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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 10 — May. 12, 2008
  • pp: 7197–7202
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Gain-guiding in transverse grating waveguides for large modal area laser amplifiers

Tsing-Hua Her  »View Author Affiliations


Optics Express, Vol. 16, Issue 10, pp. 7197-7202 (2008)
http://dx.doi.org/10.1364/OE.16.007197


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Abstract

A new optically pumped waveguide amplifier with ultra-large mode area is proposed. This amplifier is based on gain guiding in a transverse grating waveguide in which the pump is confined by the photonic bandgap while the signal is guided by optical gain. Characteristics of the propagating modes of the waveguide amplifier are analyzed theoretically using the transfer matrix method, indicating robust single-transverse-mode operation with large modal gain.

© 2008 Optical Society of America

1. Introduction

Recently Siegman has proposed the use of optical gain in index-antiguided waveguides to achieve single-transverse-mode operation with ULMA [4

4. A. E. Siegman, “Propagating modes in gain-guided optical fibers,” J. Opt. Soc. Am. A. 20, 1617–1628 (2003). [CrossRef]

]. Such a scheme has been experimentally demonstrated in a flash-lamp-pumped neodymium-doped phosphate fiber with a core diameter of a few hundreds microns [5

5. A. E. Siegman, Y. Chen, V. Sudesh, M.C. Richardson, M. Bass, P. Foy, W. Hawkins, and J. Ballato, “Confined propagation and near single-mode laser oscillation in a gain-guided, index antiguided optical fiber,” App. Phys. Lett. 89, 251101 (2006). [CrossRef]

,6

6. Y. Chen, T. McComb, V. Sudesh, M. Richardson, and M. Bass, “Very large-core, single-mode, gainguided, index-antiguided fiber lasers,” Opt. Lett. 32, 2505–2507 (2007). [CrossRef] [PubMed]

]. Index antiguiding (IAG), although effectively reducing the threshold of gain guiding (GG), could trap pump light in the cladding leading to low optical gain in the core when the waveguides are end-pumped [7

7. V. Sudesh, T. McComb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A.E. Siegman, “Diode-pumped 200 µm diameter core, gain-guided, index-antiguided single mode fiber laser,” Appl. Phys. B 90, 369–372 (2008). [CrossRef]

]. This would be an unwanted situation because end pumping is one of the most desirable attributes of waveguide lasers and amplifiers. In this article I propose a new scheme that could potentially resolve the above issue. By enabling gain guiding in transverse grating waveguides, I show that the signal could have robust single-transverse-mode operation with ULMA, and at the same time the optical pump can be confined in the same core to achieve high optical gain and conversion efficiency. This scheme can be extended to other photonic bandgap based structures, and is potentially attractive for optically pumped high-power lasers and amplifiers.

2. Principle and analysis

It is well known that a one-dimensional grating can resonantly reflect light with wavelength λ at an incident angle θR, provided the grating pitch Λ meets the Bragg condition Λ=λ/(2nclsinθR). At resonance the reflectivity of the grating equals to tanh2(κw), which approaches unity if the coupling constant κ is large and/or the length of grating w is long. [8

8. A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (John Wiley & Sons, 2003).

] Given θR, the angular bandwidth of a grating resonance is approximately 2κ/(koncl cosθR), which could be very narrow if θR is small. Thus, GG-TGW is designed to have a strong and sharp resonance at the pump wavelength by employing large κw and small (but finite) θR. In such case the pump light can be effectively trapped inside the core via Bragg resonance, even though nco is smaller than ncl. On the other hand, the signal we are after has a single-transverse mode (i.e., the lowest order mode with mode order equals 0) that has a grazing incident angle in a large core. Due to its large mismatch from the grating resonance, the signal experiences the grating as a slab with refractive index ncl, which is slightly larger than nco as previously defined. Thus, the waveguide behaves like an IAG slab waveguide for the signal. With appropriate material gain in the core via optical pumping (i.e., ni>0), gain guiding is expected to take place and yield a single-transverse mode with ULMA [4

4. A. E. Siegman, “Propagating modes in gain-guided optical fibers,” J. Opt. Soc. Am. A. 20, 1617–1628 (2003). [CrossRef]

].

