## Theoretical study on Brillouin fiber laser sensor based on white light cavity |

Optics Express, Vol. 20, Issue 27, pp. 28234-28248 (2012)

http://dx.doi.org/10.1364/OE.20.028234

Acrobat PDF (1350 KB)

### Abstract

We present and theoretically study a superluminal fiber laser based super-sensor employing Brillouin gain. The white light cavity condition is attained by introducing a phase shift component comprising an additional ring or Fabry-Perot cavity into the main cavity. By adjusting the parameters of the laser cavity and those of the phase component it is possible to attain sensitivity enhancement of many orders of magnitude compared to that of conventional laser sensors. The tradeoffs between the attainable sensitivity enhancement, the cavity dimensions and the impact of the cavity roundtrip loss are studied in details, providing a set of design rules for the optimization of the super-sensor.

© 2012 OSA

## 1. Introduction

12. G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett. **99**(13), 133601 (2007). [CrossRef] [PubMed]

17. S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. **95**(1), 013901 (2005). [CrossRef] [PubMed]

14. H. N. Yum, M. Salit, J. Yablon, K. Salit, Y. Wang, and M. S. Shahriar, “Superluminal ring laser for hypersensitive sensing,” Opt. Express **18**(17), 17658–17665 (2010). [CrossRef] [PubMed]

13. M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A **75**(5), 053807 (2007). [CrossRef]

## 2. White light cavity sensor

16. S. Wise, G. Mueller, D. Reitze, D. B. Tanner, and B. F. Whiting, “Linewidth-broadened Fabry-Perot cavities within future gravitational wave detectors,” Class. Quantum Gravity **21**(5), S1031–S1036 (2004). [CrossRef]

17. S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. **95**(1), 013901 (2005). [CrossRef] [PubMed]

*L/2,*incorporating a dispersive section of length

*l/2*. For a given frequency

*ω*

_{0}, the phase shift accumulated in a single roundtrip is given by:where

*ϕ*(

*ω*

_{res}) = 2π

*m*. In order to achieve the WLC condition we need Δ

*ϕ*to remain 2π

*m*regardless the frequency, at least within a certain vicinity of

*ω*

_{res}:Expanding Eq. (2) and subtracting Eq. (1) from it, keeping only the leading terms in Δ

*ω,*yields the negative slope necessary for the WLC condition:where

*n*is the group index of the section

_{g}*l*at

*ω*

_{res}and the dispersion relation of that section close to resonance was expanded to the first order in Δ

*ω*. Note, that Eq. (3) clearly indicate that

*n*must be smaller than one or even negative in order to satisfy the WLC condition, which means that it must have anomalous dispersion.

_{g}*ω*is a resonance frequency of the cavity,

_{res}*n*is the refractive index of the normal-dispersion medium inside the cavity,

_{p}*L'*is the cavity length,

*θ*is the phase response of the phase element,

*m*is an integer, and Δ

*ω*is an arbitrary frequency shift. Expanding Eq. (4) to first order in Δ

*ω*, i.e.

*θ*(

*ω*

_{res}+ Δ

*ω*)≈

*ω*

_{res}+

*dθ*/

*dω*⋅Δ

*ω*and

*n*

_{p}(

*ω*

_{res}+ Δ

*ω*)≈

*n*

_{p}(

*ω*

_{res}) +

*dn*

_{p}/

*dω*⋅Δ

*ω*yields:where

*n*

_{pg}is the group index of the positive dispersion medium and Δ

*ω*

_{FSR}is the free spectral range of the cavity without the fast-light phase section. Equation (5) provides a general condition for the phase shift needed to attain the WLC condition.

