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Beam combining of lasers with high spectral density using volume Bragg gratings
Optics Communications 282 (2009) 2560–2563
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Beam combining of lasers with high spectral density using volume Bragg gratings Oleksiy Andrusyak a,*, Vadim Smirnov b, George Venus a, Leonid Glebov a a b
CREOL, The College of Optics and Photonics, University of Central Florida, 4000 Central Florida Blvd., Orlando, FL 32816-2700, USA OptiGrate, 3267 Progress Drive, Orlando, FL 32826, USA
a r t i c l e
i n f o
Article history: Received 9 February 2009 Received in revised form 2 March 2009 Accepted 7 March 2009
Keywords: Laser beam combining Volume holographic gratings Photorefractive materials
a b s t r a c t Incoherent combining of multiple laser beams with offset wavelengths into a single near-diffraction-limited beam is an effective solution to increasing energy brightness and scaling output power of high-power lasers. Volume Bragg gratings (VBGs) recorded in photo-thermo-refractive (PTR) glass allow spectral beam combining with a remarkably high spectral density of channels. Spectral beam combining (SBC) of five channels within 1–2 nm bandwidth around 1064 and 1550 nm into a single near-diffraction-limited beam with absolute efficiency 92–94% is demonstrated. Scaling of this technique to multi-kW power level is discussed. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction Beam combining techniques have become an important tool in the design of high-power high-brightness laser systems [1]. Maximum power that can be obtained from single high-power amplifiers is usually limited by thermal distortion of active medium and beam quality degradation in solid-state lasers or non-linear effects and optical damage in fiber lasers. Beam combining offers an alternative solution to obtaining high-power high-brightness radiation. Output beams of an array of lower-power laser sources operating at moderate power can be combined by external optical elements, producing a single beam with increased power and brightness. Assuming that combining elements have high energy throughput and introduce no significant beam distortion, the brightness of the combined beam is increased proportionally to the number of channels. Two approaches to brightness scaling using beam combining have been considered – coherent and incoherent (spectral). A comparative review of various coherent and spectral beam combining techniques is presented in [1]. The main challenge for coherent beam combining is precise control of wavelengths and relative phases of gain elements. Coherent combining has been demonstrated for a small number of elements at low power levels, but scaling to high-power large-channel-count systems faces a number of problems. Relative phase noise between channels is a major challenge for coherent beam combining regardless of whether an active or passive phase control method is implemented [2]. Spec* Corresponding author. E-mail address: [email protected] (O. Andrusyak). 0030-4018/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2009.03.019
tral beam combining is an incoherent combining technique that does not require phase control of sources, allowing for a stable and robust system. Using this method, beams from an array of lasers with each element operated at a different wavelength are combined into a single near-diffraction-limited beam using dispersive optical elements. As a result, the energy brightness of the combined beam is increased compared to individual sources, while spectral brightness is decreased, since combined beam spectrum consists of multiple peaks corresponding to individual sources. Efficient SBC with power in combined beam on the level of a few hundred Watts and channel separation of several nanometers has been demonstrated using transmitting volume Bragg gratings [3] and multilayer dielectric surface gratings [4,5]. Both approaches offer power scalability; however, the total number of channels is limited by the ratio of available gain medium bandwidth and minimum spectral separation of channels. The total bandwidth available for SBC is typically determined by the gain bandwidth of laser medium and application requirements. For example, consider a laser system operating within a 50 nm low-altitude atmosphere transparency window around 1040 nm. With 500 W of power per channel, 100-kW-level near-diffraction-limited output can be achieved by combining 200 channels with channel separation of 0.25 nm. In order to achieve small spectral separation of channels using surface gratings, large source-tograting distances are required to spatially overlap beams from different channels, making the system impractically long. In case of transmitting VBGs, thick gratings with large Bragg angles are required, resulting in narrow angular acceptance. Reflecting VBGs used at near-normal incidence are much more advantageous for high-density SBC (2 channels/nm and higher) due to wide angular
