arXiv:1203.4843v1 [physics.ins-det] 21 Mar 2012
A Monolithic Filter Cavity for Experiments in Quantum Optics
Pantita Palittapongarnpim, Andrew MacRae, A. I. Lvovsky∗
Department of Physics and Astronomy, University of Calgary
Calgary, Alberta, Canada T2N 1N4
∗Corresponding author: firstname.lastname@example.org
Compiled December 22, 2013
By applying a high-reflectivity dielectric coating on both sides of a commercial plano-convex lens, we produce
a stable monolithic Fabry-Perot cavity suitable for use as a narrow band filter in quantum optics experiments.
The resonant frequency is selected by means of thermal expansion. Owing to the long term mechanical stability,
no optical locking techniques are required. We characterize the cavity performance as an optical filter, obtaining
a 45dB suppression of unwanted modes while maintaining a transmission of 60%.
c ? 2013 Optical Society of
Modern day experiments in quantum optics require
the isolation of single-photon level signals from an in-
tense optical background of similar wavelength. Among
the many examples there are experiments in quantum
optical engineering [1–3], quantum memory , and re-
peaters , which require the selection of a specific spec-
tral and spatial mode while simultaneously obtaining
high rejection of all other modes. This can be achieved by
means of a solid etalon filter or a cavity formed between
independent mirrors. However, both these approaches
are problematic. In the latter case, active locking of the
mirror separation is required, resulting in significant ex-
perimental complications. On the other hand, an etalon
is intrinsically stable and requires no optical locking, but
the planar cavity geometry limits the achievable cavity
finesse and provides no spatial transverse-mode filter-
Our approach is to combine the intrinsic stability of a
monolithic etalon with the high finesse and spatial mode
filtering allowed by Fabry-Perot cavities with spherical
mirrors by employing a solid plano-convex resonator con-
structed from a single substrate. This has the advantage
of not only long term stability and desirable single-pass
suppression of unwanted modes, but also experimental
Theory: The quality of a cavity filter is governed by its
finesse which in ideal case is
FR= π√R/(1 − R), (1)
where R is the reflectivity of the mirror surfaces (both
mirrors are assumed identical throughout the paper). In
reality, the finesse of a cavity can be reduced due to
intracavity loss and mismatch between the cavity and
incident optical mode:
where FR is the ideal finesse, Fdefect is the finesse as-
sociated with surface defects , Fmode is the finesse
due to the mismatch of the wavefront and the surface.
Fmode can be increased with more precise alignment
while Fdefectis determined by the optical quality of the
The effective finesse of a flat-surface etalon is limited
by the fact that this cavity configuration is at the bor-
der of the stability region. Transverse eigenmodes of the
flat-surface cavity have infinite spatial extent. Transverse
mode-matching demands that the wavefront matches the
cavity mirrors identically, but, if the incident wave is
finite, the condition of flat wavefronts cannot be met
at both mirrors owing to diffraction, limiting Fmode in
Eq. (2). This may be partially compensated by choos-
ing a wider beam diameter, but this exposes the beam
to a larger range of surface defects which in turn bounds
Fdefect. As a result, the finesse of the flat etalon is limited
to approximately 100. To obtain sufficiently high extinc-
tion, flat surface filters must employ multi-pass designs
or multiple resonators, reducing the maximum transmis-
sion at resonance and increasing experimental complex-
A Fabry-Perot cavity with spherical mirrors is more
forgiving in these regards. The focusing induced by the
curved mirrors eliminates divergence of the internal field.
Moreover, the stability of a spherical Fabry-Perot also
translates into less beam wandering  even for a non-
paraxial incoupling light which reduces the effect of sur-
face defects, so finesse levels up to the order of 105can be
routinely achieved [10,11]. Another benefit of this design
is that separate transverse modes are non-degenerate. As
a result, the cavity provides spatial as well as spectral
filtering, which is useful for applications where the signal
is not in the same spatial mode as the unwanted back-
The concave filter cavity is typically implemented us-
ing two or more spatially separated mirrors. The stabil-
ity of the resonant mode is achieved by monitoring the
transmission of an auxiliary beam and providing feed-
back to a piezoelectric transducer on which one of the
mirrors is mounted. A drawback of this method is the
locking beam adds extra light to the system which must
in turn be filtered out. Additionally, care must be taken
to minimize residual phase jitter stemming from the lock-
ing electronics as well as mechanical lability of the piezo.
A monolithic concave cavity, implemented in this
work, combines advantages of both etalons and spher-
ical Fabry-Perot filter cavity: it is mechanically stable
and permits high finesse and subsequently high extinc-
tion. It can be produced by applying a dielectric coating
to a commercial convex lens and is therefore relatively
inexpensive. An apparent challenge of this design, associ-
ated with tuning the cavity to a particular resonance, can
be easily overcome using temperature control. Changing
the temperature T of the cavity influences both the cav-
ity length L and index of refraction n, resulting in a shift
of the resonant frequency ν:
where α is the thermal expansion coefficient and ∂n/∂T
is obtained from Sellmeyer equations. Here we neglect
the change in index of refraction due to frequency as it
is much smaller than other relevant factors.
