Blue-pumped whispering gallery optical parametric oscillator

doi:10.1364/OL.37.004224

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Blue-pumped whispering gallery optical parametric oscillator

Christoph Sebastian Werner, Tobias Beckmann, Karsten Buse, and Ingo Breunig »View Author Affiliations

Optics Letters, Vol. 37, Issue 20, pp. 4224-4226 (2012)
http://dx.doi.org/10.1364/OL.37.004224

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Abstract

We demonstrate a whispering gallery optical parametric oscillator pumped at 488 nm wavelength. This millimeter-sized device has a pump threshold of 160 μW. The signal field is tunable between 707 and 865 nm wavelength and the idler field between 1120 and 1575 nm through temperature variation. Although the conversion efficiency is fundamentally limited to several percent because of absorption loss for the pump wave, the results provide evidence that such oscillators will be able to cover finally the entire visible range.

Optical parametric oscillators (OPOs) can be employed to generate coherent light at almost arbitrary frequency [1

M. H. Dunn and M. Ebrahimzadeh, Science 286, 1513 (1999). [CrossRef]

]. The only fundamental limitation is that the optical pump field has a shorter wavelength

λ_{p}

compared to the wavelengths

λ_{s}

and

λ_{i}

of the two generated fields, called signal and idler waves. Here, the relation

1 / λ_{p} = 1 / λ_{s} + 1 / λ_{i}

holds. Conventional OPOs comprise a nonlinear-optical crystal inside of a mirror cavity. The mirrors have to be specially coated for the spectral range in which the device is aimed to operate. Recently, a new class of OPOs has been demonstrated—whispering gallery OPOs [2

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010). [CrossRef]

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011). [CrossRef]

]. They do not require any external mirrors. In these exceptional devices, light is guided by total internal reflection inside the nonlinear-optical crystal. Thus, whispering gallery OPOs provide a low-loss cavity over the whole transparency range of the crystal. This has enabled pump thresholds below 10 μW [2

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010). [CrossRef]

]. The green-pumped devices demonstrated so far have a tuning range between 1010 and 1120 nm [2

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010). [CrossRef]

M. Förtsch, J. U. Fürst, C. Wittmann, D. V. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and Ch. Marquardt, “Accurate group delay measurement for radial velocity instruments using the dispersed fixed delay interferometer method,” arXiv 1204.3056 (2012).

] while the near-infrared-pumped devices are tunable between 1800 and 2500 nm [3

T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011). [CrossRef]

]. Pump lasers operating in the blue can extend the tunability into the visible spectral range. This is of interest, e.g., for coupling of nonclassical light from a whispering gallery OPO [5

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 106, 113901 (2011). [CrossRef]

] to rubidium atoms or diamond vacancies. Such experiments require signal wavelengths around 795 or 639 nm, respectively.

In this Letter, we present a whispering gallery OPO pumped in the blue at 488 nm wavelength. The experimental setup sketched in Fig. 1 comprises a spheroidally shaped monolithic cavity (1.8 mm major diameter, 0.7 mm minor diameter, 1 mm thickness) made of a

z

-cut stoichiometric lithium niobate crystal doped with 1.2% magnesium oxide. The resonator is mounted in an oven whose temperature can be varied between 30 and 170 °C. We use a rutile prism to couple the pump light with the power

P_{p}

into the resonator. The gap between the resonator and the coupling prism can be adjusted using a piezo translator. Inside the cavity, the pump wave is converted to signal and idler waves, while all interacting waves oscillate in the cavity. The pump field is extraordinarily polarized, whereas the signal and the idler fields are ordinarily polarized. This ensures type I phase matching. Two detectors are used to measure the power

P_{p}^{*}

of the transmitted portion of the pump light and the power

P_{s}

of the signal wave. The silicon-based detector for the signal wave is not influenced by the idler light (wavelength larger than 1200 nm). Furthermore, we investigate the spectrum of the light generated by the parametric process in the wavelength range between 300 and 2500 nm.

Fig. 1. Illustration of the experimental setup:

P_{p}

P_{p}^{*}

, and

P_{s}

represent powers of the pump wave at 488 nm, of its transmitted portion, and of the signal light, respectively. The inset shows a microscope picture of the resonator, whereas the arrow indicates the direction of the crystallographic

z

-axis.