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2. Volume Bragg gratings in PTR glass for spectral beam combining High-efficiency VBG recording in PTR glass has been developed [7]. While being photo-sensitive in the UV, PTR glass offers high transmittance in the near-IR and visible parts of spectrum with absorption comparable to the best available commercial optical glasses. Moreover, PTR glass has excellent thermo-mechanical properties with refractive index practically independent of temperature (dn/dT 107 K1). These features enable VBGs in PTR glass to withstand high-power laser radiation, making them ideal elements for high-power SBC. As an example, two Yb-fiber lasers with 11 nm difference in central wavelengths have been combined with 92% efficiency using a transmitting VBG to produce a single near-diffraction-limited beam with 165 W of power [3]. The behavior of narrow-band reflecting VBGs in PTR glass under high-power radiation has been studied [6,8]. It was found that diffraction efficiency and spectral bandwidth of gratings are not changed under laser irradiation with power up to 570 W and no residual phenomena were revealed in gratings irradiated by a focused laser beam with power density up to 5 kW/cm2. There is a principal difference between SBC by means of surface grating or prisms and volume gratings. The use of prisms and surface gratings is based on their angular dispersion which provides dependence of deflection angle on wavelength. From one side, high angular dispersion is required to provide spatial separation of laser sources with close wavelengths. From another side, this dispersion induces additional divergence of a deflected beam according to its spectral width [9]. SBC by means of volume Bragg gratings utilizes unique spectral response of VBGs: diffraction efficiency is close to unity when the Bragg condition is satisfied and is close to zero at multiple points corresponding to particular wavelength offsets from the Bragg condition. Two beams with shifted wavelengths incident on a grating at conjugate angles emerge overlapped and collinear (Fig. 1) if the wavelength of one (k1) matches the Bragg condition (the beam is diffracted) and the wavelength of the other (k2) is offset to match one of the zeros (the beam is transmitted). Angular dispersion of volume Bragg gratings is significant only if deflection angle is far from zero or 180°. It contributes to the divergence of beams deflected by high-spatial-frequency transmitting VBGs [10], but is insignificant for reflecting VBGs used at angles close to normal [6]. Properties of reflecting and transmitting VBGs have been described in great detail [11–13]. In this paper we will focus on spectral properties of narrow-band reflecting VBGs used for highspectral-density SBC. For a plane wave incident on an un-slanted
λ1+ λ2
reflecting Bragg grating (grating vector parallel to the front surface normal) with sinusoidal variation of refractive index, diffraction efficiency can be expressed through basic grating parameters [13]:
0 B
1
gðDkÞ ¼ B B1 þ @
2
sinh
2pnav tdn k20 f
2
k0 f 2 Dk 2nav dn
2
11 C C ; 2 1=2 C A
ð1Þ
pftk0Dk
where t is grating thickness, nav is average refractive index of the medium, dn is amplitude of refractive index modulation, and f is spatial frequency of the grating. The plane wave is incident on the grating at an angle that satisfies the Bragg condition for a wavelength k0, and Dk represents spectral offset from k0. Maximum diffraction efficiency g0 that occurs at the Bragg condition can be obtained by setting Dk = 0 in Eq. (1):
g0 ¼ tanh2
2pnav tdn k20 f
ð2Þ
:
Spectral dependence of diffraction efficiency of a narrow-band unslanted reflecting VBG used for SBC is shown in Fig. 2. Bragg condition of this grating is satisfied for k0 = 1064.0 nm when angle of incidence is 3.8° relative to the front surface normal. For a plane wave model, diffraction efficiency has a peak at k0, where diffraction efficiency is determined by Eq. (2) and a series of points at multiple wavelengths where diffraction efficiency is zero. Efficient spectral beam combining in a geometry illustrated in Fig. 1 is performed by matching k1 to the Bragg wavelength of the grating (k0) and k2 to one of the zeros. Diffraction efficiency, spectral selectivity and angular acceptance of gratings are determined by grating thickness and refractive index modulation. Following the hyperbolic tangent function of Eq. (2), diffraction efficiency g0 asymptotically approaches the 100% value as grating thickness and/or refractive index modulation are increased. However diffraction efficiency close to 100% may be undesirable for SBC of real (divergent) beams, since it also leads to an increase in diffraction efficiency for wavelengths offset from Bragg condition. For beams with finite divergence, diffraction efficiency can be calculated as a convolution of the angular efficiency of the grating and beam intensity in the angular space [13]. While peak diffraction efficiency is not changed for beams with divergence much smaller than angular acceptance of a grating, sharp minima of diffraction efficiency curve can not be matched for of the entire angular spectrum of a divergent beam. Therefore, diffraction efficiency in minima is not zero for a beam with finite divergence (Fig. 2). As a result, the transmitted beam is partially diffracted by the grating and efficiency of combining is decreased. An effective solution to minimizing these losses is to place neighboring channels into higher-order minima of spectral selectivity
100 Diffraction efficiency, %
acceptance and the small source-to-grating distances required [6]. Besides higher tolerance to beam divergence, reflecting VBGs are polarization-insensitive and are suitable for SBC of unpolarized lasers. A compact and rugged high spectral density beam-combining system can be constructed using reflecting VBGs. In this paper we discuss basic properties of reflecting VBGs recorded in PTR glass and present experimental results of 5-channel SBC with high spectral density (0.25–0.5 nm channel separation) around 1064 and 1550 nm.
Plane wave
80
0.6 mrad beam Experiment
60 40 20 0
λ1= λBragg
λ2= λBragg ± λ
Fig. 1. Spectral beam combining of two beams with offset wavelengths using a reflecting volume Bragg grating.
1063.4
1063.6
1063.8 1064.0 1064.2 Wavelength, nm
1064.4
1064.6
Fig. 2. Spectral selectivity of a reflecting VBG used for SBC with 0.43 nm channel spacing around 1064 nm.
