBG. Rays markedpurple indicate the recording beams that generate the interferencepattern at a wavelength within the photosensitivity spectrum ofthe medium. After recording and development, the grating canbe used as a transmitting grating for beams at a different wave-length marked as green or at yet another wavelength the gratingcan be used as a reflecting grating for beams indicated by red.

1040 APPLIED OPTICS / Vol. 53, No. 6 / 20 February 2014

the recording mirrors by forming a Sagnacinterferometer and monitoring the shifts of fringes.Practically speaking, this level of stability in angleis not difficult to achieve with commercially availableoptical mounts and a vibration-isolated table. Themost significant effect on the interference patterncomes from changes in φ, primarily due to vibrationsin the recording setup and air fluctuations. This re-sults in a shifting of the relative phases between therecording beams as a function of time. The recordedinterference pattern in this case is given by Eq. (2)

Ifinal�x� � I1 � I2

�Z

T

02

���������I1I2

pcos�2kx sin θ� φ�t��dt: (2)

The effect of randomly varying phase differenceabout a mean value can also be calculated to deter-mine a tolerance to phase noise allowable in a record-ing system. For this calculation, we assume arandomly varying phase difference described by aGaussian probability density function that will allowthe effect on the fringe pattern to be described by asingle parameter relating to the variance of thephase fluctuations. The probability density functionfor a randomly distributed phase variation is shownin Eq. (3)

W�φ� � 1������2π

pσe

�−φ2

2σ2

�; (3)

where σ is the root mean square error (RMSE) aboutthe average phase value. The interference patterncan then be described by the integral in Eq. (4)

Ifinal�x��I1�I2

�Z

∞

−∞W�φ� ·2

���������I1I2

pcos�2kx sin θ�φ�dφ: (4)

The fringe visibility of the resulting interferencepattern (V) is the metric that will be used to deter-mine the quality of the recorded grating. This valueis a normalized indicator for the amount of the maxi-mum possible index change that can be achieved

V � Imax − Imin

Imax � Imin: (5)

Equation (4) was integrated numerically for anumber of σ values to determine the effect of fringeshift on the visibility. The results of fringe visibilitydeterioration are shown in Fig. 2 as a function ofphase variations σ measured in units of fractionsof the recording wavelength. The value of σ in radi-ans can be determined from the x axis value bymulti-plying by 2π. As the amplitude of the phasevariations increases, the fringe visibility starts to de-crease, resulting in a weakened RIM. For high valuesof σ beyond 0.5 waves, the fringe pattern will beeffectively washed out because the phase during

recording with cover a full 2π range. Therefore,practical systems for holographic recording are mostlikely operating in the range shown in Fig. 2. The in-set in Fig. 2 shows the region of minimal phasefluctuations in that we plan to operate usingphase stabilization. In this region, the decrease ofvisibility is relatively slow. A tolerance of fluctuationamplitude less than 5% of a recording wavelengthwill guarantee fringe visibility >95% of the optimumvalue.

3. Setup and Characterization

The phase stabilization techniques described in priorart all rely on a feedback loop consisting of a phasemeasurement method, a phase shifting device, andsome signal processing. The main emphasis in thecurrent work is on the development of a sensitiveand robust method for measuring phase fluctuations.The phase shifting device is most commonly a piezo-electric transducer (PZT) placed on a turning mirrorthat allows small shifts in path length to beintroduced into one of the recording arms. A PZTis used in this system, but any phase shifting devicewith an appropriate response time is equally wellsuited. The performance of any stabilization systemcan be significantly improved by using appropriatesignal processing, and there is a wealth of informa-tion regarding various methods for processing thefeedback signal. These methods have not been imple-mented in the current system and are amatter of fur-ther improving the system that is presented here.This can lead to better frequency response and insen-sitivity to changes in incident power levels but, as wewill demonstrate, are not critical for the effective sta-bilization of our recording setup. The phase measure-ment technique has the greatest consequences interms of the recording setup and will be the focusof the technique that we demonstrate in this paper.

The entire recording setup is shown in Fig. 3.At the recording plane, a small portion of the record-ing beam is used to measure the relative phases

Fig. 2. Dependence of interference pattern visibility on phasefluctuations during recording. Phase variation σ is shown as a frac-tion of the recording wavelength. Inset shows fringe visibility forsmall phase fluctuations.

