Huanqian Loh,^{1}
Yu-Ju Lin,^{1}
Igor Teper,^{1}
Marko Cetina,^{1}
Jonathan Simon,^{2}
James K. Thompson,^{1}
and Vladan Vuletić^{1}

^{1}H. Loh (huanqian@alum.mit.edu), Y.-J. Lin, I. Teper, M. Cetina, J. K. Thompson, and V. Vuletić are with the Department of Physics, MIT–Harvard Center for Ultracold Atoms, and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139.

^{2}J. Simon is with the Department of Physics, MIT–Harvard Center for Ultracold Atoms, Harvard University, Cambridge, Massachusetts 02138.

Huanqian Loh, Yu-Ju Lin, Igor Teper, Marko Cetina, Jonathan Simon, James K. Thompson, and Vladan Vuletić, "Influence of grating parameters on the linewidths of external-cavity diode lasers," Appl. Opt. 45, 9191-9197 (2006)

We investigate experimentally the influence of the grating reflectivity, grating resolution, and diode facet antireflection (AR) coating on the intrinsic linewidth of an external-cavity diode laser built with a diffraction grating in a Littrow configuration. Grating lasers at 399, 780, and
$852\text{\hspace{0.17em}}\mathrm{nm}$
are determined to have typical linewidths between 250 and
$\text{600 kHz}$
from measurements of their frequency noise power spectral densities. The linewidths are little affected by the presence of an AR coating on the diode facet but narrow as the grating reflectivity and grating resolution are increased, with the resolution exerting a greater effect. We also use frequency noise measurements to characterize a laser mount with improved mechanical stability.

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Linewidths of 852 nm Lasers for Different Gratings in the Littrow Configuration^{
a
}

n (mm^{−1})

λ∕Δλ

R_{
G1}

R_{
G0}

Δν_{th}(kHz)

Δν_{exp}(kHz)

1200

4200

0.21

0.67

260,^{
b
} 290,^{
c
} 320^{
d
}

560 ± 140

1200

4200

0.61

0.19

260,^{
b
} 270,^{
c
} 290^{
d
}

440 ± 110

1800

8400

0.16

0.78

260,^{
b
} 290,^{
c
} 330^{
d
}

320 ± 60

Linewidths of AR-coated 852 nm lasers built with gratings 43773, 43753, 43222 from Edmund Optics for lines 1–3. For a Littrow grating laser, the first diffraction order with power reflectivity ${R}_{G1}$ is reflected back into the laser for optical feedback, while the zeroth order with power reflectivity ${R}_{G0}$ is used as the laser output. The grating resolution $\lambda /\mathrm{\Delta}\lambda $ is computed for a beam diameter of $D\simeq 3\text{\hspace{0.17em}}\mathrm{m}\mathrm{m}$ from the groove density n and the Littrow angle. The free-running laser linewidth is estimated to be $35\text{\hspace{0.17em}}\mathrm{M}\mathrm{H}\mathrm{z}$ (Ref. [28]). $\mathrm{\Delta}{\nu}_{\mathrm{t}\mathrm{h}}$ lists different theoretical predictions for the given laser parameters, and $\mathrm{\Delta}{\nu}_{\mathrm{exp}}$ is the linewidth measured using Eq. (1). $\mathrm{\Delta}{\nu}_{\mathrm{t}\mathrm{h}}=\mathrm{\Delta}{\nu}_{0}{[{\tau}_{d}/({\tau}_{d}+{\tau}_{e})]}^{2}$. $\mathrm{\Delta}{\nu}_{\mathrm{t}\mathrm{h}}=\mathrm{\Delta}{\nu}_{0}/{(1+A+B)}^{2}$, where A and B are calculated from Eq. (26) of Kazarinov and Henry (Ref. [12]).
Calculated from Eq. (8) of the paper of Sun et al. (Ref. [10]).

Table 2

Linewidths of Both Non-AR- and AR-Coated 780 nm Lasers^{
a
}

Diode Model

L_{
d
} (μm)

R_{1}

R_{2}

Δν_{th} (kHz)

Δν_{exp} (kHz)

Sanyo DL7140-201S

840

0.85

0.15

4900,^{
b
} 130,^{
c
} –^{
e
}

500 ± 80

SAL-780-40

890

0.85

8 × 10^{−5}

43,000,^{
b
} 260,^{
c
} 370^{
d
}

450 ± 80

Linewidths of $780\text{\hspace{0.17em}}\mathrm{n}\mathrm{m}$ lasers without and with an AR coating on the diode front facet, assembled with the same grating (Edmund Optics 43773). ${L}_{d}$ is the diode chip length, while ${R}_{1}$ and ${R}_{2}$ are the back and front facet power reflectivities, respectively. $\mathrm{\Delta}{\nu}_{\mathrm{t}\mathrm{h}}$ and $\mathrm{\Delta}{\nu}_{\mathrm{exp}}$ are as defined in Table 1.
Reference 28.
Δν_{th} = Δν_{0}∕(1 + A + B)^{2}, where A and B are calculated from Eq. (26) of Kazarinov and Henry’s paper (Ref. [12]12).
Calculated from Eq. (8) of the paper of Sun et al. (Ref. [10]10).
The calculations of Sun et al. do not apply for ${R}_{2}/{R}_{G1}\sim 1$ (Ref. [10]10).