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Table 1 Parameters of gratings optimized for SBC experiments. 5-Channel SBC system
Parameters of beam-combining gratings
Wavelength/channel separation (nm)
Absolute system efficiency (experiment) (%)
Bragg wavelength at normal incidence (nm)
Thickness (mm)
Refractive index modulation (ppm)
1064/0.43 1550/0.51 1550/0.25
93.7 92.6 91.7
1065.1 1552.8 1550.1
3.7 6.5 10.3
420 200 140
curve. Using an optimization procedure, gratings that simultaneously provide high efficiency for diffracted beams and low losses for transmitted beams can be designed for given channel separation and beam divergence. As an example, grating with spectral selectivity shown in Fig. 2 is optimized for high-efficiency SBC with 0.43 nm channel separation. This grating provides diffraction efficiency of 99.7% at Bragg condition and diffraction losses <1% for a beam with divergence 0.6 mrad and wavelength offset by 0.43 nm, corresponding to the 4th minimum. 3. Experimental results Three SBC systems with varying spectral separation of channels have been designed and assembled. Each system spectrally combines five beams with offset wavelengths into a single near-diffraction-limited beam by a stack of reflecting VBGs. Parameters of gratings used and absolute efficiency of 5-channel SBC systems achieved experimentally are summarized in Table 1. The optical setup is shown in Fig. 3 for a set of VBGs having the same period. Gratings are angle-tuned to diffract beams of respective wavelengths, while beams with other wavelengths are transmitted undisturbed.
Commercially available narrow-line fiber-pigtailed diode lasers terminated by high-quality adjustable collimators are used in the experiments, producing near-diffraction-limited (M2 < 1.1) beams with 3 mm diameter (FWe2M). Proper collimation is achieved by using a wedge-plate shearing interferometer [14] and by minimizing beam spot size in a focal plane of a focusing lens. Angular divergence of beams is 0.5 mrad and 0.7 mrad (FWe2M) for 1064 and 1550 nm cases respectively. Output power of each laser is set to 5 mW. Absolute system efficiency (Table 1) is calculated by dividing the power of the combined output beam by 25 mW, which is the total power of the five input beams. Central wavelengths of lasers were tuned to required separation (0.43 nm around 1064 nm, 0.5 and 0.25 nm around 1550 nm) by adjusting the angle of an intra-cavity surface grating (1064 nm) and controlling the DFB laser diode temperature (1550 nm). The output of each 5-channel SBC system is a spectrally-combined beam with total bandwidth of 1.7 nm (around 1064 nm), 2 nm and 1 nm (around 1550 nm). Spectra of output beams of the three SBC systems are shown in Fig. 4, where individual linewidths are limited by the resolution of an optical spectrum analyzer. Alignment of SBC systems is performed by using an alignment collimator pointing in a reverse direction that defines the axis of
4 2 0 1062
1063
1064
Wavelength, nm
6
Power, mW
6
Power, mW
Power, mW
Fig. 3. Spectral beam combining of five laser sources using a stack of identical reflecting volume Bragg gratings.
4 2 0 1547
1548
1549
1550
6 4 2 0 1547.5
Wavelength, nm
1548
1548.5
Wavelength, nm
Position, mm
100 80 M2=1.12 60 40 20 0 -1.5 -1 -0.5 0 0.5 1 1.5
Position, mm
120 100 80 60 40 20 0
Beam width, μm
Beam width, μm
100 80 M2=1.11 60 40 20 0 -1.5 -1 -0.5 0 0.5 1 1.5
Beam width, μm
Fig. 4. Output spectra of three SBC systems.
M2=1.13
-1.5 -1 -0.5 0 0.5 1 1.5
Position, mm
Fig. 5. Spectrally combined output beams from three SBC systems around the focal plane of a test lens: 0.43 nm channel separation around 1064 nm (left), 0.51 nm channel separation around 1550 nm (center) and 0.25 nm channel separation around 1550 nm (right).