In order to determine the quality factor of the optical whispering gallery, we scan the pump laser frequency

ν

across a cavity mode and measure the transmitted power

P_{p}^{*}

versus the frequency shift. This is shown in Fig. 2. The linewidth

Δ ν

in absence of parametric oscillation ranges from 80 (prism far from the resonator) to 140 MHz (prism touching the resonator). The first value yields the intrinsic quality factor

Q_{p} \equiv ν / Δ ν = 7.7 \times 10^{6}

for the pump wave. From here, we can deduce the absorption coefficient

α_{p} = 2 π n_{p} / λ_{p} Q_{p} \approx 3.8 m^{- 1}

with the refractive index

n_{p} = 2.25

D. H. Jundt, M. M. Fejer, and R. L. Byer, IEEE J. Quantum Electron. 26, 135 (1990). [CrossRef]

], assuming that the intrinsic cavity loss is dominated by absorption. This value agrees quite well with the previously measured coefficient

(2 \dots 3) m^{- 1}

for congruent lithium niobate [7

J. R. Schwesyg, M. C. C. Kajiyama, M. Falk, D. H. Jundt, K. Buse, and M. M. Fejer, Appl. Phys. B 100, 109 (2010). [CrossRef]

]. The ratio between the highest and lowest linewidth is smaller than two. From this, we can conclude that we are not able to achieve critical coupling or overcoupling; i.e., the internal loss is always larger than the coupling loss. The coupling efficiency

κ

was limited to 40% for a vanishing gap between the prism and the resonator.

Fig. 2. Transmitted pump power

P_{p}^{*}

and signal power

P_{s}

as a function of the frequency shift of the pump laser at 40 °C resonator temperature.

Later, we want to compare the pump threshold as well as the conversion efficiency of the OPO to the theoretically expected values. For this purpose, we take here a closer look on the measured linewidths and coupling efficiencies. With the coefficient

r_{p}

being the ratio between the coupling loss and the internal loss for the pump wave, we get [8

B. Sturman and I. Breunig, J. Opt. Soc. Am. B 28, 2465 (2011). [CrossRef]

]

Δ ν = ν (\frac{1}{Q_{p}} + \frac{1}{Q_{c}}) = Δ ν_{0} (r_{p} + 1),

(1)

κ = 4 \frac{Q_{p} Q_{c}}{{(Q_{p} + Q_{c})}^{2}} = 4 \frac{r_{p}}{{(r_{p} + 1)}^{2}},

(2)

with

Q_{c}

as the coupling quality factor and

Δ ν_{0} = ν / Q_{p}

as the linewidth determined by the intrinsic loss. At

r_{p} < 1

, the resonator is undercoupled, and at

r_{p} > 1

the resonator is overcoupled. From Eq. (1) we deduce

r_{p} = 0.75

for the prism touching the resonator. For this value, Eq. (2) shows that 98% of the pump light could be coupled into the resonator for perfect mode matching. Since we achieve 40% coupling efficiency instead, only the power

\tilde{P_{p}} = 0.41 P_{p}

is available for the parametric process. This reduction mainly originates from an imperfect spatial overlap between the pump beam and the whispering gallery mode.

If the input power exceeds the pump threshold

P_{th}

for the optical parametric oscillation, we can measure the signal power

P_{s}

while scanning the pump frequency across a cavity mode. Figure 2 shows that at

P_{p} = 200 μW

, we generate

P_{s} \approx 0.9 μW

of signal light at 40 °C resonator temperature. Using a spectrometer, we have confirmed the parametric oscillation at

λ_{s} = 800 nm

and

λ_{i} = 1250 nm

. The signal power grows with increasing pump power as shown in Fig. 3. Theoretically, this input–output curve should have a shape according to [8

B. Sturman and I. Breunig, J. Opt. Soc. Am. B 28, 2465 (2011). [CrossRef]

]

P_{s} = 4 (\sqrt{\tilde{P_{p}} / P_{th}} - 1) P_{th} \times \frac{λ_{p}}{λ_{s} (r_{p}^{- 1} + 1) (r_{s}^{- 1} + 1)},

(3)

with the pump threshold

P_{th} = \frac{π ε_{0} c_{0} n_{p}^{2} n_{s}^{2} n_{i}^{2}}{16 d^{2} λ_{p}} V_{eff} \frac{1}{Q_{p} Q_{s} Q_{i}} \times \frac{{(r_{p} + 1)}^{2} (r_{s} + 1) (r_{i} + 1)}{r_{p}} .

