Volume Bragg Grating for Coupling the Stokes

Wave Out of an Amplifier

by John E. McElhenny, Jeffrey O. White,

Steven D. Rogers, and Tigran Sanamyan

ARL-TN-0409 September 2010

Approved for public release; distribution unlimited.
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Army Research Laboratory

Adelphi, MD 20783-1197

ARL-TN-0409 September 2010

Volume Bragg Grating for Coupling the Stokes 

Wave Out of an Amplifier

John E. McElhenny, Jeffrey O. White,

Steven D. Rogers, and Tigran Sanamyan

Sensors and Electron Devices Directorate, ARL

Approved for public release; distribution unlimited. 
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Volume Bragg Grating for Coupling the Stokes Wave Out of an Amplifier

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John E. McElhenny, Jeffrey O. White, Steven D. Rogers, and Tigran Sanamyan

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U.S. Army Research Laboratory

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ARL-TN-0409

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High Energy Laser Joint Technology Office (GEK0JTO)

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

High power multimode fiber (MMF) master-oscillator power amplifiers (MOPAs) with stimulated Brillouin scattering (SBS) 

beam cleanup and wavefront reversal are under development at the U.S. Army Research Laboratory (ARL) to counter rockets, 

artillery, and mortar (CRAM). When Faraday isolators are used for outcoupling the Stokes light in the MMF MOPAs, the 

power scalability is limited. Volume Bragg gratings (VBGs) appear to be more scalable. We report here the results of tests on 

a VBG designed to separate wavelengths 0.0604 nm (16 GHz) apart, corresponding to the SBS frequency shift at 1064 nm in 

fused silica.

15. SUBJECT TERMS

Volume Bragg grating, stokes wave, Brillouin scattering

16. SECURITY CLASSIFICATION OF: 

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19a. NAME OF RESPONSIBLE PERSON

John E. McElhenny

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(301) 394-3130

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iii

Contents

List of Figures iv

1. Introduction/Background 1

2. Experiment/Calculations 2

3. Results and Discussion 6

4. Conclusions 7

5. References 8

List of Symbols, Abbreviations, and Acronyms 9

Distribution List 10
iv

List of Figures

Figure 1. The experimental setup for the high power MMF MOPA with phase conjugation. 

The Faraday rotator is the limiting factor. .................................................................................1

Figure 2. Anticipated spectral response of volume Bragg grating from OptiGrate (3). .................2

Figure 3. Using a VBG to outcouple in the wavefront reversal geometry. This geometry is 

safer than transmitting λL and reflecting λS. ..............................................................................3

Figure 4. A possible configuration to outcouple in the beam cleanup geometry. It is equally 

appropriate to reflect λL and transmit λS. ...................................................................................3

Figure 5. Steady-state temperature profile inside an 8×10×16.5 mm3 piece of PTR glass, 

with 0.16 W of heat deposited in a cylinder of the same length and 6 mm in diameter............4

Figure 6. Steady-state VBG temperature vs. distance along the y-axis from the center of 

figure 5.......................................................................................................................................4

Figure 7. Transient VBG temperature on axis with the same conditions as figure 5. ....................5

Figure 8. The VBG in its temperature-controlled holder and mounted to a tip-tilt stage...............5

Figure 9. Experimental setup to test ability of VBG to decouple the Stokes from the input 

wave. ..........................................................................................................................................6

Figure 10. (a) The input laser power reflected by the VBG (red, PD3), the input laser power 

to the SBS fiber (orange), the Fresnel reflected and backscattered Stokes power (green, 

PD4), and the Fresnel and Stokes power transmitted through the VBG (blue, PD2); and 

(b) the VBG reflectance at λL (red), VBG Stokes transmittance at λS (blue), and SBS 

reflectance (green). ....................................................................................................................7
1

1. Introduction/Background

High power multimode fiber (MMF) master-oscillator power amplifiers (MOPAs) with 

stimulated Brillouin scattering (SBS) beam cleanup and wavefront reversal are under 

development at the U.S. Army Research Laboratory (ARL) for counter rockets, artillery, and 

mortar (CRAM). 

In the wavefront reversal geometry (figure 1), a Faraday rotator-polarizer combination (Faraday 

isolator) couples the oscillator into the amplifier, and outcouples the amplified Stokes light. 