O. Andrusyak et al. / Optics Communications 282 (2009) 2560–2563
the output beam. The channels are aligned sequentially, starting with one that is closer to the output and ending with one that is transmitted through all gratings. Laser source of a respective channel is coupled to the alignment collimator and a VBG corresponding to that channel is aligned to satisfy Bragg condition for that wavelength (the beam is diffracted with highest efficiency). Next, a working collimator is placed in a location where the alignment beam is diffracted to and laser output is switched to the working collimator. The working collimator is aligned to couple light diffracted by the VBG into the alignment collimator with maximum efficiency. As this procedure is repeated to align the next channel, the beam is transmitted through VBGs of previous channels due to an offset wavelength. After all channels are aligned, output beams from all channels are overlapped and collinear, resulting in a neardiffraction-limited spectrally-combined beam. This method allows alignment with accuracy better than 20 lrad. Times-diffraction-limit factors (commonly known as M2) of spectrally-combined output beams are measured by focusing beams with a test lens [15]. Slit-based beam profiler is used to scan beams in five planes along the direction of propagation. Beam widths calculated by second moment definition are fit to a hyperbolic equation to find M2 of the beams (Fig. 5). Spectrally-combined output beams from three SBC systems are near-diffraction-limited with roughly the same M2 as input beams. This indicates that accuracy of alignment is much better than divergence of beams and combining elements do not introduce beam distortions. Brightness of output beams is enhanced by 5 times compared to individual input beams. This approach can be scaled to high power by increasing the channel count and power per channel. Low absorption in visible and near-IR regions of spectrum and excellent thermo-mechanical properties of PTR glass allow it to withstand high-power radiation. Recently, five randomly polarized fiber lasers with 0.5 nm channel separation around 1064 nm were combined using this technique with 91.7% combining efficiency, resulting in 773 W output power in a combined beam [16,17]. It was shown that at this power level VBGs introduce no significant beam distortions. SBC of high-power lasers with small spectral separation of channels provides a clear path to obtaining near-diffraction-limited spectrally-combined beams with multi-kW power levels. 4. Conclusions Reflecting volume Bragg gratings in PTR glass enable high-efficiency combining of multiple laser beams with high spectral den-
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sity. Three systems that combine five beams with channel separation 0.25–0.5 nm around 1064 and 1550 nm with absolute efficiency 92–94% are demonstrated. Output of each system is a spectrally-combined near-diffraction-limited beam with enhanced brightness. Optical and thermo-mechanical properties of volume gratings allow scaling of such systems to multi-kW power levels. Acknowledgments This work is supported by DARPA/ADHELS (contract H0011-061-0010) and HEL-JTO (contract FA9451-06-D-0015) programs. References [1] T.Y. Fan, IEEE J. Sel. Top. Quantum Electron. 11 (2005) 567. [2] S.J. Augst, J.K. Ranka, T.Y. Fan, A. Sanchez, J. Opt. Soc. Am. B 24 (2007) 1707. [3] I.V. Ciapurin, L.B. Glebov, V.I. Smirnov, in: L.N. Durvasula (Ed.), Fiber Lasers: Technology, Systems, and Applications, Proceedings of SPIE, vol. 5335, 2004, p. 116. [4] T.H. Loftus, A. Liu, P.R. Hoffman, A.M. Thomas, M. Norsen, R. Royse, E. Honea, Opt. Lett. 32 (2007) 349. [5] S. Klingebiel, F. Röser, B. Ortaç, J. Limpert, A. Tünnermann, J. Opt. Soc. Am. B 24 (2007) 1716. [6] O. Andrusyak, I. Ciapurin, V. Smirnov, G. Venus, L. Glebov, in: Donald J. Harter, Andreas Tünnermann, Jes Broeng, Clifford Headley III (Eds.), Fiber Lasers IV: Technology, Systems, and Applications, Proceedings of SPIE, vol. 6453, 2007, p. 64531L. [7] O.M. Efimov, L. Glebov, V. Smirnov, High efficiency volume diffractive elements in photo-thermo-refractive glass, United States Patent 66,73,497, January 6, 2004. [8] O. Andrusyak, V. Smirnov, G. Venus, L. Glebov, Narrow-band volume Bragg gratings in PTR glass under high-power CW laser radiation, SSDLTR-2007 Technical Digest, Paper Code P-1, 2007. [9] S.J. Augst, A.K. Goyal, R.L. Aggarwal, T.Y. Fan, A. Sanchez, Opt. Lett. 28 (2003) 331. [10] O. Andrusyak, I. Ciapurin, V. Rotar, A. Sevian, G. Venus, L. Glebov, Dense spectral beam combining with volume Bragg gratings in PTR glass, SSDLTR2006 Technical Digest, Paper Code BC-3, 2006. [11] H. Kogelnik, Bell Syst. Tech. J. 48 (1969) 2909. [12] I. Ciapurin, L. Glebov, V. Smirnov, Opt. Eng. 45 (2006) 015802. [13] I. Ciapurin, L. Glebov, V. Smirnov, in: T.H. Jeong, H. Bjelkhagen, (Eds.), Practical Holography XIX: Materials and Applications, Proceedings of SPIE, vol. 5742, 2005, p. 183. [14] M.E. Riley, M.A. Gusinow, Appl. Opt. 16 (1977) 2753. [15] ISO 11146:1999, Lasers and laser-related equipment – Test methods for laser beam parameters – Beam widths, divergence angle and beam propagation factor. [16] O. Andrusyak, I. Ciapurin, V. Smirnov, G. Venus, N. Vorobiev, L. Glebov, in: Jes Broeng, Clifford Headley (Eds.), Fiber Lasers V: Technology, Systems, and Applications, Proceedings of SPIE, vol. 6873, 2008, p. 687314. [17] O. Andrusyak, V. Smirnov, G. Venus, V. Rotar, L. Glebov, IEEE J. Sel. Top. Quantum Electron. 2009, accepted for publication.