Ej(y)=ajEj(yyj)+aj+Ej+(yyj),
(1)

where aj represents the complex field amplitude and yj is the beginning coordinate of the j-th layer. For a slab, the eigenfunctions are the well-known plane waves

E(y)=eiky,E+(y)=eiky,
(2)

where k =[(ncko)2-βc2]1/2 is the transverse wavevector of a plane wave traveling obliquely in the slab. For a grating, the forward and backward traveling waves are strongly coupled and can be calculated from coupled mode theory to be

E(y)=(eiσyreiσy)eiSy,E+(y)=(eiσyreiσy)eiSy,
(3)

where σπ/Λ is the grating resonant wavenumber, rκ/(S+k -σ), and S≡[(k -σ)2-κ 2]1/2. In the above definition, I have chosen positive roots for k and S to allow a solution of leaky modes that have outgoing phase and are unbounded in the waveguides [1

1. R. J. Lang, K. Dzurk, A. A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, “Theory of gratingconfined broad-area lasers,” IEEE J. Quantum. Electron. 34, 2196–2210 (1998). [CrossRef]

].

Fig. 1. Schematic of a one-dimensional gain-guided transverse grating waveguide. The pump (blue) is confined via Bragg resonance and the signal (red) is confined by gain guiding (GG). Dashed and solid lines indicate leaky and bound rays, respectively. Positive ni represents gain. See text for details. (Color online)

(ajaj+)=Mj1(0).(Πi=1j1Mi(di)·Mi1(0))·M0(0)·(a0a0+),
(4)

where dj is the thickness of the j-th layer and Mj is the corresponding 2×2 transfer matrix. For a slab,

M(y)=(eikyeikyikeikyikeiky)
(5)

and for a grating,

M(y)=((eiσyreiσy)eiSy(eiσyreiσy)eiSy(i(σ+S)eiσy+ir(σS)eiσy)eiSy(ir(σS)eiσyi(σ+S)eiσy)eiSy).
(6)

3. Result and discussion

I consider a TGW with the following parameters: nco=1.5, core width d=125 µm, pump wavelength λp=980 nm, signal wavelength λs=1550 nm, and κ=100 cm-1. The grating also has an average refractive index ncl=1.5005 and a resonant incident angle θR=20°. Figure 2(a) shows the loci of the complex effective indexes neff=βc/ko of the eigenmodes at 980 nm for a TGW (red curve) and a conventional IAG-slab waveguide (blue curve) with otherwise identical parameters. All modes are essentially leaky due to index antiguiding. As expected, the conventional IAG-slab waveguide exhibits a monotonically increasing loss at higher mode order. The transverse grating waveguide, on the other hand, shows a similar trend at small mode order but exhibits a sharp increase in reflectivity near θR. The eigenmode that resides in the stopband of the gratings has essentially zero propagation loss and is hereafter named the “gap mode”. This gap mode, whose transverse wavevector is set by the grating period to be π/Λ, features a very large mode order (~250) with nearly uniform interference fringes across the entire core as shown in the inset of Fig. 2(b). The amplitude of the gap mode decays exponentially into the gratings, as is typical for a Bloch mode in the stopband of a grating [9

9. P. Yeh and A. Yariv, “Bragg reflecting waveguides,” Opt. Commun. 19, 427–430 (1976). [CrossRef]

]. As a comparison, Fig. 2(b) also shows the fundamental mode (blue curve) of the IAG-slab waveguide. It has a relatively small loss coefficient ~0.05 cm-1 at 980 nm due to grazing incidence; its leaky nature, however, is evident as its field amplitude is nonzero and rises gradually in the cladding.