During the first pass through the large mode area (LMA) fiber core, the incident fundamental 

mode from the oscillator is amplified and scattered into multiple spatial modes. This light is 

coupled into a fiber designed to generate a wavefront reversed and frequency-shifted 

backscattered Stokes beam through SBS (1). As it propagates back through the LMA fiber 

(second pass), the scattering is undone and the fundamental mode quality is restored. A 

component is needed that transmits the laser light (into the fiber) and redirects the Stokes light 

(from the fiber). There is little basis by which to separate the two beams; the polarizations may 

be identical and the wavelengths differ by less than one part in 105. Faraday isolators distinguish 

between the two beams based on the fact that they are counter-propagating. Volume Bragg 

gratings (VBGs) distinguish between the two beams based on the different wavelengths, as in a 

conventional diffraction grating. 

Figure 1. The experimental setup for the high power MMF MOPA with phase conjugation. The Faraday 

rotator is the limiting factor. 

The highest power commercial-off-the-shelf Faraday isolators can handle only up to 1 kW (2). 

Compared to Faraday isolators, VBGs are a more scalable option for outcoupling the Stokes 

beam. At 1064 nm in fused silica, the wavelength shift of 0.0604 nm (16 GHz) is only one part 

in ~17,600, so to resolve the two wavelengths, i.e., reflect the laser wavelength and transmit the 

Stokes wavelength, the VBG must have ~17,600 periods. A reflection grating of period 532 nm 
2

in a material of index 1.49 (photo-thermal refractive [PTR] glass) would require a thickness of at 

least 6 mm. For a grating of thickness 12 mm, the anticipated reflectance (figure 2) was ~0.95 at 

λL and ~0.05 at λS (transmittance ~0.95). The blue line corresponds to illumination with a plane 

wave; the red line corresponds to a more realistic beam with 0.4-mrad divergence. 

Figure 2. Anticipated spectral response of volume Bragg grating from OptiGrate (3).

2. Experiment/Calculations

In the wavefront reversal MOPA geometry, the Stokes beam is coupled out after the second pass 

amplification. The safest approach is to reflect the laser beam and transmit the Stokes beam

(figure 3) rather than vice versa, because if the VBG shifts, the input light will not be coupled 

into the amplifier and no high-power 1064-nm beam will be created. In the beam cleanup

MOPA geometry, the Stokes beam is outcoupled immediately after the SBS takes place and 

there is no preferred approach regarding safety; it does not matter which beam is transmitted and 

which is reflected. For ease of alignment, we transmit the laser beam and reflect the Stokes

(figure 4).
3

Figure 3. Using a VBG to outcouple in the wavefront reversal geometry. 

This geometry is safer than transmitting λL and reflecting λS. 

Figure 4. A possible configuration to outcouple in the beam cleanup 

geometry. It is equally appropriate to reflect λL and transmit λS.

One issue is whether absorption will heat the VBG enough to shift the resonance. The index 

change and thermal expansion of PTR glass are such that the resonant wavelength red shifts 

~0.007 nm/°C. To investigate this we solved the three-dimensional (3-D) heat diffusion equation 

inside an 8×10×16.5 mm3 piece of glass with specific heat 0.84 J/gm°K and thermal conductivity

1 W/mK. An absorption coefficient α=10–3 cm–1 corresponds to an absorbed power of 0.16% of 

the incident power. Obtaining a 100-W average power from the MOPA is the goal of our Joint 

Technology Office (JTO) contract supporting this research. We, therefore, assume that 0.16 W 

is deposited uniformly in a cylinder 6 mm in diameter and 16.5 mm long. The boundary 

conditions are that two surfaces are in contact with a heat sink at 300 K. The steady-state results 

show a 1 °C temperature difference between the beam axis and the 3-mm radius of the beam 

(figures 5 and 6). This implies a 0.007-nm shift in resonance, which will produce only a small 

change in the transmission at λL and λS. 
4

Figure 5. Steady-state temperature profile inside an 8×10×16.5 mm3 piece of PTR glass, with 

0.16 W of heat deposited in a cylinder of the same length and 6 mm in diameter.

300.00

300.50

301.00

301.50

302.00

0 .4 .8 1.2 1.6 2 2.4 2.8 3.2 3.6 4

Temp (Kelvin)

Along Y (mm)

 

 

 

Figure 6. Steady-state VBG temperature vs. distance along the y-axis from the 

center of figure 5.

The thermal time constant on the order of 1 min limits the rate at which the output power of the 

laser can be changed (figure 7).
5

300.40

300.60

300.80

301.00

301.20

301.40

301.60

301.80

10.00 38.00 66.00 94.00 122.00 150.00

Temp (Kelvin)

Time (sec)

 

 yp 

 

Figure 7. Transient VBG temperature on axis with the same conditions as figure 5.