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Beam combining of lasers with high spectral density using volume Bragg gratings Oleksiy Andrusyak a,*, Vadim Smirnov b, George Venus a, Leonid Glebov a a b
CREOL, The College of Optics and Photonics, University of Central Florida, 4000 Central Florida Blvd., Orlando, FL 32816-2700, USA OptiGrate, 3267 Progress Drive, Orlando, FL 32826, USA
a r t i c l e
i n f o
Article history: Received 9 February 2009 Received in revised form 2 March 2009 Accepted 7 March 2009
Keywords: Laser beam combining Volume holographic gratings Photorefractive materials
a b s t r a c t Incoherent combining of multiple laser beams with offset wavelengths into a single near-diffraction-limited beam is an effective solution to increasing energy brightness and scaling output power of high-power lasers. Volume Bragg gratings (VBGs) recorded in photo-thermo-refractive (PTR) glass allow spectral beam combining with a remarkably high spectral density of channels. Spectral beam combining (SBC) of five channels within 1–2 nm bandwidth around 1064 and 1550 nm into a single near-diffraction-limited beam with absolute efficiency 92–94% is demonstrated. Scaling of this technique to multi-kW power level is discussed. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction Beam combining techniques have become an important tool in the design of high-power high-brightness laser systems [1]. Maximum power that can be obtained from single high-power amplifiers is usually limited by thermal distortion of active medium and beam quality degradation in solid-state lasers or non-linear effects and optical damage in fiber lasers. Beam combining offers an alternative solution to obtaining high-power high-brightness radiation. Output beams of an array of lower-power laser sources operating at moderate power can be combined by external optical elements, producing a single beam with increased power and brightness. Assuming that combining elements have high energy throughput and introduce no significant beam distortion, the brightness of the combined beam is increased proportionally to the number of channels. Two approaches to brightness scaling using beam combining have been considered – coherent and incoherent (spectral). A comparative review of various coherent and spectral beam combining techniques is presented in [1]. The main challenge for coherent beam combining is precise control of wavelengths and relative phases of gain elements. Coherent combining has been demonstrated for a small number of elements at low power levels, but scaling to high-power large-channel-count systems faces a number of problems. Relative phase noise between channels is a major challenge for coherent beam combining regardless of whether an active or passive phase control method is implemented [2]. Spec* Corresponding author. E-mail address: [email protected] (O. Andrusyak). 0030-4018/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2009.03.019
tral beam combining is an incoherent combining technique that does not require phase control of sources, allowing for a stable and robust system. Using this method, beams from an array of lasers with each element operated at a different wavelength are combined into a single near-diffraction-limited beam using dispersive optical elements. As a result, the energy brightness of the combined beam is increased compared to individual sources, while spectral brightness is decreased, since combined beam spectrum consists of multiple peaks corresponding to individual sources. Efficient SBC with power in combined beam on the level of a few hundred Watts and channel separation of several nanometers has been demonstrated using transmitting volume Bragg gratings [3] and multilayer dielectric surface gratings [4,5]. Both approaches offer power scalability; however, the total number of channels is limited by the ratio of available gain medium bandwidth and minimum spectral separation of channels. The total bandwidth available for SBC is typically determined by the gain bandwidth of laser medium and application requirements. For example, consider a laser system operating within a 50 nm low-altitude atmosphere transparency window around 1040 nm. With 500 W of power per channel, 100-kW-level near-diffraction-limited output can be achieved by combining 200 channels with channel separation of 0.25 nm. In order to achieve small spectral separation of channels using surface gratings, large source-tograting distances are required to spatially overlap beams from different channels, making the system impractically long. In case of transmitting VBGs, thick gratings with large Bragg angles are required, resulting in narrow angular acceptance. Reflecting VBGs used at near-normal incidence are much more advantageous for high-density SBC (2 channels/nm and higher) due to wide angular
