High-resolution study of composite cavity effects for p-Ge
lasers
Citation for published version (APA):
Nelson, E. W., Withers, S. H., Muravjov, A. V., Strijbos, R. C., Peale, R. E., Pavlov, S. G., Shastin, V. N., &
Fredricksen, C. J. (2001). High-resolution study of composite cavity effects for p-Ge lasers.
IEEE Journal of
Quantum Electronics
,
12
(8), 1525-1530. https://doi.org/10.1109/3.970898
DOI:
10.1109/3.970898
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Published: 01/01/2001
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IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 37, NO. 12, DECEMBER 2001 1525
High-Resolution Study of Composite Cavity Effects
for p-Ge Lasers
Eric W. Nelson, Sandra H. Withers, Andrei V. Muravjov, Remco C. Strijbos, Robert E. Peale, Sergei G. Pavlov,
Valery N. Shastin, and Chris J. Fredricksen
Abstract—The temporal dynamics, spectrum, and gain of the
far–infrared p-Ge laser for composite cavities consisting of an ac-
tive crystal and passive transparent elements have been studied
with high temporal and spectral resolution. Results are relevant to
improving the performance of mode-locked or tunable p-Ge lasers
using intracavity modulators or wavelength selectors, respectively.
It is shown that an interface between the active p-Ge crystal and
a passive intracavity spacer causes partial frequency selection of
the laser modes, characterized by a modulation of their relative in-
tensities. Nevertheless, the longitudinal mode frequencies are de-
termined by the entire optical length of the cavity and not by reso-
nance frequencies of intracavity sub-components. Operation of the
p-Ge laser with multiple interfaces between Ge, Si, and semi-in-
sulating GaAs elements, or a gap, is demonstrated as a first step
toward a p-Ge laser with an external quasioptical cavity and dis-
tributed active media.
Index Terms—Laser modes, laser tuning, submillimeter wave
lasers, submillimeter wave resonators, submillimeter wave spec-
troscopy, submillimeter wave technology.
I. INTRODUCTION
T
HE far-infrared p-Ge laser [1], based on intersubband tran-
sitions of hot holes, has a wide homogeneous gain spec-
trum [2], which allows tuning over the spectral range 50–140
cm
(70–200 m or 1.5–4.2 THz) [3]–[7] or generation of
picosecond pulses of far-infrared radiation [8]–[14]. The tradi-
tional electrodynamic cavity of a p-Ge laser consists of a bulk
p-Ge rod with external mirrors attached to its ends. Such a laser
operates on a wide spectrum of active intersubband transitions
and normally generates microsecond pulses of far-infrared ra-
diation in a broad spectrum, which consists of many longitu-
dinal modes. To generate spectrally pure single-mode emission
or ultrashort pulses, the laser design may require composite cav-
ities that include passive intracavity optical elements [3]–[7],
[14]. Examples include transparent, electrically isolating sil-
icon spacers, which have been used as part of tunable intra-
Manuscript received May 2, 2001; revised August 20, 2001. The work of S. G.
Pavlov and V. N. Shastin was supported in part by INTAS under Grant 97-0856.
This work was supported by the National Science Foundation under an AFOSR
STTR Phase I Award.
E. W. Nelson, S. H. Withers, A. V. Muravjov, and R. E. Peale are with the
Department of Physics, University of Central Florida, Orlando, FL 32816 USA
(e-mail: rep@physics.ucf.edu).
R. C. Strijbos is with JDS Uniphasen, Eindhoven, The Netherlands.
S. G. Pavlov and V. N. Shastin are with the Institute for Physics of
Microstructures, Russian Academy of Sciences, GSP-105, Nizhny Novgorod
603600, Russia.
C. J. Fredricksen is with Zauberte Inc., Orlando, FL 32826 USA.
Publisher Item Identifier S 0018-9197(01)10252-6.
Fig. 1. Schematic of p-Ge laser cavity used for wavelength selection.
cavitywavelengthselectors (Fig. 1) [3]–[7] and intracavity elec-
trooptic modulators or passive saturable intracavity absorbers
[14], which might be used for active or passive mode locking,
respectively. However, use of passive intracavity optical ele-
ments in p-Ge laser cavities can introduce undesirable effects
because of intrinsic reflections and loss at interfaces between
optical components. Intracavity spacers of Si or pure Ge have
been used by a number of authors [1], but clear understanding
of the effect of losses and reflections by intracavity interfaces
on p-Ge laser spectrum and emission dynamics was missing.
In this paper, data are presented that demonstrate potential
problems with p-Ge laser operation and tunability, which
might appear because of the presence of passive spacers in the
laser cavity. The detailed experimental measurements were
performed both in the spectral and time domains. Spectra
were measured at high resolution (0.025 cm
) sufficient to
resolve individual longitudinal modes for the laser cavity used.