*S*, of a cavity based sensor is the ratio between the change (

*δL*) in its effective length, and the corresponding shift (

*δω*) in the resonance frequency:

*S*=

*δω*/

*δL*. The larger

*S*is, the higher the sensitivity of the sensor. For a conventional cavity, the sensitivity is given by a simple expression:where

*n*and

_{p}*n*are respectively the effective and group indices of refraction for the normal dispersive section of the cavity. For a cavity incorporating a negative slope phase component, Eq. (6) is modified, yielding:

_{pg}## 3. Fiber laser implementation

*L*

_{r}k_{0}

*n*

_{eff}= 2π

*m*and Fabry-Perot satisfying 2

*L*

_{fp}k_{0}

*n*

_{eff}= 2π

*m*accordingly. The phase response of the phase element depicted in Fig. 3 is given by:where

*φ*=

*L*

_{r}n_{eff}

*ω*/

*c*=

*2L*

_{fp}n_{eff}

*ω*/

*c*,

*κ*

_{1}and

*κ*

_{2}are the power coupling coefficients as shown in Fig. 3(a) and

*r*and

_{1}*r*are the mirror reflection coefficients as shown in Fig. 3(b). Both Ring Resonator and Fabry-Perot implementations are mathematically analogous with

_{2}*κ*

_{1,2}

*= 1*-

*r*

_{1,2}

^{2}and

*L*=

_{r}*2L*. Equation (8) provides the phase shift introduced by the additional cavity. In order to attain a WLC, Eq. (8) must satisfy Eq. (5). Introducing the derivative of Eq. (8) with respect to the frequency at resonance into Eq. (5) provides the relations between

_{fp}*κ*

_{1}and

*κ*

_{2}needed to achieve the WLC condition and similarly for

*r*

_{1}and

*r*

_{2}:

*κ*

_{1}and

*κ*

_{2}for a given ratio between the cavities lengths:

*M*=

*L'*/

*L*=

_{r}*L'*/2

*L*. Introducing

_{fp}*α*

^{2}

*= r*

_{1}= 1-

*κ*and

_{1}*β*

^{2}

*= r*

_{2}= 1-

*κ*, yields the following relation between the coefficients:

_{2}*lasing*frequency (not the pump). The inset shows schematically the effective gain profile and the corresponding phase profile. The additional cavity introduces a notch in the center of the Brillouin gain profile, resulting in a negatively sloped phase profile [12

12. G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett. **99**(13), 133601 (2007). [CrossRef] [PubMed]

14. H. N. Yum, M. Salit, J. Yablon, K. Salit, Y. Wang, and M. S. Shahriar, “Superluminal ring laser for hypersensitive sensing,” Opt. Express **18**(17), 17658–17665 (2010). [CrossRef] [PubMed]

*ν*compared to the frequency of the forward traveling wave (where n is the effective refractive index of the medium,

_{B}= 2nv_{a}/λ*v*is the speed of sound in the medium and

_{a}*λ*is the vacuum wavelength of the forward traveling wave). The linewidth of the scattered wave is determined by the acoustic absorption of the medium. In optical fibers,

*ν*≈10.8GHz while the linewidth

_{B}*Δν*ranges from 10 to 30MHz. By using a cavity with a FSR larger than

*Δν*(roughly

*L'<10.5m)*while pumping the cavity using a strong tunable laser source, in a setup similar to Fig. 4, substantial gain can be provided for the desirable WLC cavity mode, overcoming losses and favoring it from the other cavity modes. As a concrete example, consider a 10m long fiber cavity, with a roundtrip loss (due to a combination of the transmission losses from the circulator and the phase component) of approximately 1.5dB (see also section 5). Using the Brillouin gain coefficient of a single mode fiber (

*γ*= 0.14 m

^{−1}W

^{−1}[18

18. A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photon. **2**(1), 1–59 (2010). [CrossRef]

## 4. Sensitivity enhancement in Brillouin ring fiber laser

*L'*. Following this modification the resonance frequency must be recalculated taking into account the dispersion of the Brillouin gain and (for the superluminal laser) the dispersion of the phase element. Designating the frequency shift in a conventional Brillouin laser by Δ

*ω*

_{c}and that in a superluminal laser by Δ

*ω*

_{s}, we define the sensitivity enhancement as

*ξ*= Δ

*ω*

_{s}/Δ

*ω*

_{c}.

*ω*

_{res}satisfying:

*θ*

_{Br}is the phase shift caused by the dispersion of the

*saturated*Brillouin lineshape. Equation (12) satisfies only the phase condition for the lasing frequency and must be supplemented by the amplitude condition. It should be noted that although the sensitivity depends on the resonance condition, the amplitude condition determines the necessary gain (pump level) for lasing which, in turn, affects the dispersion properties of the saturated gain, Δ

*θ*

_{Br}in Eq. (12). Note, that for a conventional laser, the equations are identical except that

*θ*= 0.