20 February 2014 / Vol. 53, No. 6 / APPLIED OPTICS 1041

of the beams while the rest is used to expose thephotosensitive material. The portion of the beamused for phase measurement will be called the probebeam. The phasemeasurement is achieved through acorner cube retroreflector that is placed above thesample. The probe and recording portions of thebeam trace along collinear paths to reach the record-ing plane and the probe beam is then reflected backalong this path to double the relative phase devia-tions that are incurred. At the detector plane, theback-reflected probe light forms an interference pat-tern and the corner cube is adjusted in position toachieve overlap of the two collinear probe beamsso that the entire probe beam diameter gives a zero-fringe interference pattern. One of the primarybenefits of this method is that the precision of thisalignment can be very coarse. The retroreflectorguarantees angular alignment and beam overlapcan be achieved without the use of precision stages.

As the relative phases of the paths change, the ir-radiance at the detector will vary as Eq. (1) withθ � 0. By using a retroreflector, the system can beeasily moved and realigned for recording gratingsof different period and arbitrary grating tilt angles.The detector signal is used as feedback and a PZT isplaced beneath one of the mirrors (M2 in Fig. 3) tocorrect for measured phase fluctuations by maintain-ing a constant detector signal. The feedback controlis extremely simple and, in systems control lan-guage, consists of only a proportional gain. Again,introducing other signal processing techniques canbe used to improve the performance of the system,but for what is demonstrated here only a simple con-trol system is necessary.

The phase difference between the recording beamscan be extracted from the measured variations in thedetector voltage. In order to determine the conver-sion factor between the detector’s voltage and theprobe beam phase difference, a calibration of the sys-tem was performed prior to any measurement ofphase. The calibration was accomplished by drivingthe PZT with a ramp function to generate a sinusoi-dal variation in the detector voltage with a periodcorresponding to a phase difference in the probebeams of 2π, as shown in Fig. 4. By fitting a sinusoidto this curve, a conversion function was calculated to

convert a detector voltage to a phase differencebetween the beams.

While the shifting of the phase of the two recordingbeams is important to the stability of the setup andhas many components that can contribute to errors,the displacement of the sample must not be ignored.The sample has six degrees of freedom, but primarilytilt about the y axis and displacement in the x axis ofFig. 1 can contribute to errors in the recording. Theerrors of tilt only affect the recording substantially inthe shift that they induce in various parts of thegrating relative to other parts. Therefore, the dis-placement in x, which will be referred to aslateral shift, is a critical motion to control and thequestion of whether or not the proposed system issensitive to these motions must be answered. Tothe best of our knowledge, no studies have beenconducted that relate to the sensitivity of a phase sta-bilization system to lateral motion. Since thismotion is as equally detrimental as phase changesthat occur in the delivery path, such a study isextremely important.

The sensitivity to lateral shift of the corner cuberetroreflector used in Fig. 3 will be compared tothe most common method of phase stabilization [8]that uses a transmission reference grating. Recently,reflection gratings have been shown to produce aphase shift under lateral displacement giving prom-ise to the idea that a phase stabilization systembased on transmission gratings is sensitive to the lat-eral shift of the recording media [12]. While counter-intuitive, a shift of a transmitting or surfacereflection grating by one period will shift the relativephase of the transmitted and diffracted orders by 2π.Therefore, there is a one-to-one correspondence be-tween the lateral shift in the measurement device(measured in number of wavelengths) and the shiftof the interference pattern that is monitored to mea-sure phase. This makes phase control systems usinga grating able to measure and correct for lateralshifts.

To show that a retroreflector is also sensitive tothese shifts, the nature of the optical path to and

Fig. 3. VBG recording setup showing the paths of the recording/probe beam. BS, beam splitter; M1 and M2, mirrors; PZT, piezo-electric transducer. The side view shows how the beam is split be-tween a recording portion and a probe portion for measuringphase.

-1.8

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0 1 2 3 4 5

Pha

se, r

adia

ns

Det

ecto

r Si

gnal

, V

Piezo Signal, V

Fig. 4. Phase shift between recording beams measured by thedetector in Fig. 3 as a function of voltage applied to the PZT thatcauses a position change of the recording mirror, M2. The red lineshows a sinusoidal fit to the experimental data in blue dots.

