Conversion efficiency of 85% has been achieved in cw second-harmonic generation from 1.08 to 0.54 μm with a potassium titanyl phosphate crystal inside an external ring cavity. An absolute comparison between the experimental data and a simple theory is made and shows good agreement

Kimble, H. J.

Ou, Z. Y.

Pereira, S. F.

Polzik, E. S.

English

Caltech Authors - Main

640 OPTICS LETTERS / Vol. 17, No. 9 / May 1, 1992
85% efficiency for cw frequency doubling from 1.08 to 0.54 ,um
Z. Y. Ou, S. E Pereira, E. S. Polzik, and H. J. Kimble
Norman Bridge Laboratory of Physics, M.S. 12-33, California Institute of Technology, Pasadena, California 91125
Received December 2, 1991
Conversion efficiency of 85% has been achieved in cw second-harmonic generation from 1.08 to 0.54 Am with a
potassium titanyl phosphate crystal inside an external ring cavity. An absolute comparison between the ex-
perimental data and a simple theory is made and shows good agreement.
Because of the nonlinear nature of the process and
the generally small susceptibilities involved, har-
monic generation with high conversion efficiency is
most often realized only for pulsed radiation with
high intensity for a short period.1 By contrast, the
intensity available for cw operation is usually lim-
ited to much smaller values than for pulsed opera-
tion, with a concomitant reduction in conversion
efficiency. A possible remedy to this circumstance
that was recognized long ago is to employ a high-
finesse resonator in either a passive2 or active3 con-
figuration to enhance the circulating power and
hence the overall conversion efficiency. While the
quest for efficient conversion in a cw setting might
at first sight seem to be best pursued with crystals
with large nonlinear coefficients, such as lithium
niobate and potassium niobate,4'5 unfortunately the
advantages of large nonlinear coefficient are often
mitigated by deleterious effects such as linear and
nonlinear absorption and subtle intensity-dependent
changes in refractive index, which although small
can quickly degrade the performance of a high-
finesse cavity. On the other hand, crystals with
greater transparency, with fewer thermal problems,
and with a higher damage threshold such as the
newly developed lithium triborate usually have
much smaller nonlinear coefficients and therefore
require correspondingly higher powers for the fun-
damental wave.6
For many years, potassium titanyl phosphate
(KTP) has been a well-known crystal for frequency
doubling of Nd:YAG lasers (1.064 Am).7 The large
nonlinear coefficient of KTP together with the wide
temperature width, large acceptance angle, and ex-
tremely low absorption loss make KTP a promising
candidate for high conversion efficiency. However,
because type II critical angle tuning is the only pos-
sible phase-matching scheme at 1.064 pum, the per-
formance of KTP inside a high-finesse resonator is
significantly degraded owing to the walk-off of ordi-
nary and extraordinary beams within the crystal.
To circumvent this difficulty, recently Garmash
et al.8 reported type II 90° noncritical phase match-
ing in an a-cut KTP crystal at 1.08 Am, thus sug-
gesting new possibilities for better performance of
KTP in intracavity cw frequency doubling. Follow-
ing this lead, we report in this Letter experiments
for frequency doubling from 1.08 to 0.54 Am with a
single KTP crystal inside an external ring cavity of
extremely low passive loss. Our measurements are
carried out over a range of input fundamental pow-
ers up to 700 mW, and a cw conversion efficiency of
85% is achieved. The experimental results are in
good absolute agreement with a simple theory,
which suggests that efficiencies greater than 90%
should be obtainable in our current system once the
focusing geometry is optimized.
As illustrated in Fig. 1, our frequency-doubling ex-
periment consists of a folded ring cavity of total
length 38 cm with two curved mirrors (Ml, M2) of
10-cm radius of curvature and two flat mirrors (M3,
M4). A KTP crystal is placed between the two
curved mirrors at the position of the collimated
waist (wo0 60 Am), with a small folding angle (<60)
used in the arrangement to reduce both astigmatism
and polarization imbalance. Three of the four mir-
rors have high reflectivity at 1.08 Am (R > 99.98%)
and high transmissivity at 0.54 Am (T - 94-96%).
Infrared excitation power Pi is coupled into the cav-
ity through the remaining flat mirror M4 with re-
flectivity 97% at 1.08 Am. The fundamental wave
in our experiment comes from a single-frequency,
TEMO0 -mode Nd:YO 3 laser operating at 1.08 ,m,
with the frequency of the laser locked to a stable ex-
ternal cavity and with 700 mW of infrared power
available to pump the doubling cavity. The length
of the doubling cavity is servo controlled with a