(4)

Here, the coefficients

r_{s, i}

are the ratios between the coupling losses and the intrinsic losses of the signal and idler waves, respectively. The second factor of Eq. (4),

V_{eff}

, is the effective mode volume, and

Q_{j}

are the intrinsic quality factors of the three interacting waves. The latter factor of Eq. (3) gives the maximum achievable conversion efficiency

η_{\max}

\tilde{P_{p}} = 4 P_{th}

. Only in the case of strong overcoupling for both waves it reaches

λ_{p} / λ_{s}

corresponding to the Manley–Rowe limit. We determine

η_{\max} = 2.6 %

and

P_{th} = 66 μW

(160 μW total pump threshold) by a fit of Eq. (3) to our experimental data. Reducing the gap between the resonator and the prism, hence increasing

r_{p, s}

, enhances the conversion efficiency to 7%. However, as indicated before, even for a vanishing gap we stay in the undercoupled regime for the pump wave. This limits the conversion efficiency.

Fig. 3. Signal power

P_{s}

versus total pump power

P_{p}

and versus the fraction

\tilde{P_{p}}

available for the parametric process at 40 °C resonator temperature. The dots are the experimental data, and the solid line corresponds to a fit according to Eq. (3).

The gap reduction also increases the pump threshold of the parametric oscillation up to 330 μW. According to Eq. (4), this is expected. In order to compare the measured pump thresholds with the prediction of this equation, we chose the following realistic parameters:

n_{j} = 2.2

D. H. Jundt, M. M. Fejer, and R. L. Byer, IEEE J. Quantum Electron. 26, 135 (1990). [CrossRef]

d = 5 pm / V

J. Seres, Appl. Phys. B 73, 705 (2001). [CrossRef]

V_{eff} = 10^{- 12} m^{3}

Q_{p} = 7.7 \times 10^{6}

Q_{s} = 5 \times 10^{7}

[10

A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004). [CrossRef]

], and

Q_{i} = 10^{8}

[10

A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004). [CrossRef]

]. From the linewidth measurements, we know that the pump field is undercoupled; we set

r_{p} = 0.5

. The signal and idler fields have larger wavelengths and might be critically coupled or overcoupled

r_{s} = 1

r_{i} = 2

. This yields

P_{th} = 10 μW

, which is a factor of 6 smaller than the measured value. One reason might be a significantly larger effective mode volume due to different transversal mode structures of the three interacting waves.

By changing the resonator temperature from 30 to 170 °C in steps of 10 °C, we can tune the signal and idler wavelengths. Figure 4 shows this behavior for 4 mW total pump power and a vanishing gap between the coupling prism and the resonator. At every investigated temperature value, we scan the pump frequency over 6 GHz, enabling us to couple to different transversal pump modes. The signal wavelength

λ_{s}

ranges from 707 to 865 nm, and the idler wavelength

λ_{i}

from 1120 to 1575 nm. In order to compare the measured tuning behavior to the theoretically expected one, we calculate the wavelengths

λ_{s, i}

fulfilling the phase matching condition

n_{p} / λ_{p} = n_{s} / λ_{s} + n_{i} / λ_{i}

. Here, the effective refractive index depends on the bulk refractive index [6

D. H. Jundt, M. M. Fejer, and R. L. Byer, IEEE J. Quantum Electron. 26, 135 (1990). [CrossRef]

], on the temperature, on the resonator shape, and on the transversal mode structure of the interacting waves [11

M. L. Gorodetsky and A. E. Fomin, IEEE J. Sel. Top. Quantum Electron. 12, 33 (2006). [CrossRef]

]. Figure 4 shows a good agreement between experiment and simulation.

Fig. 4. Signal and idler wavelengths versus the resonator temperature. The solid and dashed curves correspond to theoretically expected values under the assumption of different transversal mode combinations sketched in the inset for pump (

p

), signal (

s

), and idler (

i

) waves. The curved line in the inset indicates the resonator rim.

