- Email: [email protected]
Unstable, Q-switched, ruby resonator in the negative branch confocal configuration
CPL 314
Volume
27, number
OPTICS COMMUNICATIONS
2
UNSTABLE, Q-SWITCHED, RUBY RESONATOR
November 1978
IN THE
NEGATIVE BRANCH CONFOCAL CONFIGURATION A.D.E. BROWN Department
of Applied Physics, University of Hull, Hull, HU6 7RX, UK
Received 5 June 1978 Revised manuscript received
17 July
In this paper we discuss the design, Q-switched mode.
1978
performance
and merits of a ruby laser operating
1. Introduction The advantages of unstable resonators over their stable counterparts have been extensively discussed in several publications [l-3]. The large mode volume, good mode control and high energy outputs are distinct merits of the unstable resonator. Its application with gaseous active mediums is quite widespread [2 ] ; however, its use with solid state lasers has been rather limited. Ruby was the first material to be used in an unstable resonator [4], and surprising as it may seen, it has almost been neglected since. Some work has also been carried out by Mikaelian et al. [S] , by considering a self Q-switching mechanism. Ewanizky and Craig [6] have successfully used Nd:YAG in the negative branch configuration and they have drawn up a comparison between the unstable and stable performances. Investigations have been carried out by Herbst [7] with a positive branch Nd:YAG laser and Anan’ev [8] has obtained diffraction limited emission from a carefully grown Nd:YAG rod in such a configuration. Hanna and Leycock [9] have successfully used Nd:YAG in an unstable configuration for efficient S.H.G. and as a pump source for a parametric oscillator. They have also achieved single longitudinal mode selection by using a slow passive Q-switch. In this paper we present the design and operating characteristics of a negative branch, unstable, Q-switched ruby laser. The Q-switch action is achieved by means of an active modulator. The limitation of using the unstable, confocal, negative branch configuration with
in the unstable-resonator,
CO, is to be found with the internal focus which is likely to cause intracavity breakdown. At the ruby wavelength (6943 A) the problem of breakdown does not arise as the power densities attained do not exceed the breakdown threshold. To avoid possible damage all cavity components should be kept clear of the focus location. The alignment tolerances for a negative branch resonator are somewhat greater than for the positive branch [IO]. A further advantage of a confocal configuration with a laser is that the output beam is collimated, hence the beam divergance is minimised. Siegman [2] relates the magnification factor m to the geometrical loss per pass L by L = 1 - l{m2.
(1)
In ref. [l l] the geometric origin and significance of the m value is given by considering a ray matrix representation of the resonator. For a confocal resonator m is related to the radii of curvature of the mirrors (Z?1, R2) by the expression m = R,/R,.
(29
In practice the limiting stop of the resonator is the rod of radius ~2, and hence the radius of the hole in the decoupling mirror al is chosen so that m = a2/al.
(2ii)
253
Volume
21, number
2
November
OPTICS COMMUNICATIONS
Mir2-w
Fig. 1. The resonator
2. Experimental
configuration
(3)
N = (~I/W(+2),
where h is the laser wavelength and 1 the cavity length. For the parameters above N = 48 and the equivalent Fresnel number [ 1 ]
( P 2m2
’
(4)
has the value 5.8. The length of the ruby rod was 10.2 cm and its diameter 1.4 cm, thus the corresponding radius of the hole in the decoupling mirror was 0.42 cm. The orientation of the rod was 90” to the optic axis which meant that its emission was polarised and advantage was taken of this to eliminate one intracavity polariser. The rod was pumped by a close wrapped helical flash tube to ensure uniform pumping. The flash tube was driven by an optimum designed circuit of pulse duration 2.5 ms and both the rod and flash tube were placed in a water-cooled assembly. To achieve the Q-switching action a Pockels cell was employed (an A.D.P. crystal with a half-wave voltage of 23.4 kV). This was driven by a simple thyratron circuit with a rise time of = 5 ns. The decoupling mirror was a highly polished brass flat with a hole of diameter 8.4 mm drilled at 45” to its normal. The single intracavity polariser was a standard Glan-Taylor prism and the laser mirrors were dielectric coated glass substrates. 254
(100 %reflecting R, =60 cm)
with components.