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2. Volume Bragg gratings in PTR glass for spectral beam combining High-efficiency VBG recording in PTR glass has been developed [7]. While being photo-sensitive in the UV, PTR glass offers high transmittance in the near-IR and visible parts of spectrum with absorption comparable to the best available commercial optical glasses. Moreover, PTR glass has excellent thermo-mechanical properties with refractive index practically independent of temperature (dn/dT 107 K1). These features enable VBGs in PTR glass to withstand high-power laser radiation, making them ideal elements for high-power SBC. As an example, two Yb-fiber lasers with 11 nm difference in central wavelengths have been combined with 92% efficiency using a transmitting VBG to produce a single near-diffraction-limited beam with 165 W of power [3]. The behavior of narrow-band reflecting VBGs in PTR glass under high-power radiation has been studied [6,8]. It was found that diffraction efficiency and spectral bandwidth of gratings are not changed under laser irradiation with power up to 570 W and no residual phenomena were revealed in gratings irradiated by a focused laser beam with power density up to 5 kW/cm2. There is a principal difference between SBC by means of surface grating or prisms and volume gratings. The use of prisms and surface gratings is based on their angular dispersion which provides dependence of deflection angle on wavelength. From one side, high angular dispersion is required to provide spatial separation of laser sources with close wavelengths. From another side, this dispersion induces additional divergence of a deflected beam according to its spectral width [9]. SBC by means of volume Bragg gratings utilizes unique spectral response of VBGs: diffraction efficiency is close to unity when the Bragg condition is satisfied and is close to zero at multiple points corresponding to particular wavelength offsets from the Bragg condition. Two beams with shifted wavelengths incident on a grating at conjugate angles emerge overlapped and collinear (Fig. 1) if the wavelength of one (k1) matches the Bragg condition (the beam is diffracted) and the wavelength of the other (k2) is offset to match one of the zeros (the beam is transmitted). Angular dispersion of volume Bragg gratings is significant only if deflection angle is far from zero or 180°. It contributes to the divergence of beams deflected by high-spatial-frequency transmitting VBGs [10], but is insignificant for reflecting VBGs used at angles close to normal [6]. Properties of reflecting and transmitting VBGs have been described in great detail [11–13]. In this paper we will focus on spectral properties of narrow-band reflecting VBGs used for highspectral-density SBC. For a plane wave incident on an un-slanted
λ1+ λ2
reflecting Bragg grating (grating vector parallel to the front surface normal) with sinusoidal variation of refractive index, diffraction efficiency can be expressed through basic grating parameters [13]:
0 B
1
gðDkÞ ¼ B B1 þ @
2
sinh
2pnav tdn k20 f
2
k0 f 2 Dk 2nav dn
2
11 C C ; 2 1=2 C A
ð1Þ
pftk0Dk
where t is grating thickness, nav is average refractive index of the medium, dn is amplitude of refractive index modulation, and f is spatial frequency of the grating. The plane wave is incident on the grating at an angle that satisfies the Bragg condition for a wavelength k0, and Dk represents spectral offset from k0. Maximum diffraction efficiency g0 that occurs at the Bragg condition can be obtained by setting Dk = 0 in Eq. (1):
g0 ¼ tanh2
2pnav tdn k20 f
ð2Þ
:
Spectral dependence of diffraction efficiency of a narrow-band unslanted reflecting VBG used for SBC is shown in Fig. 2. Bragg condition of this grating is satisfied for k0 = 1064.0 nm when angle of incidence is 3.8° relative to the front surface normal. For a plane wave model, diffraction efficiency has a peak at k0, where diffraction efficiency is determined by Eq. (2) and a series of points at multiple wavelengths where diffraction efficiency is zero. Efficient spectral beam combining in a geometry illustrated in Fig. 1 is performed by matching k1 to the Bragg wavelength of the grating (k0) and k2 to one of the zeros. Diffraction efficiency, spectral selectivity and angular acceptance of gratings are determined by grating thickness and refractive index modulation. Following the hyperbolic tangent function of Eq. (2), diffraction efficiency g0 asymptotically approaches the 100% value as grating thickness and/or refractive index modulation are increased. However diffraction efficiency close to 100% may be undesirable for SBC of real (divergent) beams, since it also leads to an increase in diffraction efficiency for wavelengths offset from Bragg condition. For beams with finite divergence, diffraction efficiency can be calculated as a convolution of the angular efficiency of the grating and beam intensity in the angular space [13]. While peak diffraction efficiency is not changed for beams with divergence much smaller than angular acceptance of a grating, sharp minima of diffraction efficiency curve can not be matched for of the entire angular spectrum of a divergent beam. Therefore, diffraction efficiency in minima is not zero for a beam with finite divergence (Fig. 2). As a result, the transmitted beam is partially diffracted by the grating and efficiency of combining is decreased. An effective solution to minimizing these losses is to place neighboring channels into higher-order minima of spectral selectivity
100 Diffraction efficiency, %
acceptance and the small source-to-grating distances required [6]. Besides higher tolerance to beam divergence, reflecting VBGs are polarization-insensitive and are suitable for SBC of unpolarized lasers. A compact and rugged high spectral density beam-combining system can be constructed using reflecting VBGs. In this paper we discuss basic properties of reflecting VBGs recorded in PTR glass and present experimental results of 5-channel SBC with high spectral density (0.25–0.5 nm channel separation) around 1064 and 1550 nm.
Plane wave
80
0.6 mrad beam Experiment
60 40 20 0
λ1= λBragg
λ2= λBragg ± λ
Fig. 1. Spectral beam combining of two beams with offset wavelengths using a reflecting volume Bragg grating.
1063.4
1063.6
1063.8 1064.0 1064.2 Wavelength, nm
1064.4
1064.6
Fig. 2. Spectral selectivity of a reflecting VBG used for SBC with 0.43 nm channel spacing around 1064 nm.