Fig. 2. (a) Loci of the eigenmodes for a passive TGW and an IAG-slab waveguide at 980 nm, and for a passive TGW at 1.55 nm. (b) Field amplitudes of the gap mode for the TGW and the fundamental mode for the IAG waveguide as described in a at 980 nm. The inset shows the high-order-mode nature of the gap mode. (Color online)

Fig. 3. (a) Modal gain as a function of the pump gain in the core for the fundamental mode (i=0) and the first two higher-order modes (i=1, 2). (b) Field amplitudes of the fundamental mode at various material gains g up to the gain-guiding threshold of the first HOM. The wavelength is 1.55 µm. (Color online)

The bandwidth of a Bragg grating at its resonance is Δλ=λp2κ/(πnclsinθR), and this in principle imposes a minimum spectral separation between the pump and signal used in the proposed TGW scheme. For the present example, this corresponds to 15 nm which is smaller than the spectral separation in practical rare-earth-ion-doped laser/amplifier systems. In practice, however, the spectral separation is desired to be a few times larger than Δλ to avoid the finite reflectivity at the side lobes of the gratins. On the other hand, Δλ in principle can be made very small if a weak grating (and correspondingly a long grating length) is employed.

4. Conclusion

Acknowledgments

References and links

1.

R. J. Lang, K. Dzurk, A. A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, “Theory of gratingconfined broad-area lasers,” IEEE J. Quantum. Electron. 34, 2196–2210 (1998). [CrossRef]

2.

A. Yariv, Y. Xu, and S. Mookherjea, “Transverse Bragg resonance laser amplifier,” Opt. Lett. 28, 176–178 (2003). [CrossRef] [PubMed]

3.

W. Liang, Y. Xu, J. M. Choi, and A. Yariv, “Engineering transverse Bragg resonance waveguides for large modal volume lasers,” Opt. Lett. 28, 2079–2081 (2003). [CrossRef] [PubMed]

4.

A. E. Siegman, “Propagating modes in gain-guided optical fibers,” J. Opt. Soc. Am. A. 20, 1617–1628 (2003). [CrossRef]

5.

A. E. Siegman, Y. Chen, V. Sudesh, M.C. Richardson, M. Bass, P. Foy, W. Hawkins, and J. Ballato, “Confined propagation and near single-mode laser oscillation in a gain-guided, index antiguided optical fiber,” App. Phys. Lett. 89, 251101 (2006). [CrossRef]

6.

Y. Chen, T. McComb, V. Sudesh, M. Richardson, and M. Bass, “Very large-core, single-mode, gainguided, index-antiguided fiber lasers,” Opt. Lett. 32, 2505–2507 (2007). [CrossRef] [PubMed]

7.

V. Sudesh, T. McComb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A.E. Siegman, “Diode-pumped 200 µm diameter core, gain-guided, index-antiguided single mode fiber laser,” Appl. Phys. B 90, 369–372 (2008). [CrossRef]

8.

A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (John Wiley & Sons, 2003).

9.

P. Yeh and A. Yariv, “Bragg reflecting waveguides,” Opt. Commun. 19, 427–430 (1976). [CrossRef]

10.

A. E. Siegman, “Gain-guided, index-antiguided fiber lasers,” J. Opt. Soc. Am. A 24, 1677–1682 (2007). [CrossRef]

11.

K. Liu and E. Y. B. Pun, “Modeling and experiments of packaged Er3+-Yb3+ co-doped glass waveguide amplifiers,” Opt. Commun. 273, 413–420 (2007). [CrossRef]

12.

K. Liu and E. Y.B. Pun, “K+-Na+ ion-exchanged waveguides in Er3+-Yb3+ co-doped phosphate glasses using field-assisted annealing,” Appl. Opt. 43, 3179–3184 (2004). [CrossRef] [PubMed]

13.

D. L. Veasey, D. S. Funk, N. A. Sanford, and J. S. Hayden, “Arrays of distributed-Bragg-reflector waveguide lasers at 1536 nm in Yb/Er co-doped phosphate glass,” Appl. Phys. Lett. 74, 789–791 (1999). [CrossRef]

14.