If the whispering gallery OPO is aimed to generate tunable signal light in the green or yellow spectral range, the system should be pumped at wavelengths around 400 nm. Based on our experimental results, we can predict that in this case the pump threshold will increase to hundreds of microwatts. This is mainly due to decreasing values for the intrinsic quality factor

Q_{p}

and for the ratio

r_{p}

. Furthermore, the decreasing

r_{p}

will limit the maximum achievable conversion efficiency to several percent, which can be seen from Eq. (3). Thus, for a practical device with some 10% conversion efficiency, a material with significantly lower absorption in the ultraviolet region compared to that of lithium niobate is required. Possible candidates are lithium tantalate and borates. Lithium tantalate is transparent down to 300 nm wavelengths [12

A. L. Alexandrovski, G. Foulon, L. E. Myers, R. K. Route, and M. M. Fejer, Proc. SPIE 3610, 44 (1999). [CrossRef]

] and can be periodically poled to achieve quasi phase matching [13

J.-P. Meyn and M. M. Fejer, Opt. Lett. 22, 1214 (1997). [CrossRef]

]. Borates are transparent even below 200 nm wavelengths [14

C. Chen, Y. Wang, B. Wu, K. Wu, W. Zeng, and L. Yu, Nature 373, 322 (1995). [CrossRef]

]. However, here birefringent phase matching is the only current option since no method to grow orientation-patterned borates is known so far.

In conclusion, we demonstrated and characterized a blue-pumped whispering gallery OPO. This monolithic device with about 2 mm diameter has a submilliwatt pump threshold and is tunable over hundreds of nanometers between the red and near infrared. Furthermore, our experiments show that the conversion efficiency is limited to several percent because of absorption loss for the pump wave. We consider this special OPO as a step to a compact system that covers the whole visible spectral range with tunable nonclassical light.

Acknowledgments

We gratefully acknowledge the financial support from the Deutsche Forschungsgemeinschaft.

References

1.	M. H. Dunn and M. Ebrahimzadeh, Science 286, 1513 (1999). [CrossRef]
2.	J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010). [CrossRef]
3.	T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011). [CrossRef]
4.	M. Förtsch, J. U. Fürst, C. Wittmann, D. V. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and Ch. Marquardt, “Accurate group delay measurement for radial velocity instruments using the dispersed fixed delay interferometer method,” arXiv 1204.3056 (2012).
5.	J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 106, 113901 (2011). [CrossRef]
6.	D. H. Jundt, M. M. Fejer, and R. L. Byer, IEEE J. Quantum Electron. 26, 135 (1990). [CrossRef]
7.	J. R. Schwesyg, M. C. C. Kajiyama, M. Falk, D. H. Jundt, K. Buse, and M. M. Fejer, Appl. Phys. B 100, 109 (2010). [CrossRef]
8.	B. Sturman and I. Breunig, J. Opt. Soc. Am. B 28, 2465 (2011). [CrossRef]
9.	J. Seres, Appl. Phys. B 73, 705 (2001). [CrossRef]
10.	A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004). [CrossRef]
11.	M. L. Gorodetsky and A. E. Fomin, IEEE J. Sel. Top. Quantum Electron. 12, 33 (2006). [CrossRef]
12.	A. L. Alexandrovski, G. Foulon, L. E. Myers, R. K. Route, and M. M. Fejer, Proc. SPIE 3610, 44 (1999). [CrossRef]
13.	J.-P. Meyn and M. M. Fejer, Opt. Lett. 22, 1214 (1997). [CrossRef]
14.	C. Chen, Y. Wang, B. Wu, K. Wu, W. Zeng, and L. Yu, Nature 373, 322 (1995). [CrossRef]

OCIS Codes
(190.4360) Nonlinear optics : Nonlinear optics, devices
(190.4970) Nonlinear optics : Parametric oscillators and amplifiers
(230.5750) Optical devices : Resonators

ToC Category:
Nonlinear Optics

History
Original Manuscript: August 7, 2012
Manuscript Accepted: August 21, 2012
Published: October 5, 2012

Virtual Issues
October 17, 2012 Spotlight on Optics

Citation
Christoph Sebastian Werner, Tobias Beckmann, Karsten Buse, and Ingo Breunig, "Blue-pumped whispering gallery optical parametric oscillator," Opt. Lett. 37, 4224-4226 (2012)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-37-20-4224