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Table 1 Parameters of gratings optimized for SBC experiments. 5-Channel SBC system
Parameters of beam-combining gratings
Wavelength/channel separation (nm)
Absolute system efficiency (experiment) (%)
Bragg wavelength at normal incidence (nm)
Thickness (mm)
Refractive index modulation (ppm)
1064/0.43 1550/0.51 1550/0.25
93.7 92.6 91.7
1065.1 1552.8 1550.1
3.7 6.5 10.3
420 200 140
curve. Using an optimization procedure, gratings that simultaneously provide high efficiency for diffracted beams and low losses for transmitted beams can be designed for given channel separation and beam divergence. As an example, grating with spectral selectivity shown in Fig. 2 is optimized for high-efficiency SBC with 0.43 nm channel separation. This grating provides diffraction efficiency of 99.7% at Bragg condition and diffraction losses <1% for a beam with divergence 0.6 mrad and wavelength offset by 0.43 nm, corresponding to the 4th minimum. 3. Experimental results Three SBC systems with varying spectral separation of channels have been designed and assembled. Each system spectrally combines five beams with offset wavelengths into a single near-diffraction-limited beam by a stack of reflecting VBGs. Parameters of gratings used and absolute efficiency of 5-channel SBC systems achieved experimentally are summarized in Table 1. The optical setup is shown in Fig. 3 for a set of VBGs having the same period. Gratings are angle-tuned to diffract beams of respective wavelengths, while beams with other wavelengths are transmitted undisturbed.
Commercially available narrow-line fiber-pigtailed diode lasers terminated by high-quality adjustable collimators are used in the experiments, producing near-diffraction-limited (M2 < 1.1) beams with 3 mm diameter (FWe2M). Proper collimation is achieved by using a wedge-plate shearing interferometer [14] and by minimizing beam spot size in a focal plane of a focusing lens. Angular divergence of beams is 0.5 mrad and 0.7 mrad (FWe2M) for 1064 and 1550 nm cases respectively. Output power of each laser is set to 5 mW. Absolute system efficiency (Table 1) is calculated by dividing the power of the combined output beam by 25 mW, which is the total power of the five input beams. Central wavelengths of lasers were tuned to required separation (0.43 nm around 1064 nm, 0.5 and 0.25 nm around 1550 nm) by adjusting the angle of an intra-cavity surface grating (1064 nm) and controlling the DFB laser diode temperature (1550 nm). The output of each 5-channel SBC system is a spectrally-combined beam with total bandwidth of 1.7 nm (around 1064 nm), 2 nm and 1 nm (around 1550 nm). Spectra of output beams of the three SBC systems are shown in Fig. 4, where individual linewidths are limited by the resolution of an optical spectrum analyzer. Alignment of SBC systems is performed by using an alignment collimator pointing in a reverse direction that defines the axis of
4 2 0 1062
1063
1064
Wavelength, nm
6
Power, mW
6
Power, mW
Power, mW
Fig. 3. Spectral beam combining of five laser sources using a stack of identical reflecting volume Bragg gratings.
4 2 0 1547
1548
1549
1550
6 4 2 0 1547.5
Wavelength, nm
1548
1548.5
Wavelength, nm
Position, mm
100 80 M2=1.12 60 40 20 0 -1.5 -1 -0.5 0 0.5 1 1.5
Position, mm
120 100 80 60 40 20 0
Beam width, μm
Beam width, μm
100 80 M2=1.11 60 40 20 0 -1.5 -1 -0.5 0 0.5 1 1.5
Beam width, μm
Fig. 4. Output spectra of three SBC systems.
M2=1.13
-1.5 -1 -0.5 0 0.5 1 1.5
Position, mm
Fig. 5. Spectrally combined output beams from three SBC systems around the focal plane of a test lens: 0.43 nm channel separation around 1064 nm (left), 0.51 nm channel separation around 1550 nm (center) and 0.25 nm channel separation around 1550 nm (right).
