Optical: systems and elements – Optical frequency converter – Parametric oscillator
Reexamination Certificate
2001-06-29
2003-10-21
Lee, John D. (Department: 2874)
Optical: systems and elements
Optical frequency converter
Parametric oscillator
C359S326000, C359S328000
Reexamination Certificate
active
06636343
ABSTRACT:
BACKGROUND OF THE INVENTION
This invention relates in general to a system and method for nonlinear frequency conversion tunable laser light using achromatic phase-matching, and in particular to an achromatic phase-matching optical system and method which exactly matches the high order dispersion characteristics of nonlinear optical materials.
Many applications require broadly tunable UV light. No such laser source exists, however, so tunable UV is usually obtained by frequency-doubling a tunable laser in the visible and near-IR by using nonlinear optical effects such as a second harmonic generation process. Such processes are phenomenon which derive from nonlinear polarization effects of certain material media. The effect depends upon crystal structure, particularly anisotropic structure. Commonly used crystals are &bgr;-barium borate (“BBO”), potassium dihydrogen phosphate (“KDP”) and lithium triborate (“LBO”).
Because frequency-doubling, therefore, involves passing light through a nonlinear crystal, the effects of its wavelength-dependent refractive index must be taken into account. In particular, in order for frequency doubling to take place in the crystal, the refractive index of the incident light at the “fundamental” wavelength and with its polarization must equal the refractive index of the frequency doubled light (with its own polarization) to be produced. Since the refractive index of the crystal varies both with the angle of incidence and with the frequency of the input beam it is apparent the that absent extraordinary precaution only a very narrow range of frequencies of a broadband beam can enter a crystal at the appropriate incident angle for efficient frequency doubling.
Second-harmonic generation of light (hereafter referred to as “SHG”) the generation of light of twice the optical frequency of input laser light, has been an essential tool of laser research for many years. It is used widely to generate ultraviolet light because such wavelengths are difficult to generate directly from a laser. Indeed, this technique is often used to generate visible light from a near-infrared laser because it is easier to generate near-infrared laser light than it is to generate visible light. In general, however, it is possible to frequency-double light from virtually all visible and near-infrared lasers.
A particular type of laser light which is important to frequency-double is broadband light. However, the use of SHG processes to frequency-double broadband light which is incoherent has proved to be difficult and inefficient. (In general, ultrashort pulses generated by lasers can be considered broadband light whose frequencies are in phase while incoherent light can be considered broadband light whose frequencies are randomly phased.) These two types of light are difficult to frequency-double due to their respective large bandwidths. As a result of the large bandwidths, efficient methods for frequency-doubling both of these types of light have not been developed.
The efficiency &eegr; of a SHG process depends on several factors. A first factor is the nonlinear coefficient of the SHG crystal used. This factor depends on internal properties of the crystal and can only be improved by manipulating the composition of the crystal.
Second, &eegr; is proportional to the square of the length of the crystal, L, the distance through which light ray propagate through the crystal. Thus, thick crystals yield much higher efficiency than thin ones.
Third, &eegr; depends on the laser intensity and is, typically, directly proportional to the laser intensity. Consequently, continuous-beam lasers, which have relatively low intensity, frequency-double inefficiently while pulsed lasers, which generally achieve higher intensity, frequency-double more efficiently. In general, the shorter the pulse the more efficiently it frequency-doubles, given a fixed energy per pulse.
As earlier noted, in order for frequency-doubling to take place in an SHG crystal, the refractive index of the input laser light (again, the “fundamental” wavelength) must equal the refractive index of the frequency-doubled light to be produced. Since the refractive index of a crystal is a function of both the incidence angle and frequency of the input beam different incidence angles must be used to obtain maximum efficiency &eegr; for different wavelengths. The requirement that a wavelength enter the crystal at the appropriate angle necessary to frequency-double most efficiently will be referred to hereinafter as the “phase-matching condition,” or simply “phase-matching” for short. The angle will be referred to as the “phase-matching angle,” and is a function of wavelength.
Because the efficiency &eegr; of the SHG process is strongly “peaked” with respect to the entrance angle for a given wavelength and also with respect to wavelength for a given angle, only a very narrow range of wavelengths near the exact phase-matching wavelength can yield highly efficient SHG process. The range of wavelengths that achieves high-efficiency frequency-doubling for a single angle is called the crystal's “phase-matching bandwidth” for that angle. If the input laser light contains frequencies outside this bandwidth, such frequencies will not produce their corresponding second harmonic (i.e., will not be frequency-doubled) and the efficiency of the overall process is reduced.
When the crystal bandwidth is greater than the input light bandwidth, the above effect can be neglected. However, when the crystal bandwidth is less than the bandwidth of the input light, the SHG efficiency is proportional to the crystal bandwidth, yielding a fourth factor. In this case, the efficiency can be written approximately as:
η
∝
d
2
×
l
×
L
2
(
Δ
λ
cr
Δ
λ
l
)
where d is the nonlinear coefficient of the crystal, l is the intensity of the light, L is the length of the crystal through which the light propagates, &Dgr;&lgr;
cr
is the bandwidth of the crystal, and &Dgr;&lgr;
l
is the bandwidth of the incident light. Furthermore, the bandwidth, &Dgr;&lgr;
cr
, of an SHG crystal is given by:
Δ
λ
cr
=
λ
4
l
(
ⅆ
n
ⅆ
λ
)
f
-
(
ⅆ
n
ⅆ
λ
)
s
where &lgr; is the wavelength of light and dn/d&lgr; is the derivative of the refractive index n with respect to wavelength at the appropriate polarization of the fundamental wavelength and second harmonic wavelength, indicated by the subscripts, f and s, respectively.
Thus, the bandwidth of an SHG crystal is a function of the crystal's refractive-index vs. wavelength curve: a fundamental property of the crystal. Furthermore, the bandwidth is inversely proportional to the crystal length. Hence, if one attempts to increase the conversion efficiency by increasing the crystal length, one must also increase the precision of the phase-matching thereby reducing the tolerance for error in the entrance angle of the incoming beam.
Various attempts to improve the efficiency of the SHG process have been and continue to be made. Several researchers have introduced achromatic phase-matching (APM) devices that use angular dispersion so that each wavelength enters the nonlinear crystal at its appropriate phase-matching angle as a way of increasing the bandwidth of the crystal and therefore, increase its efficiency. The crystal and all dispersing optics remain fixed. Because such systems have no moving parts, they are inherently instantaneously tunable, and can be used for nonlinear conversion of tunable or broadband (such as ultrashort) radiation. Most of these devices have used diffraction gratings or prisms in combination with lenses which are sensitive to translational misalignment. Also, previous work has considered only the lowest order (linear) term of the media-created dispersion and the phase-matching angle tuning function. Bandwidths of about 10 times the natural bandwidth of the crystal were achieved; larger bandwidths were only obtained by using a divergent beam at the expense
Evans Timothy P.
Lee John D.
Sandia National Laboratories
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