design
In our arrangement the unstable Q-switched ruby resonator had two 100% reflecting mirrors at the wavelength 6943 A (fig. 1). Their respective radii of curvature were 100 cm and 60 cm which give a magnification factor of 1.66. Siegman [ 1 ] places importance upon the Fresnel number of a cavity; it is useful to think of the Fresnel number as the ratio of the “cavity divergence” to the “internal beam divergence”, i.e.
m-l Neq =__
1978
Fig. 2. Q-switched
output
from ruby resonator.
50 ns/div.
Output beam patterns from the resonators are annular shaped as expected, with an internal diameter of 8.0 mm and an external diameter of 15 mm.
3. Measurements Measurements of the pulse shape (temporal profile) were achieved with a Tetronix 5 19 oscilloscope and a Barlow photodiode. The bandwidth of such an arrange. ment is oscilloscope limited to 1 GHz. Fig. 2 shows a typical output. The width at half maximum is 50 ns. Energy measurements were obtained by the use of a pyroelectric calibrated detector. The energy in the pulse shown in fig. 2 was 500 mJ, the output from a
Fig. 3. Near-field
burn pattern.
OPTICS COMMUNICATIONS
Volume 27, number 2
stable resonator containing the same component would be about 50 mJ in a TEMou mode. Fig. 3 shows the near field burn pattern from the resonator; the central dark region is known as the Poisson or Arago spot. An expression for the far field pattern is given in ref. [12]. I(r) = h2 C(?ra2) 2 2 ;“:‘:“_($F)i’.
(5)
and Zi = kraJf where of the far field image and f the focal length of the imaging system. From eq. (6) the far field intensity is zero when In this expression C is a constant
k = 27r/X r is the radial component
J1(z2>lz2
= @lla2)2Jl(zlYZl
,
November 1978
value of 0.8 f 0.1 mrd. This is eight times greater than the diffraction limit. The difference is attributable to the poor quality of the laser rod. If a rod of good quality is used in a plano-concave configuration with a mirror curvatur of 200 cm and a cavity length of 80 cm, the diffraction limit would be about 1 mrd for the TEM,, mode. This is greater than what we obtained using an unstable resonator with a rod of poor quality. The spectral line width was measured by using a Fabry Perot interferometer with a plate spacing of 1 mm and reflectivity of 96%. The discrete ring pattern that was formed was focused onto Kodak Pan X film (A.S.A. 600) with a 20 cm lens. From measuring the widths and diameters of the rings we arrived at a value of = 0.23 A as the spectral width of the laser output.
(69
or J,(x)
= (l/m) J, (x/m).
(6ii)
With a near field pattern ofal = 0.42 and a2 = 0.7 cm (m = 1.66) at 6943 A eq. (7) may be expressed as JI(6.335a)
=0.6J1(3.816a),
(7)
where a = (r/f) X 104. From the solution of eq. (7) we are able to determine the focal length of the imaging system which will give a prominent ring pattern in the far field. Solving eq. (7) numerically we have al = 0.47, a2 = 1.08 and a3 = 1.68. For the first minimum to have a diameter of 0.5 cm, it is necessary to use a lens combination of focal length 53.2 m which is impractical, By considering the energy distribution in the far field, which is obtained by integrating eq. (5) and plotting this against x, we obtain the diffraction limited beam divergence. From this we deduce that if the beam is of good quality we would expect 80% of the beam’s energy to be within 0.1 mrd. Measurements were made to determine the beam divergence by employing thin glass slides and calibrated neutral density filters. The glass slides are arranged equally spaced in a parallel stack with the neutral density filters placed between them. The beam, which is focused by a 4 m lens, has an incident angle of 60” upon the glass slides which reflect 8% each. The reflections from each slide are collected by a lens and focused onto Polaroid to form a row of burn patterns. By plotting the burn pattern diameter against percentage reflected one can determine the approximate beam divergence from the half width. This measure gave a
4. Conclusion We have shown that ruby can be successfully used with an unstable resonator in the Q-switched mode. The advantages over the stable configuration (high energy extraction and good beam divergence in spite of the poor quality rod) have been demonstrated. By efficiently using all the available gain medium to produce a beam of good phase uniformity, one obviously reduces the cost of a laser system. This has enabled us to construct a ruby laser to give 100 MW with only one amplifier [l 11.