The size of the actual VBG is state-of-the-art at 8×10×12 mm3 and mounted in a temperaturecontrolled holder (figure 8). To test the VBG, we used a setup (figure 9) in which the laser light 

is reflected and the Stokes light is transmitted. This is the preferred setup for the wavefront 

reversal geometry and will also work for beam cleanup.

Figure 8. The VBG in its temperature-controlled holder and mounted to a tip-tilt stage.
6

Figure 9. Experimental setup to test ability of VBG to decouple the Stokes from the input wave.

We collimate the input light with a 35-mm focal length doublet (to a 4.9-mm-diameter beam), 

use the half-waveplate and Faraday isolator as a variable optical attenuator (VOA) and couple

into the fiber with a 19-mm focal length doublet. Uncoated beam samplers at a small angle of 

incidence monitor the power. The input angle and the VBG angle are chosen to maximize the 

Bragg reflection of the input light. 

3. Results and Discussion

The threshold of the OFS graded-index (GI) 50/125 fiber is 0.2 W. The VBG reflectance of the 

input light (λL) is 85% while the maximum VBG transmittance of the Stokes light (λS) is ~84%. 

The VBG Stokes transmittance is calculated from

TStokes

VBG = Ptrans

VBG −�1−Rlaser

VBG �0.04PreflVBG

Pback

fiber−0.04Prefl

VBG (1)

where Ptrans

VBG is the power transmitted through the VBG from the fiber (PD2), Prefl

VBG is the input 

laser power reflected by the VBG (PD3), Rlaser

VBG is the reflectance of the VBG at the laser 

wavelength, Pback

fiber is the backscattered power (both the SBS-generated Stokes wave and Fresnel 

reflection) from the fiber (PD4), and 0.04 corresponds to the Fresnel reflection from the input 

face of the fiber. 

Figure 10 shows the input laser power reflected by the VBG, the input laser power to the SBS 

fiber, the Fresnel reflected and backscattered Stokes power, and the Fresnel and Stokes power 

transmitted through the VBG, as well as the VBG reflectance at λL, VBG Stokes transmittance at 

λS, and SBS reflectance.
7

0 1 2 3 4 5 6 7 8

0

1

2

3

4

5

6

7

 VBG Input Reflected

 Input to Fiber

 Backscattered

 VBG Backscattered Transmitted

2.7km GI 50/125 - VBG: f1=35mm, f2=19mm

Power (W)

Input Power (W)

201008.26

0 1 2 3 4 5 6 7 8

0.0

0.2

0.4

0.6

0.8

1.0

 VBG Laser Reflectance

 Fiber SBS Reflectance

 VBG Stokes Transmittance

2.7km GI 50/125 - VBG: f1=35mm, f2

=19mm

Transmittance/Reflectance

Input Power (W)

201008.26

Figure 10. (a) The input laser power reflected by the VBG (red, PD3), the input laser power to the SBS fiber 

(orange), the Fresnel reflected and backscattered Stokes power (green, PD4), and the Fresnel and 

Stokes power transmitted through the VBG (blue, PD2); and (b) the VBG reflectance at λL (red), VBG 

Stokes transmittance at λS (blue), and SBS reflectance (green).

4. Conclusions

The scalability of the high-power MMF MOPAs was previously limited by the Faraday isolators

available, which can handle a maximum of 1 kW. Compared to a Faraday isolator, a VBG made 

from PTR glass appears to be a more scalable option for outcoupling the Stokes beam. 

The VBG, fabricated by OptiGrate (3), is designed to separate wavelengths 0.0604 nm apart (the 

wavelength shift between the input and Stokes waves operating at 1064 nm in fused silica). It 

reflects up to 85% of the input laser light while transmitting up to 84% of the backscattered 

Stokes light. Faraday isolators outcouple based on the direction of propagation, while VBGs 

outcouple based on the wavelength difference between the two waves. 
8

5. References 

1. Boyd, R.W. Nonlinear Optics; Academic Press Inc., San Diego, p 331, 1992.

2. Passat Ltd. Web Page, 720 N. Hammonds Ferry Rd., Linthicum, MD 21090, USA.

www.passatltd.com (accessed 2010).

3. OptiGrate Corp. Web page, 3267 Progress Drive, Orlando, Florida 32826.

www.optigrate.com (accessed 2010).
9

List of Symbols, Abbreviations, and Acronyms

3-D three-dimensional 

ARL U.S. Army Research Laboratory 

CRAM counter rockets, artillery, and mortar

GI graded-index

JTO Joint Technology Office

LMA large mode area

MMF multimode fiber

MOPA master-oscillator passive-amplifier

PTR photo-thermal refractive

SBS stimulated Brillouin scattering

VBG volume Bragg grating

VOA variable optical attenuator
10

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