1042 APPLIED OPTICS / Vol. 53, No. 6 / 20 February 2014

from the retroreflector must be considered. Theoptical path encountered by a ray that has traveledfrom a particular phase plane, reflected off of anypart of the retroreflector and back to that plane, isequal to twice the distance from the initial phaseplane to the optical center of the corner cube [13].Therefore, it is possible to model optical path lengthin an interferometer by geometrically drawing a linefrom a reference point in the beam path to the opticalcenter of the corner cube. Since this system dealswith measuring relative lateral shifts, the locationof this optical center is not important and can be con-sidered to be located at the corner cube vertex [14].With this understanding, it is intuitive from Fig. 5that a shift of δ will cause a relative phase shift be-tween two incident beams. This is because the opticalpath for one beam will shorten, while the other willlengthen. Mathematically this takes the form

OPD � 2n0

� ������������������������������x� δ�2 � y2

q−

�����������������������������x − δ�2 � y2

q �;

where y � x∕ tan θglass; (6)

OPD is the optical path difference, θglass is theangle within the glass, n0 is the refractive index ofthe corner cube, and the planes of equal phase areconsidered the entrance of the beams into the cornercube for simplicity. Assuming the square of the

displacement is negligible, Eq. (6) can be simplifiedto the result in Eq. (7)

OPD � 4n0δ sin θglass: (7)

The period of the grating that is recorded is givenby λrec∕�2n0−rec sin θglass-rec�. Due to the invariance ofthe product of n0 sin θ by Snell’s law, and the use ofthe same beam as the probe and for recording, themedium of the retroreflector is insignificant. There-fore, if the retroreflector shifts by one grating period,the measured OPD will be twice the period. This cor-responds exactly with the results we expect from thissystem because it is designed to measure fringeshifts caused by phase variations before the record-ing plane in a double-pass configuration.

Experimental verification of the sensitivity tolateral motion was conducted to confirm the accuracyof our approximations. The experimental setups forcomparing the sensitivity of the retroreflector to thesensitivity of a transmitting VBG are shown in Fig. 6.Along with verifying the presence of lateral sensitiv-ity in a retroreflector, experimental verification ofthe lateral sensitivity of a transmitting VBG is im-portant since all previous discussion of grating sen-sitivity to lateral motion was conducted using thingratings.

In the setups of Fig. 6, the PZT was oriented suchthat it could induce lateral shifts of the two phasemeasurement devices. Both interferometers werealigned to measure the interference of a He–Ne laseroperating at 633 nm and incident on the devicesat approximately 13.5°. The transmitting VBG isdesigned to diffract light at this angle with approx-imately 50% diffraction efficiency. When each inci-dent beam is aligned to the Bragg angle and theyoverlap spatially, the diffracted beam of one armand the transmitted beam of the other arm of theinterferometer will be collinear. The detected inten-sity will be a measure of the relative phase differencebetween the two arms. To observe the sensitivity tolateral motion of each of the setups, the PZT wasramped through a voltage range and the intensity

Fig. 5. Diagram of a retroreflector in a phase stabilization systemwith designation of variables for calculating lateral sensitivity.

Fig. 6. Experimental setup to study the sensitivity of phasemeasurement to lateral displacement for (A) a transmitting VBG and for (B) acorner cube retroreflector. The PZT is used to shift the respective measurement device. The effect of lateral shift on the signal measured atthe detector is monitored.

20 February 2014 / Vol. 53, No. 6 / APPLIED OPTICS 1043

change at the detection plane was monitored. Thetwo signals that were received are shown in Fig. 7.Both methods result in periodical signals at the de-tectors caused by phase incursion between theinterfering beams and, therefore, demonstrate meas-ureable sensitivity to lateral shifts induced by thePZT. The most important feature to note is theroughly twice higher frequency of the oscillationsin the retroreflector signal, as expected by theory.The difference between the frequencies of each signalis not exactly a factor of two. This discrepancy is sim-ply due to not precisely controlling the direction ofthe PZT motion to be exactly orthogonal to the axisof interference.