*θ*

_{Br}, in is necessary to solve for the laser threshold conditions and employ the relations between the real and imaginary part of the susceptibilities [19]:where

*ω*

_{0}is the frequency at which the Brillouin gain peaks (set to the resonance frequency of the WLC) and Δ

*ω*

_{Br}is the linewidth of the Brillouin gain.

*χ’*and

*χ”*are respectively the real and imaginary parts of the dielectric susceptibility. When the system is lasing, the gain compensates the overall roundtrip losses of the cavity. Denoting the roundtrip transmission as

*T*, then

*χ’*and

*χ”*are given by:where

*k*

_{0}and

*n*are respectively the wavenumber and the refractive index of the fiber.

*f*

_{Brillouin}= 40MHz and

*T*= 0.9, the effective additional length induced by the Brillouin phase shift is ~1m.

*κ*

_{1}and

*κ*

_{2}and for various ratios between

*L'*and

*L*(a Fabry-Perot based arrangement is completely analogous, as shown above). Figure 5 depicts the optimal relation between the coupling coefficients for

_{r}*L'/L*of 1/3, 0.5, 1, 2, 3, and 4 as calculated from Eq. (12). For the simulations, the chosen parameters were

_{r}*L'*= 10m, Δ

*f*

_{Brillouin}= 40MHz, and “central” wavelength of 1.55μm. The ring laser circumference was chosen in order to ensure a single cavity mode within the Brillouin gain line. Note that as the cavity of the phase element becomes shorter, the optimal κ

_{2}for a given κ

_{1}becomes smaller, pushing the phase element closer to the critical coupling regime. However, it should be clear that the closer the phase element cavity to critical coupling, the larger the loss induced by this element (i.e. lower

*T*in Fig. 3).

## 5. Nonlinearity of the sensitivity enhancement

*δL*in the cavity length and is expected to decrease for larger

*δL*. Specifically, the sensitivity enhancements depicted in Figs. 6 and 7 were found for

*δL*= 0.1nm but it is expected to increase for smaller changes and to decrease for larger changes.

*δω*and

*δL*, yielding the following Eq. for

*δω*:

*R*1-

_{i}=*κ*. Assuming the sensor is set to the WLC Eq. (9), then Eq. (18) yields a simple cubic equation for

_{i}*δω*which can be readily solved:

*δL*(the measured quantity) which means that the sensitivity enhancement is not a constant but rather depends on the measured quantity:

*L*/

^{'}*L*2,

_{r}=*κ*

_{1}= 0.5 and

*κ*

_{2}= 0.7414, corresponding to an optimal configuration. As shown in the figure, the sensitivity enhancement increases dramatically for small

*δL*, exceeding 400 for

*δL*~10pm. However, the sensitivity enhancement drops rapidly as

*δL*is increased although the enhancement for

*δL*≈1nm still exceeds 20.

## 6. Design tradeoffs

*M*also affects the relations between

*κ*

_{1}and

*κ*

_{2}, as can be seen from Eq. (11). However, the improvement in the sensitivity enhancement is accompanied by larger excess roundtrip losses induced by the phase component. Figure 9 depicts the dependence of the sensitivity enhancement on δ

*L*for several values of M, where

*κ*

_{1}= 0.03 and

*κ*

_{2}for each

*M*is found from Eq. (11). The inset zooms in on smaller

*δL*range (in linear scale). The enhancement is shown in a logarithmic scale in order to clarify the difference between the various

*M*levels. Figure 10 depicts the excess roundtrip losses induced by the phase component. For M = 1 the phase component introduces excess losses of 30% per roundtrip while for M = 5 the loss exceeds 50% per roundtrip. Thus, although the phase components with shorter cavities provide larger enhancement level, the substantial excess loss they induce may pose a serious problem.

*κ*

_{2}is determined directly by

*κ*

_{1}, it is the choice of

*κ*

_{1}which eventually determines the enhancement and the excess loss. Figure 11 depicts the sensitivity enhancement as a function of

*δL*for several coupling coefficients (

*κ*

_{1}). The inset depicts the corresponding excess losses. Decreasing

*κ*

_{1}results in an overall lower sensitivity enhancement factor but also lower excess losses. Therefore, Fig. 11 provides the necessary design tradeoffs allowing for optimizing and balancing between desired enhancement levels and acceptable roundtrip losses.