When designing the cavity, one needs to decide upon
its length (thickness) L, surface curvature radii r1, r2
and reflectivity R. These parameters can be calculated
from the desired final specifications of the filter, such as
the free spectral range, linewidth and extinction ratio,
based on the following considerations. Neglecting the de-
fects associated with the imperfect mode matching and
surface defects, the transmission of a Fabry-Perot cavity
as a function of the frequency is given by 
1 − R
where δ is the frequency-dependent per-roundtrip phase
shift and T is the transmission of the mirror surface
(which may not equal to 1 − R due to losses inside
the cavity or at reflection). From the above, we find the
transmission at the center of a resonant mode (δ = 0)
and in the middle between modes (δ = π) to equal, re-
1 − R
1 − R
and hence, assuming R close to unity, the extinction ratio
Tmax/Tmin≈ 4/(1 − R)2≈ (2FR/π)2.
In this way, the desired extinction ratio determines the
requirements on the finesse and surface reflectivity. One
must, however, keep in mind the degrading effects asso-
ciated with losses and surface defects. Choosing the re-
flectivity too high, such that T ≪ 1−R or π/(1 −R) <
Fdefect, will degrade the cavity transmission on resonance
without significantly improving the extinction ratio.
Once the reflectivity is known, the cavity length is
obtained from the desired linewidth ∆ν via ∆ν =FSR
with FSR = c/2nL being the free-spectral range.
The choice of the mirror curvature is determined
by the spatial filtering requirements. The resonance of
Hermite-Gaussian mode TEMmnis located at 
νqmn= FSR (7)
q +1 + m + n
where the first term represents the plane-wave resonance
condition (q being an integer number defining the longi-
tudinal mode) and the second gives the Gaussian mode
correction. A few special cases are of interest here. For a
plane cavity, the second term vanishes and all transverse
modes are frequency degenerate; no spatial filtering oc-
curs. For a confocal cavity, such that e.g. r1= r2= L,
transverse modes are separated by half-integer number of
FSRs. In this case, if the cavity is aligned to the TEM00
mode, it will also transmit all even TEM modes; only
partial spatial filtering occurs. The advantage of the con-
focal configuration, however, is that if the cavity is con-
figured to reject a particular frequency in both TEM00
and TEM01modes, it can be certain to reject that fre-
quency in all other transverse modes.
In the regime where L ≪ r1,r2 (corresponding to
our experiment), adjacent transverse modes are gener-
ally nondegenerate and are separated by
L/r1+ L/r2. (8)
In this case, full spatial filtering occurs for a specific
frequency provided that ∆ν⊥ is larger than the cavity
linewidth. Although the cavity may transmit undesired
spectral components in other transverse modes, these
components can be eliminated by spatial filtering of the
TEM00mode transmitted through the cavity.
Construction and Design: Our filter cavity consists
of a commercial plano-convex lens from Lambda Re-
search Optics with a surface quality of λ/10 at 633
nm, a scratch/dig of 10/5, and high reflectivity coating
(R = 99.0% ± 0.1%) on each surface. For the purpose
of our experiments on Raman-like effects in atomic ru-
bidium , where we filter single photons from a strong
pump, separated in frequency by 3 to 7 GHz, we choose
substrates with centre thicknesses L = 4.3, 5.3, and 7.8
mm. The curvature radius is chosen as r = 40.7 mm,
which satisfies the stability condition for plano-convex
lenses: 0 < 1−L/r < 1. We choose BK7 as the substrate
material owing to its high transmission in the near in-
frared and its high coefficient of thermal expansion.
The cavity is placed in a standard lens mount with a
thermally coupled AD590 sensor measuring the tempera-
ture to within 0.1◦C. Temperature control is achieved
through a Peltier thermoelectric cooler which couples the
mount to a large aluminum block which acts as a heat
sink. The temperature sensor and Peltier element are
connected to a standard PID temperature control system
(Thorlabs ICT100) with a long-term stability of 0.004
◦C. The entire system is enclosed to minimize environ-
0510 1520 25
Fig. 1. (a) The transmission of the cavity over a FSR.
The transverse intensity profile of the first three eigen-
modes is shown in the inset. (b) The transmission profile
of the TEM00mode with green line showing the exper-
imental data and the blue showing the theoretical fit.
The FWHM is found to be 84 MHz
mental coupling. The optical field for probing the cav-
ity is provided by a continuous-wave Ti:Sapphire laser
aligned to match the TEM00mode of the cavity.