standard locking system9 to obtain coincidence be-
tween the fundamental input frequency and the fre-
quency of a TEMoo longitudinal-mode resonance for
the ordinary polarization. The harmonic light gen-
erated in the KTP crystal is transmitted principally
through the curved mirror M2 (with transmission
at 0.54 Aum of 94%) as shown in Fig. 1.
The nonlinear medium for frequency doubling is a
3 mm X 3 mm X 10 mm flux-grown, a-cut KTP
crystal with two faces antireflection coated for low
loss at both fundamental and harmonic wavelengths.
Type II noncritical 90° phase matching at 1.08 ,um
[2n0 (2co) = nfe(C) + n0 (w)] is achieved near 630 C
with a temperature width of 30°C for our crystal
(note that this phase-matching temperature is sig-
nificantly different from the temperature of 153°C
reported in Ref. 8).1o Because type II phase match-
ing requires both ordinary (o) and extraordinary (e)
beams for the generation of harmonic light, the in-
0146-9592/92/090640-03$5.00/0 © 1992 Optical Society of America
May 1, 1992 / Vol. 17, No. 9 / OPTICS LETTERS 641
Ml M2
Fig. 1. Schematic of the experimental setup.
piezoelectric transducer.
PZT,
put infrared light is polarized at 450 with respect to
the b or c axis of the crystal. The generated green
light is polarized along the b axis. One problem en-
countered in type II doubling in a resonant cavity is
that the indices of refraction are different for the
ordinary and extraordinary beams circulating
through the KTP crystal, so that longitudinal modes
of the doubling cavity corresponding to the e and o
polarizations are generally not simultaneously reso-
nant for a given geometrical length of the cavity.
However, the indices of refraction for the e and
o beams have different temperature dependencies so
that temperature tuning over a range of approxi-
mately 10'C within the wide phase-matching width
suffices to bring longitudinal modes for e and
o beams simultaneously into resonance. The tem-
perature tolerance for maintaining overlapping reso-
nance is approximately 20 mK for our arrangement.
In fact, during the experiment, we actively stabilize
the temperature of the crystal to a few millikelvins,
so that the generated green power is stable to a few
percent over 5-10 min.
For measurements of power a calibrated thermal
power meter (Coherent Model 210) is employed for
both input fundamental (Pi) and output harmonic
(P2) waves, except at low input power (<20 mW),
where a calibrated photodiode is used. From these
measured powers, we compute the total conversion
efficiency 7 = P2/P1 = (P 2'/0.94)/P1 , where the fac-
tor 0.94 is the measured transmission at 0.54 ,um
of the cavity mirror M2. In Fig. 2 we display the
results of our measurements over a range of fun-
damental input powers from 5 to 700 mW, with
Fig. 2(a) giving the dependence of the harmonic out-
put P2 on infrared input Pi and Fig. 2(b) displaying
the dependence of the conversion efficiency i1 on Pi.
In particular, for an infrared input power P1 =(700 ± 10) mW, a green output power P2' = (560 ±
5) mW is obtained, representing a directly measured
conversion efficiency of 80%. After considering the
94% transmission of mirror M2, we obtain an over-
all conversion efficiency of (85 ± 1)% for frequency
doubling from 1.08 to 0.54 ,.m. We stress that the
correction for the 6% Fresnel loss at the curved mir-
ror is the only adjustment made to the data.
For frequency doubling in either external passive
cavities or active laser cavities, thermal effects
driven by absorption of fundamental and/or har-
monic radiation can have an adverse impact on the
harmonic conversion.5 Fortunately we have found
that for our range of operating power, the KTP crys-
tal shows only slight thermal effects. In particular,
the temperature of the crystal rises as the fun-
damental wave builds up in the cavity, with the mag-
nitude of the temperature rise varying by as much
as 0.50 C for an infrared input power of 700 mW
(note that P1 = 700 mW corresponds to approxi-
mately 30 W of circulating infrared power). This
small temperature rise seems to be associated with
no major deleterious thermal effects, as we can see
from the good agreement in Fig. 2 between the ex-
perimental data and the theoretical curves. These
theoretical results are derived from a simple analysis
of second-harmonic generation in an external cav-
ity.2'5 If we denote the overall conversion efficiency
by 7- P2/P1 with total generated harmonic power
P2 and input fundamental power P1 , it is straightfor-
ward to show that
4TVENi E
[2 - ViT (2 - L - JNLp)] 2 (1)
where T is the transmission coefficient of the infra-
red input coupler (M4 in Fig. 1), L is the total infra-
red round-trip loss in the cavity excluding T, and
ENL is the single-pass nonlinear conversion effi-
ciency without the cavity (ENL = P2 /P1 2 for T = 1,