Acknowledgement
I would like to thank my mother, Mrs. M.J. Brown, for her kindness and financial support. My gratitude is also due to Dr. B.J. Rye and Professor S.A. Ramsden for their guidance and encouragement. I would also like to thank Dr. Forrst of the Culham Laboratory for the loan of a Fabry Perot interferometer.
References [l] [2] [3] [4] [S]
A.E. Siegman, Laser Focus (May 1971) 42. A.E. Siegman, 3. Appl. Opt. 13 (1974) 353. Yu.A. Anan’ev, Sov. J.Q.E. 1 (1972) 565, Review. A.E. Siegman, Proc. IEEE 53 (1965) 277. A.L. Mikaelian et al., Sov. J.Q.E. 1 (1971) 74.
25.5
Volume
27, number
2
OPTICS COMMUNICATIONS
[6] T.F. Ewanizky and J.M. Craig, J. Appl. Opt. 15 (1976) 1465. [7] R.L. Herbst, H. Komine and R.L. Byer, Opt. Comm. 21 (1977) 5. [E] Yu.A. Anan’ev et al., Sov. J.Q.E. 1 (1972) 403. [9] DC. Hanna and C. Laycock, ECOSA 1, 1st European
256
November
Conf. on Optical systems and applications (1978) (Brighton U.K.). [lo] W.E. Krupke and W.R. Sooy, IEEE J.Q. 21 (1969) [ 111 A.D.E. Brown, internal report, University of Hull. [12] A.I. Mahan et al., J. Opt. Sot. Am. 54 (1964) 721.
1978
575
Volume
27, number
OPTICS COMMUNICATIONS
2
UNSTABLE, Q-SWITCHED, RUBY RESONATOR
November 1978
IN THE
NEGATIVE BRANCH CONFOCAL CONFIGURATION A.D.E. BROWN Department
of Applied Physics, University of Hull, Hull, HU6 7RX, UK
Received 5 June 1978 Revised manuscript received
17 July
In this paper we discuss the design, Q-switched mode.
1978
performance
and merits of a ruby laser operating
1. Introduction The advantages of unstable resonators over their stable counterparts have been extensively discussed in several publications [l-3]. The large mode volume, good mode control and high energy outputs are distinct merits of the unstable resonator. Its application with gaseous active mediums is quite widespread [2 ] ; however, its use with solid state lasers has been rather limited. Ruby was the first material to be used in an unstable resonator [4], and surprising as it may seen, it has almost been neglected since. Some work has also been carried out by Mikaelian et al. [S] , by considering a self Q-switching mechanism. Ewanizky and Craig [6] have successfully used Nd:YAG in the negative branch configuration and they have drawn up a comparison between the unstable and stable performances. Investigations have been carried out by Herbst [7] with a positive branch Nd:YAG laser and Anan’ev [8] has obtained diffraction limited emission from a carefully grown Nd:YAG rod in such a configuration. Hanna and Leycock [9] have successfully used Nd:YAG in an unstable configuration for efficient S.H.G. and as a pump source for a parametric oscillator. They have also achieved single longitudinal mode selection by using a slow passive Q-switch. In this paper we present the design and operating characteristics of a negative branch, unstable, Q-switched ruby laser. The Q-switch action is achieved by means of an active modulator. The limitation of using the unstable, confocal, negative branch configuration with
in the unstable-resonator,
CO, is to be found with the internal focus which is likely to cause intracavity breakdown. At the ruby wavelength (6943 A) the problem of breakdown does not arise as the power densities attained do not exceed the breakdown threshold. To avoid possible damage all cavity components should be kept clear of the focus location. The alignment tolerances for a negative branch resonator are somewhat greater than for the positive branch [IO]. A further advantage of a confocal configuration with a laser is that the output beam is collimated, hence the beam divergance is minimised. Siegman [2] relates the magnification factor m to the geometrical loss per pass L by L = 1 - l{m2.