Results: We characterize the spectral properties of the
cavity by scanning the laser over one cavity FSR and
monitoring the transmission as shown in Fig. 1. For the
4.3 mm cavity, we measure FSR = 23.1±0.2 GHz which
is consistent with the expected value of c/2nL = 23.07
GHz. Since the laser linewidth (100 kHz) is much less
than the cavity linewidth we neglect its contribution and
find ∆ν = 84 ± 5 MHz [Fig. 1(b)] corresponding to a
finesse of F = 275±19, which is somewhat less than the
value of F = 312±30, expected according to (1), due to
various defects as discussed above.
The on-resonance transmission reaches Tmax≈ 0.6, in-
dicating that the mirror defects and losses do not play a
significant role in the cavity performance. For the spec-
tral component located 6.8 GHz away from the cavity
resonance, we find an extinction ratio of over 45dB, in
agreement with Eq. (6). Given that the intracavity losses
are low in this configuration, at least a 10 dB higher
extinction ratio can be obtained with a similar lens by
choosing a higher reflectivity coating. Further improve-
ments can be achieved by using a substrate lens with
superior surface characteristics.
Even with the present cavity, the extinction ratio can
be greatly improved by placing a spatial filter at the
output and if polarization filtering is available. Acting
in this fashion, in a separate experiment, we achieved
over 180 dB suppression of a strong pump beam, tuned
≈ 3 GHz from the resonance . Thus our design pro-
vides an attractive compromise between simultaneous
high transmission of the desired signal and attenuation
of unwanted modes.
A key figure of merit in our filter is the suppres-
sion of unwanted spectral and spatial modes. Imperfect
mode-matching results in the appearance of higher or-
der transverse modes which cause intermittent resonance
peaks along the spectrum [Fig. 1(a)] and thus lowers the
suppression. However, these peaks are sparse and for a
broad range of frequencies do not significantly degrade
the extinction. The distance between adjacent peaks is
2.4 GHz, which is consistent with Eq. (8).
Fig. 2. Temperature tuning of the resonant frequency.
The frequency change of TEM00 mode is displayed,
which is linear within 4 K with the slope of −2.88
In order to characterize the temperature tunability
of the system, we monitor the deviation of the TEM00
transmission maximum as a function of temperature as
shown in Fig. 2. The behaviour is seen to be linear with
slope dν/dT = −2.88 GHz/K. The calculation gives
dν/dT = −3.32 GHz. The discrepancy is most likely due
to inaccuracy in the stated values for BK7, which vary
by up to 20% depending on the source.
The long term stability of the cavity system depends
largely on the accuracy of the temperature-control sys-
tem. To characterize this parameter, we observe the fre-
quency deviation of the transmission maximum with re-
spect to a local oscillator which is stabilized to an atomic
transition. We observe a rms drift of 0.057∆ν for data
taken over 25 minutes and 0.0950∆ν for 2 hours. The
latter value corresponds to an rms temperature drift of
0.003 K, indicating that the temperature controller is
likely the limiting factor in the cavity stability. Figure
3 shows the measured frequency fluctuations over a 25-
Since even minor differences in the path length cause
significant shifts in the resonant frequency, any birefrin-
gence in the cavity material will cause separate peaks for
the ordinary and extraordinary polarizations. As shown
in Fig. 4(a), the s and p polarization resonances are sep-
Fig. 3. Long term drift of cavity resonance frequency.
The shaded area represents the cavity line-width. We
observe a drift of 0.057∆ν over the 25 minute interval.
Fig. 4. (a) The transmission profile of different polar-
izations through the 5.3-mm cavity showing a frequency
separation of 181 MHz between the resonances for the
s and p polarizations. (b) The delay of a laser pulse
propagating through the cavity is found to be 4.40 ns.
The signal is obtained from a setup shown in the inset
arated by ∼ 181 MHz for this particular cavity.
Another figure of interest for time-domain experiments
is the delay introduced by our filter cavity due to its on-
resonance dispersion. To determine this, we measure the
delay of a 40 ns pulse with respect to a reference pulse
[Fig. 4(b)] and observe a value of 4.4 ns. A calculation
using the Kramers-Kronig relations yields the effective
group velocity to be 1.04 × 106m/s which corresponds
to a 5.3 ns delay. The discrepancy with the experimental
result can be attributed to uncertainties in the measure-
ments of the arrival time or approximations used in the
group velocity calculation.
Summary: We have built and characterized a mono-
lithic filter cavity for use in quantum optics experiments.
The cavity consists of a simple plano-convex lens sub-
jected to dielectric high-reflection coating on both sides,
and is tuned by changing its temperature. In a non-
confocal geometry, it is possible to obtain stability and
transverse mode filtering as well as high extinction ratio
in a single-pass configuration.
The work was supported by NSERC and CIFAR. We
thank Irina Novikova and Ben Buchler for helpful dis-
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