Table 3

Best Achieved Linewidths^{
a
}

Atoms

λ (nm)

AR Coating

n(mm^{−1})

λ∕Δλ

R_{
G1}

Δν_{exp}(kHz)

Cs

852

Yes

1800

8400

0.16

320 ± 60

Rb

780

Yes

1200

4100

0.27

450 ± 80

Yb

399

No

2400

8200

0.60

2508 ± 70

Narrowest linewidths achieved with 852 and $780\text{\hspace{0.17em}}\mathrm{n}\mathrm{m}$ lasers and their corresponding diode and grating parameters as defined in Table 1.

Tables (3)

Table 1

Linewidths of 852 nm Lasers for Different Gratings in the Littrow Configuration^{
a
}

n (mm^{−1})

λ∕Δλ

R_{
G1}

R_{
G0}

Δν_{th}(kHz)

Δν_{exp}(kHz)

1200

4200

0.21

0.67

260,^{
b
} 290,^{
c
} 320^{
d
}

560 ± 140

1200

4200

0.61

0.19

260,^{
b
} 270,^{
c
} 290^{
d
}

440 ± 110

1800

8400

0.16

0.78

260,^{
b
} 290,^{
c
} 330^{
d
}

320 ± 60

Linewidths of AR-coated 852 nm lasers built with gratings 43773, 43753, 43222 from Edmund Optics for lines 1–3. For a Littrow grating laser, the first diffraction order with power reflectivity ${R}_{G1}$ is reflected back into the laser for optical feedback, while the zeroth order with power reflectivity ${R}_{G0}$ is used as the laser output. The grating resolution $\lambda /\mathrm{\Delta}\lambda $ is computed for a beam diameter of $D\simeq 3\text{\hspace{0.17em}}\mathrm{m}\mathrm{m}$ from the groove density n and the Littrow angle. The free-running laser linewidth is estimated to be $35\text{\hspace{0.17em}}\mathrm{M}\mathrm{H}\mathrm{z}$ (Ref. [28]). $\mathrm{\Delta}{\nu}_{\mathrm{t}\mathrm{h}}$ lists different theoretical predictions for the given laser parameters, and $\mathrm{\Delta}{\nu}_{\mathrm{exp}}$ is the linewidth measured using Eq. (1). $\mathrm{\Delta}{\nu}_{\mathrm{t}\mathrm{h}}=\mathrm{\Delta}{\nu}_{0}{[{\tau}_{d}/({\tau}_{d}+{\tau}_{e})]}^{2}$. $\mathrm{\Delta}{\nu}_{\mathrm{t}\mathrm{h}}=\mathrm{\Delta}{\nu}_{0}/{(1+A+B)}^{2}$, where A and B are calculated from Eq. (26) of Kazarinov and Henry (Ref. [12]).
Calculated from Eq. (8) of the paper of Sun et al. (Ref. [10]).

Table 2

Linewidths of Both Non-AR- and AR-Coated 780 nm Lasers^{
a
}

Diode Model

L_{
d
} (μm)

R_{1}

R_{2}

Δν_{th} (kHz)

Δν_{exp} (kHz)

Sanyo DL7140-201S

840

0.85

0.15

4900,^{
b
} 130,^{
c
} –^{
e
}

500 ± 80

SAL-780-40

890

0.85

8 × 10^{−5}

43,000,^{
b
} 260,^{
c
} 370^{
d
}

450 ± 80

Linewidths of $780\text{\hspace{0.17em}}\mathrm{n}\mathrm{m}$ lasers without and with an AR coating on the diode front facet, assembled with the same grating (Edmund Optics 43773). ${L}_{d}$ is the diode chip length, while ${R}_{1}$ and ${R}_{2}$ are the back and front facet power reflectivities, respectively. $\mathrm{\Delta}{\nu}_{\mathrm{t}\mathrm{h}}$ and $\mathrm{\Delta}{\nu}_{\mathrm{exp}}$ are as defined in Table 1.
Reference 28.
Δν_{th} = Δν_{0}∕(1 + A + B)^{2}, where A and B are calculated from Eq. (26) of Kazarinov and Henry’s paper (Ref. [12]12).
Calculated from Eq. (8) of the paper of Sun et al. (Ref. [10]10).
The calculations of Sun et al. do not apply for ${R}_{2}/{R}_{G1}\sim 1$ (Ref. [10]10).

Table 3

Best Achieved Linewidths^{
a
}

Atoms

λ (nm)

AR Coating

n(mm^{−1})

λ∕Δλ

R_{
G1}

Δν_{exp}(kHz)

Cs

852

Yes

1800

8400

0.16

320 ± 60

Rb

780

Yes

1200

4100

0.27

450 ± 80

Yb

399

No

2400

8200

0.60

2508 ± 70

Narrowest linewidths achieved with 852 and $780\text{\hspace{0.17em}}\mathrm{n}\mathrm{m}$ lasers and their corresponding diode and grating parameters as defined in Table 1.