(1)
In ref. [l l] the geometric origin and significance of the m value is given by considering a ray matrix representation of the resonator. For a confocal resonator m is related to the radii of curvature of the mirrors (Z?1, R2) by the expression m = R,/R,.
(29
In practice the limiting stop of the resonator is the rod of radius ~2, and hence the radius of the hole in the decoupling mirror al is chosen so that m = a2/al.
(2ii)
253
Volume
21, number
2
November
OPTICS COMMUNICATIONS
Mir2-w
Fig. 1. The resonator
2. Experimental
configuration
(3)
N = (~I/W(+2),
where h is the laser wavelength and 1 the cavity length. For the parameters above N = 48 and the equivalent Fresnel number [ 1 ]
( P 2m2
’
(4)
has the value 5.8. The length of the ruby rod was 10.2 cm and its diameter 1.4 cm, thus the corresponding radius of the hole in the decoupling mirror was 0.42 cm. The orientation of the rod was 90” to the optic axis which meant that its emission was polarised and advantage was taken of this to eliminate one intracavity polariser. The rod was pumped by a close wrapped helical flash tube to ensure uniform pumping. The flash tube was driven by an optimum designed circuit of pulse duration 2.5 ms and both the rod and flash tube were placed in a water-cooled assembly. To achieve the Q-switching action a Pockels cell was employed (an A.D.P. crystal with a half-wave voltage of 23.4 kV). This was driven by a simple thyratron circuit with a rise time of = 5 ns. The decoupling mirror was a highly polished brass flat with a hole of diameter 8.4 mm drilled at 45” to its normal. The single intracavity polariser was a standard Glan-Taylor prism and the laser mirrors were dielectric coated glass substrates. 254
(100 %reflecting R, =60 cm)
with components.
design
In our arrangement the unstable Q-switched ruby resonator had two 100% reflecting mirrors at the wavelength 6943 A (fig. 1). Their respective radii of curvature were 100 cm and 60 cm which give a magnification factor of 1.66. Siegman [ 1 ] places importance upon the Fresnel number of a cavity; it is useful to think of the Fresnel number as the ratio of the “cavity divergence” to the “internal beam divergence”, i.e.
m-l Neq =__
1978
Fig. 2. Q-switched
output
from ruby resonator.
50 ns/div.
Output beam patterns from the resonators are annular shaped as expected, with an internal diameter of 8.0 mm and an external diameter of 15 mm.
3. Measurements Measurements of the pulse shape (temporal profile) were achieved with a Tetronix 5 19 oscilloscope and a Barlow photodiode. The bandwidth of such an arrange. ment is oscilloscope limited to 1 GHz. Fig. 2 shows a typical output. The width at half maximum is 50 ns. Energy measurements were obtained by the use of a pyroelectric calibrated detector. The energy in the pulse shown in fig. 2 was 500 mJ, the output from a
Fig. 3. Near-field
burn pattern.
OPTICS COMMUNICATIONS
Volume 27, number 2
stable resonator containing the same component would be about 50 mJ in a TEMou mode. Fig. 3 shows the near field burn pattern from the resonator; the central dark region is known as the Poisson or Arago spot. An expression for the far field pattern is given in ref. [12]. I(r) = h2 C(?ra2) 2 2 ;“:‘:“_($F)i’.