Single-shot transient recordings of the laser emission were
collected at a temporal resolution (
100 ps), which is much
faster than the cavity round-trip time. Also, the effect on gain of
passive intracavity elements was studied qualitatively in terms
of threshold electric and magnetic fields.
Silicon, pure Ge, and GaAs were chosen as cavity inserts
because all have low absorption at p-Ge laser emission wave-
lengths and active p-Ge has relatively low small-signal gain
[15]. Also, the refractive index of these materials is sufficiently
close to that of Ge in that only
1% reflection is expected at
each interface when the interface is of optical quality. The op-
eration of a p-Ge laser with a liquid-helium filled gap between
active crystal and back mirror was demonstrated in anticipation
of future open-cavity configurations.
0018–9197/01$10.00 © 2001 IEEE
1526 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 37, NO. 12, DECEMBER 2001
Fig. 2. Experimental cavity constructions. In each case, additional elements
were sandwiched between a 27.975-mm active p-Ga crystal and a 7-mm Cu
back mirror. The constructions were: (a) 25-
m teflon/active p-Ge/25-
m
teflon; (b) teflon/active p-Ge/12 0.5-mm GaAs plates/two 0.5-mm intrinsic Ge
plates/9-mm Si spacer; (c) teflon/active p-Ge/two GaAs plates/Ge plate/GaAs
plate/Ge plate/GaAs plate/Si spacer; and (d) teflon/27.975-mm crystal/gap
provided by a Si ring.
II. EXPERIMENT
Laser crystals were cut from monocrystalline Ge doped by
Ga with
cm in the form of a rectangular
parallelepiped
mm ( mm
and
mm) with the long axis along the
[110] crystallographic axis. Electric field pulses of 1–2-
s du-
ration were applied along the [
] axis via ohmic contacts
evaporated on opposite lateral sides. The crystal end faces were
polished parallel to each other within 1 arc minute accuracy.
The surface roughness in the central portion of the active crystal
ends was determined to be
nm. The edges were uninten-
tionally rounded during polishing, giving a final deviation from
flatness of 100 nm. The basic laser cavity was formed by two
copper mirrors attached to the sample end faces via 20
mof
isolating teflon film (Fig. 2). The output mirror had a diameter
of 4 mm, which was smaller than the active sample cross sec-
tion to allow some radiation to escape around the mirror edge.
The system was cooled by liquid helium and immersed in an
external magnetic field created by a superconducting solenoid
in Faraday configuration (
[110]), or by a room temperature
external electromagnet in Voigt configuration (
[001]). The
strengths of the applied electric and magnetic fields could be in-
dependently varied to determine the
and lasing thresholds.
The laser beam propagated along the long crystal axis [110]
was conducted out of the cryostat using a brass light pipe and
was detected after a teflon lens with a fast whisker-contacted
Schottky diode.
1
The signal was amplified
2
and recorded on a
transient digitizer
3
with 4.5-GHz analog bandwidth, oversam-
pled at 200 Gs/s. For spectral measurements, the radiation was
1
1T17(82), University of Virginia.
2
Picosecond Pulse Labs 5840, 10-GHz bandwidth.
3
Tektronix SCD5000.
Fig. 3. Transient recording of 50.240-mm p-Ge crystal laser emission:
(a) without and (b) with a Si spacer in the cavity.
directed to a Bomem DA8 Fourier spectrometer with an un-
apodized instrumental line width of 0.025 cm
, equipped with
an event-locking accessory (Zaubertek) for low duty sources
[16]. The modulated signal was detected by a liquid-helium
cooled Si composite bolometer.
The laser operation was tested using cavities that contained
spacers made of Si, pure Ge, semi-insulated GaAs, and also
a liquid-helium filled gap between the laser crystal and back
mirror [Fig. 2(b)–(d)]. Si spacers were cut to a length of
8
mm from monocrystalline Si and had the same flatness and par-
allelism of the surfaces as p-Ge samples. The GaAs was stan-
dard semi-insulating substrate material cut from 0.5-mm wafers
purchased from the M.T.I. Corporation. These double-side pol-
ished commercial wafers had a 3 arc minute wedge, which was
compensated by using pieces in pairs, cut from neighboring re-
gions of the wafer, with one of the pieces rotated 180
about
the plane normal. The pure Ge sample (approximately 7
14
mm
) was cut from a single-side polished 0.5-mm wafer from
Atramet. The rough side was hand polished using a low-speed
glass wheel with a nylon pad and Buehler 1
m diamond sus-
pension in water as the final step. After that, the sample piece
was cut in half and the residual wedge compensated as for the
GaAs.