Another important feature is the higher visibilityof the fringes produced by the retroreflector. Whilethis increased visibility is not necessarily relatedto a difference between the systems, it does highlightthe ease of alignment afforded by the use of theretroreflector. A reference grating system requiresthat the grating be aligned to the interfering beamsin tip about the y axis and roll about the z axis andfor small beams, displacement about the z axis toobtain good beam overlap. In a system that uses adynamically formed grating to measure phase,this alignment is automatic. For a stabilization sys-tem using a reference grating, this alignment re-quires a high level of accuracy and can be difficultto obtain high visibility of the phase measurement.Despite these differences it is clearly shown thatboth methods have sensitivity to lateral motionand the relative sensitivity confirms the resultsin Eq. (7), making both methods equally suitablefor correcting these detrimental motions in aholographic recording.

4. Effect of Phase Stabilization on VBG Performance

It is important to note that the performance of aphase stabilization system cannot be completelyevaluated by detecting the feedback signal withthe system operating in an open feedback loop and

then closing the loop and comparing the relativeamplitudes of fluctuations between the stabilizedand unstabilized system. While this would demon-strate the effectiveness of the feedback system, itdoes not directly show the effect that this has onthe quality of the VBG recording. If phase stabiliza-tion results in no change in the grating performance,the system is either measuring incorrectly or phasefluctuations are not responsible for quality of record-ing. Based on the analysis of the effects of phase fluc-tuations presented in Section 2, the primary effect ofan unstabilized system is to reduce the RIM. There-fore, by demonstrating an improvement of a grating’sRIM we can conclude that phase fluctuations weredeteriorating the RIM depth and that phase stabili-zation was successful in controlling these fluctua-tions. This experiment was conducted using thesetup depicted in Fig. 3 to record reflecting VBGswith a resonant wavelength of 978 nm and the timefor each recording was 22 min. The recordingmaterial for these experiments is photo-thermo-refractive glass, which has proven in recent yearsto be an excellent material for recording high-qualityVBGs [15,16]. This material is photosensitive to UVradiation and develops a permanent RIM after ther-mal development.

From these recordings, an increased RIM due toincreased fringe visibility in the phase-stabilizedrecordings is expected to be observed. In a reflectingVBG with high-diffraction efficiency, an increasedRIM will correspond to a higher bandwidth. TheRIM can be calculated by matching measuredspectral response to those calculated by coupledwave theory using measured parameters for thick-ness and resonant wavelength [17,18]. After expo-sure and development, the recorded gratings werecut to a thickness of 3.75 mm and transmission spec-tra were measured using a tunable laser. The trans-mission spectrum of each grating was used todetermine the RIM induced in each recording [18].

The first grating was recorded with no stabiliza-tion present. Figure 8(A) shows the phase differencecalculated from the measured feedback signal beforeand during the recording, using Fig. 4 for conversion.The relative phase of the beams has both high-frequency noise and slow oscillations. These oscilla-tions are the result of phase drift in one directionbecause the detector is measuring the sinusoid of aphase term and there is a 2π phase ambiguity.

The phase during recording [Fig. 8(A)] was ana-lyzed by using Eq. (2) to determine the expectedfringe visibility that can be achieved by recordingin this condition. The measured data predicts thatthe RIM will be 76% �5% of a perfect recording withno phase shifts. Uncertainty in this measurement isdue to changes in the average intensity in the record-ing beam and is evident only when observing achange in the inflection points of the signal in the re-gion near �π∕2. The measured transmission spec-trum is shown in Fig. 9(A) together with thetheoretical spectrum that provides the same spectral

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8 9 10

Det

ecto

r Si

gnal

, V

Piezo Signal, V

Fig. 7. Dependence of signals measured by the detectors inFigs. 6(A) and 6(B) on a signal applied to the PZT controlling lat-eral displacement of a TBG (red) and a retroreflector (blue). Thedifference in the visibility of these fringes is not inherent tothe measurement device but is determined by alignment ofcomponents.

1044 APPLIED OPTICS / Vol. 53, No. 6 / 20 February 2014

width. The RIM was calculated by matching themeasured spectrum to a theoretical spectrum. An ex-cellent agreement of the shapes of both spectra canbe seen in the figure. For a 3.75 mm thick RBG withresonant wavelength of 978 nm, a 430 pm bandwidthcorresponds to a RIM of 490 ppm.