(5)
and Zi = kraJf where of the far field image and f the focal length of the imaging system. From eq. (6) the far field intensity is zero when In this expression C is a constant
k = 27r/X r is the radial component
J1(z2>lz2
= @lla2)2Jl(zlYZl
,
November 1978
value of 0.8 f 0.1 mrd. This is eight times greater than the diffraction limit. The difference is attributable to the poor quality of the laser rod. If a rod of good quality is used in a plano-concave configuration with a mirror curvatur of 200 cm and a cavity length of 80 cm, the diffraction limit would be about 1 mrd for the TEM,, mode. This is greater than what we obtained using an unstable resonator with a rod of poor quality. The spectral line width was measured by using a Fabry Perot interferometer with a plate spacing of 1 mm and reflectivity of 96%. The discrete ring pattern that was formed was focused onto Kodak Pan X film (A.S.A. 600) with a 20 cm lens. From measuring the widths and diameters of the rings we arrived at a value of = 0.23 A as the spectral width of the laser output.
(69
or J,(x)
= (l/m) J, (x/m).
(6ii)
With a near field pattern ofal = 0.42 and a2 = 0.7 cm (m = 1.66) at 6943 A eq. (7) may be expressed as JI(6.335a)
=0.6J1(3.816a),
(7)
where a = (r/f) X 104. From the solution of eq. (7) we are able to determine the focal length of the imaging system which will give a prominent ring pattern in the far field. Solving eq. (7) numerically we have al = 0.47, a2 = 1.08 and a3 = 1.68. For the first minimum to have a diameter of 0.5 cm, it is necessary to use a lens combination of focal length 53.2 m which is impractical, By considering the energy distribution in the far field, which is obtained by integrating eq. (5) and plotting this against x, we obtain the diffraction limited beam divergence. From this we deduce that if the beam is of good quality we would expect 80% of the beam’s energy to be within 0.1 mrd. Measurements were made to determine the beam divergence by employing thin glass slides and calibrated neutral density filters. The glass slides are arranged equally spaced in a parallel stack with the neutral density filters placed between them. The beam, which is focused by a 4 m lens, has an incident angle of 60” upon the glass slides which reflect 8% each. The reflections from each slide are collected by a lens and focused onto Polaroid to form a row of burn patterns. By plotting the burn pattern diameter against percentage reflected one can determine the approximate beam divergence from the half width. This measure gave a
4. Conclusion We have shown that ruby can be successfully used with an unstable resonator in the Q-switched mode. The advantages over the stable configuration (high energy extraction and good beam divergence in spite of the poor quality rod) have been demonstrated. By efficiently using all the available gain medium to produce a beam of good phase uniformity, one obviously reduces the cost of a laser system. This has enabled us to construct a ruby laser to give 100 MW with only one amplifier [l 11.
Acknowledgement
I would like to thank my mother, Mrs. M.J. Brown, for her kindness and financial support. My gratitude is also due to Dr. B.J. Rye and Professor S.A. Ramsden for their guidance and encouragement. I would also like to thank Dr. Forrst of the Culham Laboratory for the loan of a Fabry Perot interferometer.
References [l] [2] [3] [4] [S]
A.E. Siegman, Laser Focus (May 1971) 42. A.E. Siegman, 3. Appl. Opt. 13 (1974) 353. Yu.A. Anan’ev, Sov. J.Q.E. 1 (1972) 565, Review. A.E. Siegman, Proc. IEEE 53 (1965) 277. A.L. Mikaelian et al., Sov. J.Q.E. 1 (1971) 74.
25.5
Volume
27, number
2
OPTICS COMMUNICATIONS
[6] T.F. Ewanizky and J.M. Craig, J. Appl. Opt. 15 (1976) 1465. [7] R.L. Herbst, H. Komine and R.L. Byer, Opt. Comm. 21 (1977) 5. [E] Yu.A. Anan’ev et al., Sov. J.Q.E. 1 (1972) 403. [9] DC. Hanna and C. Laycock, ECOSA 1, 1st European
256
November
Conf. on Optical systems and applications (1978) (Brighton U.K.). [lo] W.E. Krupke and W.R. Sooy, IEEE J.Q. 21 (1969) [ 111 A.D.E. Brown, internal report, University of Hull. [12] A.I. Mahan et al., J. Opt. Sot. Am. 54 (1964) 721.
1978
575