S. Pissadakis and C. Pappas, “Planar periodic structures fabricated in Er/Yb co-doped phosphate glass using multi-beam ultraviolet laser holography,” Opt. Express 15, 4296–4303 (2007). [CrossRef] [PubMed]

OCIS Codes
(130.2790) Integrated optics : Guided waves
(140.3280) Lasers and laser optics : Laser amplifiers
(140.3490) Lasers and laser optics : Lasers, distributed-feedback
(140.3570) Lasers and laser optics : Lasers, single-mode
(140.4480) Lasers and laser optics : Optical amplifiers
(130.5296) Integrated optics : Photonic crystal waveguides

ToC Category:
Integrated Optics

History
Original Manuscript: March 17, 2008
Revised Manuscript: April 30, 2008
Manuscript Accepted: April 30, 2008
Published: May 2, 2008

Citation
Tsing-Hua Her, "Gain-guiding in transverse grating waveguides for large modal area laser amplifiers," Opt. Express 16, 7197-7202 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-10-7197


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References

  1. R. J. Lang, K. Dzurk, A. A. Hardy, S. Demars, A. Schoenfelder, and D. F. Welch, "Theory of grating-confined broad-area lasers," IEEE J. Quantum. Electron. 34, 2196-2210 (1998). [CrossRef]
  2. A. Yariv, Y. Xu, and S. Mookherjea, "Transverse Bragg resonance laser amplifier," Opt. Lett. 28, 176-178 (2003). [CrossRef] [PubMed]
  3. W. Liang, Y. Xu, J. M. Choi, and A. Yariv, "Engineering transverse Bragg resonance waveguides for large modal volume lasers," Opt. Lett. 28, 2079-2081 (2003). [CrossRef] [PubMed]
  4. A. E. Siegman, "Propagating modes in gain-guided optical fibers," J. Opt. Soc. Am. A. 20, 1617-1628 (2003). [CrossRef]
  5. A. E. Siegman, Y. Chen, V. Sudesh, M.C. Richardson, M. Bass, P. Foy, W. Hawkins, and J. Ballato, "Confined propagation and near single-mode laser oscillation in a gain-guided, index antiguided optical fiber," App. Phys. Lett. 89, 251101 (2006). [CrossRef]
  6. Y. Chen, T. McComb, V. Sudesh, M. Richardson, and M. Bass, "Very large-core, single-mode, gain-guided, index-antiguided fiber lasers," Opt. Lett. 32, 2505-2507 (2007). [CrossRef] [PubMed]
  7. V. Sudesh, T. McComb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A.E. Siegman, "Diode-pumped 200 μm diameter core, gain-guided, index-antiguided single mode fiber laser," Appl. Phys. B 90, 369-372 (2008). [CrossRef]
  8. A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (John Wiley & Sons, 2003).
  9. P. Yeh and A. Yariv, "Bragg reflecting waveguides," Opt. Commun. 19, 427-430 (1976). [CrossRef]
  10. A. E. Siegman, "Gain-guided, index-antiguided fiber lasers," J. Opt. Soc. Am. A 24, 1677-1682 (2007). [CrossRef]
  11. K. Liu and E. Y. B. Pun, "Modeling and experiments of packaged Er3+-Yb3+ co-doped glass waveguide amplifiers," Opt. Commun. 273,413-420 (2007). [CrossRef]
  12. K. Liu and E. Y.B. Pun, "K+-Na+ ion-exchanged waveguides in Er3+-Yb3+ co-doped phosphate glasses using field-assisted annealing," Appl. Opt. 43,3179-3184 (2004). [CrossRef] [PubMed]
  13. D. L. Veasey, D. S. Funk, N. A. Sanford, and J. S. Hayden, "Arrays of distributed-Bragg-reflector waveguide lasers at 1536 nm in Yb/Er co-doped phosphate glass," Appl. Phys. Lett. 74, 789-791 (1999). [CrossRef]
  14. S. Pissadakis and C. Pappas, "Planar periodic structures fabricated in Er/Yb co-doped phosphate glass using multi-beam ultraviolet laser holography," Opt. Express 15, 4296-4303 (2007). [CrossRef] [PubMed]

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