The cavity construction shown in Fig. 2(d) had a Si ring with
an inner diameter of 6 mm, an outer diameter of 9 mm, and
1.5-mm thickness, inserted between the active crystal and the
back mirror. The purpose of the ring was to create a gap while
keeping the back mirror parallel to the active crystal face.
III. R
ESULTS
The periodic temporal structure of the single laser shot from
the 50.240-mm crystal with mirrors [Fig. 2(a)] is shown in
Fig. 3(a). The period of main oscillations equals the calculated
roundtrip time
ps (
[17]). The same structure with an 8.375 0.005-
mm-long polished Si spacer (
[17]),
installed between the Ge crystal and back mirror, reveals
a high-frequency component superimposed onto lower fre-
quency oscillations. The observed period of fast oscillations is
215 ps.
The average of a series of Fourier transforms of data such
as in Fig. 3(a) and (b) are presented in Fig. 4(a) and (b).
For the laser cavity with the 50.240-mm crystal without an
NELSON et al.: HIGH-RESOLUTION STUDY OF COMPOSITE CAVITY EFFECTS FOR p-Ge LASERS 1527
Fig. 4. Fourier transform of transient records for 50.240 mm p-Ge laser
emission: (a) without and (b) with a Si spacer in the cavity. Dashed line: the
4.5-GHz instrumental bandwidth.
Fig. 5. Fourier transform of transient records for 27.975 mm p-Ge laser
emission: (a) without and (b) with a Si spacer in the cavity (
E
=1
:
43
kV/cm,
B
=0
:
92
T for both cases). Dashed line: the 4.5-GHz instrumental bandwidth.
insert [Fig. 4(a)], harmonics (numbered) of the fundamental
round-trip frequency 760.0 MHz (“1”) are observed up to the
seventh. Harmonics 5 and up are attenuated by the 4.5-GHz
bandwidth of the electronics. For the same laser with the Si
spacer [Fig. 4(b)], harmonics up to the ninth are observed and
their spacing is smaller than in Fig. 4(a), owing to the smaller
round-trip frequency 664.5
0.5 MHz for the combined cavity.
Compared to Fig. 4(a), the second and third harmonics are
strongly suppressed and the higher harmonics are relatively
more pronounced.
Fig. 5 shows similar results for the 27.975-mm crystal.
Without a Si spacer, three harmonics of the 1.365-GHz
fundamental are observed [Fig. 5(a)]. With a Si spacer, fast
oscillations are again observed with a period
ps.
Harmonics of the combined cavity’s 1.085
0.001-GHz
fundamental can be seen [Fig. 5(b)] up to the fifth, where the
fourth and fifth have grown at the expense of the second. The
periods and frequencies of the prominent oscillations noted so
far are summarized in Table I for both long and short active
crystals.
Fig. 6 shows a spectrum of the p-Ge laser with tunable
frequency selector (see Fig. 1). The cavity consisted of the
27.975-mm active crystal with a 7.865
0.005 mm long Si
spacer, giving
of 177.6 0.2 ps and of 910.1 0.7 ps
for this construction. A lamellar-type wavelength selector with
agap
m [3]–[6] was included in this cavity (Fig. 1).
Recently, it was discovered that the selection efficiency (active
cavity finesse) strongly depends on the precise position of
the tunable mirror [6]. For Fig. 6, a spectrum was chosen
for which the laser failed to operate in a single frequency
mode, generating multiple modes instead, for the purpose of
investigating the causes of such behavior. Four modes with
peaks at 106.06, 106.24, 106.42, and 106.60
0.02 cm are
apparent, for a spacing of 0.18
0.02 cm . This separation is
nearly five times the axial mode spacing 0.0366 cm
of the
entire cavity. No other peaks appear in the range 40–140 cm
.
Fig. 7 presents the observed
generation zones for the
four cavity constructions shown in Fig. 2.
IV. D
ISCUSSION
The laser intensity seen in Fig. 3 is clearly periodic, with a
period equal to the round-trip cavity time. In addition, there
is a finer pattern of mode interference within one period that
depends on the initial random-phase distribution of the modes,
which differs for each laser shot. The calculated round-trip
times of the full cavities (active Ge crystal with Si spacer)
c are given for each setup in
Table I. The optical thickness of the teflon film on the mirror
and the phase shift on the boundaries where neglected in cal-
culations of round-trip times because the optical length of the
active Ge crystal and Si spacer is
to times larger than
the teflon film thickness and the radiation wavelength. The time
of propagation of the radiation inside the teflon film less than
0.2 ps, which is less than the uncertainity in
. The calculated
round-trip time
c for internal reflections within
the 8.375-mm Si spacer is also given in Table I. The observed
fast oscillation periods
in Fig. 3(b) is (within experimental
uncertainty) an exact harmonic of
, i.e., , where
is 7 for the cavity consisting of a 50.240-mm Ge crystal
and a Si spacer and
is 4 for the 27.975-mm crystal and Si
spacer. In each case,
differs significantly from . This
confirms that the development of the p-Ge laser radiation
occurs at longitudinal mode frequencies of the fall laser cavity
defined by the end mirrors. Within the accuracy of the data
presented here, reflections and scattering of the laser radiation
on intracavity interfaces do not affect the laser mode spacing.