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References

M. H. Dunn and M. Ebrahimzadeh, Science 286, 1513 (1999). [CrossRef]
J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010). [CrossRef]
T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011). [CrossRef]
M. Förtsch, J. U. Fürst, C. Wittmann, D. V. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and Ch. Marquardt, “Accurate group delay measurement for radial velocity instruments using the dispersed fixed delay interferometer method,” arXiv 1204.3056 (2012).
J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 106, 113901 (2011). [CrossRef]
D. H. Jundt, M. M. Fejer, and R. L. Byer, IEEE J. Quantum Electron. 26, 135 (1990). [CrossRef]
J. R. Schwesyg, M. C. C. Kajiyama, M. Falk, D. H. Jundt, K. Buse, and M. M. Fejer, Appl. Phys. B 100, 109 (2010). [CrossRef]
B. Sturman and I. Breunig, J. Opt. Soc. Am. B 28, 2465 (2011). [CrossRef]
J. Seres, Appl. Phys. B 73, 705 (2001). [CrossRef]
A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004). [CrossRef]
M. L. Gorodetsky and A. E. Fomin, IEEE J. Sel. Top. Quantum Electron. 12, 33 (2006). [CrossRef]
A. L. Alexandrovski, G. Foulon, L. E. Myers, R. K. Route, and M. M. Fejer, Proc. SPIE 3610, 44 (1999). [CrossRef]
J.-P. Meyn and M. M. Fejer, Opt. Lett. 22, 1214 (1997). [CrossRef]
C. Chen, Y. Wang, B. Wu, K. Wu, W. Zeng, and L. Yu, Nature 373, 322 (1995). [CrossRef]

Aiello, A.
Alexandrovski, A. L.
Andersen, U. L.
Beckmann, T.
Breunig, I.
Buse, K.
Byer, R. L.
Chekhova, M. V.
Chen, C.
Dunn, M. H.
Ebrahimzadeh, M.
Elser, D.
Falk, M.
Fejer, M. M.
Fomin, A. E.
Förtsch, M.
Foulon, G.
Fürst, J. U.
Gorodetsky, M. L.
Haertle, D.
Ilchenko, V.
Jundt, D. H.
Kajiyama, M. C. C.
Leuchs, G.
Linnenbank, H.
Maleki, L.
Marquardt, Ch.
Matsko, A.
Meyn, J.-P.
Myers, L. E.
Route, R. K.
Savchenkov, A.
Schwesyg, J. R.
Seres, J.
Silberhorn, C.
Steigerwald, H.
Strekalov, D. V.
Sturman, B.
Wang, Y.
Wittmann, C.
Wu, B.
Wu, K.
Yu, L.
Zeng, W.

Appl. Phys. B

J. R. Schwesyg, M. C. C. Kajiyama, M. Falk, D. H. Jundt, K. Buse, and M. M. Fejer, Appl. Phys. B 100, 109 (2010). [CrossRef]
J. Seres, Appl. Phys. B 73, 705 (2001). [CrossRef]

IEEE J. Quantum Electron.

D. H. Jundt, M. M. Fejer, and R. L. Byer, IEEE J. Quantum Electron. 26, 135 (1990). [CrossRef]

IEEE J. Sel. Top. Quantum Electron.

M. L. Gorodetsky and A. E. Fomin, IEEE J. Sel. Top. Quantum Electron. 12, 33 (2006). [CrossRef]

J. Opt. Soc. Am. B

B. Sturman and I. Breunig, J. Opt. Soc. Am. B 28, 2465 (2011). [CrossRef]

Nature

C. Chen, Y. Wang, B. Wu, K. Wu, W. Zeng, and L. Yu, Nature 373, 322 (1995). [CrossRef]

Opt. Lett.

J.-P. Meyn and M. M. Fejer, Opt. Lett. 22, 1214 (1997). [CrossRef]

Phys. Rev. A

A. Savchenkov, V. Ilchenko, A. Matsko, and L. Maleki, Phys. Rev. A 70, 051804 (2004). [CrossRef]

Phys. Rev. Lett.

J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 105, 263904 (2010). [CrossRef]
T. Beckmann, H. Linnenbank, H. Steigerwald, B. Sturman, D. Haertle, K. Buse, and I. Breunig, Phys. Rev. Lett. 106, 143903 (2011). [CrossRef]
J. U. Fürst, D. V. Strekalov, D. Elser, A. Aiello, U. L. Andersen, Ch. Marquardt, and G. Leuchs, Phys. Rev. Lett. 106, 113901 (2011). [CrossRef]

Proc. SPIE

A. L. Alexandrovski, G. Foulon, L. E. Myers, R. K. Route, and M. M. Fejer, Proc. SPIE 3610, 44 (1999). [CrossRef]

Science

M. H. Dunn and M. Ebrahimzadeh, Science 286, 1513 (1999). [CrossRef]

Other

M. Förtsch, J. U. Fürst, C. Wittmann, D. V. Strekalov, A. Aiello, M. V. Chekhova, C. Silberhorn, G. Leuchs, and Ch. Marquardt, “Accurate group delay measurement for radial velocity instruments using the dispersed fixed delay interferometer method,” arXiv 1204.3056 (2012).

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