## 7. Some practical considerations

*δL*. As shown in Fig. 8, the sensitivity enhancement varies over an order of magnitude for

*δL*ranging between 10pm to 1nm. Such nonlinear response makes it difficult to use the induced resonance shift as a direct measure to the change in the cavity length in an “open-loop” configuration. Thus, in order to take advantage of the large sensitivity enhancement at small

*δL*, it is advantageous to operate such sensor in a “closed-loop” configuration in which a counter modification in the cavity length is introduced in order to return the resonance frequency to its “original” value.

*ξP*

^{1/2}). For a given Brillouin pump power available, the power of the sensing laser,

*P*, generally decreases with increasing Λ. The exact variation of P as a function of Λ depends on the nature of gain saturation. In the limit of a lasing condition where loss equals unsaturated gain,

*P*is proportional to 1/Λ. Taking this as the limiting case, we can see that the minimum measurable perturbation is proportional to (Λ

^{ε}/ξ), where the exponent ε has a value somewhere between 1 and 3/2. This dependence should be used as a guide in determining the optimal operating condition for the sensor. Of course, we must also ensure that the loss is small enough so that the available pump power is above the lasing threshold. Note that in Eq. (23) the sensitivity enhancement parameter,

*ξ*, itself depends on

*δL*. Specifically,

*ξ*increases with decreasing

*δL*. Thus, Eq. (23) has to be solved in a self-consistent manner. Numerically, this can be done by evaluating the right hand side (RHS) of Eq. (23) for decreasing values of

*δL*until it (the RHS) matches the value of

*δL.*

*δL*

_{min}for a 1 m WLC fiber laser with intrinsic losses of 5% per revolution where the pump is set to attain a value of

*P*= 10mW inside the cavity in the absence of the additional phase component. Figure 12 shows

*δL*

_{min}as a function of

*κ*

_{1}for a WLC laser where

*M*= 1 and

*κ*

_{2}is set to meet the WLC condition. For comparison,

*δL*

_{min}for a conventional fiber laser with the same length and 1 sec averaging time is ~4.4x10

^{−17}m. As can be seen, the minimal measurable

*δL*

_{min}is smaller by nearly 8 orders of magnitudes for a relatively large range of coupling coefficients

*κ*

_{1}. This is a highly attractive property because it means that the precise values of parameters are relatively unimportant as long as the laser lases and the WLC is satisfied.

*F*~10 and

*P*= 10mW in the above example), the impacts of the Kerr effect and Raman scattering are not expected to impair significantly the performance of the sensor, as discussed below. Four wave mixing process is also inefficient because the pump and signal are counter-propagating and the pump is not resonant in the cavity (single pass). Second, control of polarization is also required in order to ensure single mode operation. This can done either by introducing a polarization controller to the cavity (as in Fig. 4) or by using a polarization maintaining fiber. Finally, Rayleigh scattering in the lasing frequency cannot build up because of the circulator located in the cavity forcing uni-directional lasing.

23. S. Huang, L. Thevenaz, K. Toyama, B. Y. Kim, and H. J. Shaw, “Optical Kerr-effect in fiber-optic Brillouin ring laser gyroscopes,” IEEE Photon. Technol. Lett. **5**(3), 365–367 (1993). [CrossRef]

## 8. Conclusions

*δL*) is accompanied by larger roundtrip loss. This relation is important because larger losses are expected to increase the minimal measurable

*δL*. The overall sensitivity enhancement and excess losses are determined by phase component coupling coefficients and cavity length. Larger coupling coefficients provide higher enhancement factors but also larger excess losses. The length of the phase component cavity is also important: shorter cavities can provide larger sensitivity enhancements which are, again, accompanied by higher losses. Nevertheless, the impact on the minimal measurable perturbation is relatively small because of the large enhancement levels at small perturbations.