Rather, the only observed effect of an interfaces is modulation
of the relative mode intensities, as well be shown below.
Harmonics of the fundamental round-trip frequency occur in
Figs. 4 and 5 because of beating between different pairs among
the ensemble of evenly spaced [14] axial modes. These modes
are defined by frequencies
, where the mode index
is an integer. The redistribution of energy in the frequency
spectrum of mode beating caused by the insertion of the optical
spacer [Figs. 4(b) and 5(b)] can be explained in terms of losses
and scattering at the Si/Ge interface and competition between
modes in the active Ge crystal. Small loss modes will be more
prominent in the laser output. Losses, which can occur from in-
terface absorption or scattering, are expected to be largest for
those modes having a large amplitude of the oscillating elec-
tric field at the interface and smallest for modes with interface
nodes, as shown schematically in Fig. 8. Small loss modes are,
therefore,
, where is as close as possible to an
integer. Thus, for the 50.240-mm sample, minimum-loss com-
bined cavity modes occur when
or
1528 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 37, NO. 12, DECEMBER 2001
TABLE I
S
UMMARY OF ROUND-TRIP TIMES FOR CONSTRUCTIONS USED IN MEASURING
EMISSION DYNAMICS.
C
ORRESPONDING FREQUENCIES ARE GIVEN TO THE IMMEDIATE RIGHT OF EACH TEMPORAL VALUE
Fig. 6. Emission spectrum of p-Ge laser with intracavity wavelength selector.
Fig. 7. Laser generation zones for four cavity constructions with different
passive intracavity elements, corresponding to Fig. 2.
Fig. 8. Composite Si/Ge cavity showing low- and high-loss modes (left and
right, respectively). Modes with nodes at the Si/Ge interface will experience the
smallest loss.
. The requirement for low loss that be nearly in-
tegral means that periods
should be prominent in transient
recordings of the composite laser and the eighth harmonic of
the fundamental round-trip frequency should be the strongest
in the Fourier transform of such data. Similar analysis for the
27.975-mm crystalargues that thefifth harmonic shouldbe most
prominent. The experimental fact that the seventh and the fourth
harmonics appear strongest in Figs. 4(b) and 5(b), respectively,
isexplained bythe
5-GHz instrumentalbandwidth limitations.
This discussion is clarified by a simple model. The intensity
of a given mode with wave vector
after passes through
the composite Si/Ge cavity in a linear regime of laser emission
development is
(1)
where
is the active Ge crystal length and is the gain coef-
ficient. Scattering or absorption at the Si/Ge interface with loss
coefficient
is assumed to be proportional to the squared am-
plitude of the oscillating electric field of certain modes (
)at
the interface. The wavenumber
in the Ge crystal for modes
having allowed frequencies for the combined cavity is
. The time dependence caused by beating between
a pair of modes with mode indices
and , where are and
are integers, is given by
(2)
The third term represents beat oscillations with frequencies
, which cannot be observed with our detection electronics
not beyond about 5–6 GHz. For a given
, the amplitude of
the beat oscillation depends on the mode number
. Since
hundreds of modes can oscillate simultaneously, the spectrum
of observable beats
is found by averaging (summing) the
amplitude over many
values
(3)
Fig. 9 shows the calculated beat spectrum, according to (3) for
the Si plus 50.240-mm Ge cavity, as the white bars. Parame-
ters used were
, cm and .
The gain value of
corresponds to a typical experimental value
[15]. The number of passes (
) is a realistic value
for a characteristic 1
s emission pulse duration. The minimum
and maximum
values correspond to minimum (70 cm ) and
maximum (90 cm
) frequencies when fields of approximately
T and kV/cm are appliedtoa cavityconsisting
of the 50.240 mm Ge crystals with the 8.375-mm Si spacer. The
dashed lineis a possible power attenuationfunction,which is the
product ofa firstorder filterwith a 4.5-GHz cutoff (modelingthe
SCD 5000 transient digitizer) and a second filter term modeling
all other components in the detection circuit. The solid bars plot
the product of the calculated beat spectrum with the frequency
attenuation function. A loss coefficient
of 0.007 gave a beat