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the output beam. The channels are aligned sequentially, starting with one that is closer to the output and ending with one that is transmitted through all gratings. Laser source of a respective channel is coupled to the alignment collimator and a VBG corresponding to that channel is aligned to satisfy Bragg condition for that wavelength (the beam is diffracted with highest efficiency). Next, a working collimator is placed in a location where the alignment beam is diffracted to and laser output is switched to the working collimator. The working collimator is aligned to couple light diffracted by the VBG into the alignment collimator with maximum efficiency. As this procedure is repeated to align the next channel, the beam is transmitted through VBGs of previous channels due to an offset wavelength. After all channels are aligned, output beams from all channels are overlapped and collinear, resulting in a neardiffraction-limited spectrally-combined beam. This method allows alignment with accuracy better than 20 lrad. Times-diffraction-limit factors (commonly known as M2) of spectrally-combined output beams are measured by focusing beams with a test lens [15]. Slit-based beam profiler is used to scan beams in five planes along the direction of propagation. Beam widths calculated by second moment definition are fit to a hyperbolic equation to find M2 of the beams (Fig. 5). Spectrally-combined output beams from three SBC systems are near-diffraction-limited with roughly the same M2 as input beams. This indicates that accuracy of alignment is much better than divergence of beams and combining elements do not introduce beam distortions. Brightness of output beams is enhanced by 5 times compared to individual input beams. This approach can be scaled to high power by increasing the channel count and power per channel. Low absorption in visible and near-IR regions of spectrum and excellent thermo-mechanical properties of PTR glass allow it to withstand high-power radiation. Recently, five randomly polarized fiber lasers with 0.5 nm channel separation around 1064 nm were combined using this technique with 91.7% combining efficiency, resulting in 773 W output power in a combined beam [16,17]. It was shown that at this power level VBGs introduce no significant beam distortions. SBC of high-power lasers with small spectral separation of channels provides a clear path to obtaining near-diffraction-limited spectrally-combined beams with multi-kW power levels. 4. Conclusions Reflecting volume Bragg gratings in PTR glass enable high-efficiency combining of multiple laser beams with high spectral den-
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sity. Three systems that combine five beams with channel separation 0.25–0.5 nm around 1064 and 1550 nm with absolute efficiency 92–94% are demonstrated. Output of each system is a spectrally-combined near-diffraction-limited beam with enhanced brightness. Optical and thermo-mechanical properties of volume gratings allow scaling of such systems to multi-kW power levels. Acknowledgments This work is supported by DARPA/ADHELS (contract H0011-061-0010) and HEL-JTO (contract FA9451-06-D-0015) programs. References [1] T.Y. Fan, IEEE J. Sel. Top. Quantum Electron. 11 (2005) 567. [2] S.J. Augst, J.K. Ranka, T.Y. Fan, A. Sanchez, J. Opt. Soc. Am. B 24 (2007) 1707. [3] I.V. Ciapurin, L.B. Glebov, V.I. Smirnov, in: L.N. Durvasula (Ed.), Fiber Lasers: Technology, Systems, and Applications, Proceedings of SPIE, vol. 5335, 2004, p. 116. [4] T.H. Loftus, A. Liu, P.R. Hoffman, A.M. Thomas, M. Norsen, R. Royse, E. Honea, Opt. Lett. 32 (2007) 349. [5] S. Klingebiel, F. Röser, B. Ortaç, J. Limpert, A. Tünnermann, J. Opt. Soc. Am. B 24 (2007) 1716. [6] O. Andrusyak, I. Ciapurin, V. Smirnov, G. Venus, L. Glebov, in: Donald J. Harter, Andreas Tünnermann, Jes Broeng, Clifford Headley III (Eds.), Fiber Lasers IV: Technology, Systems, and Applications, Proceedings of SPIE, vol. 6453, 2007, p. 64531L. [7] O.M. Efimov, L. Glebov, V. Smirnov, High efficiency volume diffractive elements in photo-thermo-refractive glass, United States Patent 66,73,497, January 6, 2004. [8] O. Andrusyak, V. Smirnov, G. Venus, L. Glebov, Narrow-band volume Bragg gratings in PTR glass under high-power CW laser radiation, SSDLTR-2007 Technical Digest, Paper Code P-1, 2007. [9] S.J. Augst, A.K. Goyal, R.L. Aggarwal, T.Y. Fan, A. Sanchez, Opt. Lett. 28 (2003) 331. [10] O. Andrusyak, I. Ciapurin, V. Rotar, A. Sevian, G. Venus, L. Glebov, Dense spectral beam combining with volume Bragg gratings in PTR glass, SSDLTR2006 Technical Digest, Paper Code BC-3, 2006. [11] H. Kogelnik, Bell Syst. Tech. J. 48 (1969) 2909. [12] I. Ciapurin, L. Glebov, V. Smirnov, Opt. Eng. 45 (2006) 015802. [13] I. Ciapurin, L. Glebov, V. Smirnov, in: T.H. Jeong, H. Bjelkhagen, (Eds.), Practical Holography XIX: Materials and Applications, Proceedings of SPIE, vol. 5742, 2005, p. 183. [14] M.E. Riley, M.A. Gusinow, Appl. Opt. 16 (1977) 2753. [15] ISO 11146:1999, Lasers and laser-related equipment – Test methods for laser beam parameters – Beam widths, divergence angle and beam propagation factor. [16] O. Andrusyak, I. Ciapurin, V. Smirnov, G. Venus, N. Vorobiev, L. Glebov, in: Jes Broeng, Clifford Headley (Eds.), Fiber Lasers V: Technology, Systems, and Applications, Proceedings of SPIE, vol. 6873, 2008, p. 687314. [17] O. Andrusyak, V. Smirnov, G. Venus, V. Rotar, L. Glebov, IEEE J. Sel. Top. Quantum Electron. 2009, accepted for publication.