## Acknowledgment

## References and links

1. | P. Hariharan, |

2. | G. Gauglitz, “Direct optical sensors: principles and selected applications,” Anal. Bioanal. Chem. |

3. | B. J. Meers, “Recycling in laser-interferometric gravitational-wave detectors,” Phys. Rev. D Part. Fields |

4. | G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rudiger, and K. Danzmann, “Experimental demonstration of a suspended dual recycling interferometer for gravitational wave detection,” Phys. Rev. Lett. |

5. | M. B. Gray, A. J. Stevenson, H.-A. Bachor, and D. E. McClelland, “Broadband and tuned signal recycling with a simple Michelson interferometer,” Appl. Opt. |

6. | B. J. Meers, “The frequency response of interferometric gravitational wave detectors,” Phys. Lett. A |

7. | P. Lambeck, “Integrated optical sensors for the chemical domain,” Meas. Sci. Technol. |

8. | A. Leung, P. M. Shankar, and R. Mutharasan, “A review of fiber-optic biosensors,” Sens. Actuators B Chem. |

9. | R. Ulrich, “Fiber-optic rotation sensing with low drift,” Opt. Lett. |

10. | R. E. Meyer, S. Ezekiel, D. W. Stowe, and V. J. Tekippe, “Passive fiber-optic ring resonator for rotation sensing,” Opt. Lett. |

11. | A. Lenef, T. D. Hammond, E. T. Smith, M. S. Chapman, R. A. Rubenstein, and D. E. Pritchard, “Rotation sensing with an atom interferometer,” Phys. Rev. Lett. |

12. | G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett. |

13. | M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A |

14. | H. N. Yum, M. Salit, J. Yablon, K. Salit, Y. Wang, and M. S. Shahriar, “Superluminal ring laser for hypersensitive sensing,” Opt. Express |

15. | J. Schaar, H. Yum, and M. S. Shahriar, “Theoretical Description and Design of a Fast-Light Enhanced Helium-Neon Ring-Laser Gyroscope,” Proc. SPIE 7949, Advances in Slow and Fast Light |

16. | S. Wise, G. Mueller, D. Reitze, D. B. Tanner, and B. F. Whiting, “Linewidth-broadened Fabry-Perot cavities within future gravitational wave detectors,” Class. Quantum Gravity |

17. | S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett. |

18. | A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photon. |

19. | M. O. Scully and W. E. Lamb, |

20. | T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, and H. Statz, “Laser gyro at quantum limit,” IEEE J. Quantum Electron. |

21. | J. D. Cresser, W. H. Louisell, P. Meystre, W. Schleich, and M. O. Scully, “Quantum noise in ring laser gyros. I. Theoretical formulation of the problem,” Phys. Rev. A |

22. | B. T. King, “Application of superresolution techniques to ring laser gyroscopes: exploring the quantum limit,” Appl. Opt. |

23. | S. Huang, L. Thevenaz, K. Toyama, B. Y. Kim, and H. J. Shaw, “Optical Kerr-effect in fiber-optic Brillouin ring laser gyroscopes,” IEEE Photon. Technol. Lett. |

**OCIS Codes**

(280.3420) Remote sensing and sensors : Laser sensors

(290.5830) Scattering : Scattering, Brillouin

**ToC Category:**

Sensors

**History**

Original Manuscript: September 25, 2012

Revised Manuscript: October 28, 2012

Manuscript Accepted: October 29, 2012

Published: December 5, 2012

**Citation**

Omer Kotlicki, Jacob Scheuer, and M.S. Shahriar, "Theoretical study on Brillouin fiber laser sensor based on white light cavity," Opt. Express **20**, 28234-28248 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-27-28234