A second RBG was recorded using the sameparameters. During the recording process, the PZTwas used to maintain a constant relative phase ofthe recording beams. Figure 8(B) shows the phasevariations before and during recording. Monitoring

the phase variations before recording allowsphase noise present in the recording environmentto be determined. The remaining noise duringstabilization has a RMSE of 0.0052λ and the ex-pected visibility of this recording is 99.8%. The signalsent to the PZT during the recording is shown onthe same plot to demonstrate how it was used tocounteract the phase noise. The spectral responseof this grating was also measured and fit totheory in Fig. 9(B). At a thickness of 3.75 mm,the bandwidth of 660 pm corresponds to a RIM of740 ppm.

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(b)

Fig. 8. Phase fluctuations at a detector depicted in Fig. 3 for therecording of gratings (A) without and (B) and (C) with phase sta-bilization. The relative phase of the recording beams with no sta-bilization shows both high-frequency noise and long-termvariations. The relative phase of the recording beams with stabi-lization shows dramatic decrease of both high-frequency noise andlong-term variations. The correction voltage applied to the PZT isshown in blue.

00.10.20.30.40.50.60.70.80.9

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976.5 977 977.5 978 978.5 979

Tra

nsm

itta

nce

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rans

mit

tanc

e

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(b)

Fig. 9. Transmission spectra of 3.75 mm thick gratings with thesame periods recorded (A) without and (B) and (C) with phase sta-bilization. The FWHM bandwidths are 430, 660, and 670 pm forplots (A), (B), and (C), respectively. Red, experiment; blue, coupledwave theory simulation.

20 February 2014 / Vol. 53, No. 6 / APPLIED OPTICS 1045

The demonstration of improvement of RIM wassignificant but does not rule out all possible noisesources that deteriorate the recording conditions.For example, the grating shown in Fig. 9(B) didnot undergo a long-term phase drift as was presentin the unstabilized case. To address these concerns, athird reflecting VBG was recorded when the environ-mental phase variation [Fig. 8(C)] was demonstrat-ing different behavior. This environment differsfrom the environment in Fig. 8(B) in that there isa slow, long-term drift and the amplitude of thehigh-frequency phase noise is much lower. Thesetwo different scenarios are evidence of the variousoperating conditions that can be encountered in atypical laboratory environment. When recording inthis environment, the relative phase difference be-tween the recording beams was again significantlydecreased by the use of phase stabilization and theRMSE noise is 0.0057λ. The predicted visibility fromthis phase is 99.7%. The correction voltage applied tothe PZT shows a linear drift during the recording, in-dicating that it is working against the linear drift inthe environment as expected. The measured trans-mission spectrum in Fig. 9(C), at a thickness of3.75 mm, gave a bandwidth of 670 pm correspondingto a RIM of 750 ppm. This value matches well withthat of the grating in Fig. 9(B), confirming propermeasurement of relative phase and effective correc-tion. Thus, the grating recorded without phase stabi-lization has a RIM that is 66% of the RIM in thegrating recorded with stabilization. This deviatesfrom the calculation that predicts 76% but is of theright general scale given the uncertainty in themeasurement and typical homogeneity of about 5%for RIM. The use of this phase stabilization systemis shown to correct the phase to a level where consis-tent high-visibility fringes can be recorded over longexposure times. The increase in fringe visibility man-ifests itself as a broader reflection bandwidth in theexperiments presented here and we have demon-strated an increase of RIM by 50%. Using this systemwill allow longer recording times, meaning thatlower irradiance beams can be used for recordinglarger aperture gratings.

5. Conclusion

For holographic recordings of volume Bragg gratingswith fringe visibility exceeding 95%, random noisevariations must be maintained below 0.05λ. The ac-tive stabilization system proposed here producesphase stabilization well below this level by using acorner cube retroreflector to sample the recordingbeams and measure the relative phase difference.This system is versatile in the sense that it can beused to stabilize an interference pattern with anyspatial period. The lateral sensitivity of the retrore-flector system was verified experimentally to showthat it is comparable to other common methods ofphase stabilization. The effectiveness of the systemwas verified by recording reflecting volume Bragggratings both with and without phase stabilization.

By reducing phase noise during recording, thevisibility of the interference pattern was improved,leading to an increase of the RIM in the finalVBG. An increase in the RIM by 50% was demon-strated in PTR reflecting Bragg gratings using thisphase stabilization system. The system can be usedto ensure fringe visibility of >99% in a holographicrecording, independent of the recording media andis applicable to any grating period or tilt.

This work was funded by HEL/JTO and ARO(contract W911NF-10-1-0441).

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