L = 0). For our experiment ENL was determined by
P2
ci
._
CL
0.2 0.4 0.6 P (W) .8
Fig. 2. (a) Second-harmonic power P2 as a function of in-
put infrared power P1 , (b) conversion efficiency rq as a
function of input infrared power P1 . The solid curves are
derived from Eq. (1) with the measured values ENL =
6.3 X 10-4 W-1 , L = 0.32%, and T = 3%.
642 OPTICS LETTERS / Vol. 17, No. 9 / May 1, 1992
In conclusion, we have demonstrated an efficient
avenue for cw frequency doubling. Conversion effi-
ciency of 85% has been achieved by using a KTP
crystal cut for type II noncritical phase matching
near 1.08 Am. Although we have employed a con-
ventional discharge-pumped cw neodymium laser, a
doubling cavity with capabilities such as ours should
have broad application as an element in a system for
frequency conversion from a semiconductor diode
laser. There are as well a number of important
H 0.7 0.8 0 problems in quantum optics for which a system with
P0 (W) such high conversion efficiency can be gainfully
employed. including operation in a conjugate mode
Fig. 3. Theoretical conversion efficiency '1 as a function
of input infrared power P1 with ENL = 2 X 10-3 W- 1,
L = 0.32%o, and T = 3.9%o.
removing the input coupler (M4) and measuring the
generated green light, which thus preserved the fo-
cusing geometry used in the actual resonant cavity.
The result for the single-pass efficiency is ENL =
6.3 X 10' W-1 . One important aspect of our ex-
periment is that the total internal loss L is quite
small because of the extremely low losses of the cav-
ity mirrors and the good quality of the KTP crystal.
We determined that L = 0.32% from measurements
of the finesse of the doubling cavity, with the princi-
pal contribution coming from reflection losses at the
surfaces of the KTP crystal. The transmission T
was directly measured to be 3%, which is close to the
optimized value of 2.3% for 700 mW of infrared in-
put power [Eq. (2) of Ref. 5]. Knowledge of T, L,
and ENL allows us to calculate the expected theoreti-
cal efficiency rq for second-harmonic generation
from Eq. (1) together with the expected power
P2 = 'qP1, with the results shown in Fig. 2 (solid
curves) together with the experimental data. Note
that there is no fitting of the theory to the data; the
comparison is in absolute terms without adjustable
parameters.
As for the possible improvement of these results,
we note that the optimum waist for second-
harmonic generation for our 10-mm KTP crystal is
approximately 20 Am,11 which is considerably
smaller than the actual waist of 60 ,m in our ex-
periment. This lack of optimum focusing is re-
flected in the fact that our measured value of ENL is
approximately three times smaller than the best
value of ENL -2 X 10-3 W-1 that we infer for this
crystal from separate measurements with a longer
crystal in a geometry free from the constraints im-
posed by the cavity. We are currently constructing
a new cavity with curved mirrors (Ml, M2) of radii
of curvature of 5 cm, so that a waist of approxi-
mately 20 ,m can be obtained in a regime of broad
stability for the cavity. We should then be able to
achieve ENL = 2 X 10-3 W'1, which with the loss
L = 0.32% (as demonstrated already in the current
cavity) and with the optimized value T = 3.9% for
PI = 700 mW [Eq. (2) in Ref. 5] should lead to con-
version efficiency greater than 90%, as illustrated in
Fig. 3.
as an efficient nondegenerate optical parametric
oscillator.
This research was supported by the U.S. Office of
Naval Research (N00014-90-J-1059), by the National
Science Foundation (PHY-9014547), and by the
Venture Research Unit of British Petroleum. We
gratefully acknowledge the contributions of J. T. Lin,
who directed our attention to the research in Ref. 8
and who helped to obtain KTP crystals of such high
quality. We likewise benefited greatly from the
skillfully fabricated dielectric coatings provided by
R. Lalezari of PMS Electrooptics and G. Enzor of
Thin Film Lab.
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9. A small dither at the frequency 3.5 kHz is applied to
mirror M4 to produce a peak excursion of the cavity
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piezoelectric transducer on which M4 is mounted to
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0.92
cD
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a)
0.91-


85% efficiency for cw frequency doubling from 1.08 to 0.54 μm

This difference may be due to shifts in the phasematching temperature associated with focusing geometry (see Ref. 11). Such shifts are observed in our study for different cavity beam waists with a given crystal.

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85% efficiency for cw frequency doubling from 1.08 to 0.54 μm

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