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### References

- P. Hariharan, Basics of Interferometry, 2nd ed (Academic Press, 2006).
- G. Gauglitz, “Direct optical sensors: principles and selected applications,” Anal. Bioanal. Chem.381(1), 141–155 (2005). [CrossRef] [PubMed]
- B. J. Meers, “Recycling in laser-interferometric gravitational-wave detectors,” Phys. Rev. D Part. Fields38(8), 2317–2326 (1988). [CrossRef] [PubMed]
- G. Heinzel, K. A. Strain, J. Mizuno, K. D. Skeldon, B. Willke, W. Winkler, R. Schilling, A. Rudiger, and K. Danzmann, “Experimental demonstration of a suspended dual recycling interferometer for gravitational wave detection,” Phys. Rev. Lett.81(25), 5493–5496 (1998). [CrossRef]
- M. B. Gray, A. J. Stevenson, H.-A. Bachor, and D. E. McClelland, “Broadband and tuned signal recycling with a simple Michelson interferometer,” Appl. Opt.37(25), 5886–5893 (1998). [CrossRef] [PubMed]
- B. J. Meers, “The frequency response of interferometric gravitational wave detectors,” Phys. Lett. A142(8-9), 465–470 (1989). [CrossRef]
- P. Lambeck, “Integrated optical sensors for the chemical domain,” Meas. Sci. Technol.17(8), R93–R116 (2006). [CrossRef]
- A. Leung, P. M. Shankar, and R. Mutharasan, “A review of fiber-optic biosensors,” Sens. Actuators B Chem.125(2), 688–703 (2007). [CrossRef]
- R. Ulrich, “Fiber-optic rotation sensing with low drift,” Opt. Lett.5(5), 173–175 (1980). [CrossRef] [PubMed]
- R. E. Meyer, S. Ezekiel, D. W. Stowe, and V. J. Tekippe, “Passive fiber-optic ring resonator for rotation sensing,” Opt. Lett.8(12), 644–646 (1983). [CrossRef] [PubMed]
- A. Lenef, T. D. Hammond, E. T. Smith, M. S. Chapman, R. A. Rubenstein, and D. E. Pritchard, “Rotation sensing with an atom interferometer,” Phys. Rev. Lett.78(5), 760–763 (1997). [CrossRef]
- G. S. Pati, M. Salit, K. Salit, and M. S. Shahriar, “Demonstration of a tunable-bandwidth white-light interferometer using anomalous dispersion in atomic vapor,” Phys. Rev. Lett.99(13), 133601 (2007). [CrossRef] [PubMed]
- M. S. Shahriar, G. S. Pati, R. Tripathi, V. Gopal, M. Messall, and K. Salit, “Ultrahigh enhancement in absolute and relative rotation sensing using fast and slow light,” Phys. Rev. A75(5), 053807 (2007). [CrossRef]
- H. N. Yum, M. Salit, J. Yablon, K. Salit, Y. Wang, and M. S. Shahriar, “Superluminal ring laser for hypersensitive sensing,” Opt. Express18(17), 17658–17665 (2010). [CrossRef] [PubMed]
- J. Schaar, H. Yum, and M. S. Shahriar, “Theoretical Description and Design of a Fast-Light Enhanced Helium-Neon Ring-Laser Gyroscope,” Proc. SPIE 7949, Advances in Slow and Fast LightIV, 794914 (2011).
- S. Wise, G. Mueller, D. Reitze, D. B. Tanner, and B. F. Whiting, “Linewidth-broadened Fabry-Perot cavities within future gravitational wave detectors,” Class. Quantum Gravity21(5), S1031–S1036 (2004). [CrossRef]
- S. Wise, V. Quetschke, A. J. Deshpande, G. Mueller, D. H. Reitze, D. B. Tanner, B. F. Whiting, Y. Chen, A. Tünnermann, E. Kley, and T. Clausnitzer, “Phase effects in the diffraction of light: beyond the grating equation,” Phys. Rev. Lett.95(1), 013901 (2005). [CrossRef] [PubMed]
- A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photon.2(1), 1–59 (2010). [CrossRef]
- M. O. Scully and W. E. Lamb, Laser Physics (Westview Press, Boulder, CO, 1974).
- T. A. Dorschner, H. A. Haus, M. Holz, I. W. Smith, and H. Statz, “Laser gyro at quantum limit,” IEEE J. Quantum Electron.16(12), 1376–1379 (1980). [CrossRef]
- J. D. Cresser, W. H. Louisell, P. Meystre, W. Schleich, and M. O. Scully, “Quantum noise in ring laser gyros. I. Theoretical formulation of the problem,” Phys. Rev. A25(4), 2214–2225 (1982). [CrossRef]
- B. T. King, “Application of superresolution techniques to ring laser gyroscopes: exploring the quantum limit,” Appl. Opt.39(33), 6151–6157 (2000). [CrossRef] [PubMed]
- S. Huang, L. Thevenaz, K. Toyama, B. Y. Kim, and H. J. Shaw, “Optical Kerr-effect in fiber-optic Brillouin ring laser gyroscopes,” IEEE Photon. Technol. Lett.5(3), 365–367 (1993). [CrossRef]

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